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Overlapped Transmission in Wireless Networks

Permanent Link: http://ufdc.ufl.edu/UFE0022041/00001

Material Information

Title: Overlapped Transmission in Wireless Networks
Physical Description: 1 online resource (134 p.)
Language: english
Creator: Boppana, Surendra
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: adhoc, broadcasting, cellular, mac, mud, ocsma, tcp
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In wireless networks, interference is one of the major impairments that deteriorates the performance of a system. Conventional channel-sharing schemes such as TDMA, FDMA, CDMA, etc, orthogonalize the channel resources among users to minimize interference. However, information-theoretic results indicate that orthogonalization of the channel resources is not the most efficient way to transmit to multiple users. We use the term overlapped transmission to describe non-orthogonal transmission schemes because these schemes allocate the same channel resources to more than one user, thus overlapping their transmissions. We conducted an investigation into the potential benefits of overlapped transmissions as well as practical approaches to overlapped transmission in both cellular and ad hoc wireless networks. We first analyzed the potential of overlapped transmissions to improve the performance of wireless cellular networks. We considered the use of cooperative broadcasting techniques in the downlink of a cellular network to support additional users compared to a system that orthogonalizes the channel resources among the users, such as TDMA, FDMA, CDMA, etc. We evaluated the performance gains of cooperative broadcasting techniques in terms of number of users that can be supported by the base station in a cellular network when the number of users in the system is finite. We also evaluated the user capacity of a cooperative broadcasting system, when the number of users in the system is large. We compared the performance of the optimal broadcasting to several optimal and suboptimal forward-link channel-sharing schemes. Next, we studied the use of overlapped transmission in ad hoc networks to improve the spatial re-use and throughput of the network. We showed how multihop routing can result in mobile radios having knowledge of interfering signals during the reception of a transmission. We then demonstrated how this knowledge can be exploited to schedule additional transmissions by performing interference cancellation at the physical layer. We evaluated the performance limits of employing overlapped transmissions in wireless ad hoc networks with randomly distributed nodes. We developed a MAC protocol that takes advantage of the knowledge of the interfering signals to schedule additional transmissions, thereby increasing the spatial re-use and throughput of the network. We evaluated the performance of this MAC protocol in a variety of network scenarios and compared to that of IEEE 802.11 MAC protocol. We also analyzed the impact of overlapped transmissions on the performance of Transmission Control Protocol (TCP) in wireless ad hoc networks.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Surendra Boppana.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Shea, John M.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022041:00001

Permanent Link: http://ufdc.ufl.edu/UFE0022041/00001

Material Information

Title: Overlapped Transmission in Wireless Networks
Physical Description: 1 online resource (134 p.)
Language: english
Creator: Boppana, Surendra
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2008

Subjects

Subjects / Keywords: adhoc, broadcasting, cellular, mac, mud, ocsma, tcp
Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: In wireless networks, interference is one of the major impairments that deteriorates the performance of a system. Conventional channel-sharing schemes such as TDMA, FDMA, CDMA, etc, orthogonalize the channel resources among users to minimize interference. However, information-theoretic results indicate that orthogonalization of the channel resources is not the most efficient way to transmit to multiple users. We use the term overlapped transmission to describe non-orthogonal transmission schemes because these schemes allocate the same channel resources to more than one user, thus overlapping their transmissions. We conducted an investigation into the potential benefits of overlapped transmissions as well as practical approaches to overlapped transmission in both cellular and ad hoc wireless networks. We first analyzed the potential of overlapped transmissions to improve the performance of wireless cellular networks. We considered the use of cooperative broadcasting techniques in the downlink of a cellular network to support additional users compared to a system that orthogonalizes the channel resources among the users, such as TDMA, FDMA, CDMA, etc. We evaluated the performance gains of cooperative broadcasting techniques in terms of number of users that can be supported by the base station in a cellular network when the number of users in the system is finite. We also evaluated the user capacity of a cooperative broadcasting system, when the number of users in the system is large. We compared the performance of the optimal broadcasting to several optimal and suboptimal forward-link channel-sharing schemes. Next, we studied the use of overlapped transmission in ad hoc networks to improve the spatial re-use and throughput of the network. We showed how multihop routing can result in mobile radios having knowledge of interfering signals during the reception of a transmission. We then demonstrated how this knowledge can be exploited to schedule additional transmissions by performing interference cancellation at the physical layer. We evaluated the performance limits of employing overlapped transmissions in wireless ad hoc networks with randomly distributed nodes. We developed a MAC protocol that takes advantage of the knowledge of the interfering signals to schedule additional transmissions, thereby increasing the spatial re-use and throughput of the network. We evaluated the performance of this MAC protocol in a variety of network scenarios and compared to that of IEEE 802.11 MAC protocol. We also analyzed the impact of overlapped transmissions on the performance of Transmission Control Protocol (TCP) in wireless ad hoc networks.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Surendra Boppana.
Thesis: Thesis (Ph.D.)--University of Florida, 2008.
Local: Adviser: Shea, John M.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2008
System ID: UFE0022041:00001


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OVERLAPPED TRANSMISSION IN WIRELESS NETWORKS


By
SURENDRA BOPPANA



















A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2008



































S2008 Surendra Boppana





































To my parents.










ACKNOWLEDGMENTS

My stay at the University of Florida has been a very enriching experience. A few

people have made a tremendous impact on my life, personally and professionally. My

sincerest thanks go to my advisor Dr. John AI. Shea, whose guidance, expertise, and

professionalism were instrumental in my growth as a researcher. I thoroughly enjoi- .1

working with him.

I thank Dr. Womg, Dr. Fang, Dr. McNair and Dr. Presnell for their guidance,

s-II_~-1;- -Huns and interest in my work. I thank my friends who made my stay in Gainesville

enjoi- l1l1.'. Special thanks to Sarva and Dehdeep for the lively discussions we had, and for

making my life at WING that much more interesting.

Lastly, I dedicate this work to my parents, IUsha and N ,g 1.11x!1-1! .1, .In who have been

a constant source of inspiration in my life.










TABLE OF CONTENTS


page


ACK(NOWLED GMENTS


LIST OF TABLES.


LIST OF FIGURES

ABSTRACT


CHAPTER


1 INTRODUCTION


Cellular- Nuetwor-ks
Ad Hoc Networks.
Dissertation Outline


2 OVERLAPPED TRANSMISSION IN CELLULAR NETWORKS.

2.1 Introduction.
2.2 System Description.
2.3 Maximizing the User Capacity .. ...... .
2.4 User Capacity under Average Power Constraint ....
2.4.1 Cellular Network without BC
2.4.2 Cellular Network employing BC .......
2.4.3 Cellular Network employing GWBE Sequences .....
2.5 User Capacity under Total Power Constraint .......
2.6 Suninary

:3 ITSER CAPACITY OF DOWNLINK( CELLULAR NETWORKS


:3.1 Introduction.
:3.2 System Description.
:3.3 User Capacity of TDMA System .
:3.3.1 System Description
:3.3.2 Asyniptotic User Capacity of TDMA System.
:3.4 User Capacity of DPC System.
:3.4.1 System Description
:3.4.2 Asyniptotic User Capacity of DPC System
:3.5 Results and Discussion.
:3.5.1 User Capacity in Exponential Path-Loss C'I .Ill., I
:3.5.2 User Capacity in Exponential Path-Loss C'I .Ill., I


no Fadingf
with Fading


:3.6 Suninary











4 PERFORMANCE COMPARISON OF OPTIMAL AND SUBOPTIMAL DOWNLINK(
CHANNEL-SHARING SCHEMES . ...... .. 49

4.1 Introduction ......... . .. .. 49
4.2 System Model ............. ..... ... ....... 50
4.3 Asymptotic Analysis for Required Minimum SNR per MS .. .. .. .. 52
4.3.1 Broadcasting over the Whole Band .... .. .. 52
4.3.2 Fixed Frequency Division Multiplexing .. .. . .. 54
4.3.3 Two-Level Broadcasting . ..... .. .. 54
4.3.4 Three-Level Broadcasting . .... .. .. 55
4.3.5 Optimal Frequency Division Multiplexing .. .. . .. 56
4.4 Results .......... ......... 57
4.5 Summary ........ .. .. 63

5 OVERLAPPED TRANSMISSION IN WIRELESS AD HOC NETWORKS .. 65

5.1 Introduction ......... . .. .. 65
5.2 Motivation. ............ ... .. ...... 68
5.3 Overlapped Transmission in Wireless Ad Hoc Networks .. .. .. .. 71
5.3.1 System Model ......... .. 71
5.3.2 Interference due to Secondary Transmission ... .. .. 73
5.3.3 Probability of Secondary Transmission ... .. 76
5.4 Summary ......... ... .. 80

6 THE OVERLAPPED CARRIER SENSE MULTIPLE ACCESS PROTOCOL .82

6.1 Introduction ......... .. .. .. 82
6.2 The Design of OCSMA Protocol . .... .. 82
6.2.1 Primary Handshaking ....... ... .. 82
6.2.2 Secondary Handshaking . ..... .. 85
6.2.3 Primary Transmission ....... ... .. 88
6.2.4 Secondary Transmission . ..... .. 88
6.2.5 Data Acknowledgments . .... .. 89
6.3 Design Considerations ........ ... .. 90
6.3.1 Cross-L .vr-i Interaction . ...... .. .. 90
6.3.2 Complexity of the Protocol ...... .. . 90
6.3.3 Reduced Overhead ......... ... .. 91
6.4 Simulation Results ......... . .. 91
6.5 Summary ......... ... .. 101

7 IMPACT OF OVERLAPPED TRANSMISSION ON THE PERFORMANCE
OF TCP IN AD HOC NETWORKS . ..... .. .. 102

7.1 Introduction .......... ...... ..... 102
7.2 Interaction between TCP and OCSMA ... .. .. .. 103
7.2.1 Impact of TCP Congestion Window Size ... .. . .. 104
7.2.2 Impact of Collisions on TCP Throughput .. .. . .. 109










111
116i
117
120
123


. . 124


124
125


. .. 126


7.2.3 Fairness Issues and Medium Contention .. .. .
7.3 OCSMA with Look Ahead Capability (OCSMA_LA) .
7.3.1 OCSMA_LA Protocol Description . .
7.3.2 Simulation Results .....
7.4 Summary .....

8 CONCLUSION AND DIRECTIONS FOR FUTURE WORK( .

8.1 Conclusion .........
8.2 Directions for Future Work . .

APPENDIX

A DERIVATION OF THE JOINT PDF OF XAD, XCD . .

REFERENCES ......_._ .....

BIOGRAPHICAL SETH .. .. ..........


. .. 134










LIST OF TABLES


Table page

6-1 NS2 simulation setup. ......... . .. 92

6-2 Comparison of events at the MAC level in a ten-node linear network with packet
size 400B. .. .......... ........... 94

6-3 Comparison of events at the MAC level in a ten-node linear network with packet
size 1800B. ......... ... .. 95

7-1 Simulation setup for evaluating the impact of OCSMA on TCP performance. .104

7-2 Events at the MAC level in a ten-node linear network under OCSMA protocol. 106

7-3 Performance comparison of OCSMA and OCSMA_DA. ... .. .. 111

7-4 MAC-level events in a ten-node linear network under OCSMA_LA. .. .. .. 121










LIST OF FIGURES


Figure page

2-1 Power disparities in a cellular network. . ..... 22

2-2 Pairingf strategies in a six-node cellular network. .... .. 24

2-3 User capacity of systems employing BC and GWBE sequences under average
power constraint and infinite user assumption. NV = 10, y = 10 dB, p = 0.05. :32

2-4 Average user capacity of systems employing BC and GWBE sequences with fixed
user population and total power constraint. NV = 10, y' = 10 dB, a~ = 4. .. .. 3:3

:3-1 User capacities of TDMA and DPC in an exponential path-loss channel. .. 44

:3-2 Efficiency of TDMA compared to DPC in an exponential path-loss channel. .. 45

:3-3 User capacities of TDMA and DPC in an exponential path-loss channel with
fading. ............... .. .. 47

:3-4 Efficiency of TDMA compared to DPC in a exponential path-loss channel with
fadingf ............ .......... ... 48

4-1 Broadcastingf over the whole hand for n~ = 2 and D = 50 for various service
factors, 6. ......... .... . 58

4-2 Two-level BC for n~ = 2 and D = 50 for various service factors, 6. .. .. .. 58

4-:3 Three-level BC for n~ = 2 and D = 50 for various service factors, 6. .. .. .. 59

4-4 Optimal FDM for n~ = 2 and D = 50 for various service factors, 6. .. .. .. 59

4-5 Fixed FDM for n~ = 2 and D = 50 for various service factors, 6. .. .. .. .. 60

4-6 Comparison of all the schemes for n~ = 2, D = 50 and 6 = 0.8. .. .. .. .. 61

4-7 Comparison of all the schemes for n~ = 4, D = 50 and 6 = 0.8. .. .. .. .. 62

4-8 Ratios of S, for the FDM schemes and the suboptinmal BC schemes to that for
broadcasting over whole hand for n~ = 2, D = 50 and 6 = 0.8. .. .. .. .. .. 6:3

5-1 Four-node linear network with conventional scheduling. ... .. .. 68

5-2 Four-node linear network with overlapped transmissions. .. .. .. 69

5-:3 Ad hoc network with overlapped transmission. ..... .. 72

5-4 Distribution of signal-to-interference ratio, y. ..... .... 75

5-5 Probability of finding a secondary transmitter. ..... .. 78

5-6 IUpper bound on probability of reception by node B. .. .. .. 79










5-7 Upper bound on the probability of a successful secondary transmission, p(S). ..

6-1 Typical frame exchanges in OCSMA protocol. ..........

6-2 Timeline of the OCSMA protocol. ..........

6-3 Frame formats of the OCSMA protocol. ..........

6-4 Ten-node linear network. ..........

6-5 Throughput comparison in a ten-node linear network with TCP traffic. .....

6-6 Throughput comparison in a ten-node linear network with CBR traffic. .....

6-7 Throughput comparison in linear network with multiple CBR flows. .......

6-8 Effect of varying the number of nodes in a linear network on the throughput
gain of OCSMA and OCSMA_RO. ..........

6-9 Binary-tree network. ..........

6-10 Throughput gain of OCSMA and OCSMA_RO in a tree network. ........

6-11 Throughput gain in a random network with mobility. ..........

7-1 Ten-node linear network under OCSMA. ..........

7-2 End-to-end throughput comparison in a ten-node linear network with TCP traffic.

7-3 MAC-level performance comparison of OCSMA and IEEE 802.11 in a ten-node
linear network. ..........

7-4 Transmitter congestion window evolution in a ten-node linear network. .....

7-5 Effect of short and long retry counts on throughput gains of OCSMA and OCSM~
in a ten-node linear network. ...........

7-6 Networks with multiple flows. ..........

7-7 Throughput comparison in a network with multiple parallel flows. ........

7-8 Throughput comparison in a network with multiple linear flows. .........

7-9 Ten-node linear network under OCSMA_LA. ..........

7-10 Frame formats of the OCSMA_LA protocol. ..........

7-11 Throughput comparison of OCSMA, OCSMA_LA and IEEE 802.11 in a ten-node
linear network. ..........

7-12 Throughput comparison of OCSMA_LA and IEEE 802.11 in a ten-node linear
network with CBR traffic. ..........


80

83

84

85

92

93

96i

96;


97

98

99

100

104

105


107

108

A_RO
110

112

113

115

117

118


120


122










A-1 Circle-circle intersection for analysis. . ..... .. 127


























































11










Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

OVERLAPPED TRANSMISSION IN WIRELESS NETWORKS

By

Surendra Boppana

August 2008

C'I !.v: John M. Shea
Major: Electrical and Computer Engineering

In wireless networks, interference is one of the us!I i ~r impairments that deteriorates

the performance of a system. Conventional channel-sharing schemes such as TDMA,

FDMA, CDMA, etc, orthogonalize the channel resources among users to minimize

interference. However, information-theoretic results indicate that orthogonalization of

the channel resources is not the most efficient way to transmit to multiple users. We

use the term overlapped transmission to describe non-orthogonal transmission schemes

because these schemes allocate the same channel resources to more than one user, thus

overlapping their transmissions. We conducted an investigation into the potential benefits

of overlapped transmissions as well as practical approaches to overlapped transmission in

both cellular and ad hoc wireless networks.

We first an~ li. .1 the potential of overlapped transmissions to improve the performance

of wireless cellular networks. We considered the use of cooperative broadcasting techniques

in the downlink of a cellular network to support additional users compared to a system

that orthogonalizes the channel resources among the users, such as TDMA, FDMA,

CDMA, etc. We evaluated the performance gains of cooperative broadcasting techniques

in terms of number of users that can be supported by the base station in a cellular

network when the number of users in the system is finite. We also evaluated the user

capacity of a cooperative broadcasting system, when the number of users in the system is










large. We compared the performance of the optimal broadcasting to several optimal and

suboptinial forward-link channel-sharing schemes.

Next, we studied the use of overlapped transmission in ad hoc networks to improve

the spatial re-use and throughput of the network. We showed how niultihop routing can

result in mobile radios having knowledge of interfering signals during the reception of a

transmission. We then demonstrated how this knowledge can he exploited to schedule

additional transmissions by performing interference cancellation at the physical 1 ca cr. We

evaluated the performance limits of employing overlapped transmissions in wireless ad

hoc networks with randomly distributed nodes. We developed a MAC protocol that takes

advantage of the knowledge of the interfering signals to schedule additional transmissions,

thereby increasing the spatial re-use and throughput of the network. We evaluated the

performance of this MAC protocol in a variety of network scenarios and compared to that

of IEEE 802.11 MAC protocol. We also analyzed the impact of overlapped transmissions

on the performance of Transmission Control Protocol (TCP) in wireless ad hoc networks.










CHAPTER 1
INTRODUCTION

With recent advancements in wireless technologies, wireless networks have emerged to

phI i- an important role in our d~i--to-d~i- communications. They provide greater flexibility,

mobility, and, when used in ad hoc configuration, do away with the necessity of any

infrastructure for their deployment. They are being increasingly used in applications

such as tactical communications, environmental monitoring, and commercial data

communications. Unlike wireline communications, all the nodes in a wireless network

share the same physical medium, which results in challenges specific to wireless networks.

Interference is one of the most challenging impairments that exist in a wireless environment.

Due to the broadcast nature of the wireless channel, simultaneous transmissions by radios

may result in interference at the receiving radios. Several channel-sharing schemes

have been developed and deploi-c II based on the configuration of the wireless network

(infrastructure or ad hoc).

1.1 Cellular Networks

In a cellular network, the transmissions are coordinated by the base station (BS).

The channel resources are allocated by the BS to those mobile users that either transmit

data to the BS or receive data from the BS. C'!I.!! .i. -sharing schemes such as time-division

multiple access (TDMA), frequea s l-i-division multiple access (FDMA), code-division

multiple access (CDMA), etc., are emploi-. I to accomplish the allocation of channel

resources. These schemes orthogonalize the channel resources such that there is minimal

interference among the transmissions. However, it is well known that orthogfonalizingf the

system resources [1] is not the optimal approach for simultaneous transmission to multiple

users.

The focus of [1] is a typical broadcast channel, such as the downlink of a cellular

network, with the BS and each of the mobile stations (j!ss) equipped with single

antennas. When the signal at each receiver is corrupted only by thermal noise in the









receiver front-end, this is the classical single-input single-output (SISO) Gaussian

broadcast channel (GBC), which has been extensively studied in the literature. The

SISO GBC belongs to the class of degraded broadcast channels, and its capacity region

is well known. The capacity of the GBC can he achieved by either superposition coding

(SPC) [1, 2] or dirty paper coding (DPC) [3-6]. Several practical schemes have been

proposed based on SPC [7, 8] and DPC [9, 10] that exploit the spatial diversity in cellular

networks that achieve improved performance.

In the first part of this dissertation, we analyzed the performance of overlapped

transmission in cellular networks. We define overlapped transmissions as those additional

transmissions which are a result of BS employing cooperative broadcasting techniques

compared to a cellular network employing conventional channel-sharing schemes such

as TDMA, FDMA CDMA, etc. We evaluated the performance gain of cooperative

broadcasting in terms of the number of users that can he supported by a BS (also see [11,

12]), and compared the performance of broadcasting to several optimal and sub-optimal

channel-sharing schemes (also see [13]).

1.2 Ad Hoc Networks

In wireless ad hoc networks, Medium Access Control (j1!AC) protocols such as the

IEEE 802.11 MAC protocol [14] are designed to coordinate transmissions among nodes

such that there is minimum interference at the receiving nodes. However, the strategies

emploi- II by these MAC protocols, such as the popular RTS/CTS strategy used in the

distributed coordination function (DCF) of the IEEE 802.11 MAC protocol, result in

inefficient utilization of the channel resources. For a survey on the current research on the

design of MAC protocols, please refer to [15] and references therein.

Multiuser detection (j!UD) in wireless networks has been proposed by several

authors [16-21] as a means to increase the spatial re-use in wireless networks hv increasing

the number of simultaneous transmissions in the network. However, in most cases, the

nodes might not have sufficient processing power to perform complex MUD schemes. The










complexity of the MUD schemes could be significantly simplified and the performance

enhanced if the interfering signal were completely known at the receiver. In wireless

ad hoc networks, the interfering signal may be known at the receiver due to multihop

routing. We introduced the idea of employing MUD schemes with known-interference

cancellation in multihop networks to increase the number of simultaneous transmissions

in [22]. A similar idea that employs network coding at the physical1.?,-;-r to increase

simultaneous transmissions in wireless ad hoc networks was recently proposed in [23,

24]; these network coding papers consider the physical-l o,-;r aspects of employing such

overlapped transmission schemes, but do not address the MAC level implications. In

the second part of this dissertation, we introduced overlapped transmission schemes

for ad hoc networks based on cancellation of known interference. We analyzed some of

the fundamental limits on employing overlapped transmission in ad hoc networks (also

see [22, 25]). We designed a MAC protocol which exploits this feature to improve the

throughput and spatial re-use in wireless networks (also see [26]). The performance of the

resultant OCSMA protocol is evaluated in a variety of network scenarios and its impact on

the performance of TCP flows is investigated (also see [27]).

1.3 Dissertation Outline

The rest of the dissertation is organized as follows. In C'!s Ilter 2, we introduced the

notion of overlapped transmission in cellular networks. We investigated the performance

of a cellular network employing cooperative broadcasting and compared it to that of a

system employing Generalized Welch Bound Equality (GWBE) sequences. In C'!s Ilter 3,

we defined the user capacity of a cellular network. We evaluated the user capacity of

systems employing dirty paper coding (DPC) and TDMA, and compared the performance

of a system employing DPC to that of a system employing TDMA. The performance

of optimal and suboptimal forward-link channel-sharing schemes in cellular networks

are compared in (I Ilpter 4. In ChI Ilpter 5, we introduced the notion of overlapped

transmission in wireless ad hoc networks. We investigated some limits on employing










overlapped transmission in an ad hoc network. In C'!s Ilter 6, we developed the Overlapped

Carrier Sense Multiple Access (OCSMA) protocol to coordinate transmissions so that

knowledge of the interfering signals in the network can be exploited to schedule overlapped

transmissions in the network. The performance of the OCSMA protocol under various

network topologies is evaluated using Network Simulator (ns2), and is compared to that

of a system employing the IEEE 802.11 MAC protocol. The interaction between OCSMA

and TCP is investigated in OsI Ilpter 7, where we evaluated the impact of overlapped

transmissions on the performance on TCP flows in a variety of network scenarios. The

dissertation is concluded and future research directions are discussed in (I Ilpter 8.









CHAPTER 2
OVERLAPPED TRANSMISSION IN CELLULAR NETWORKS

2.1 Introduction

In [1], Cover introduced the broadcast channel (see also [28, 29]) and demonstrated

that it is more efficient to simultaneously transmit to multiple users than to time-share

or otherwise use orthogonal division of the channel resources among users. Consider a

standard two-user degraded Gaussian broadcast channel defined by


yri = ix + ni

y2 2 ha2n (2-1)

where x is the signal transmitted by the sender, yl and y2 are the signals received by

user 1 and user 2, respectively, nl and n2 are i.i.d. ~ #1(0, 1), hi and h2 are the channel

gains of users 1 and 2, respectively with |h1|2 2 l12. The sender has a total power

constraint of P. The capacity region of this channel can be obtained by two different

coding techniques. In [1], Cover proposed the use of superposition coding (SPC) and

successive decoding to achieve better performance than orthogonal division of the channel

and found the achievable rate region. The transmitter generates two codebooks, one with

power aP at rate R1, and another codebook with power (1 a)P at rate R2, Where P is

the total power available at the transmitter, and a s [0, 1]. User 1, which has the better

channel, decodes user 2's codeword first, subtracts this from the received signal, and then

decodes its codeword. The rate region is given by



U (1alz\(2-2)
aE[o,1] 0


Bergmans [2] showed that this rate region is the capacity region for Gaussian broadcast

channels. The second technique is based on the coding for channels with known

interference [3-6]. The transmitter first generates the codeword for user 2 with power









aP. Once the codeword is generated, the transmitter has non-causal information about

the interference that this code causes at user 1. Hence the rate [3, 4]


R1 = max {I(U; Y) I(U; S)} (2-3)


is achievable for user 1, where S ~ #1(0, (1 a)|hl|2P). From Costa [5], we know

that by letting U = X1 + PS, and appropriately choosing P, R1 in (2-3) becomes

log(1 + alhl|2P), Which is the best possible rate for user 1. However, the codewords of

user 1 cause interference at user 2. Hence, the achievable rates at user 2 are given by

Ra I ~ ~ ~~~~ (1 a)|Iha2P1+ahlPi(4


Broadcast strategies for temporal fading channels were introduced by Shamai in [30],

and extended to multiple-user and multiple-input multiple-output (jl\!llO) channels

in [31-33]. A summary of information-theoretic work focused on cellular communications

is given in [34]. Practical schemes based on SPC were proposed by Pursley and Shea [7, 8],

which exploit spatial differences among receivers and improve the throughput in wireless

networks .

In this chapter, we evaluated the use of information-theoretic broadcasting (BC)

techniques such as SPC and DPC in a cellular CDMA communication system that

employs orthogonal spreading sequences and power control. In such systems, orthogonal

spreading codes are used for different users' signals. Power control is applied to minimize

multipath interference to users in that cell and to minimize interference to users in

.Il1i Il:ent cells. Ideally, each user sees the same signal-to-noise ratio (SNR) for the signal on

their designated spreading code. However, if a user despreads another user's signal, power

control may result in vastly different SNRs. BC may offer some significant advantages

in such scenarios by simultaneously transmitting messages to multiple users on a single

spreading code. Although the focus of this chapter is on a cellular CDMA network, the










ideas presented here can he applied to other channel-sharing schemes such as FAIDA,

TDMA, etc.

In this work, we use an abstract model of a CDMA system in which the required

transmit powers are determined according to Shannon capacity or the capacity region

of the additive white Gaussian noise (AWGN) broadcast channel. As in [:35], our goal is

to assess the number of users that can he supported at some target rate under a power

constraint.

We compare the user capacity of a system employing BC to that of a system

employing GWBE sequences with the same power constraint. The use of generalized

Welch hound equality (GWBE) sequences to accommodate more users than the processing

gain of a cellular system was considered in [:36] (see also [:37]) for a synchronous AWGN

channel with linear MAISE receivers. The design of spreading sequences to maximize

user capacity for a CDMA forward link in a fading channel was considered in [:38]. The

.I- i-alchronous CDMA system was addressed in [:39]. Iterative construction of the optimum

sequences that maximize the user capacity with minimum total transmitted power was

-II_0---- -1.. in [40]. In [:36], it is shown that for a CDMA cellular system in which each user

is assigned a unique spreading code and an AINSE receiver is emploi-, I1 the user capacity

K for a common target SNR of y, is limited by K < NV(1 + #), where NV is the processing

gain of the system.

The remainder of the chapter is organized as follows. In Section 2.2, the system

model is described and the notion of BC is introduced. In Section 2.3, we constructed an

optimum pairing strategy that minimizes the total power transmitted for a given number

of pairs. In Section 2.4, we compared the performance of a system employing BC with a

system employing GWBE sequences under an average power constraint and infinite user

population. In Section 2.5, we compared the user capacity of this broadcasting system to

that of a system employing GWBE sequences under a total power constraint and fixed

user population. The chapter is concluded in Section 2.6.









2.2 System Description

We consider a cellular system that uses orthogonal spreading and power control on

the forward link, which is typically seen in commercial systems, such as IS-95, WCDMA

and CDMA2000 [41]. Consider the BS at the center of a circular area of coverage.

Without loss of generality, we assume that the circular region has unit radius and the

BS is at position (0, 0). The users are uniformly distributed in the area of coverage. Let

Di denote the distance from the BS to mobile user ifl The probability density function

(pdf) of Di is given by

2d, 0 f~i (d) 0, otherwise. (5

Another quantity we shall be referring to later is Ui, the square of the distance from the

BS to the mobile user if It is easy to see that Ui is uniformly distributed in [0,1]. We

assume that the thermal noise, multiple-access interference and .ll11 Il:ent-cell interference

can be modeled as a single additive white Gaussian noise (AWGN) source with two sided

power spectral density & [42]. (The assumption is reasonable since the .I.11 I.:ent-c~ell

interference is highest at the cell boundaries and multiple-access interference is highest

in the interior of the cell). Let W be the bandwidth each user sees after despreading the

received signal and NV denote the number of orthogonal channels in the system.

Power control is used to ensure that each mobile user receives sufficient power to

achieve the desired quality of service while minimizing the interference to other mobiles.

We consider the case in which perfect power control is used to maintain a constant

signal-to-noise ratio (SNR) at each mobile user receiving information from the BS. In

such a scenario, it is often possible to identify pairs of users such that one of the users

receives a much higher power than the target power level when that user demodulates

the other user's signal. Figure 2-1 depicts such a scenario, in which power control is

used to achieve the same received power at each of the mobile users MI1, -T T. and if .

An exponential path loss model without the effects of fading and shadowing is assumed




















Target SNR level




Distance from the base station ->

Figure 2-1. Power disparities in a cellular network.



for the sake of exposition. In the figure, the abscissa denotes the distance of the mobile

users from the BS, and the ordinate denotes the power of the signals intended for each

user. The users are indexed in increasing order of their distance from the BS. It can he

seen from the figure that when the BS transmits information to ii T., maintaining the

target SNR level, the SNR seen by both All and if ., is much greater than their target

SNR levels (by amounts A + B and C respectively). Similarly, when the BS transmits

information to T., All receives an additional ,4 dB of power above its target SNR level.

This implies that All has sufficient SNR to decode messages intended for both i T. and i T.,

and ifl. has sufficient SNR to decode the messages intended for f.11. The power disparities

at users Aft, if.1 and if -II__- -r that information for if.1 and All can he included in

the transmission to if.1 through the use of BC. Similarly, we can include information

for All while transmitting information to T.. The dotted line in Figure 2-1 indicates

BS transmitting information to if ., while transmitting to if i. at the target SNR level

by employing BC. Such additional transmissions that occur due to the BS employing

cooperative broadcasting strategies are termed as overlapped transmissions.

We can exploit such disparities to increase the user capacity of the system by

employing BC [1, 3-6, 28, 29]. 1\oreover, we show that this additional system capacity










comes at very little expense to the performance of the network. In our broadcasting

strategy, the BS uses two-level superimposed codes to transmit to pairs of users which are

allocated the same spreading sequence. The broadcast codes are composed of information

at two different rates designed for two different SNR requirements for their accurate

reception. The message with the lower SNR requirement for its accurate reception

is known as the basic message, and the message with higher SNR requirement for its

accurate reception is known as the additional message. The user capacity of such a system

is dependent on the number of suitable pairs that exist and also on which users pair.

To analyze the performance of such a system, we index the mobile users in decreasing

order of their channel gains. We define a pairing str:1 rl ;, f(i) as a one-to-one function

which associates/pairs user Ml with the user Myf(i, f(i) > i for 1 I i I NV. This means

that users Ml and Myf(i share the same spreading code, and Ml pairs with Myf(i to recover

an additional stream of information that is superimposed on the message for Myf(i (Note

that Ml has a better channel than Myf(i). The constraint on the domain of i indicates that

the maximum number of pairs using our two-level BC is equal to the number of orthogonal

channels available. Here the one-to-one condition implies that no two users pair with the

same user. This restriction is required by our use of two-level BC. The fact that f(i) is a

function restricts each user to pair with at most one user. Although these requirements

are not necessary from a theoretical standpoint, they represent a scenario that is of more

practical interest. Two such examples of pairing strategies are depicted in Figure 2-2 for

a six-node cellular network. Assume that the users are indexed in the decreasing order of

their channel gains. For example, user My has a better channel than M. 1, M. 1 has a better

channel than M. 1, and so on. The pairing strategy f(i) = i + 3, indicates that user Mi and

user if I ,3 Share the same spreading sequence, and user Mi recovers an additional message

on top of the transmission for user if 1+3 (Note that user Mi has a better channel than

user if I ,3). Under the pairing strategy f (i) = 7 i, users Mi and My7- share the same












cI, cI,

nAJ
BS


OO@@@ O


*****
I I I 11 T T
*ci *ci *ci *ci *i *


f(i)-- 7 i


Figure 2-2. Pairing strategies in a six-node cellular network.



spreading sequence, and user ifl recovers an additional message from the transmission for

user Afy_4.

An exponential path loss model with Rayleigh flat fading is assumed, where the power

Pr, received by user Af,, is related to the transmitted power Pt by


Pr =KI dL h|,|2 Pt,


(2-6)


where KI is a constant, d, is the distance of the mobile user from the BS, a~ is the path

loss exponent, and |h,| is the magnitude of the fading at the user Af,, which is assumed to

be constant over many symbols. The information rates Rbm and Ranz of the basic and the

additional messages under two-level BC are given by [29]


(1 a)K ObPt
a~pxbPt 0 ~W
aK ~ P,


Rbm


Rn,


(2-7)


(2-8)


og 10a (










where Pt is the power transmitted by the BS, za and zb are the channel gains of users

receiving the basic and additional messages, respectively, and 0 < a < 1 is fraction of the

power allocated for the transmission of the additional message. Under an average power

constraint, the transmission of an additional message while maintaining the same target

SNR at the user receiving the basic message results in an increase of the total transmit

power by the BS. In the context of a cellular network, this additional transmit power

will result in increased interference to users in .Il11 Il:ent cells and to users in the current

cell from multi-path. Hence our focus is on increasing the capacity of the system while

maintaining the same average transmit power at the BS. Such a throughput gain can be

achieved by decreasing the information rate or the target SNR of the users. For the sake

of simplicity, henceforth we assume that the target SNRs of both the additional and the

basic messages are same.

2.3 Maximizing the User Capacity

In this section, we derived an optimum pairing strategy for BC that minimizes the

total power transmitted by the BS for a given user capacity (we are interested in the case

where the user capacity is greater than the number of orthogonal channels). First we need

the following result to construct a pairing strategy that maximizes the user capacity.

Theorem 2.1. Consider a cellular network with K users and N or'/;. ~i. .t..al channels such

that NV < K < 2NV. The total power transmitted by the BS using NV or it..y. .t..rl channels

and two-level BC is greater than that of direct transmission to the K users through K

or'l,~ vi. .t..l channels.

Proof. Since we are considering only a two-level broadcast code, it is sufficient to show

that the total power transmitted to two users with two orthogonal channels, maintaining

a constant SNR at the users is less than the power transmitted to the users with one

channel and a two-level broadcast code and maintaining the same SNR at both the users.

Consider a network with two users My1 and if with channel gains zz and z2, With zz > z2*

Let P1 and P2 be the powers transmitted by the base station to the users Mr and it.,,









respectively, through two orthogonal channels, such that a target SNR of y is maintained

at the users. Hence we have y =p1 = .2P Note that P2 P. In order for these

users to pair using a two-level broadcast code with one channel such that both My and

M.1 have a target SNR of y, there should exist a pair of (a, P) satisfying the following

constraints.


aZ P

(1 a) Z2

a Z2 0 i


0



(2-9)

(2-10)

(211)

(212)


where Zi = K~zi, i = 1, 2, NVo/2 is the two sided noise power spectral density of the

AWGN channel, and W is the effective bandwidth seen by each user after despreading the

orthogonal code. Constraints (2-9) and (2-10) state that the SNRs of basic and additional

messages should satisfy the target SNR requirement. We show that no such pair (a, P)

exists that satisfy the above constraints. From (2-9) we have


Z1P
4 a = (. 7


Z P,
) ~


(2-13)


Substituting (2-13) in (2-10),






m z2( 1p)

+ P Pi


y P1 Z2 0 Io)

=Z2(P 7P1 2 / 7

= YP1 + P2

=Pi (1 + y) + P2

> P1 + P2


Z2 p2
No~w










which violates constraint (2-12).


Corollary 2.1.1. The minimum additional power required for BC to a pair of users

having the same spreading sequence is yPs, where y is the inr, SNR and Pi is the power

required by the BS to maintain a constant SNR of y at the user Mi with better channel

gain and without 1,,I'l. c;/.:,i~ BC.

A pairing strategy that minimizes the total power transmitted for a given number of pairs

k
f(i)/= i + Nv, 1< i < k. (214)

Note that, even though the choice of the optimum pairing strategy is not unique, the

minimum total transmitted power is unique.

2.4 User Capacity under Average Power Constraint

In this section, we compared the user capacity of a system employing BC to that of

a system employing GWBE sequences under the same average total power constraint.

Since our focus is on increasing the capacity of a cellular network without increasing the

total transmit power, we derive the average power constraint from a cellular system that

supports NV users through NV orthogonal channels.

2.4.1 Cellular Network without BC

Consider a cellular system with infinite user population and NV orthogonal channels

supporting NV users We assume that all the users are uniformly distributed in the

circular area of coverage and have a target SNR requirement of y and a maximum outage

probability of p. Let z denote the instantaneous channel gain between the BS and the user




1 By population we mean the number of mobile radios requesting service and by users
we mean the actual number of mobile radios which are supported by the BS.









M~. The distribution of the channel gain x (cf. (2-6)) is given by


Fz (x) = Fz (x = d-2 F 2)

= +e- -1 > 0. (215)

An outage event occurs if the instantaneous SNR at the user falls below y. The probability
of outage is given by


Pr(KI~xP,1VW~ ) C

=r( rlvoIc~t

e-zo 1 q*Nolf
S1 + Zo KI> F

Let Z,, denote the maximum value of the channel gain which results in an outage event.
When an outage occurs, the BS doesn't transmit to that particular user (since perfect

power control is assumed, the BS has information about the channel gains of all the users).
Since we are assuming an infinite user population, it is ah-li- possible to find NV users

with channel gains x > Z,,, such that they are supported by the BS. Under this conditional
distribution of the channel gains (i.e. F,(x|: > Z,,)), the average power transmitted by the
BS, such that a target SNR of ]* is maintained at a user is given by

{(PT(Z,,) }l~w = E| >Z (2-17)

[ 1 + Zarn2,(0, eZ,,) e-zp (1 + Z,,)


where C' = yiNoWT(KI>)-l and r(.) is the incomplete gamma function given by

F~, ) t-l -tdt. (2-18)

Since the BS transmits to NV users, the average total transmitted power is given by
NE { Pr( Z,,)}.









2.4.2 Cellular Network employing BC

Consider the cellular network employing BC of Section 2.2. We assume that there is

an infinite user population, and let K, NV < K < 2NV denote the number of users served in

a transmission duration (we again assume that it is alr- we possible to find K users with

channels gains greater than Z,,, such that they are served by the base station). In this

section, we assume that the number of users served by the BS is constant across all the

symbol durations. Hence, in a network with K users (users supported by the BS) and NV

orthogonal channels, the total power Pbc transmitted by the BS under the pairing strategy

of (2-14) is given by




I (K K-N l X

=P,"bc aC, (2-19)

where




k =1 "


and y,' is the common target SNR of all the users, not necessarily equal to -,. We are

aware of the fact that an increase in the user capacity under the same average power

constraint would result in the decrease of the target SNR. The term PiTb ca be

interpreted as the total power required to transmit to K users using K orthogonal

channels and APfe can he interpreted as the increase in the transmitted power due

to employing BC to support these K users over NV orthogonal channels (refer to

Corollary 2.1.1). The expected value of P,"bc iS giVen by














Ky'No;WI K


K~y'
E P(pTZ,)}


E{(Pu"b"( ')}


(2-20)


where E {PT(Z,)} is given by (2-17). Similarly, the expected value of Abc iS giVen by

E {A Abfe ,l 7/2 0E, zl > z2 > K. (2-21)


The distribution of pk


k~-1 can be evaluated from the principles of order statistics. Let


P, =Z1. The conditional density of pi, 1 < i; < K is given by [43, 44]


Kt!


f, (plp < P,)


x 1


(2-22)


where F,(P,)- is- givn b

F,(P,) = P,(1 e ep).

Hence, the expected value,, of A~e is


(2-23)


K-N~i p~


E {APfe q,)


(2-24)


where f,,(plp < P,), 1 < k < K is given by (2-22). The expected value of Pfe is the sum
of the expected values of Pu"bc and APfe


(2-25)


([1 i-1
p l~i 1aii ( en K-i


-e1+ ,/1


E {Pfe(q')} = E {Panbc /)} +E {APfe(q')} .









2.4.3 Cellular Network employing GWBE Sequences

Consider a cellular system with infinite user population and K, > NV supported users

such that each user is associated with a unique GWBE signature sequence [45] (we assume

that it is ah-li-w possible to find K, users with channels gains greater than Z,, such that

they are served by the BS). Let the target SNR of all the users be y'. Assuming that all

the orthogonal channels are equally occupied by the users, the total transmitted power by

the BS in a symbol duration is given by [38]


P9 =S y)lo (2-26)
N Kg(y') k=1 zk

where gi(q) = is the effective bandwidth of each user and Ki, < N(1 + 6) and zk, is

the channel gain of user M.l [36]. The average total power transmitted is


E{"(') ="EPrZ,} (2-27)

where E{(PT(Z,)} is given by (2-17).

We numerically evaluate the user capacities of systems employing BC and GWBE

sequences such that the average transmit power in both the cases is equal to that of the

system in Section 2.4.1. The results in Figure 2-3 compare the user capacities of systems

employing BC and GWBE sequences for a~ = 2, 4, as a function of the degradation in

the target SNR -10 log ,: compared to the target S\NR y of the system in Section 2.4.1.
The number of orthogonal channels NV = 10, outage probability p = 0.05, target SNR of

the non-broadcasting system y = 10 dB, PSD of the AWGN channel NVo = 1 x 10-10

bandwidth W = 1 x 106 Hz, and K(,= 1 x 10-2

For NV = 10, and for a degradation of about 1 dB in the target SNR, using BC, 12

users can be supported for a~ = 4 and 11 users for the case of a~ = 2. This translates to an

increase of 211' in the user capacity of the system for a~ = 4 and 101' for a~ = 2. Higher

values of a~ lead to greater disparity in the channel gains of the mobile users, and BC

can be effectively used to support more users. The user capacity of a system employing













GWBE sequences remains constant at 10 for target SNRs ranging from 10 dB to 7 dB.

The maximum number of users that can be supported using GWBE sequences is given

by~ ~ 1 Kr < ( +6 adfr N = 10, and 7 dB < yi < 10 dB, K, < 10. Hence no


additional users can be accommodated using GWBE sequences in this particular scenario.

The results indicate that significant increase in the user capacity can be achieved using

two-level BC with little degradation in the target SNR.



14.5-
Sa=4, BC
-e- a=2, BC
e-a=2,GWBE
13.5-





S11.5-


11 -


10.5-


U 0.5 1 1 .5 2 2.5
Decrease in the target SNR (dB)

Figure 2-3. User capacity of systems employing BC and GWBE sequences under average
power constraint and infinite user assumption. NV = 10, y = 10 dB, p = 0.05.



2.5 User Capacity under Total Power Constraint

In this section, we evaluated the user capacities of a system employing BC and a

system employing GWBE sequences under a finite user population. Instead of limiting

the average total power transmitted by the BS, we constrain the total power transmitted

by the BS during a transmission duration. Since the user population is finite, the number

of users that can be served in any transmission duration is random and depends on the

channel gains of the users in that symbol duration. We evaluate the average user capacity
















-M- BC
-*-GWBE


16

14

12


10 15 20 25 30 35 40 45 50
Node population

Figure 2-4. Average user capacity of systems employing BC and GWBE sequences with
fixed user population and total power constraint. NV = 10, y' = 10 dB, a~ = 4.


(averaged over all transmission durations) of both the systems under the same total power

constraint. We arbitrarily choose the total power constraint per symbol duration equal to

the average power constraint considered previously (cf. (2-17)). The results in Figure 2-4

show the average user capacity of systems employing BC and GWBE sequences for a~ = 4,

number of orthogonal channels NV = 10, K, = 10-2, 0V = 10-10, W = 106 Hz, and

y' = y = 10 dB. We do not impose any outage constraint in this case. It can be noted

that there is no gain in the user capacity of the system employing GWBE sequences

(maximum user capacity is 10 in this scenario). However, the average user capacity of the

system employing BC increases non-linearly with increasing user population and reaches

the theoretic maximum of 2NV when the user population is about 5 times the number of

orthogonal channels available. With sufficiently large population, it is alr-ws- possible to

find 2NV users with channel gains which satisfy the total power constraint under BC. With

fixed user population and total power constraint, an increase in average user capacity is

possible with BC without any degradation in the target SNR.










2.6 Summary

In this chapter, we evaluated the performance of BC in increasing the user capacity of

the forward link of CDMA cellular systems. The disparities that exist in a network with

power control were exploited to superimpose information to users with better channel

conditions. We have compared the performance of such a system employing BC to that of

a system employing GWBE sequences under both average- and fixed-power constraints.

The results indicate that on an average, 211' increase in the capacity is possible for a~ = 4

under an average power constraint by employing BC at a degradation of 1 dB in the target

SNR. With a fixed power constraint, the increase in the user capacity is far greater than

that of a system employing GWBE sequences. In the next chapter, we evaluated the

user capacity of a cellular network employing broadcasting and compared it to the user

capacity of a cellular network employing TDMA.









CHAPTER 3
USER CAPACITY OF DOWNLINK( CELLULAR NETWORKS

3.1 Introduction

As we have seen in C'!s Ilter 2, cooperative broadcasting techniques such as SPC

and DPC can be used to simultaneously transmit to multiple users, which are more

efficient than time-sharing or otherwise use orthogonal division of the channel resources

among users. In this chapter, we investigate the performance of information-theoretic

broadcasting (BC) when all the users share the entire channel resources. Unlike

orthogonalization schemes or two-level broadcasting schemes of C'!s Ilter 2, under BC,

the BS uses the entire channel resources to transmit simultaneously to all the users in

the system. We focus on the use of DPC, which has been shown to achieve the capacity

of MIMO Gaussian broadcast channels [46]. As noted earlier, DPC is one of the coding

schemes that can achieve the capacity of a scalar Gaussian broadcast channel. However,

DPC is a complicated scheme that has yet to be implemented in practical systems. ?1 itiv

present d or systems use time-division multiple access (TDMA), in which the base station

supports several users by transmitting to only one user at a time. The performance gains

of DPC over TDMA in a MIMO Gaussian broadcast channel in terms of sum-rate capacity

were first evaluated in [47]. Viswanathan et al. [48] have considered the performance gain

of DPC over TDMA in terms of downlink user capacity in a MIMO cellular network.

Simulation results in [48] so-----~ -r that the performance gain of DPC over TDMA is not

significant for system employing single antennas at each radio. However, no analytical

results were provided. In this chapter, we evaluate the downlink user capacity of a

single-cell communication system under TDMA and DPC and analyze the performance

gains of DPC over TDMA when the number of users in the cell is large.

The rest of the chapter is organized as follows. Section 3.2 describes the system

model of the cellular network emploi-e I in evaluating the user capacities under TDMA

and DPC. In Section 3.3, we evaluated the user capacity of a cellular network employing










TDMA, and in Section 3.4, we evaluated the user capacity of a cellular network employing

DPC. Section 3.5 evaluates the gain of DPC over TDMA under several network scenarios.

The chapter is concluded in Section 3.6.

3.2 System Description

Consider a scalar Gaussian broadcast channel with NV receivers and single antennas

at the transmitter and at each of the receivers. This is representative of the forward link

of a single cell of a cellular communication network. Let x denote the complex baseband

transmitted signal and hk, 1 < k < NV, denote the channel gain from the transmitter to

user/receiver k. The complex baseband channel output at user k, yk, is


yk = k~x k nk, 1 < k < NV, (3-1)


where nrk ~ #1(0, NVo), Vk, is circularly symmetric complex Gaussian noise. The

transmitter/base station is subject to a total power constraint of Prot and all the users

have a common target date rate Ro. We assume that the channel gains are perfectly

known at the transmitter and the receivers. The total bandwidth of the system is assumed

to be W Hz.

In this chapter, we characterized the user capacity of TDMA and DPC in a scalar

Gaussian broadcast channel. We define the user -r'~ra. HuI to be the expected number of

users that can be supported by the base station under a total transmit power constraint,

and a common target data rate at the users. The user capacity of cellular systems

employing DPC and TDMA are an~ li. .1 using an information-theoretic framework, and

the performance is evaluated for large user populations.

3.3 User Capacity of TDMA System

3.3.1 System Description

We consider a TDMA system in which the base station serves only one user per time

slot using the entire transmit power Prot available to it. If hk denotes the complex channel










gain of user k, the received power Pk, is giVen by


Pk, = K(,|hk 2Ptot, (3-2)


where Prot is the total transmit power available at the base station and K, is a constant.

Time is divided into fmames, and each frame is divided into time slots, not necessarily

of equal duration, during which the base station transmits to different users based on

their channel gains. The channel gains of all the users are independent and identically

distributed with a continuous and strictly increasing distribution function. Although the

channels gains are randomly distributed, they are assumed to be constant throughout the

duration of a frame, and are uncorrelated across the frames.

Let zi, z2, *** Nx 1 2~ > N r) denote the ordered squared-channel-magnitudes

(i.e., zk k l12) of the mobile users in the cellular network, and Ro denote their common

target information rate. The channel capacity of user k is [29]




To achieve the target rate of Ro, the base station has to transmit to user k for a fraction

of time Ro/Ok~. Hence the user capacity K~TDM/A of this system is given by





= kPr i7T < ~To, T To where
k= 1 i= 1 i= 1

Ti =,(3-4)


To = W/Ro, and with the convention that



i= 1 N+i= 1 ) P ,,i= 13










Proposition 3.1. Consider a single-cell of a cellular network employing TDM~A with total

transmit power Prot, common .:yIr information rate Ro at the users, and a population of

NV users. Then the downlink user i nt'r~ .:; H KTDMA iS given by


K~TDMA i TO T2 I TN. (3-6)


where Tis are given by (3-4).

Proof. For NV = 2, we have from (3-4)


K~TDMA PrT T1 TO,T T1 2 TO) 2Pr (T + T2 TO)

=Pr (T, < To, T + T2 TO)

Pr T, < To, T, + T2 TO) P T T1 T2 TO)

=Pr(T I5 + Pr ( + T ,


For NV > 2, (3-6) follows from induction. O

3.3.2 Asymptotic User Capacity of TDMA System

We can find the e nm i nd ic'l~ user capacity of a cellular system employing TDMA by

invoking a theorem on the distribution of the trimmed mean of ordered random variables.

To that end, we introduce the following notation. Let


M.l =,>T~ Tk 1 2, TN (7
i= 1
1 k
(yp~vl Tc~lv> C Ti, Gk = 0, pk =
i= [areN] +1

denote the trimmed mean of the ordered random variables T T2 TN With continuous

and monotonically increasing parent distribution FT(t) [49], where [.] denotes the ceiling

function. Let Ik, and uk, denote the cOkth and Pkth percentiles of the parent distribution









FT(t) i.e, Ik = F,-1 k~) and uk, = F-~1 k). Further, define

0, x < I


1, X > Uk,

and let

pk = x~k~x)(3-9)

and

o =i" Z2dGk (X) p ~. (3-10)

The following theorem from [49] states that if FT(t) is continuous almost everywhere and

strctl inresin an { xdFT(x) < 00, the .I-i-ph.1 Ic '~ distribution (as NV 00o) of the

trimmed mean converges to the normal distribution.

Theorem 3.1. 2(Ni~(M pl)) 2 (Z), with Z = (P a~)-1(Y~ + (u p)Y2) + 1-I3)

and E(Z) = 0, where Yi is #1(0, (p a)O.2) Gnd indep688Ren Of (Y2, 3)1 and 2 ~3) aTC

#1(0, C), where

C = P (1 P) a(1 P)
-a( ) (1 a~)

and 2(X) denotes the distribution of the random variable X.

Proof. Refer to [49]. O

Although the theorem has not been proven for values of akr and PIk that vary with k, we

apply the theorem to get an approximation on the distribution of the trimmed means Ml,

The .I-i-mptotic user capacity of a TDMA system can be expressed as


K~TDMA o
k=1k

N ~ V~i 31










where Mi ,, pks ak are given by (:37), (:39), and (:310), respectively, and #(.) denotes the

unit normal distribution function.

3.4 User Capacity of DPC System

3.4.1 System Description

In a cellular system that employs the DPC multiple access scheme, the base station

encodes the users' signals in a sequential manner. By doing so, when the transmitter

encodes a user's signal, the signals to be transmitted to all the previously encoded users

are fully known at the transmitter. The DPC technique ensures that the user being

presently encoded doesn't suffer any interference from the previously encoded users. The

users are encoded in order of increasing channel gains, which ensures that DPC achieves

the sum-rate capacity of the scalar Gaussian broadcast channel.

When the base station uses DPC, it transmits to each of the selected users for the

entire duration of the frame. Thus the target rate Ro can he translated to a target SNR of

yo = 2TY 1. We consider the channel model described in (:32). The following proposition

gives the user capacity of a cellular system employing DPC.

Proposition 3.2. Consider a cellular network employing DPC' with total treenstait power

Ptot. common isr, 1 SNR of yo and user population NV. A-tn ;1,.,1 that the users are

ordered in decreasing order of channel maagnitude~s x 1 < i < N., the user -r'~ra. //t I DPC is

given by

KDPCv Wy, iO '07 tot (:312)
,= 1 P i= -
Proof. When DPC is emploi- II at the transmitter, the information of the user with the

best channel gain (xl) is encoded last and hence he doesn't see interference from any of

the previously encoded users. Since yo is the target SNR, the power required to transmit

to the first user P1 (with the best channel gain) is given by




Ky ~









Similarly, user 2 with channel gain z2 SeeS interference only from user 1's signal. The

power required to transmit to user 2, P2 to maintain a target SNR of To is given by [29]

To=
N~oW + z2 K,
(No W70 +~p

Kv, z 2



Inductively, it can be shown that the power required to transmit to user k, Pk, maintaining

a target SNR of To at the receiver is given by


(NoW7 k-1 x0 70 k-1-
t;Kr, zi, zklYo

Since the total transmit power available at the base station is Prot, the user capacity of a
cellular system employing DPC is


KDP = klr Pi< ot, k+i >tot (3-14)
k= 1 i= 1 i= 1
with the convention that

i= 1 i=1 i= 1


By appealing to the technique used in Proposition 3.1, the user capacity of DPC system
can be expressed as


= 1 ~i= 1

N~ 0I rv0 k~i-1 +07 -1-


=~ Pr i (1 + o)-i Ptot, (3-15)
k= 1 =

where Plot = ProtKi(Nnr/'oW70
O










3.4.2 Asymptotic User Capacity of DPC System

We use a similar approach to Section 3.4.2 to find a closed form expression for the

user capacity of DPC system when the user population tends to infinity. To that end, we

introduce the following notation. Let




Xk "N Zi 21 2 N(3 16)
i= 1


1i=l 1 V 1) 37

where pi = z l, and A(u), O < a < 1 is the weight function defined as

k1+y)-u(N+1) k Jk 8) 0 u lN+1 (3 8)
N+1

Note that Xk, can be interpreted as a linear combination of the ordered random variables

pi < p2 PN p With A(.) as the weight function. Let Fp(p) denote the parent

distribution of p, which is assumed to be continuous and strictly increasing. Define


kLcA k FP) = k ~U F-(U)1U (319)

and


of (Ak, Fp)= (Fx)(Fy)[Fmix,))-F)Fy /.i (3-20)


The following theorem from [50] states that, under very general conditions, the linear

combination of ordered random variables .-i-mptotically (as NV c o) converges to the

normal distribution.

Theorem 3.2. Assume that f_ p2dFp < OO, and 8() iS bounded and continuous a.e.

F, Then

oX- I(J, Fp)( P









where 2(X) denotes the distribution of the random variable X.


Proof. Refer to [50]. O

Although the theorem has not been proven for weight function, Jk(u) that varies

with k, we apply the theorem to get an approximation on the distribution of Xk*

Using Theorem 3.2, the .-i-mptotic user capacity of a DPC system can be written as


KDPCi= y0 k-ifi Ptot

k = 1Vr, i =- 1J) p


Jk, ~ Pr, Xkl totI ~Vl Y rlI





TDMA~N~ kfiiny rl aP


where Xk, k, k, and ofDP are given by (3-16),31) 31) and (3-20), respectively, W andlz h



In fordanertcoprthusrcpiie of TDMA and DPC systems a xoetl thos anl, weeinethean


TDMA1 eficen apcy, y in asoeta ahLssCanl oF



9 =DiP (3-21)

where KDMA istedand DC e gitwen t bys (3-11)n and (31) resper ,ctivey We panalyzeth




Ianexponent a i al posanth-loss hannel withosut fading the powers rectived by uer P















independent and uniformly distributed in a circular area of unit radius with the base

station at the center, the density function for Di is




2d, 0
f~i(d) r0, otherwise. 3)


Under this channel assumption, it is easy to see that the channel magnitudes ze are related

to Di as ze = Do" and that their parent distribution is given by


(Z 2
Fiz =z-,0Ot

(324)


Similarly, the T~s defined in (3-4) are i.i.d. with parent distribution



Fr () = K,P, ot 2 -1 1 ,O< 1.
No W log





65-
yo=0dB
60-
u=2,TDMA,Analytical

u=2,DPC,Analytical
[- 8 -u=2,DPC,Simulation
50 a =2,TDMA,Analytical
O- u=2,TDMA,Simulation
~45 u=2,DPC,Analytical
8 u=2,DPC,Simulation
a =4,TDMA,Analytical
40t =4,TDMA,Simulation
a =4,DPC,Analytical
-u=4,DPC,Simulation
35~ -~ =4,TDMA,Analytical
r,=5dB =4,TDMA,Simulation
30 _B- a =4,DPC,Analytical
4 =4,DPC,Simulation

25 0 ^


(3-25)


20 200 400 600 800 1000 1200 1400 1600
Node population (N)


Figure 3-1. User capacities of TDMA and DPC in an exponential path-loss channel.

The .I-i-mpllicl~ user capacities of the TDMA and DPC systems can be evaluated

from the parent distributions FT(t) and Fz(z) as shown in Section 3.3.2 and Section 3.4.2,



















yo=0dB
0 92' yo=5dB

00=4







0 200 400 600 800 1000 1200 1400 1600
Node population

Figure 3-2. Efficiency of TDMA compared to DPC in an exponential path-loss channel.


respectively. The results in Figure 3-1 illustrate the user capacities of TDMA and DPC

systems for user population NV > 100, target SNR To=0,5 dB, total transmit power

Ptot = 240, the bandwidth of the system W = 106 Hz, noise density NVo = 10-10 and

K, = 10-2. Note that Ro = W log2( + 0). The simulated results (dashed lines)

are provided alongside the analytical results (solid lines), and it can be seen that the

analytical results are in good agreement with the simulated results. Note that the user

capacities of both the TDMA and DPC systems increase with an increase in the path-loss

exponent a~. This is because larger values of a~ provide greater disparity in channel gains,

which TDMA and DPC can take advantage to increase the system capacity.

The relative efficiency rl of TDMA in comparison to DPC is plotted for several

different target SNRs To and for Pros = 240 in Figure 3-2. It can be seen that for all

the three target SNRs To shown, rl is above 0.93 for a~ = 2, and above 0.89 for a~ = 4.

This indicates that the gain in user capacity achieved by employing DPC is at most 1"'

compared to the user capacity of a TDMA system in this scenario. Also note that an

increase in the path-loss exponent decreases the TDMA efficiency, since as the disparity










in the channel gains increases, DPC more efficiently exploits the channel disparities to

increase the user capacity.

3.5.2 User Capacity in Exponential Path-Loss Channel with Fading

Since closed form expressions for user capacities in a fading channel for any general

path-loss exponent do not exist, in this section, we only consider an exponential path-loss

model with Rayleigh fading where the path-loss exponent a~ = 2. Assuming that the users

are uniformly distributed in a circular area of unit radius, and the base station is at the

center of the coverage area, the channel magnitudes ze can be expressed as





where Di is the distance of user i from the base station (refer to (3-23)) and ri is the

magnitude of fading experienced by user i, which is Rayleigh distributed. Assuming that

the fading experienced by the users is i.i.d., the distribution function Fz(z) of the channel

gains can be expressed as
e- 1
Fz (z) =1 + z > 0. (3-26)

However, since the first and second order moments of z are not finite, the conditions

of Theorem 3.1 and Theorem 3.2 are not satisfied, and closed form expressions for the user

capacity of TDMA and DPC systems cannot be evaluated directly. Hence we consider the

truncated distribution

Fiz) = (3-27)
0Fz(z)-Fz(zo) Z 1- Fz (zo) z zoX
where zo is chosen such that Fz(zo) < p for some specified p. The reason behind the

choice of this particular truncated distribution is that we assume that the users in the

cell can be identified as being over-faded and non-c; ., Jral..l based on their channel

conditions in a particular frame. The truncation on the distribution function indicates

that only the non-overfaded users, with channel gains greater than zo are eligible to receive














transmission from the base station. The ..-i sph.1li~ user capacities of TDMA and DPC

can be evaluated~ from the paren distribution,, of F (z) ; give in 3-7)








~tTDMA,Analytical
40 TDMA,Simulation
45C ~DPC, Analytical
DPC, Simulation
35 TDMA,Analytical
40- B -TDMA,Simulation
~ ~- DPC, Analytical
30 5B DPC, Simulation

2 5 DAAayla

20 PSmlto




10


ll 200 400 600 800 1000 1200 1400 1600
Node population (N)

Figure 3-3. User capacities of TDMA and DPC in an exponential path-loss channel with
fading.



The results in Figure 3-3 show the user capacities of systems employing TDMA and

DPC in a fadingf channel with path-loss exponent a~ = 2, for three different target SNRs

To, total transmit power Pros = 240 and p = 0.05. It can be seen from the plots that the

analytical results (solid lines) are in good agreement with the simulated results (dashed

lines). The TDMA efficiency r for three different target SNRs To is plotted in Figure 3-4.

It can be seen that TDMA efficiency is greater than 0.93 for all the three SNRs. Hence the

gain of DPC over TDMA in terms of user capacity is at most >' for this scenario. Thus

DPC provides little gain in user capacity in comparison to TDMA for this scenario.

3.6 Summary

In this chapter, we derived closed form expressions for the user capacity of single-cell

networks employing TDMA and DPC schemes for large user populations under a total













0 948-

0 946-

0 944-

0 942-

O 094~ yo=0dB

0 938 -Y=d
yo=10dB
0 936-

0 934-

0 932-


ll 200 400 600 800 1000 1200 1400 1600
Node population (N)

Figure :3-4. Efficiency of TDMA compared to DPC in a exponential path-loss channel with
fading.



transmit power constraint. In exponential path-loss channels with and without f .11,!

our results indicate that TDMA is generally at least 0' .~ as efficient as DPC. The results

in this chapter corroborate the existing findings on the performance gain of DPC over

TDMA [1:3, 47, 48]. It was shown in [48], that DPC provides very little gain over TDMA

in terms of user capacity in a scalar Gaussian broadcast channel. The results reported

in [1:3] indicate that cooperative broadcasting provides significant gains over TDMA

only when the required spectral efficiency, and the service factor are high. Thus for the

downlink of cellular systems that employ single antennas at the base station and mobile

users, the increase in user capacity provided by using broadcasting techniques likes DPC

instead of TDMA may not offset the increase in complexity associated with the former.

In the next chapter, the performance gains of broadcasting techniques such as SPC

and BC in a cellular system are further investigated by comparing several optimal and

suboptimal forward-link channel-sharing schemes in a variety of network scenarios.









CHAPTER 4
PERFORMANCE COMPARISON OF OPTIMAL AND SUBOPTIMAL DOWNLINK(
CHANNEL-SHARING SCHEMES

4.1 Introduction

The results in ChI Ilpter 3 indicate that broadcasting techniques such as DPC and SPC

may not provide substantial gains over simpler schemes such as TDMA in the downlink

of a cellular network. In the present chapter, the performance gains of BC are further

investigated by comparing various optimal and suboptimal channel-sharing schemes for

Gaussian broadcast channels in the downlink/forward-link under an equal-rate constraint.

In the recent past there has been some related work reported, namely [12, 47, 48], that

compared dirty paper coding (DPC) to time-division multiple access (TDMA) for the

Gaussian broadcast channel. In [48], the authors consider algorithms for ordering users

in a cellular system using DPC and provide simulation results on the number of users

that can be supported with multiple-input multiple-output (j\! [MO) transmission under

an equal-rate constraint. DPC and TDMA schemes are compared in [47] on the basis of

the sum-rate capacity (instead of an equal-rate constraint) for MIMO Gaussian broadcast

channels, and it is shown that the DPC gain (over the TDMA sum-rate capacity) is

upper bounded by the minimum of the number of transmit antennas and the number

of receivers. In [12], the authors provide analytical approximations for the user capacity

under an equal-rate constraint for single-input single-output (SISO) transmission as the

user population becomes large.

The present work differs from previous work in that we provide a true .I-i-inidlli'lc

analysis of the various schemes in terms of the required minimum signal-to-noise ratio

(SNR) per mobile station (jlS) at a given bandwidth efficiency. Analytical results are

provided for the following schemes: optimal frequency division multiplexing (FDM) with

optimal allocation of frequency and power, fixed FDM with equal bandwidth allocation,

BC over the whole band, two-level BC in conjunction with fixed FDM, and three-level BC

in conjunction with fixed FDM. We perform the analysis under .I-i-misind ic~ conditions,










i.e., as the number of MSs in the system and the total bandwidth goes to infinity. The

results obtained show that BC schemes provide significant performance advantage only

under certain scenarios. We also observe that it is sufficient to use three-level BC to

achieve performance very close to the best performance guaranteed by broadcasting over

the entire band (for example, the .I-i-intlllnd ic minimum SNR per MS is less than 1.15

times that for broadcasting over the whole band at a spectral efficiency of 5.5 bits/s/Hz).

This is in contrast to FDM, for which the required .I-i-mptotic minimum SNR per MS is

about 2.55 times that for broadcasting over the whole band at a spectral efficiency of 5.5

bits/s/Hz. In the following section, the system model is introduced, and in Section 4.3 the

analysis of the different channel-sharing schemes are presented. The results are discussed

in Section 4.4, and the chapter is concluded in Section 4.5.

4.2 System Model

Consider the forward link from the base station (BS) to M~ mobile stations (j!ss)

of an infrastructure network. Assume that a frequency band of W Hz is available for the

BS to send information to the M~ MSs. Assuming an exponential path-loss model with

Rayleigh flat f ..111, for i = 1, 2, M~, the power Pri received by the ith MS, is related

to the transmitted power Pi, by



Pi = ~13 Zid- h1 i,(1

where K, is a constant, d is the close-in distance for the system, di(> d) is the distance

between the ith MS and the BS, a~ is the path-loss exponent, and |hi| is the magnitude of

the fading at the MS, which is assumed to be constant over many symbols. We assume

an annular region of coverage with all distances from the BS to an MS normalized by

the close-in distance. Thus, we have an annular region with an inner radius do = 1 and

an outer radius D. To statistically characterize the channel gain factors Zi's, we assume

that all the MSs are uniformly distributed in this annular area of coverage with the BS

at the center. With independent block Rayleigh fading (with second moment 2o.2),









can be shown that, for the special cases of path-loss exponent a~ = 2 and a~ = 4, the

channel gains are independent and identically distributed (i.i.d.) random variables with

the cumulative distribution functions (cdfs):

Fzz)= -zD2 e -e- z > 0~ (4-2)


and

Fz(z) =1 .! erf D T 43


respectively.

It is also assumed that the BS has perfect information about the channel gains

Zi ( wi through a separate feedback channel from each MS), and, without loss of

generality, we order the gains in descending order, i.e., Z1 > Z2 > ZM.r Under

perfect power control for the Rayleigh fading model, it can be shown that it is not possible

to transmit to every MS while maintaining finite transmission power per MS because

E~[1/Zi] is unbounded. To avoid this modeling problem, we assume that the system does

not transmit to a set of or [.:.1, MSs (cf. [38]) whose channel gains are such that Zi < zo

for some small value of zo. Thus, the overfaded MSs are those that experience outage

during those intervals in which their channel gains are too bad. Clearly, this assumption is

reasonable from a practical view-point. With this assumption, the cdf of the channel gains

of the serviceable MSs: becomes F'(z-;zo), for z- > zo, where F'(z; ui) = Fi z for z > n,1

is the conditional cdf of Z given that Z > u.

Now suppose that during each (long) transmission time slot, the BS is to service the

best K of the M n1on-or; [:./..1 users. The ratio 5 = is called Ithe servicce faictor of the

forward link. It specifies the fraction of serviceable MSs to be served in each transmission



1 The case of general a~ can also be considered, but the cdf expression is more
complicated. Here, we will focus on the cases when a~ = 2 and a~ = 4 for simplicity.










interval. Note that we have 0 < 6 < 1. In addition, we require that each serviced MS

has to be supported at an equal rate of R nats/s. The spectmal e~ff. .:. ,: ;I of the system

is defined as the ratio i3 = in Iterms of nats/s/Hz that c~an be supported ove~r the

band. We assume that the channel from the BS to each MS is corrupted by AWGN with a

two-sided noise power spectral density of NVo/2. Let Pt be the total power transmitted by

the BS to support the transmission to the K MSs, when possible.

We quantify the performance of a channel-sharing scheme by the minimum SNR per

MS required to achieve a target rate of R nats/s at each of the K MSs. More precisely,

the minimum SNR per MS is defined by


SK = mln 4-4)
NoK R

Below we present an .l-i-injull'tic analysis under which the values of W, M~ and K

all approach infinity while maintaining a fixed service factor 6 and spectral efficiency P.

The various transmission approaches mentioned in Section 4.1 are compared in terms of

the .I- i-ini d ul ic minimum SNR per MS, i.e. So, = limK->o SK. Note that this .I- i-ini d aticc

consideration is not unreasonable as the values of W, M~ and K are usually quite large in

practical wideband infrastructure networks.

4.3 Asymptotic Analysis for Required Minimum SNR per MS

In this section, the .I-i-n npi nd ic analysis of different approaches are presented towards

achieving the goals mentioned in the previous section. The five schemes studied in this

chapter are: broadcasting over the whole band, fixed FDM, two-level BC, three-level BC

and optimal FDM.

4.3.1 Broadcasting over the Whole Band

Under this scheme, the BS transmits to the K MSs using K-level BC and using the

entire available bandwidth. For i = 1, 2, K, let 0 < ai < 1 be the fraction of the

total power Pt allocated for transmission to the ith MS. Note that CK-1 as = 1. Then for










i= 1,2, --- ,K,

W log 1l +vw zpa > R. (4-5)

When K = 1, P = R/W and it is easy to see that al = 1 is feasible if and only if

Pt (e -1 1
> ~(4-6)
NVoR P Z1

For the case of two users, K = 2, p = 2R/W and from equation (4-5) we obtain,

(e /* 1)
at Pt > No oW (4-7)


and

a2Pt > e/ R/W 0Z (8

Thus, there exists a feasible choice of al and a2 (With al + a2 = 1) if and only if

Pt 64 2 -Pi/2
> -( /2_ 9)
2 No R P Z,
i= 1

From the above, it can be proved using induction on the number of users K, that

there exists a choice of the power fractions al, a2, aK that satisfies the above set

of inequalities if and only if

Pt eP K-Pi/K
> -(6/ 10)
NVoKR P Z,
i= 1

Hence, using the definition of SK in (44),

eP 60/K P/ Kt 6-Pi/KZ.
SK 41



Clearly, as K approaches infinity, B in (4-11) approaches P. To investigate the .I-oi-nd ic'l~

behavior of C above, we first observe that 1/Z1, 1/Z2, 1/ZM~ are order statistics of M~

i.i.d. random variables distributed according to 1 F(1/z) (for 0 < z < 1/zo), which has a










finite second moment. Hence, using the result in [51, Example 1], it can be shown that


1: K -Pi/K 00
lim x{p1-Fz o)'d~;z)w .1
K->oo K1 i=] Zi p(-S ~;zo 6

(4-12)


As a consequence, the .I-i-inidlli'lc minimum SNR per MS for broadcasting is given by

e~'- C-) PX exp {#F~z; zo)/6}
SoI = F(z; zo) w. p. 1. (4-13)
6 p-1(1-S;zo)

4.3.2 Fixed Frequency Division Multiplexing

In this scheme, the K best non-overfaded users are served using a fixed allocation of

bandwidth, with every user being allocated an equal share of the total bandwidth, viz.

W/K Hz.2 For this scheme, we have

1 1
SK = ( )4-14)
i= 1

and as before, using [51, Example 1] we can show that in the ..-iinidull~lc case,

eP -1 "o 1
So, = dF(z; zo). (4-15)
P6 p-1(1-S;zo)

4.3.3 Two-Level Broadcasting

We consider two-level BC in conjunction with fixed FDM allocation. The entire
bandwidth W is divided into L = [K1 equa~l Sub-bands andr two-level BC; is used to

support a pair of users over each such sub-band.

For a typical pair of users, ;?i users i and j with Zi > Zj, we have

lo 1 + > R (4-16)
L No~w




2 Here, we note that the performance of the fixed time division multiplexing (TDM)
scheme would be identical to that of the fixed FDM scheme as proved in [28].









and

WC rw(1 a) jLZjptL

where pt is the total power expended in supporting the two users over the particular

sub-band. It can be easily shown [11] that a choice of 0 < a < 1 exists if and only if

LR
pt > Pi + Pj + (e w 1)Ps


(4-17)






(4-18)


where P, = e "-)o is the power requ~ired if a bandwidth of W/~L Hz is availablle

exclusively for user a without BC.

Therefore, the minimum SNR per MS required to support the best K non-overfaded users


SK =min






PL

Noting that 1/Z I< 1/Z2 < -

variables distributed according to 1 -

[51, Example 1], we obtain


K R


i= 1 i l i= 1)


1)1 (e w -1)
zi LR~c zi(4-19)
i= 1 i= 1

< 1/ZM/ are order statistics of M~ i.i.d. random

F(1/z) (for 0 < z < 1/zo) and invoking the result in


(4-20)


4.3.4 Three-Level Broadcasting

We consider the three-level BC in conjunction with fixed FDM allocation. The entire
bandwidth W is divided into L = [K~ equa~l Sub-baindsi a~nd three-level BC is usedr to

support three users over each such sub-band.


2(eP/2 00 ~o
ps p-(1-S;zo)









Following the same manner as for two-level BC, we get

3(e#/3 ) 0011 ;o
So F, zo +(e3 0o)
ps p-1(1-S;zo) -1~z~ (d3-1F(1-Z;o X;zo )1

+t(e2i'/3l )
J -1(1- ;zo) Ii; ]
(4-21)

4.3.5 Optimal Frequency Division Multiplexing

In this scheme, the BS optimizes the SNR per MS by optimal allocation of power and

bandwidth to each of the K MSs according to their channel gains such that each user is

provided with a data rate of R nats/s/Hz. We have, for i = 1, 2, K,

log 1 + >R (4-22)
K iNociW R

where ci/K and Pi are the the fraction of total bandwidth and the transmitted power for

the ith MS, respectively. Thus, 1 PK-1C adl Pt L= E Pi. Fr-om the above and the

definition of SK it can be seen that


OSSK min 1 -:'~~ I)
i= 1

= mm i~- (4-23)
i= 1

where g(x) = x(ePl" 1).

Thus, the problem reduces to findings the ce's that minimize the right hand side of

(4-23) subjct to th~e constrain~t ( C,K-1 C7i = 1. This standard optim~iza~tion? problem? canl
be solved using Lagrange multipliers. Writing the functional as



J(cy, C2 *, CK) =1 Cs 1i (4-24)












and differentiating with respect to ci, we have

8 J 1 g' (ci) A
8ci K Zi IK
s '(ce) = AZe


(4-25)


where~~ g'x e( ) 1 is the derivative of the function g(x).

We let h denote the inverse function of g'. Now, h(- AZi) is a continuous function,

decreasing in A > 0, and thereby it can be shown that there exists AK Such that


K
K h(-AK~)) = and ce = h(-AK~).
i= 1


(4-26)


In the .I-i-inpind ic~ case, as K, M~ and W go to infinity, it can be proved using the result in

[51, Example 1] that


lim ( A )=
K->oo K
i= 1


1"


h(-Az)dF(z; zo) w. p. 1.


(4-27)


As a result of (4-27), A,, = limK->o XK can be obtained by equating the right side o

(4-27) to 1 and solving for Am.

Finally, using the above and the result in [51, Example 1] one more time, we get


So, = dF(z; zo) w. p. 1.(


f


:428)


4.4 Results

Using the expressions derived in the previous section, we compute the .I-i-mptotic

minimum SNR per MS (So,) required for each of the schemes described before. The

coverage area for the BS is the annular region with an inner radius of do = 1 and an outer

radius of D, with all distances being normalized by the close-in distance of the cell, which














0 7000-


S6000 ---- =0 4
z -e-- 8=0 6
S 5000 -- =


4000- a-2a~nd D=50

~-3000-







S2 3 4 5 6
Spectral Efficiency, (3 (bits/s/Hz)


Figure 4-1. Broadcastingf over the whole band for a~ = 2 and D = 50 for various service
factors, 6.

12000-


10000-

-4-- 6=0 4
8000t -e- =0 6
-4- 8=0 8
-8- 8=1 0
,6000-

a=2 and D=50
S4000-


S2000


S2 3 4 5 6
Spectral Efficiency, (3 (bits/s/Hz)


Figure 4-2. Two-level BC for a = 2 and D = 50 for various service factors, 6.






is typically 100 m or 1 km for outdoor environments. As the size of macro-cells typically


range from 1 km to 30 km, typical values for D can range between 10 to 300. A mobile


station is considered overfaded if its channel gain falls below zo = Fi (0.05), i.e., when the


service factor is unity (6 = 1), the outage probability is 0.05. We study the variation of So,


with spectral efficiency P and the service factor 6 as parameters. The path-loss exponents


















0 8000


a,7000


m 6000
E
E
~5000


S4000




E
S2000


-8=02
-a- 6=0 4
-8- 80 6
-4- 6=0 8
-a--81 0


a=2 and D=50


05 1 15 2 25 3 35 4 45 5 55 6
Spectral Efficiency, (3 (bits/s/Hz)


Figure 4-3. Three-level BC for a


2 and D = 50 for various service factors, 6.


0 16


14



S 1




0- 06



E 04


- 8=0 2
-E-- 6=0 4
-9- 6=0 6
-4- 80 8 a=2 and D=50
-9- 6=1 0


05 1 15 2 25 3 35 4 45 5 55 6
Spectral Efficiency, (3 (bits/s/Hz)



Figure 4-4. Optimal FDM for a~ = 2 and D = 50 for various service factors, 6.







considered are a~ = 2 and a~ = 4. We choose the Rayleigh fading second moment equal to 1


so that the fadingf process neither adds nor subtracts power.
















S 2.5 -


z 2-

E -8=0.2
c-*--8=0.4
Z 1.5-
-0 -9- =0.6
-#--8=0.8 a2nD5
86=1.0



< 0.5-



0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Spectral Efficiency, (5 (bits/s/Hz)


Figure 4-5. Fixed FDM for a~ = 2 and D = 50 for various service factors, 6.


Figure 4-1 through Figure 4-5 show the performance of different schemes for the

path-loss exponent a~ = 2, and outer radius of coverage, D = 50, with spectral efficiency

Sfor the service factor 6. Figure 4-1, Figure 4-2, and Figure 4-3 show the performance of

applying broadcasting over the whole band, two-level BC and three-level BC, respectively.

These figures demonstrate that the .eimpi- ndic'l minimum SNR per MS required for

three-level BC exceeds that for the optimal method of broadcasting over the whole band

by not more than 101' for low and moderately high values of the spectral efficiency

(p < 3.5 bits/s/Hz). On the other hand, two-level BC performs a little worse, with

S, within 101' and between 101' to 211' more than that for the optimal method when

p < 2.5 bits/s/Hz and 2.5 bits/s/Hz< P < 4.0 bits/s/Hz, respectively.3 We further

note that for all the schemes, the increase in S, with increasing p becomes more rapid





3 Note that S, has not been plotted in dB so that the actual rate of change of S, with
Scan be observed directly from the figures.












Fixed FDM
-at Optimal FDM
12000 -E--Two-level BC
-e-Three-level BC
-Q- BC over the entire band
10000-

E a=2, 8=0.8 and D=50
.5 8000-


S6000-


4000-


2000-

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Spectral Efficiency, B (bits/s/Hz)


Figure 4-6. Comparison of all the schemes for n~ = 2, D = 50 and 6 = 0.8.





for higher values of 6; i.e., when the service factor is low, the effect of an increase in the

spectral efficiency on the S, value is low. This is because, when the service factor is

lower, the BS enjoys more freedom in choosing the best K out of M~ users and thereby can

maintain a comparatively low S,, even for high values of spectral efficiency because of the

benefits of niulti-user diversity.

Figure 4-4 and Figure 4-5 show the performance of optimal FDM and fixed FDM,

respectively. The degradation in the performance for the suboptinmal method of fixed

FDM when compared to optimal FDM is very similar to that for the case of the two-level

BC and broadcasting over the whole hand. For example, for a service factor of 0.8, S,

for fixed FDM is about 211' more than that for the optimal FDM scheme at 79 = 4.0

bits/s/Hz.

In Figure 4-6 and Figure 4-7, we show the performance comparison of the different

schemes when the service factor is 0.8. For example, in Figure 4-6, when /9 = 3.0 bits/s/Hz

we have S, for broadcasting over the whole hand, three-level BC and two-level BC at













-- Fixed FDM
(n16 -II Optimal FDM
-ll Two-level SPC
g -9- Three-level SPC
8 14 -# Cooperative Broadcasting over whole band

12 =4, 6=0.8 and D=50


.5 10





C4



0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Spectral Efficiency, P (bits/s/Hz)


Figure 4-7. Comparison of all the schemes for n~ = 4, D = 50 and 6 = 0.8.


189:3.8, 2027.5 and 2194.76, respectively, whereas for optimal FDM and fixed FDM these

values are 2729.5 and :3150.62, respectively. The differences in the performance for the

different methods widen with an increase in P. Thus, for n~ = 2, at /9 = 6.0 bits/s/Hz, we

have S, at 5108.1 and 60:31.4 for broadcasting over the whole hand and three-level BC,

respectively, while 11212.1 and 14177.8 for optimal FDM and fixed FDM, respectively.

We note that for different values of the path-loss exponent c0, although the values of S,

change, the shapes of the curves are almost unaltered.

Finally, in Figure 4-8 we plot, as a function of /S, the ratio of S, for different schemes

to that for broadcasting over the whole hand. It has been observed that this plot does

not significantly vary for different values of D or c0. Front this figure, we observe that for

/9 < 5.5 bits/s/Hz, S, for three-level BC is within 1.15 times that of broadcasting over the

whole hand, whereas even for optimal FDM, S, is more than twice that for broadcasting

over the whole hand at high spectral efficiencies. Thus, front these results we conclude

that the performances obtained front two- or three-level BC schemes are much closer to












~2.6-

-Fixed FDM
2. El Optimal FDM
S-8- Two-level SPC
o 2.2C e Three-level SPC
.E ~a=2, 6=0.8 and D5


m1.8-

8 1.6-

1.4-




0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6
Spectral Efficiency, (5 (bits/s/Hz)

Figure 4-8. Ratios of So, for the FDM schemes and the suboptimal BC schemes to that for
broadcasting over whole hand for a~ = 2, D = 50 and 6 = 0.8.


that for optimal broadcasting over the whole hand than for the other two FDM schemes,

especially at moderate and high spectral efficiencies.

4.5 Summary

In this chapter, we compared the performance of various forward-link channel-sharing

schemes with the consideration of both path-loss and f ..111, under an equal-rate

constraint, in terms of the .I-i-ini!!lle'~ minimum SNR per MS. We found that the

suboptimal method of three-level BC with fixed FDM allocation requires an .I- in ipi ni le

minimum SNR per MS that is within 1.15 times that of the optimal method of broadcasting

over the whole hand when the spectral efficiency is below 5.5 bits/s/Hz. On the other

hand, fixed FDM or even optimal FDM perform much worse, except for very low spectral

efficiencies. These results motivate the use of practical methods like two- or three-level

BC in multiband operation instead of the optimal but practically difficult schemes

like broadcasting over the whole hand or optimal FDM. Moreover, the fact that the

performance degradation from using the suboptimal three-level BC method is less than

1'.even for high values of spectral efficiency motivates the use of three-level BC not only










for the traditional cellular networks but also for systems that operate in the high spectral

efheciency regions.

In the following chapters, the problem of channel-sharing in wireless ad hoc networks

is considered, where we focus on the design, development and analysis of niediunt

access control (j1! C) protocols that improve the performance of wireless networks.

We developed a 1\AC protocol, and through analysis and network simulations, evaluated

its impact on the throughput of the network and its interaction with other lI w< v.










CHAPTER 5
OVERLAPPED TRANSMISSION IN WIRELESS AD HOC NETWORKS

5.1 Introduction

In wireless ad hoc networks (WANets) that do not employ code-division multiple

access, medium-access control (\!A9C) protocols, such as IEEE 802.11 [52], are used to

allocate the channel resources to specific transmitters and receivers so as to minimize

the interference in the network. Traditionally, the design of the MAC protocol is carried

out independently of the physical-1.,-;-r design, assuming a simplistic collision channel

model. In these models, a packet is successfully received by a node if there are no other

transmissions in its interference range. These MAC protocols schedule transmissions such

that the collisions in the network are minimized.

Multiuser detection (j!UD) [17, 18, 20, 21, 53, 54] in wireless networks has been

proposed as a means to increase spatial re-use by increasing the number of simultaneous

transmissions in the network. AllD techniques are emploi-u 0 at the physical l o,-;- (PHY)

to recover information from colliding packets at the receiver. These signal processing

techniques used at the PHY enable a node to receive packets in the presence of other

transmissions in its communication range. This multipacket reception (1\! PR) capability of

the nodes at the PHY leads to greater spatial re-use in the network. MAC protocols were

proposed in [19, 21] that take advantage of the MPR capabilities of the PHY to increase

the spatial re-use in networks to provide high-throughput in heavy traffic and low delay in

light traffic.

In most cases, mobile radios do not have sufficient processing power to perform

complex hilD schemes. Recent work on the transport capacity of wireless networks [55]

indicates that in the low-attenuation regime, multi-stage relaying using cancellation

of known interference is order optimal. Here, the interference is known from the use

of multihop routing. Using interference cancellation for only known interference may

significantly improve network performance at a reasonable complexity.









To explain how an interfering signal may be known in multihop routing in a WANet,

consider a four-node linear network consisting of nodes A, B, C and D, where A transmits

a packet to D using multihop routing. In a slotted communication system employing a

conventional MAC protocol, a typical sequence of transmissions for a packet would be


1 : A B, 2 : B C, 3 : C D,


where the notation 1 : A B indicates that node A transmits a packet to node B in time

slot 1, etc. Under conventional MAC protocols, in the time slot when C forwards a packet

to D, A is not allowed to transmit to B since C's transmission will cause interference at

B. However when a MPR-based MAC protocol is emploi-. I simultaneous transmissions of

A B and C D are possible, since MUD techniques can be emploi-- II at B to recover the

packet transmitted by A. Note that the packet transmitted by C to D is the same packet

that B forwarded to C in an earlier time slot (ignoring the differences in the headers). If

B were to retain a copy of the packet that it forwarded to C, B would have information

regarding the interfering transmission. This greatly reduces the complexity of the MUD

algorithms emploi-- II at the PHY to recover the packet transmitted by A. This example is

revisited in Section 5.2.

The idea of employing this type of known-interference cancellation (IC) technique

to increase simultaneous transmissions in WANets was first analyzed in [22]. In [22],

knowledge of the interfering signal is assumed at both the transmitter and the receiver,

and the receiver performs MUD/IC to recover additional messages. Limitations on

scheduling such simultaneous transmissions were analyzed and a MAC protocol that

supports such simultaneous transmissions was proposed.

The idea of employing network coding to increase spatial re-use and throughput in

WANets has recently received considerable attention from the research community [56-66].

A transmitting node exploits the broadcast nature of the physical medium along with

the knowledge of the interfering messages at the receiving nodes to combine/encode










multiple independent messages at the network 11s-c v and transmit to several nodes.

A node receiving the encoded message uses the knowledge of the other interfering

messages available at the network 1.,-:-r to recover the message intended for it. Practical

channel-sharing schemes that support network coding in WANets were proposed

in [57, 60, 64, 66].

Our approach is similar to some network coding approaches to increase simultaneous

transmissions in WANets [23, 24, 67, 68]. In physical-1.,-:-r network coding [24], relay

nodes may receive signals consisting of several simultaneous transmissions. These signals

are decoded, re-encoded and rellai- II on to their final destinations. The destination, which

has the knowledge of the other interfering signals, mitigates the interference and recovers

the intended transmission. However, this approach requires perfect synchronization

among those transmissions that interfere at a relay node. An alternative strategy called

analog network coding [67] does not require the intermediate relay nodes to decode

the signal. When a relay node receives a signal consisting of interfering transmissions,

the node amplifies the signal and broadcasts it. Only packet-level synchronization is

necessary between the interfering transmissions. The intended destinations leverage the

information they have about the interfering transmissions to mitigate them, and recover

the intended transmission. These approaches are similar to the idea of employing MUD

with known-interference cancellation. These works analyze the physical-111-< v aspects

involved, but do not address the MAC-1.,-:-r implications of employing such simultaneous

transmission schemes in ad hoc networks.

In this chapter, we analyzed some of the fundamental limits on performing overlapped

transmissions in a WANet. Our analysis provides an understanding of the performance

gains of such transmissions, and an insight into the PHY and MAC interaction required

for scheduling such transmissions. In C'!s Ilter 6, we designed a MAC protocol based on

the IEEE 802.11 MAC protocol that exploits this feature to improve the spatial re-use and

throughput in wireless networks.











ABCD



ABCD
***
ABC

t!ABCD
e -
~ ABCD




Figure 5-1. Four-node linear network with conventional scheduling.




The rest of the chapter is organized as follows. Section 5.2 introduces the idea of

employing overlapped transmission in a linear network. In Section 5.3, some limits on

performing overlapped transmissions in wireless networks are evaluated. The chapter is

concluded in Section 5.4.

5.2 Motivation

In this section, the idea of overlapped transmissions in a four-node linear network is

illustrated, which is shown in Figure 5-1. We assume that the nodes can communicate

only with the .Il11 Il:ent nodes and operate in half-duplex mode. Node A transmits

packets to node D through multihop routing. A typical transmission sequence under a

conventional scheduling scheme is depicted in Figure 5-1, in which it takes three time

slots for a packet from A to reach D. The scheduled transmissions in a given time slot

are marked by solid directed arrows along with the packet identifiers, and the interference

caused by these transmissions are marked by dashed arrows. Under typical carrier-sense

multiple access protocols with collision avoidance (CSMA/CA), when packet mi is being

forwarded by C in time slot 3, A cannot transmit the message m2 SinCe C'S tranSmission

will cause interference at B.











ABCD


ABCD

ABCD1

t!ABCD

ii **
~ ABCD




Figure 5-2. Four-node linear network with overlapped transmissions.


The throughput of this network can he improved by employing simultaneous

transmissions as described below. We observe that in the time slot iS, C forwards the

packet ni1 that it received from B in the earlier time slot 2. If B were to retain a copy

of the message mi locally, it knows the message being transmitted by C in time slot ;3

(assuming that linkr-1 we;r encryption is not used and any differences in the headers are

ignored). If A is allowed to transmit the message n?2 in the time slot iS, B can use the

stored information regarding mi to mitigate the interference caused by C's transmission.

We call this additional transmission that results due to the interference mitigation of

known-interference as overlapped transmission.

A scheduling scheme employing the idea of overlapped transmission for the four-node

linear network is depicted in Figure 5-2. Under this scheduling scheme, a packet is

transmitted from A to B hy employing overlapped transmission during the time slot

that C forwards a packet to D. Since the transmission of the packet from A to B did

not involve the allocation of a separate time slot for its transmission, a packet requires

on average only two time slots to be transmitted from A to D. These two time slots are

required for the scheduling of transmissions from B to C, and C to D, respectively. The

performance gain of this scheduling scheme can he measured in terms of transmission

efficiency, which is defined as the ratio of the time taken for the transmission of M~ packets










under conventional scheduling scheme and the scheduling scheme employing overlapped

transmissions. The transmission efficiency 04 of this scheme is given by


F4 At >1, (5-1)
2 ( Af- 1) + 3 2

where Af is the total number of packets transmitted by A. Note that under conventional

scheduling, it takes three time slots for every packet from A to reach D. However, using

the scheduling scheme employing overlapped transmissions, it takes two time slots on

average for a packet from A to reach D 1

Similarly, in an NV(N > 4) node linear network, the transmission efficiency FN can he

shown to be
Nv 1 + 3( Af 1) :3
FN = N -) At > 1. (5-2)
NV- 12( -1 2

We observe that the centralized scheduling scheme that employs overlapped transmissions

has the potential to improve the efficiency of a linear network by up to approximately

50I' over the conventional scheme. In Section 5.3, we look at some of the limitations

of employing overlapped transmissions in WANets. Since the focus of this work is on

developing a 1\AC protocol for overlapped transmission, the PHY aspects of the protocol

are not evaluated here.

We identify a transmission between two nodes as a I,.:l,,or,; treenstaission if the

transmission is not predicated on the use of non-causal knowledge of the interfering

signals during that transmission interval. For example, in the network of Figure 5-2,

the transmission of message mi from C to D in time slot is is theI,e. *.7
and the nodes C and D are called theI,<.:lt.;lt transmitter and the I, : a.~r;l receiver,

respectively. Similarly, a transmission between two nodes is a .<.. .7 i~:lr; treenstaission if at

least one of the nodes has non-causal information about the primary transmissions in the




1 The first packet requires three time slots.










present transmission interval and performs MUD/IC to mitigate the interference. In the

network of Figure 5-2, the transmission of the message m2 from node A to B in time slot

iS for which B performs MUD/IC to mitigate the interference from C's transmission is the

.<... t.'.LI, ,i transmission, and the nodes A and B are called the secot.'.litti transmitter and

the .'. .- -t~l~r t r receiver, respectively

5.3 Overlapped Transmission in Wireless Ad Hoc Networks

In this section, some fundamental limits on performing overlapped transmission in a

wireless network are analyzed. The purpose of the analysis is to provide insights into the

types of scenarios in which overlapped transmission may be appropriate, and the design of

a MAC protocol to efficiently utilize the simulcasting capability.

5.3.1 System Model

Consider first a wireless ad hoc network with nodes distributed according to a

two-dimensional homogeneous Poisson point process with density A nodes per unit

area. Each node is equipped with a transceiver and communicates with other nodes in

half-duplex mode. We assume that each node has an infinite packet suffer, and each

radio retains copies of the packets it forwards unless that packet is transmitted to its

final destination or until that packet has been forwarded on hv one of its neighbors. To

investigate some of the issues that will limit the performance of overlapped transmission,

we analyze the use of overlapped transmission in a system using slotted communications.

In this model, each node transmits in a given time slot with probability p. This assumption

is only to facilitate the analysis of overlapped transmissions in ad hoc networks in

Section 5.3. However, no such assumption is made during the development of the MAC

protocol in C'!s Ilter 6. We also assume that the secondary transmitter is informed of the




2 The terms pI ll!!Ia .y" and "semiI. lliy3 are also used in the cognitive radio literature
to classify users according to their regulatory status, and should not he confused with
the terminology emploi- I1 here, in which users are classified according to their roles in an
overlapped transmission.











corresponding primary transmission and that the overlapped transmission is synchronized

with its corresponding primary transmission. The received power Pr (in the far field) can

he expressed as

Pr = KIdr P,, (5-3)

where P, is the transmitted power, dr is the distance between the transmitter and the

receiver, KI is a constant, and a~ is the path-loss exponent. In the absence of interference,

we assume that a transmission at the nmaxiniun power level will be received correctly if

and only if the intended receiver is within a distance of one unit front the transmitter.

We also assume that there is some interference range, which is typically larger than the

transmission range. Nodes within the interference range but outside the transmission

range of a transmitter can detect the presence of a transmission but will not he able to

correctly decode the packet being transmitted.














Figure 5-3. Ad hoc network with overlapped transmission.


In this section, we consider some limitations on the ability to utilize overlapped

transmissions to improve the throughput in a wireless ad hoc network. These limitations

come front the following two sources:

*Interference due to seco,:.1.n; ta hn~syisesion: Since the secondary receiver has

non-causal knowledge of the primary transmission, it can mitigate the interference

due to the primary transmitter and recover the intended message. However, the

secondary transmission causes interference, possibly to several primary transmissions.










In Section 5.3.2, we evaluated the amount of interference that a secondary

transmission may cause at the primary receiver, and -II__- -r how this interference

can he controlled by adapting the power level of the secondary transmission to meet

specified signal-to-interference ratio (SIR) and outage requirements or by careful

selection of the secondary transmitter.

*,~~ Pr l~.l.:7:;i of .<. ..t.'. I, ; ti hnsynisesion: Overlapped transmissions depend on the

availability of suitable secondary transmitters and the successful reception of the

messages at the secondary receiver.

The analytical results in Section 5.3.2 and Section 5.:3.3 are based on the network

shown in Figure 5-3, which can he considered to be a part of a larger network. Nodes A

and C are in the transmission range of B, and B transmits packets to D through C by

employing niultihop routing. Hence D is in the transmission range of C, but not in the

transmission range of B. This particular region is shown in Figure 5-:3 with dashed lines.

We also assume that A has packets for B. The network of Figure 5-:3 is used to simplify

the analysis, yet illustrate the important aspects of overlapped transmission.

5.3.2 Interference due to Secondary Transmission

Consider first the ad hoc network of Figure 5-3, and the time slot during which node

C forwards to D a packet that it has received front B in an earlier transmission. The

transmission front C to D is a primary transmission, and a possible secondary transmission

is front node A to node B. We assume that both nodes A and B are informed of C's

transmission to D. Node A is allowed to transmit only if it is not in the transmission range

of D. This restriction on A's transmission reduces the amount of interference at D, but it

is still non-negligible. However, A is allowed to transmit even if it is in the transmission

range of C. We also assume that B can perform perfect interference cancelation of C's

transmission and recover the packet transmitted by A. However, A's transmission causes

interference at node D. In order to analyze the impact of the secondary transmission at










the primary receiver, we evaluate the Signal-to-Interference Ratio (SIR) at node D. We

assume that the secondary transmission is the only source of interference at D.

For conciseness, we introduce the following notation. Let Xij be the random variable

denoting the distance between the nodes i and j. Also, let Al(rl, r2, d) denote the area of

the lens formed by the intersection of two circles of radii rl and T2 With centers separated

by a distance d. Mathematically,

Sr o-1 r7 d2 ~~+ro-1 d2 2 p2
2rld 2r2d



Let p denote the ratio of the distances between nodes C and D, and A and D respectively.

Mathematically,

p= XCD < 1, XAD > 1. 55
XAD

The constraint XCD < 1 indicates that D is in the transmission range of C and the

constraint XAD > 1 TeffeCtS the fact that the secondary transmitter A is allowed to

transmit only if it is not in the transmission range of D. Hence we have p < 1. In an

exponential path-loss channel without f llla! the ratio y of the powers of the primary

transmission to the secondary transmission at node D can be expressed as


Y= p- o,-" p< 1. (5-6)


The density of p can be expressed as


f,,(r)= sfACD(,r>s (5-7)


where fxA,,XCD 8s, y) is the joint probability density function (pdf) of XAD and XCD.

The joint pdf of XAD and XCD is eValuated in Appendix A and is given by (A-7). The











truncated distribution of p is given by


(5-8)


Then front (5-6) and (5-8), the pdf of SINR y, is


fr(r) =1 ,q |d <1,


(5-9)


where nr is the path-loss exponent.



0.9

0.8

0.7-

0.6

"L 0.5


0.3

0.2~ -

0.1 -


20 30
Signal to Interference Ratio (y) in dB


Figure 5-4. Distribution of signal-to-interference ratio, y.


The distribution function Fr (y) of SIR at D, y, for path-loss exponent n~ = 2, 4

are numerically computed and plotted in Figure 5-4. Let yo denote the nxininiun SIR

requirement for the successful reception of a message. An outage event occurs when

y < yo. Let /9 denote the outage probability, Pr(y < yo) = /S. Since the radio locations

are random, it may not he possible to achieve /9 = 0 for a particular yo. For example, let

n~ = 4, /9 = 0.05 and Yo = 12 dB. This SIR requirement roughly translates to a value of

p = 0.5. Fr-om Figure 5-4, we have for /9 = 0.05, SIR of Fr 1(f) = 4 dB, which is less than


S fp r)d p<1
fp(r~lr < 1) = frdr
0, otherwise.










the required SIR. The interference caused by the secondary transmission can be controlled

by using the location information of the nodes in choosing the secondary transmitter.

Another way to meet the target SIR requirement without increasing the interference to

other nodes is to reduce the power of the secondary transmission.

5.3.3 Probability of Secondary Transmission

In this section, the conditional probability of a secondary transmission given that

there is a primary transmission that permits a secondary transmission is evaluated. With

respect to the network of Figure 5-3, given that C successfully forwards B's packet to D,

we evaluate the probability of a successful secondary transmission from node A to B. The

probability of a successful secondary transmission depends on the following factors.

1. A cril~rlt..l.;, of a e... .'.lit ti transmitter (arbitrarily called node A here): All the

nodes that are in the transmission range of the secondary receiver (node B), but

not in the transmission range of the primary receiver (node D) are identified as

potential secondary transmitters. One of them is arbitrarily chosen as the the

secondary transmitter. We note that identification of a secondary transmitter

does not guarantee a successful secondary transmission. In this analysis, we do

not address the issue of how a secondary transmitter is chosen, but investigate the

factors that limit the availability of a secondary transmitter.

2. A on ri.lhr~i;, of packets at the secot.'.lit ti receiver: In order to simplify the analysis,

we assume that a secondary transmitter ahr-l-w has packets for the corresponding

receiver.

3. Scheduling a secot.'.lit ti transmission: We assume that, once a secondary transmitter

is identified, it transmits a packet to the secondary receiver, independent of the state

of the medium. This assumption results in an upper bound on the probability of

scheduling a secondary transmission in a time slot, as the secondary transmission

may not be possible if it will interfere with other primary transmissions.










4. S;,. -ful reception of the overlapped dates
receiver can successfully receive the message provided that no node in its interference

range (with the exception of the primary transmitter) transmits. We do not consider

the effect of other secondary transmissions at this secondary receiver, again yielding

an upper bound on the number of successful overlapped transmissions that can occur

in an ad hoc network.

Using the example network of Figure 5-3, we evaluate the probability of a successful

secondary transmission from A to B while C forwards to D the packet it has received from

B in an earlier transmission. Based on the above discussion, the probability of a successful

secondary transmission, p(S) can he bounded by


p(S) < p(T)p(T|FT), (5-10)


where FT denotes the event that there is a suitable secondary transmitter (denoted as A in

our example network), and T denotes the event that the secondary receiver (denoted as

B in our example network) successfully receives the packet transmitted by the secondary

transmitter.

The probability of the event FT is equivalent to finding a non-transmitting node that is

in the transmission range of B, but not in the transmission range of D. This region ,4,(X)

is given by

4,(X) = iTr At~(1, 1, X), 1 < X < 2, (5-11)

where Al(TI, T2, d) is given by (5-4) and x is the distance between B and D, whose pdf is

given by

fxBD(~ XC'D,XBD (y~x, |c= ) fxec(:r.Ii1 2 -2

where fxC',,XBD(Y, |XIXc = r) and fxec.(:) are given by (A-3) and (A-1), respectively.

Since the nodes are Poisson distributed with node density A, the probability p(FT), of











0.9

S05




S0.75


~'0.65



90.55

0.5

0.45
0 0.05 0.1 0.15 0.2
Probability of transmission in a time slot (p)


Figure 5-5. Probability of finding a secondary transmitter.



finding a secondary transmitter is given by


0(XAFy(z))ne-XAA(z)
p(F) = n! (1 ") fxBxDx
zn=0

= 1 e-Ap~z(1-p /XD (zdz,(5-13)


where p is the probability of transmission by a node in a time slot. The probability p(FT),

of finding a secondary transmitter is shown in Figure 5-5 for three different node densities,

A. It can be seen that for a given probability of transmission in a time slot, the probability

of finding a secondary receiver increases with an increase in the node density. Also note

that for stable operation of the network, the probability of transmission p, should be less

than the average number of nodes in the interference range of a node. For instance, if we

assume that the interference range is twice the transmission range, we have p < (4XA) 1,

where A is the node density, and the interference range of a node is assumed to be 2 units.

With p = (4~X) 1, p(F) is 0.51, 0.74 and 0.85 for A = 1, 2, and 3, respectively.



















~0.6 -+

S0.5 -

S0.4~ -

S0.3 -



o~~~- -e-a-e-oa

0 0.05 0.1 0.15 0.2
Probability of transmission in a time slot (p)


Figure 5-6. Upper bound on probability of receipt y oeB


The probability of successful reception at B of the secondary transmission from A,

p(T|FT), can be upper bounded by the probability that no primary transmissions occur

in the non-overlapping interference regions of B and D. Under the assumption that the

interference range is twice the transmission range, the area of this region is given by


Ai(z) = 47r Az~(2, 2, z), (5-14)


where Al(rl, r2, d) is giVen by (5-4). Using the same approach as in (5-13), p(T|FT) can be

bounded by


p(T|FT) < e-uzllz)pfxBD (z)dz. (5-15)


The probability of reception by node B was numerically evaluated and the pdf is plotted

in Figure 5-6 for three different node densities, A, and path-loss exponent, a~ = 4. As the

node density increases, the probability of receipt eraewihi u oteices

in the interference around node B. For an ad hoc network with probability of transmission












p = (4rXA)-1, the probability of node B receiving A's message is 0.53 for all the node

densities A.


0.9

0.8

0.7

0.6



B 0.4

O. O.3

0.2

0.1


0 0.05 0.1 0.15 0.2
Probability of transmission in a time slot (p)


Figure 5-7. Upper bound on the probability of a successful secondary transmission, p(S).



The upper bound on the probability of successful secondary transmission p(S) (cf.

(5-10)) is shown in Fig. 5-7 for several values of node densiy A. When the probability

of transmission, p = (41XA)- the value of the upper bound is 0.27, 0.39, and 0.41 for

A = 1, 2, and 3, respectively. For p = (81XA) 1, the value of the upper bound is 0.37, 0.54,

and 0.61 for A = 1, 2, and 3, respectively.

5.4 Summary

In this chapter, we proposed the idea of overlapped transmission to enhance the

spatial re-use and throughput of wireless networks. By taking advantage of a priori

knowledge of the interfering packet, the receiver can employ a simplified IC scheme to

receive a packet in the presence of interference. We analyzed some of the factors that limit

the use of overlapped transmissions in an ad hoc network. The analysis shows that there

is a high probability of successful secondary transmission given that there is a primary










transmission in a time slot. Although this secondary transmission causes interference

to several primary transmissions, this interference can be minimized by either selecting

secondary transmissions that are outside of the primary receiver's interference range, or by

reducing the power of the secondary transmission. In the following chapters, we developed

a MAC protocol that supports overlapped transmission and evaluated its performance

under various network scenarios.











CHAPTER 6
THE OVERLAPPED CARRIER SENSE MULTIPLE ACCESS PROTOCOL

6.1 Introduction

In this chapter, we develop the Overlapped Carrier Sense Multiple Access (OCSMA)

protocol, which is based on the IEEE 802.11 MAC protocol. The OCSMA protocol

supports overlapped transmission in ad hoc networks and exploits knowledge of the

interfering transmissions to schedule additional transmissions, which improve the spatial

re-use and throughput in wireless ad hoc networks.

The organization of the chapter is as follows. Section 6.2 describes the OCSMA

protocol. The design issues of the protocol are considered in Section 6.3, and Section 6.4

provides performance evaluation of the protocol. The chapter is concluded in Section 6.5.

6.2 The Design of OCSMA Protocol

The OCSMA protocol is based on the distributed coordinated function (DCF)

mode of the IEEE 802.11 MAC protocol [52, Section 9.2]. Unless stated explicitly, the

terminology used in the following sections corresponds with that in the IEEE 802.11

standard.

The design of the OCSMA protocol is best described with the example network

of Figure 6-1(a). The timeline of the protocol for the example network is shown

in Figure 6-2, and the frame formats are shown in Figure 6-3. The operation of the

protocol can he divided into five phases as follows:

6.2.1 Primary Handshaking

This phase of the OCSMA protocol is similar to the RTS/CTS exchange of the IEEE

802.11 protocol. When a node has data to transmit to another node in its transmission

range, it initiates the handshake by sending a Request To Send (RTS) frame. The node

that receives the RTS sends a Clear To Send (CTS) frame if it senses the medium to

be free. The node initiating the handshake is the n Mr.:,,~r; ta nsmitter and the node











ODATA
~S Rn. C~T CODATA~ ACKI ACIU


RTS CTS


A


C


(b) RTS


(a) Ad hoc network


B

G







B

G


B


(c) CTS









(e) RTT


(d) PTS


(f) C'TT


s~B


r


r


(g) DATA


(h) ODATA


A


CD


(j) ACEK2


(i) ACEK1


Figure 6-1. Typical frame exchanges in OCS1\A protocol.


that responds to the RTS is the pItent,,r a receiver. All the other nodes that receive the

handshake set their transmit allocation vectors (TAV) for the duration of the transmission.

The transmit allocation vector is similar to the network allocation vector (NAV) defined










RTS PTS DATA

ACK1
~~SCTS _(_RTT~iR illj
D f U TA1'0 (PTS)

B TAY0 (RTS)
CTT ODAT DIFS

Al ~ ~ ~ ~ A (CTS)S F~wc~s

Other$ TA1' (RTS) | I Contention Window
TA1' (PTS)
; ______~~_TA1' (RTT)
I TA1' (CTT)


Figure 6-2. Timeline of the OCSMA protocol.


in the IEEE 802.11 standard [52, Section 9.2.5.4], with a few significant differences as

described below.

Each node is equipped with a transmit allocation matrix (TAX) that is responsible

for the virtual carrier sense mechanism. The TAX is an array of several TAVs. Nodes

receiving a valid frame that is not destined for them update their TAV with the

information in the Duration/ID field. Unlike the NAV vector of IEEE 802.11, the TAX

allocates a TAV for each valid frame (not addressed to the receiving node) it receives,

even if the new TAV value is not greater than any of the current TAVs. Thus the TAX

maintains an array of TAVs for each frame that it receives. The medium is considered

busy if any of the TAVs is set. The TAVs also store information regarding the transmitter

and receiver of the frame, if that information is available. The implementation of the TAX

greatly simplifies the design of OCSMA protocol, as discussed in later sections. Another

important distinction between NAV and TAV is that a node can transmit even if the TAV

of a node is set. The conditions under which this is possible are discussed later.

Consider the WANet in Figure 6-1(a), where at some point of time, node C intends to

forward a packet to D that it has received from B in an earlier transmission. C transmits

an RTS to D, and D responds with a CTS, as shown in Figure 6-1(b) and Figure 6-1(c),












respectively. The frame formats of the RTS and CTS (refer to Figure 6-3) in OCSMA are

the same as in the IEEE 802.11 protocol [52, Section 7.2.1].

Octets: 2 2 6 6 4

C olDuration RA TA FCS
RTS Frame

Octets: 2 2 6 4
C lDurationl RA FCS
CTS Frame
Octets: 2 2 6 6 6 4 4

CFolDuatonRA TA DA PID FCS

PTS Frame

Octets: 2 2 6 6 6 4

C olDuratio RA TA PA FCS
RTT Frame

Octets: 2 2 6 4

C olDurationl RA FCS
CTT Frame
Octets: 2 2 6 6 6 2 6 0-2312 4

CF01Duaio/ dAddressddes Address3 Squnc Address41 Frame Bodyl FCS

DATA/ODATA Frame

Octets: 2 2 6 4
C olDurationl RA FCS

ACK Frame

Figure 6-3. Frame formats of the OCSMA protocol.


6.2.2 Secondary Handshaking

The secondary handshaking can be thought of as a secondary RTS/CTS exchange

to determine the possibility of performing overlapped transmission with the primary

transmission. Upon receipt of the CTS, the primary transmitter sends a Prepare To Send

(PTS) frame to the node from which it received the present DATA frame in an earlier

transmission. If the data is locally generated, no PTS is sent, and transmission of the

DATA frame starts after a duration of SIFS [52, Section 9.2.5]. If the PTS is sent, the










primary transmitter defers the transmission of the DATA frame until the completion of

the secondary handshaking.

Continuing our example using Figure 6-1(a), after the completion of the RTS/CTS

exchange between C and D, node C sends a PTS to B. The PTS frame format is shown

in Figure 6-3. The format is similar to the format of an RTS frame except for the

additional fields DA and PID. The Destination Address (DA) field contains the address of

the primary receiver, and the Packet ID (PID) field contains the unique ID of the DATA

frame that is being transmitted to the primary receiver. The node receiving the PTS

frame is called the a... -m/.oa,; receiver. Being a secondary receiver implies that the present

node has information regarding the primary transmission and is capable of receiving an

overlapped transmission.

Upon receipt of the PTS, the secondary receiver ensures that its TAV is set only by

the primary transmitter. Note that the TAVs store information regarding the transmitter

and the receiver of any valid frame it receives that is not addressed to the receiving node.

This is to ensure that there are no other transmissions occurring in the range of the

secondary transmitter except for the primary transmission. If this is true, it identifies a

suitable partner for secondary transmission as described below.

Once the secondary receiver identifies the medium to be free except for the primary

transmission, it generates a list of potential partners. The nodes are identified based on

the following criteria:

1. The node should not cause excessive interference to the primary transmission. In

this chapter, we consider only one of the two approaches described in Section 5.3.2,

in which the secondary receiver knows the locations of the neighboring nodes and

uses this information to identify potential candidates for the secondary transmitter.

2. The node should have transmitted a frame to the secondary receiver in an earlier

time slot. The information regarding receipt of frames from all the other nodes is

maintained in a cache at the MAC level.









The second condition is based on the heuristic that if a node has transmitted a frame

to the secondary receiver in an earlier time slot, it is very likely that there might be more

frames destined for the secondary receiver. This ensures that there is a greater probability

of secondary transmission for any particular partner. A node is chosen randomly from

the potential candidates to be the a. m /.ol ta nsmitter.

The secondary receiver sends a Request to Transmit (RTT) frame to the selected

secondary transmitter. The format of the RTT is similar to the format of the RTS except

that it also contains an additional field, Primary Address (PA), which contains the address

of the primary transmitter. The secondary transmitter compares the address of the

primary transmitter against the transmitter info of the TAVs (if it is available), and all

the TAVs that are set by the primary transmitter are reset. This ensures that the TAV

of the secondary transmitter is not set by either the RTS or the PTS sent by the primary

transmitter. If it finds the medium to be free and has a suitable packet to transmit,

it responds with a Clear to Transmit (CTT) frame whose format is the same as the

CTS (Figure 6-3). Transmission of CTT implies that the secondary transmitter is capable

of transmitting overlapped data without causing interference to any of the transmissions

(including the primary transmission) in its communication range.

In the example network of Figure 6-1(a), when B receives the PTS from C, it ensures

that its TAV is set only by C's transmission of RTS to D (refer to the TAVO setting of

B shown in Figure 6-2). Since B is not in the transmission range of D, it will be able

to detect D's transmission of CTS but will not be able to decode it. This would cause

B's TAV1 to be set to a duration of Extended Inter Frame Spacing (EIFS) [52, Section

9.2.3.5], but it would expire before the PTS frame is received (refer to TAV1 setting of

B in Figure 6-2). Based on the selection criteria for choosing a partner, assume node B




1 Using other approaches, such as round robin scheduling, may increase the probability
of choosing a node with a packet for the secondary receiver.









chooses node A to send the RTT. When A receives the RTT, it ensures that its TAV is

not set (refer to the TAV settings of A in Figure 6-2). If it senses the medium to be free,

it responds with a CTT frame. In the present example, if we assume that A is in the

interference range of C (it can sense C's transmission but not decode it), it would have set

its TAV (when C transmits PTS to B) to a duration of EIFS, which would have expired

by the time A receives the RTT frame.

6.2.3 Primary Transmission

A timer at the primary transmitter is set to expire in synchronous with the

completion of the secondary handshaking. Note that its TAV timer will not be set during

secondary handshaking (refer to the TAV settings of node C in Figure 6-2). We note

that this differs from the typical NAV implementation of IEEE 802.11 protocol. When

the timer expires, it transmits its DATA frame to the primary receiver. In the example

network of Figure 6-1(a), upon completion of the secondary 1. .141 11:;0s, C starts the

primary transmission to D, as shown in Figure 6-1(g). The frame format of the DATA

frame (refer to Figure 6-3) is the same as in the IEEE 802.11 protocol [52, Section 7.2.2].

6.2.4 Secondary Transmission

The secondary transmitter starts its overlapped transmission ao seconds after the

commencement of the primary transmission (refer to Figure 6-2). This overlapped I1.I A ;I ao

is designed to allow the secondary receiver to acquire the timing and phase of the primary

transmission, which greatly simplifies the interference cancellation (IC) mechanism at

the PHY. It does not ensure perfect symbol or phase synchronization of the primary and

secondary transmissions at the secondary receiver. The format of the overlapped data

(ODATA) frame is the same as the DATA frame. The secondary receiver cancels the

interference and recovers the overlapped data. This phase is illustrated in Figure 6-1(h),

which depicts node B receiving an ODATA frame while canceling out the interference

caused by C's transmission (primary transmission). Note that the secondary transmission

is allowed to terminate al seconds after the end of the primary transmission.










6.2.5 Data Acknowledgments

If the DATA and ODATA frames are successfully received, the primary and

secondary transmitters acknowledge their successful reception as shown in Figure 6-1(i)

and Figure 6-1(j), respectively. The format of the ACK( frames are the same as in the

IEEE 802.11 protocol [52, Section 7.2.1.3].

How the nodes then contend for channel access is an important design consideration

that significantly affects the performance of OCS1\A. Consider first the primary and

secondary receivers. If the DATA and ODATA packets were successful, both of these

nodes have packets to transmit and will contend for channel access. If the primary receiver

sends an RTS before the secondary receiver, then it will become the primary transmitter

for that packet, and the secondary receiver from the previous overlapped transmission

will have the appropriate packet to act as a secondary transmitter for an overlapped

transmission. However, if the secondary receiver gains access to the channel before the

primary receiver, then an overlapped transmission will depend on the availability of

appropriate packets further back in the network. The behavior of the primary receiver is

similar to that of a successful receiver in IEEE 802.11 protocol [52, Section 9.2.4, Section

9.2.5.1]. To give the secondary receiver a high probability of choosing to defer longer than

the primary receiver, it will choose a random backoff value in a window that is twice the

size of the current contention window, once it senses the channel to be idle.

Next, consider the reception of acknowledgments at the primary and secondary

transmitters. Upon reception of ACK(, the primary transmitter resets it contention window

parameter as in the IEEE 802.11 [52, Section 9.2.5.5] protocol. If it has a packet to

transmit, the channel access mechanism is the same as the mechanism in the IEEE 802.11

protocol. However, the secondary transmitter does not reset its contention window. This

ensures that, with high probability, the secondary transmitter does not contend with

the primary transmitter for channel access. The contention window parameter of the

secondary transmitter is reset when it receives an ACK( for any DATA frame (and not an










ODATA frame) that it transmits later. We observed that, in networks with linear flows,

this design leads to a greater probability of overlapped transmission.

6.3 Design Considerations

In this section, we discuss various design issues concerning the OCSMA protocol. In

particular, we compare and contrast the OCSMA protocol with the IEEE 802.11 MAC

protocol, on which it is based.

6.3.1 Cross-Layer Interaction

The design of OCSMA protocol involves a greater level of cro;-l~iver interaction

compared to the IEEE 802.11 protocol. For instance, when a node receives an RTT,

the MAC needs to interact with the higher 1 owni~ to determine if a packet of suitable

length can he sent to the secondary receiver. It is also possible that a packet might

need fragmentation such that the transmission of overlapped data is terminated within

al seconds of the termination of the primary transmission (refer to the timeline of the

protocol in Figure 6-2). Similarly, when the secondary receiver receives a CTT, the MAC

needs to indicate to the PHY 11i; v that interference mitigation will be needed to recover

the overlapped transmission. Cro;-l~iver interaction is also needed at the secondary

transmitter when identifying potential partners for overlapped transmission.

6.3.2 Complexity of the Protocol

The OCSMA protocol involves greater computational complexity than the IEEE

802.11 protocol. This is a result of employing MUD at the PHY and also increased

bookkeeping at the MAC level. However, the increase in the computational complexity

at the MAC level is minimal, and we believe that the design of the protocol can greatly

reduce the computational complexity at the PHY 11i;< v in comparison to other MUD

approaches. We also note that the protocol overhead of OCSMA is more than that of

IEEE 802.11 because of an increase in the number of control frames. However, as the

results in Section 6.4 indicate, this overhead becomes negligible as the size of the DATA

frame increases.










6.3.3 Reduced Overhead

The design of the protocol and the frame formats are to a large extent compatible

with the existing 802.11 frame formats. Hence they can he integrated with existing IEEE

802.11-hased wireless networks with nxininmal changes. The overhead of the OCSMA

protocol can he reduced considerably if no such conformity is required. For instance the

CTT packet can he eliminated without a significant penalty on the throughput. The

elimination of CTT packet results in reduced protocol overhead but increases the power

consumption at the PHY of the secondary receiver since interference cancelation has

to be turned on more often. In addition, the DA and PA fields of the PTS and RTT

frames, respectively, can he eliminated without any significant performance penalty

(refer to Figure 6-3). We call this protocol the OCSMA protocol with reduced overhead

(OCSMA_RO). The performance of this reduced-overhead protocol is simulated in the

next section. The PTS can also be eliminated by including the information of the PTS

frame in the RTS. In this case, the RTS format will be much different front the format of

RTS of the IEEE 802.11 protocol. However, we did not observe any significant change in

the throughput with this modification. Finally, the frame formats of all the frames can

he modified to reduce the overhead, although we did not evaluate such approaches in this

work.

6.4 Simulation Results

We evaluated the performance of the OCSMA protocol under different network

topologies and traffic conditions using Network Simulator (ns2) [69]. Since we evaluate

only the performance of the MAC protocol, we assume perfect interference cancellation at

the PHY and that the ODATA packet can he recovered whenever there is an overlapped

transmission with the corresponding primary transmission being the only source of

interference. The simulations are based on the 1 Mbps DSSS mode (cf. [52, Section

15]) of IEEE 802.11; except where specified, the parameters are given in Table 6-1.

The overlapped delay ao of 240 ps corresponds to about 30 bytes of data, which is












slightly larger than the sunt of the lengths of PLCP header and PLCP preamble (24

bytes) [52, Section 15.2.2]. For other system parameters, the default values of the 802.11

intplenientation in ns2 are used. Henceforth, we refer to a MAC service data unit (jlrsl>)I

as a frame, and a transport 1 e s, r service unit (TSDIT) as a packet.

Table 6-1. NS2 simulation setup.
Parameter Default value
Data rate 1 Mbps
Simulation duration 4000 s
Warnmup time 400 s
Routing protocol ADDV
CI. ill. I mdelTwo ray propagation
RTS Threshold 150 Bytes
Transmission radius 250 ni
Carrier-sensing radius (Interference range) 550 ni
IFQ length 100
Overlapped Delay ao 240 p-s
a, 240 p-s
STA Retry Limits (Short, Long) (7,4)


*---y *
:1 2 3 4 5


e---- **
~7 8 9 10


Figure 6-4. Ten-node linear network.


We first evaluate the OCSMA protocol in a fixed ten-node linear network as shown

in Figure 7-1, with the source and the destination located at either end of the network.

The nodes are placed at regular intervals of 200 nt. This translates to the .Il11 Il-ent nodes

being in the coninunication range of each other, and nodes two hops apart being in the

interference range of each other. The transmission power of the secondary transmission











is the same as that of the primary transmission. The traffic model is based on FTP

-!us!!11 Il.d application", in which the TCP queue is never empty. TCP is used for

flow control, with a nmaxiniun window size of 32. The end-to-end throughputs of the

network under the OCSMA, OCSMA_RO, and IEEE 802.11 MAC protocols are shown

in Figure 6-5.

10000

9500

9000

8500~ -Y --- IEEE 802.11
I //-e-- OCSMA
.Y 8000 -4-- OCSMA RO





6500

60000
400 600 800 1000 1200 1400 1600 1800 2000
Packet size (Bytes)

Figure 6-5. Throughput comparison in a ten-node linear network with TCP traffic.


We observe that the throughput of the IEEE 802.11 MAC protocol increases until

the data packet length reaches 1000 bytes, beyond which it starts decreasing. However,

the throughput of both OCSMA and OCSMA_RO increase until the packet length reaches

1400 bytes, beyond which the throughput decreases. The OCSMA protocol provides

throughput gains of !I' to t:' I' over the range of packet lengths shown in Figure 6-5. The

nmaxiniun throughput under OCSMA is achieved for a packet length of 1400 bytes, at

which point it provides 21 throughput gain over IEEE 802.11. Similarly, the reduced

overhead version of OCSMA (OCSMA_RO) provides throughput gains of 11- 111' over the

packet lengths simulated, and provides a throughput gain of 2' over IEEE 802.11 for a

packet length of 1400 bytes.












The MAC-level events across the network for all three protocols are tabulated

in Table 6-2 and Table 6-3 for data packet lengths of 400 and 1800 bytes, respectively. The

average rate of RTS frames received for OCSMA and OCSMA_RO is higher than the rate

of RTS frames received in the case of IEEE 802.11. We observe that the proportion of the
averge ate f rception of PTS to that of RTS is very high, indicating that there is a

very high probability of an overlapped transmission from the perspective of the primary

transmitter. However, the ratio of the reception of CTT to that of RTT is significantly

low, which indicates that the actual number of ODATA transmissions is significantly less

than the potential number of overlapped transmissions. This might be due to the lack of

suitable packets at the secondary transmitter or the medium being perceived as busy by

the secondary transmitter. To investigate the reason for the low CTT to RTT ratio, we

created a No Packet to Transmit (NPT) frame. The secondary receiver transmits an NPT

in response to an RTT if it finds the medium to be free but doesn't have a suitable frame

for the secondary receiver. The NPT frame was introduced only for simulation purposes,

and is not a part of the OCSMA protocol. We did not observe any adverse effect on the

system throughput from the inclusion of the NPT frame.

Table 6-2. Comparison of events at the MAC level in a ten-node linear network with
packet size 400B.
Received frame IEEE 802.11 OCSMA OCSMA_RO
type (Events/s) (Events/s) (Events/s)
RTS 161.8 193.6 201.0
CTS 1363.2 127.9 140.0
PTS 110.8 105.8
RTT 79.1 78.9
CTT 22.8
NPT 41.8
DATA 134.0 117.0 127
ODATA 22.8 22.7
Collision 9.3 15.5 10.1










Table 6-:3. Comparison of events at the MAC level in a ten-node linear network with
packet size 1800B.
Received frame IEEE 802.11 OCSMA OCSMA_RO
type (Events/s) (Events/s) (Events/s)
RTS :36;.0 59.5 61.0
CTS :32.4 :39.5 41.5
PTS : 34.4 :36.0
RTT 26.0 28.0
CTT 6.7
NPT 16.4
DATA :32.3 :39.0 41
ODATA 6.7 7. 1
Collision 0.7 :3.2 :3.2



As can he seen in Table 6-2 and Table 6-3, the ratio of CTT to NPT is about 5 1' .

and 41 for packet lengths of 400 bytes and 1800 bytes, respectively. This indicates that

the full potential of the overlapped transmissions is not realized due to lack of suitable

packets. The ratio of overlapped data (ODATA) packets received to that of data (DATA)

packets is 19.5' and 17.C,' for OCSMA and OCSMA_RO, respectively, for a packet

size of 400 bytes. The ratio is 17.',' and 17.;:' respectively, when the packet size is

increased to 1800 bytes. It is also worth noting that the average number of collisions at

the MAC level in the case of both the OCSMA protocols is higher than that of the IEEE

802.11 protocol. We observed that these collisions are mainly due to the control frames

during the secondary handshaking (RTT and CTT) causing collisions in the vicinity of the

secondary transmitter. However, these collisions are offset by the increase in throughput

due to overlapped transmissions. The interaction between TCP and OCSMA is thoroughly

investigated in OsI I pter 7.

The throughput of the ten-node linear network of Figure 7-1 with constant hit rate

(CBR) traffic is shown in Figure 6-6 for several packet arrival rates. The packet size

is 1000 bytes. We observe that the throughput of all three protocols is the same until

the packet arrival rate reaches 20 packets/s. As the packet rate increases, there is a

dramatic fall in the rate of packets delivered hv IEEE 802.11. However, under OCSMA















S- 22-


S20-


18-


S16
16 802.11
-0- OCSMA
w d ~OCSMA_RO
14-


12-



10 15 20 25 30 35 40 45 50
Packet arrival rate (packets/s)


Figure 6-6. Througfhput comparison in a ten-node linear network with CBR traffic.




and OCSMA_RO, the decline in the throughput is more gradual, and the throughput gains

provided by OCSMA protocols over IEEE 802.11 are significant.


1.7

03 1.6








S1.2


4 6
Packet arrival rate


Figure 6-7. Throughput comparison in linear network with multiple CBR flows.












Next, we consider the effect of multiple-flows in a linear network. Three sources and

three destinations are placed at either end of a ten-node linear network, and the traffic

type is CBR. The throughput gains of OCSMA and OCSMA_RO over 802.11 with CBR

traffic and multiples flows in a linear network are shown in Figure 6-7. The packet arrival

rate indicates the common rate at which packets arrive at each of the sources. It can he

observed that even in the presence of multiple flows, OCSMA and OCSMA_RO provide

significant gains over IEEE 802.11 in a ten-node linear network.

1.0

1.7

1.6



a. -x- OCSMA
0-e-- OCSMA RO



1.2

1.1


5 10 15 20 25 30
Number of nodes in the linear network

Figure 6-8. Effect of varying the number of nodes in a linear network on the throughput
gain of OCSMA and OCSMA_RO.


Next, we vary the number of nodes in the linear network. FTP -!nu!11 II application"

traffic with TCP congestion control was simulated. The TCP packet size is 1400 bytes,

and the congestion window size is 32. The end-to-end throughput gains of the OCSMA

and OCSMA_RO protocols over IEEE 802.11 are shown in Figulre 6-8 as a function of

the number of nodes in the linear network. It can he seen that OCSMA and OCSMA_RO

provide maximum throughput gains of 72' and '7;' respectively, when the network

consists of six nodes. The gain decreases with an increase in the number of nodes in the












network. In a thirty-node network, the throughput gains of OCSMA and OCSMA_RO

are lu~' and 10I' respectively. For a fixed TCP congestion window size, under OCSMA

and OCSMA_RO, we observed that, as the size of the linear network increases, the ratio

of ODATA to DATA frames decreases and the collision rate increases. When the size of

the network is large, we noticed that the full potential of overlapped transmissions is not

realized due to the lack of availability of packets at secondary transmitters. Increasing

the CW size increases the probability of overlapped transmission, but doesn't completely

eliminate the packet starvation issue. In ChI Ilpter 7, the interaction between OCSMA and

TCP in ad hoc networks is analyzed and the OCSMA protocol is modified to improve the

performance of TCP flows.

(340,1160) (820.1160)

(240.1060) t(340.1060) (820.1060) (920.1060)


(0,20 (100,820) (340.820) (820.820) (1060 820)t (16 80


(100.720) (1060. 20)

(340.580) (580.580) (820.580)
(100.440) (1060.440)


(0.340) (100 340) (340.340) (820.340) (1060 340) (1160.340)





(340.0) (820,0)


Figure 6-9. Binary-tree network.


We also evaluated the throughput gains of OCSMA and OCSMA_RO over IEEE

802.11 in a hinary-tree network shown in Figure 6-9. The location of the nodes are given

in paranthesis. In this topology, each node of the tree network has exactly two children,

and the root (located at (580,580)) transmits independent messages to each of the leaf

nodes. The traffic type is CBR, and the packets meant for each of the leaf nodes arrive at













the source with same rate. The rest of the simulation parameters are given in Table 6-1.

The performance gains of OCSMA and OCSMA_RO in a binary tree network with a depth

of four is shown in Figure 6-10. It can he observed that for packet arrival rates greater

than 3, OCSMA and OCSMA_RO provide at least ;::".' throughput gain over the IEEE

802.11 protocol.


1.4

1.35

1.3

'i 1.25

c. -x- OCSMA
.c 1.2
U~ I -- OCSMARO
2- 1.15

1.1

1.05


S1.5 2 2.5 3 3.5 4 4.5 5
Packet arrival rate


Figure 6-10. Throughput gain of OCSMA and OCSMA_RO in a tree network.


We next consider a random topology with 50 nodes distributed in a 1500m x 1500m

square. This scenario corresponds to an average node density of four nodes in a circle of

radius equal to the transmission range of a node (set to 250m). The mobility model chosen

is the random waypoint model, which is the default model in ns2. The nodes move with

a speed that is uniformly distributed in the interval [0, max_speed], where we consider

different values of max_speed. Twenty TCP connections were randomly generated with

packet size 1400 bytes, and the rest of the system parameters are given in Table 6-1. The

throughput gains of OCSMA and OCSMA_RO over IEEE 802.11 are averaged over 500

instantiations of the random network. The performance gain of OCSMA protocols over














1 25-
OCSMA
OCSMARO
12 --


1 15-





1 05-





0 95-


09-
0 2 5 10 15 20
Maximum speed (m/s)


Figure 6-11. Throughput gain in a random network with mobility.


IEEE 802.11 as a function of the maximum speed of the nodes in the network is shown

in Figure 6-11. We observe that the throughput gains of the OCSMA protocols decrease as

the mobility in the network increases. When there is no mobility in the network, OCSMA

provides an average throughput gain of about 1;:' with a standard deviation of 11 The

high standard deviation indicates that in certain scenarios, OCSMA provides significant

gains over IEEE 802.11. Similarly, OCSMA_RO provides an average throughput gain

of 1'7' with a standard deviation of 1_' Under high mobility (max_speed = 20m/s),

OCSMA and OCSMA_RO provide average throughput gains of 5' (standard deviation =

5' .) and '7' (standard deviation =~ 5'), respectively. The results indicate that, in general,

the throughput gain from overlapped transmissions is small when there is high mobility in

the network. However, in certain scenarios, OCSMA provides significant gain over IEEE

802.11.










6.5 Summary

We developed the OCSMA protocol based on the IEEE 802.11 MAC protocol to

support overlapped transmissions in a wireless network. Network simulations employing

OCSMA protocol and its reduced overhead variant, OCSMA_RO, show that the

end-to-end throughput can he improved by as much as '7;' over the IEEE 802.11 protocol

in a linear network with TCP traffic. Under CBR traffic, OCSMA and OCSMA_RO are

more robust to the traffic load and multiple flows than the IEEE 802.11 protocol. In a

random network with 50 nodes and 20 TCP connections, the OCSMA and OCSMA_RO

protocols provide an average throughput gain of 1;:' and 1'7' respectively, when there is

no mobility in the network. The throughput gain of the OCSMA protocols decrease with

an increase in the mobility in the network. Although the average gain provided by the

OCSMA protocols in high mobility conditions is only 5' to '7' the throughput gain in

certain scenarios can he much higher.









CHAPTER 7
IMPACT OF OVERLAPPED TRANSMISSION ON THE PERFORMANCE OF TCP IN
AD HOC NETWORKS

7. 1 Introduction

In the previous chapter, we developed the OCSMA protocol and compared its

performance to the IEEE 802.11 MAC protocol in a variety of network scenarios using

ns2. In this chapter, the performance of OCSMA is further investigated with an emphasis

on its impact on networks that employ Transmission Control Protocol (TCP). In wireless

networks, congestion control mechanisms are emploi-o I in conjunction with MAC protocols

to provide reliable and efficient end-to-end service.

The interactions between the TCP and MAC protocols, like IEEE 802.11, in wireless

ad hoc networks have been well investigated by the research community (see [70-76] and

the references therein). In wireless networks, TCP suffers from poor bandwidth utilization

and network unfairness. This is primarily due to the unique characteristics of the wireless

environment such as half-duplex links, channel noise, and mobility.

To alleviate the issues associated with TCP in wireless networks, several schemes have

been proposed (cf. [76-78]). These schemes aim to achieve better cro ;-1 .ver interaction

between the MAC and transport 1... ris by either modifying the MAC level behavior or

the congestion control mechanism at the transport 1... -r. For a survey of the work on

improving TCP performance in wireless networks, refer to [76].

In the present chapter, the interaction between TCP and OCSMA is investigated in

multihop networks with linear flows. Through network simulations, we study the impact of

overlapped transmission on the behavior of TCP flows. The focus is on identifying factors

(at the MAC and transport 1... ris) that impact the performance of the network. The

results show that when TCP is used for congestion control, OCSMA provides significant

performance advantages over the IEEE 802.11 MAC protocol in several scenarios of

interest.











The rest of the chapter is organized as follows. The interaction between TCP and

OCSMA in a variety of network scenarios is investigated in Section 7.2. In Section 7.3, we

modify the OCSMA protocol to increase the throughput of TCP flows in linear networks.

Through network simulations, we show that the modified OCSMA protocol improves the

performance of both TCP and ITDP traffic in linear networks. The chapter is concluded

in Section 7.4.

7.2 Interaction between TCP and OCSMA

In this section, the cro;-l~iver interaction between TCP and OCSMA is investigated.

We present results from ns2 simulations for a variety of scenarios and study the interaction

between the two l~i-;-v We compare and contrast the OCSMA protocol with the IEEE

802.11 MAC protocol. In the following sections, we refer to a MAC service data unit

( !l)~lU) as a frame, and a transport 1... -r service unit (TSDIT) as a packet. A MAC level

acknowledgment is denoted by a capitalized ACK(, while a transport 1... -r acknowledgment

is represented by an italicized ack.

We first consider a ten-node linear network, as depicted in Figure 7-1. Node 1 is

the source, and node 10 is the destination. The nodes are placed at regular intervals of

200 m. The communication radius is 250 m, and the sensing range is 550 m. In the linear

network of Figure 7-1, the transmission ranges of nodes 3 and 9 are denoted hv solid

circles, and their respective sensing ranges are denoted by dashed circles. The default

values of simulation parameters are summarized in Table 7-1.




























Table 7-1. Simulation setup for evaluating the impact of OCSMA on TCP performance.
Parameter Value
Data rate 1 Mbps
Congestion Control TCP Reno
Simulation duration 2000 s
Warnt-up time 200 s
Routing protocol ADDV
CI. ill. I mdelTwo ray propagation
RTS Threshold 150 Bytes
Transmission radius 250 ni
Carrier-sensing radius (Interference range) 550 ni
IFQ length 100
Overlapped Delay ao 240 p-s
STA Retry Limits (Short, Long) (7,4)
TCP packet size 1400 Bytes
Application type FTP "simulated application"


7.2.1 Impact of TCP Congestion Window Size

In this subsection, we evaluated the impact of the TCP congestion window (CW) size

on the end-to-end throughput of the network. In ns2, the CW parameter represents the

receiver advertised window size, and defines the nmaxiniun number of packets to be sent at

every round-trip-tinle. TCP is designed to adjust the flow hased on the CW size and the

congestion in the network. In the following sections, unless otherwise stated, CW refers to

the receiver's advertised CW.


1 2 3 4 5


~7 8 9 10


Figure 7-1. Ten-node linear network under OCSMA.
















S 12



10 -0
o -x--OCSMA
F I-F--OCSMA RO
S9~1 -0- IEEE 802.11





5 10 15 20 25 30
TCP Congestion Window Size (packets)

Figure 7-2. End-to-end throughput comparison in a ten-node linear network with TCP
traffic .


The end-to-end throughput under the OCSMA, OCSMA_RO and IEEE 802.11 MAC

protocols in the ten-node linear network of Figure 7-1 as a function TCP CW size are

shown in Figure 7-2. In the case of IEEE 802.11, the throughput of the network increases

with an increase in CW size until the CW size is 4, beyond which it decreases. This

behavior of TCP throughput under IEEE 802.11 has been reported in the literature [78,

79], where it was noted that the optiniun performance is achieved when the CW size of

TCP is a fraction (usually 1/4) of the number of nodes in the linear network.

However, the behavior of OCSMA protocols is quite different front that of the IEEE

802.11 protocol. The TCP throughput under OCSMA (and OCSMA_RO) increases with

an increase in CW size, and the throughput saturates for CW sizes greater than 14. This

behavior of OCSMA can he better understood by analyzing the link throughput.

The link throughput (j1\! C level) under OCSMA and IEEE 802.11 are shown

in Figure 7-3(a). The left ordinate scale is for DATA frames, and the right ordinate is

for ODATA transmission. Note that under OCSMA, both DATA and ODATA frames












contribute to the link throughput. The DATA (and ODATA) loss rate for OCSMA and

IEEE 802.11 are plotted in Figure 7-:3(b).

We observe that the link throughput under IEEE 802.11 mimics the end-to-end

throughput curve of Figure 7-2. Note that the rate at which DATA frames are dropped

due to collisions increases as the CW size increases as shown in Figure 7-:3(b). In the case

of OCSMA, both the DATA and ODATA reception rate increases with an increase in the

CW size, and saturates for CW sizes greater than 14. Increasing the CW size increases

the number of frames available for overlapped transmission in the network. Note that the

DATA reception rate under OCSMA is less than the DATA reception rate under IEEE

802.11. However, the combination of DATA and ODATA frames in OCSMA provides a

greater end-to-end throughput over IEEE 802.11. Although the collision rate in the the

case of OCSMA is very high, the ability to perform overlapped transmissions offsets these

collisions to provide high throughput even when CW size is high.

Table 7-2. Events at the MAC level in a ten-node linear network under OCSMA protocol.
Frame CW = 1 CW = 2 CW = 4 CW =8 CW =16
type (Events/s) (Events/s) (Events/s) (Events/s) (Events/s)
RTS 6:3.8 84.9 155.4 182.4 190.0
CTS 6:3.8 76.3 10:3.2 106.6 107.1
PTS 49.6 59.3 78.9 80.1 79.6
RTT 49.6 52.0 58.6 57.8 56.6
CTT 0 11.2 11.5 18.3 21.5
NPT 49.6 :38.4 :38.5 28.7 2:3.4
DATA 6:3.8 72.8 94. 11 96.0 95.8
ODATA 0 11.2 11.5 18.3 21.5
COLL 0 :3.4 7.8 8.7 8.8


We further investigate the behavior of OCSMA by analyzing the MAC-level events

across the network. The MAC-level events under OCSMA are tabulated in Table 7-2 for




1 In this scenario, events correspond to either reception of a frame or a collision





















-e-OCSMA, DATA

Y80-





2 4 6 8 10 12 14 16 18
TCP Congestion Window size (packets)

(a) Link throughput in a ten-node linear network







6 --OCSMA
-#- IEEE 802.11
~t5

L4




O 01
3- ogsinWndwsz pces
o b rm-rprt na e-oelna ewr






(b)ea Frm-do rt i enndelnernewr


802.11 in a ten-node


several values of CW size. We see that the average rate of RTS frames received increases

as the CW size increases. We also note that the reception of RTT frames increases

indicating that the opportunity to perform overlapped transmissions (as perceived by

the secondary receiver) increases. However, the ratio of the reception of CTT to that of

RTT is significantly lower than one, which indicates that the actual number of ODATA

transmissions is significantly less than the potential number of overlapped transmissions.











The NPT frame was introduced in Section 6.4 during the simulations to investigate the

reason for the low rate of overlapped transmissions in the system. It is not a part of the

OCSMA protocol, and we did not observe any adverse effect on the system throughput

due to its inclusion. In Table 7-2, we note that the ratio of NPT to RTT is very high

indicating that a lot of opportunities of overlapped transmissions are missed because of a

lack of suitable frames for overlapped transmission at the secondary transmitters. We note

that the number of overlapped transmissions increases with an increase in the CW size,

yet, the full potential of overlapped transmissions is not realized. For instance, for a CW

size of 16, the ratio of CTT/(NPT+CTT) is only I This is mainly due to the lack of

interaction between OCSMA and TCP as explained below.



as0
.6 20 Rx CW =3


1 0
4 00 10 20 30 40 50 60 70 80 90 100
v, Rx CW =5

S10
S20 10 20 30 40 50 60 70 80 90 100


E 20 G 1
? ~Rx CW=1

E- 10
0 10 20 30 40 50 60 70 80 90 100
Time (s)

Figure 7-4. Transmitter congestion window evolution in a ten-node linear network.


Consider the network of Figure 7-1 and assume that TCP is operating in congestion

avoidance phase and the queue at node 1 is empty. When the source receives an ack

packet for a TCP packet that it transmitted to node 9, it pushes a packet (most of the

time) to the interface queue at the MAC level. The MAC of node 1 transmits this "DATA

ft...to node 2, which it forwards to node 3, and so on. When node 3 forwards this











frame to node 4, there is a possibility of an overlapped transmission between nodes 1 and

2. However, this is possible only if the transport 1 m-;-r at node 1 receives a new ack for a

TCP packet that it transmitted earlier. We observed that when the receiver CW size is

small, the probability of this happening is very small, and the opportunity for overlapped

transmissions are wasted every time a TCP packet is forwarded along the linear network

during the congestion avoidance phase. When the CW size increases, the collisions in

the network increase, and there is a high probability that a node is in backoff state,

which indicates that its queue is non-empty. This increases the probability of overlapped

transmission. The results in Figure 7-4 plot the evolution of the source contention

window.2 Note that when the CW size is low, TCP is in the congestion avoidance phase,

which implies that the probability of transmitting one packet upon reception of an ACK(

is very high. As the CW size increases, TCP experiences fast start phases quite often,3

which implies that the TCP at node 1 releases multiple packets quite often in response to

an ack packet. This increases the probability of overlapped transmission in the system.

However, this cannot completely eliminate packet starvation in an overlapped transmission.

The observation made regarding OCSMA apply to the OCSMA_RO protocol too, the only

difference being that there is no CTT frame in OCSMA_RO.

7.2.2 Impact of Collisions on TCP Throughput

In the previous section (cf. Table 7-2), we observed that the collision rate under

OCSMA protocols is very high. This is due to an increase in the number of control frames

in OCSMA (compared to IEEE 802.11). In this section, we consider strategies that negate

the impact of the higher collision rate in OCSMA and increase the TCP throughput.




2 The actual number of packets transmitted by the source is minimum of the
transmitter and receiver CWs.

SThe TCP variant TCP-Reno is used for congestion control.













1.32
(20,10

1.3
C (1 0,6)
I (14,8)
1.28

03 (7,4)
2 1.26
F (10,6) / t OCSMA
1.24 -e-- OCSMA RO

1.22 (7,4)


1.2
6 8 10 12 14 16 18 20
STA Short Retry Count (ssrc) limit

Figure 7-5. Effect of short and long retry counts on throughput gains of OCSMA and
OCSMA_RO in a ten-node linear network.


First, we analyze the impact of the STA Short Retry Count (SSRC), and STA

Long Retry Count (SLRC) limits [52, Section 9.2.5.3] on the throughput of OCSMA

and OCSMA_RO. The results in Figure 7-5 show the throughput gains of OCSMA and

OCSMA_RO over IEEE 802.11 for various values of the SSRC and SLRC limits. The TCP

window size is :32 and the packet size is 1400 hvtes. The values of the SLRC and SSRC

limits used are shown in parenthesis. We observe that the throughput gain of OCSMA

and OCSMA_RO increase monotonically with an increase in the SSRC and SLRC limits.

The increase in collisions in the case of OCSMA protocols are offset by the increase in

the SSRC and SLRC limits. We observe that when SSRC and SLRC are 20 and 10,

respectively, the throughput gain of OCSMA over IEEE 802.11 is :31 For these values of

retry limits, the reduced overhead variant OCSMA_RO, provides a throughput gain of :3 .

over IEEE 802.11.

Next, we consider the strategy of sending one ack per multiple received packets, i.e.

d. T w.- I1-ack. The destination node transmits one ack for two consecutive packets received.

This changes the granularity at the transmitting node. For each ack that the transmitter












receives, TCP sends multiple packets to the interface queue. We expect this strategy to

decrease the number of collisions in the system (due to fewer acks being transmitted), and

increase the number of overlapped transmissions.

Table 7-:3. Performance comparison of OCSMA and OCSMA_DA.
Frame OCSMA OCSMA_DA OCSMA OCSMA_DA
Type (CW=2) (CW=2) (CW=16) (CW=16)
TPITT 9.3 9.7 1:3.0 15.1
RTS 84.9 6;6.3 190.1 196.1
CTS 76.3 65.8 107. 1 112.1
PTS 59.3 51.6 79.6 84.63
RTT 52.0 51.3 56.6 61.7
CTT 11.2 18.1 21.5 :30.0
NPT 49.6 :32.0 2:3.4 18.0
DATA 6:3.8 65.1 95.8 105.4
ODATA 11.2 18.1 21.5 :30.0
COLL :3.4 0.0 8.8 5.4


The end-to-end throughput and the MAC level events under OCSMA and OCSMA

with d.l 1 i-, I1-ack (OCSMA_DA) are tabulated in Table 7-:3. When the CW size is 2, the

end-to-end throughput (TPITT) under OCSMA and OCSMA_DA are the same. However,

the number of collisions in the case of OCSMA_DA is much lower than in the case of

OCSMA. Note that the number of overlapped transmissions are greater in the case of

OCSMA_DA. When the CW size is 16, OCSMA_DA provides lu~' throughput gain over

OCSMA. Also note the increase in overlapped transmissions and reduction in collisions in

the case of OCSMA_DA.

7.2.3 Fairness Issues and Medium Contention

In this subsection, we investigated the inter-flow contention issues when TCP is

used in conjunction with OCSMA. Medium contention is a 1!n I in t- source of unfairness in

niultihop ad hoc networks. Different flows may experience different congestion issues, and

the resources allocated to then nay be different. Starvation is another 1! in .ju problem

which results due to the greediness of TCP flows. In order to evaluate these issues in the










Flowl

1 2 3 4 5 6
Flow2

7 8 9 10 11 12
Flow3

13 14 15 16 17 18
(a) Network with parallel flows







S10

Flow 1






S12


S13
(b) Network with intersecting flows

Figure 7-6. Networks with multiple flows.



context of OCSMA, we consider the two network topologies illustrated in Figure 7-6(a)

and Figure 7-6(b). Figure 7-6(a) shows a network with three parallel flows each traversing

through six nodes. The .Il11 Il-ent nodes in a flow are placed at a distance of 200 m, and the

.Il1i Il-ent flows are separated by a distance of 400 m.

The results in Figure 7-7 plot the throughput evolution of each of the three flows

under the OCSMA and IEEE 802.11 MAC protocols. We chose a TCP CW size of 2 for

each of the flows. The TCP packet size is 1400 bytes, and the short and long retry limits

are 20 and 10, respectively. We observed that a CW size of 2 gave the best performance

under both OCSMA and IEEE 802.11. We observe that under 802.11, flows 1 and 3
























0 10 20 30 40 50 60 70 80 90 100
16
-x- IEEE 802.11, flow3
14C 4-OCSMA, flow3

12-

104
0 10 20 30 40 50 60 70 80 90 100
Time (s)

Figure 7-7. Throughput comparison in a network with multiple parallel flows.


have non-zero throughput at all times, where as the throughput of flow 2 is zero. The

nodes of flow 2 experience interference from both the flows 1 and :3, which results in zero

throughput for flow 2. This is the classic starvation problem encountered in multihop

networks that arises because of the greediness of TCP flows.

However, under OCSMA, the throughput of flow 2 is non-zero, but still lower than

that of flows 1 and :3. Since flow 2 experiences interference from nodes in flow 1 and :3, it

is not surprising that the throughput of flow 2 is lower than that of flows 1 and :3. The

non-zero throughput of flow 2 under OCSMA is primarily due to the effect of increased

collisions, and the ability to perform overlapped transmission. Since the collision rate

under OCSMA is very high, nodes (including the nodes in flows 1 and :3) spend more time

in backoff, which provides a greater chance for nodes in flow 2 to compete and succeed in

accessing the channel. On the other hand, the increase in collisions across all the flows is

offset to a large extent by an increase in spatial re-use due to overlap transmissions. For

instance, in Figure 7-7, note the throughputs of flows 1 and :3 under OCSMA are similar

(although lower) to the case of IEEE 802.11.










We compare the fairness of IEEE 802.11 and OCSMA by employing Jain's fairness

index [80]. Jain's fairness index is defined as





where xl, x2, xn are the flow throughputs of each of the a flows, respectively. Using

Jain's fairness index (cf. (7-1)), and evaluating the average throughput of each of the

three flows over a simulation duration of 1800 s (cf. Table 7-1), we have with IEEE 802.11,


f802.11 1l, 2a, 3) = 0.67, (7-2)

and with OCSMA

fOCSM/Axl 1a 2 3) = 0.89. (7-3)

The closer the fairness index is to unity, the greater the fairness in the network. The

fairness index of 0.67 in the case of IEEE 802.11 is due to the channel resources being

equally divided between two flows (flow 1 and flow 3), and the third flow (flow 2) is

completely deprived of the channel resources. However, we note that in the case of

OCSMA, flow 2 has non-zero throughput, which is reflected by a higher value of fairness

index.

Next, we simulate the network of Figure 7-6(b), and evaluate the throughput of each

the flows under OCSMA and IEEE 802.11. The TCP CW size is 2 (this provided the

best performance for both OCSMA and IEEE 802.11). TCP packet size is 1400 bytes,

and the retry limits are (20,10). The throughput evolution of each of the two flows under

OCSMA and IEEE 802.11 MAC protocols are depicted in Figure 7-8. In the case of IEEE

802.11, we see that at any point of time, one of the flows captures the resources, while the

other flow is completely deprived of the channel resources. This exemplifies the greediness

of TCP flows. However, in the case of OCSMA, we note that the channel resources are

more evenly distributed among both the flows, and the throughput of the flows is similar










12
10-





\-x-- OCSMA, Flow 1
2~ -P ---IEEE 802.11, Flow 1
S0
0 10 20 30 40 50 60 70 80 90 100
,n12
g 10t -P -x-- OCSMA, Flow 2
E-~ -Q- IEEE 802.11, Flow 2







0 10 20 30 40 50 60 70 80 90 100
Time (s)


Figure 7-8. Throughput comparison in a network with multiple linear flows.


during the entire observation interval. We observed the same trend even when the CW

size is increased. This indicates that OCSMA introduces a certain amount of fairness in

situations involving inter-flow contention.

To evaluate short-ternt fairness, we first computed the average throughput of each

flow over consecutive windows of 10 s. Jain's fairness index was computed for each 10 s

window, and the average fairness over all the windows was computed. The fairness indices

under IEEE 802.11 and OCSMA are



f802.11 = 0.50, (7-4)


and

focum4r = 0.99, (7-5)


respectively. A fairness index of 0.5 under IEEE 802.11 indicates that one of the flows

is completely deprived of the channel resources. However, under OCSMA, the fairness

index is very close to unity, indicating a fair allocation of the channel resources. Next, we










evaluate the long-term fairness by calculating the average throughput of each of the flows

over a simulation duration of 1800 s. The fairness indices under IEEE 802.11 and OCSMA

are

f802.11 = 0.98, (7-6)

and

focsM/A = 0.99, (7-7)

respectively. Note that while IEEE 802.11 provides only long-term fairness, OCSMA

provides both long-term and short-term fairness.

7.3 OCSMA with Look Ahead Capability (OCSMA_LA)

In the previous sections, we analyzed the impact of OCSMA on the performance of

TCP flows in wireless networks. The simulation results ell----- -r that OCSMA provides

better end-to-end throughput and fairness over IEEE 802.11 protocol. Based on network

simulations, we identified parameters that impact the performance of the network.

However, the discussions of Section 7.2 so-----~ -r that the full potential of overlapped

transmissions is not realized. We attributed this to packet starvation, and lack of

interaction between the two 111-;- rs. In this section, we modify the OCSMA protocol to

address the issue of packet starvation.

Motivated by the work in [81], we introduce the concept of Look Ahead. Upon the

completion of an overlapped transmission, both the primary and secondary receivers

contend for the channel access. The OCSMA protocol was designed to allow for the

secondary receiver to backoff for a greater duration and allow for the primary receiver

to have a greater chance for channel access (please refer to Section 6.2.5 for more

details). However, this design doesn't ahr-l-as guarantee the occurrence of an overlapped

transmission. In networks with linear flows, the probability of an overlapped transmission

can he increased by ensuring that the primary receiver of the current overlapped

transmission rl;, tr;, gets access to the channel before the secondary receiver. This is

accomplished with the help of the Look Ahead feature, as explained below.












7.3.1 OCSMA_LA Protocol Description

e----- *
1 2 3 4 5 6 7 8 9 10

Figure 7-9. Ten-node linear network under OCSMA_LA.


Since OCSMA_LA is based on OCSMA protocol, we highlight only the differences

between the two protocols. We will use the example network of Figure 7-9 to describe

the design of OCSMA_LA protocol. For a complete description of OCSMA protocol, refer

to Section 6.2. The differences between OCSMA and OCSMA_LA are during the primary

treenstaission and acknow, 1. Jrites.;. 4 phases, as described below.

In the network of Figure 7-9, assume that node 3's transmission to node 4 is the

rIt,.I,, r ,I treenstaission, and node 1's transmission to node 2 is the .< ..-t.'.lit ti treenstaisesion.

After the completion of the secondary handshaking phase (refer to Figure 6-1(d), Figure 6-1(e),

and Figure 6-1(f)), node 3 commences the transmission of the DATA frame to node 4.

Upon successful reception of the DATA frame, node 4 acknowledges it with a modified

ACK(, the AK(M (AcEK Modified) frame. The frame format of the AK(M frame is shown

in Figure 7-10. The AK(M frame, in addition to the Receiver Address (R A) field, contains

the additional fields TA, NA and NFD. The Transmitter Address (TA) field contains the

address of the node transmitting the AK(M frame. The Next Address (NA) field contains

the address of the node for which the present node (the node transmitting the AK(M) has

a DATA frame, and the Next Frame Duration (NFD) contains the duration information of

the DATA frame. Continuing with our example, upon successful reception of the DATA

frame, node 4 uses the contents of the first available DATA frame in its queue to fill

the fields, NA and NFD. If node 4 does not have a DATA frame in its queue, and if the

present frame is to be forwarded on by D, it generates the required info before sending it

to the higher lIwr-is as follows.










Octets: 2 2 6 6 4
FaeDuration RA TA FCS
Control
RTS Frame

Octets: 2 2 6 4

C 1Duration RA FCS

CTS Frame

Octets: 2 2 6 6 6 4 4
FaeDuration RA TA DA PID FCS
Control

PTS Frame

Octets: 2 2 6 6 6 4

C 1Duratio RA TA PA FCS

RTT Frame

Octets: 2 2 6 4

C 1Duration RA FCS

CTT Frame
Octets: 2 2 6 6 6 2 6 0-2312 4

C 1DuatonAddress Addes Address3 Sequec Addres Frame Bod FCS

DATA/ODATA Frame

Octets: 2 2 6 4

C1Durationl RA FCS

ACK Frame

Octets: 2 2 6 6 6 2 4
FaeDurationl RA TA NA NFD FCS
Control

AKM Frame

Figure 7-10. Frame formats of the OCSMA_LA protocol.


When node 4 receives the DATA frame, before forwarding it to the higher 1.,-c cs, the

MAC 1.,-c c uses information contained in the frame to determine the next hop receiver of

this frame. We assume that the MAC 1.,-c c has access to the routing tables. The MAC










address of the receiver is copied into the NA field of the AK(M frame, whose format is

shown in Figure 7-10.

Continuing with the example network of Figure 7-9, once node 4 receives the DATA

frame, and assuming that there is a frame already in the queue for node 5, it appropriately

sets the NA and NFD fields and transmits the AK(M frame. When the AK(M frame is

received by the primary transmitter, node :3, it resets its retry limits, and performs backoff

just like in the case of the reception of an ACK( frame. When the next hop receiver,

node 5 receives the AK(M frame, it waits for a duration equal to the transmission of an

ACK( frame (to allow for node 2's transmission of ACK( to node 1), and transmits a CTS

frame if the niediunt is free. Note that the information necessary for updating the fields

RA and Duration of the CTS frame (refer to Figure 7-10) are available through the TA

and NFD fields of the AK(M frame (refer to Figure 7-10). When node :3 receives the

CTS frame, it ensures that this frame is in response to either an RTS frame or an AK(M

frame. If this is true, it proceeds with the secondary handshaking phase of the OCSMA

protocol (refer to Section 6.2).

Since the next hop receiver (node 5 in the present example) requests for the DATA

frame even before the secondary and primary receivers have a chance to contend for the

channel access, the secondary receiver, node :3 has the suitable frame for an overlapped

transmission when node 4 transmits the DATA frame to node 5. Once an overlapped

transmission occurs in the linear network, with high probability, the capability to perform

overlapped transmission is retained until the DATA/ODATA frames reach the destination.

For instance, in the example network of Figure 7-9, when node 4 transmits a DATA frame

in response to the CTS sent by node 5 (which responds to an AK(M frame sent by node 4),

node :3 has a suitable frame for an overlapped transmission, and in the next transmission

duration when node 5 transmits the DATA frame in response to the CTS sent by node 6,

node 4 would have a suitable frame (the ODATA frame that it received front node :3) for

an overlapped transmission, and so on. The probability of overlapped transmission is high












only when the collisions in the network are low. When the collision rate increases, there

is a high probability that the primary data transmission might not be successful, which

affects the performance gain of the Look Ahead variant.


. 14
O



I
n11
LI.


5 10 15 20 25 30
TCP Congestion Window size (packets)


Figure 7-11. Throughput comparison of OCSMA, OCSMA_LA and IEEE 802.11 in a
ten-node linear network.



7.3.2 Simulation Results

In this subsection, the performance of OCSMA_LA is evaluated using ns2, and

compared to that of OCSMA and IEEE 802.11. The first scenario we consider is the

ten-node linear network of Figure 7-1. The parameters used for the simulation are

tabulated in Table 7-1. We employ the de 1li- Il-ack version of TCP Reno described

in Section 7.2.2. The results in Figure 7-11 compare the end-to-end throughput of the

OCSMA, OCSMA_LA, and IEEE 802.11 protocols as a function of the TCP CW size (also

see Figure 7-2). We note that the throughput of the network under IEEE 802.11 increases

until the CW size equals 5, beyond which it decreases. The throughputs under OCSMA

and OCSMA_LA increase with an increase in CW size, and the throughputs saturate for












CW sizes greater than 14. For CW size greater than 20, we note that OCSMA provides a

throughput gain of ::Il' over IEEE 802.11, while OCSMA_LA provides a throughput gain

of ::' I' over IEEE 802.11.

Table 7-4. MAC-level events in a ten-node linear network under OCSMA_LA.
Frame OCSMA_LA OCSMA_LA OCSMA_LA OCSMA_LA OCSMA_LA
Type (CW=2) (CW=4) (CW=8) (CW=16) (CW=:32)
TPUJT 11.54 1:3.7 15.1 15.7 15.71
RTS 19.0 55.5 10:3.8 118.6 119.6
CTS 71.9 97.6 115.3 115.7 116.2
PTS 58.2 80.0 88.8 74.3 74.6
RTT 57.2 7:3.5 76.4 74.0 74.9
CTT :38.0 :31.8 :30.7 :36; 37.2
NPT 15.7 :31.0 :32.5 2:3.0 20.0
DATA 65.9 91.1 10:3.5 10:3.3 104.2
ODATA :38.0 :34.0 :30.7 :36;.0 :37.2
COLL 0.0 6;.6; 12.4 14.4 15.4


The MAC-level events under OCSMA and OCSMA_LA are tabulated in Table 7-4 for

three different values of CW size. Note that the congestion control algorithm is TCP with

d.1 0-. .1-ack. Note that under OCSMA_LA, the number of CTS frames received can he

greater than the number of RTS frames received. A CTS is transmitted either in response

to an RTS or an AK(M. We note that when CW size is 2, the ratio of CTT/(CTT+NPT)

is 71 and DATA loss due to collisions is zero. As the CW size increases, the end-to-end

throughput under OCSMA_LA increases; however, the number of overlapped transmissions

(ratio of CTT to CTT+NPT) decreases until a CW size of 8, and then increases. This

behavior is in contrast to the behavior of OCSMA. We noted that when the CW size

increases, the increase in the number of packets at the nodes (as evidenced by the increase

in the number of RTS frames) decreases the effectiveness of the Look Ahead capability

of OCSMA_LA, as other transmissions in the network may collide with the primary

transmission initiated by an AK(M frame. However, hevond a certain CW size, the increase














~20

S 18

r16
E at-x--OCSMA LA
ic -4- IEEE 802.11
-0 1 4-


4 12-





10 15 20 25 30 35 40 45 50
Packet arrival rate (packets/s)

Figure 7-12. Throughput comparison of OCSMA_LA and IEEE 802.11 in a ten-node linear
network with CBR trafiic.


in the collision rate in the network causes most of the nodes to be in backoff state, which

ensures that there are more packets available for overlapped transmission.

The OCSMA_LA protocol is designed to address the issue of packet starvation in

TCP flows. However, we expect the Look Ahead feature of OCSMA_LA to benefit UDP

traffic also. We evaluate the performance of OCSMA_LA in a ten-node linear network with

CBR traffic. The results in Figure 7-12 compare the end-to-end throughput of a ten-node

linear network under OCSMA_LA and IEEE 802.11 with CBR traffic as function of packet

arrival rate at the source, node 1 (also see Figure 6-7). The packet size is 1400 bytes, and

the short and long retry limits are 20 and 10, respectively. We note that OCSMA_LA

has a higher throughput than IEEE 802.11, and when the packet arrival rate increases

beyond 22 packets/s, the degradation in the throughput is more gradual compared to

IEEE 802.11. For packet arrival rates greater than 22 packets/s, OCSMA_LA provides at

least I gain over IEEE 802.11 protocol.










7.4 Summary

In this chapter, we investigated the impact of overlapped transmissions on the

throughput of TCP in multihop networks with linear flows. Through network simulations,

we analyzed the interactions between OCSMA and TCP protocols. We identified some

of the key parameters at the MAC and transport 1.>. ris that impact the performance of

the system. By modifying these parameters, we showed that OCSMA can improve the

performance of TCP flows in av .vi'. iv of network scenarios and is more efficient than

IEEE 802.11 in addressing fairness and medium contention issues associated with TCP

flows. Later, we modified the OCSMA protocol to address the issue of packet starvation

in TCP flows. We evaluated the performance of the resultant OCSMA_LA protocol in

linear networks. Through network simulations, we demonstrated that OCSMA_LA can

significantly improve the throughput of both TCP and UDP traffic in wireless ad hoc

networks .










CHAPTER 8
CONCLUSION AND DIRECTIONS FOR FITTIRE WORK(

8.1 Conclusion

In this work, we studied the use of overlapped transmissions to improve the spatial

re-use and throughput in wireless networks. In CDMA-hased cellular networks, the

base station can exploit the spatial diversity along with cooperative broadcasting

techniques to schedule additional transmissions in the system. The results indicate

that such overlapped transmissions can lead to significant gain in user capacity over a

conventional CDMA system. We also evaluated the user capacity of a cellular network

employing DPC as a broadcasting technique when the user population is large, and

compared it to that of a system employing TDMA. The results indicate that under low

spectral-efficiency requirement, the gain in user capacity by employing DPC over TDMA

is very modest, at most 1"' for the system parameters that we considered. This is not

very surprising considering the fact that recent research in this area has shown that in

a single-input single-out (SISO) degraded Gaussian broadcast channel, DPC provides

significant gains over TDM only when there is limited multi-user diversity and the

spectral efficiency requirement of the users is very high [13, 47, 48]. Next, we evaluated

the performance of optimal and sub-optimal forward-link channel-sharing schemes. We

observed that under high spectral-efficieny regime, there is a significant performance gain

in employing cooperative broadcasting over conventional channel-sharing schemes, and

that computationally simpler schemes like two- and three-level broadcasting techniques

provide performance close to the optimal scheme.

In wireless ad hoc networks, overlapped transmissions have the potential to

significantly improve the spatial re-use and the throughput of the network. We have

analyzed some of the limits on performing overlapped transmissions in ad hoc networks.

We developed the OCSMA MAC protocol, that exploits the knowledge of the interfering

signals along with MITD/IC capabilities of the PHY to schedule overlapped transmissions










in the network. Network simulations indicated that systems with linear flows show

a significant throughput intprovenient with OCSMA over conventional IEEE 802.11

protocol. In networks with random topology and mobility, OCSMA still provides

considerable throughput gain over conventional MAC protocols like IEEE 802.11. We also

investigated the interaction between OCSMA and TCP, and through network simulations

we demonstrated the superiority of OCSMA over conventional MAC protocols like IEEE

802.11 in addressing the fairness and niediunt contention issues associated with TCP in

wireless ad hoc networks. We modified the OCSMA protocol to increase the probability of

overlapped transmission under TCP flows. Through network simulations, we demonstrated

that the resultant OCSMA_LA protocol improves the performance of both TCP and ITDP

flows in wireless ad hoc networks.

8.2 Directions for Future Work

The development and performance evaluation of the OCSMA MAC protocol were

carried out assuming that the physical 1 e -< c can perform perfect interference cancellation.

Clearly, this is not the case in reality. The performance of overlapped transmission at

the physical 1 .,-< c can he evaluated by modeling the system of four nodes involved in the

transmission as an interference channel. Since the primary receiver is not effected by the

secondary transmitter, we can further reduce the system to a 'Z'-intererence channel [82].

Since the secondary receiver is aware of the interference (due to primary transmission),

it would be reasonable to assume that the secondary transmitter has partial information

regarding the interference. In such a scenario, it would be interesting to look at strategies

that the secondary transmitter can use to improve the performance of the MITD/IC

schemes at the secondary receiver.

In this work, we evaluated the impact of overlapped transmissions on the performance

of TCP in wireless networks. It would be interesting to investigate the interaction between

OCSMA and routing protocols in wireless ad hoc networks.










APPENDIX A
DERIVATION OF THE JOINT PDF OF X,4D, XCD

Consider the four-node network of Figure 5-:3. In order to evaluate the joint

distribution of X,4D and XCD, we first look at the relative positions of nodes A and D

with respect to node B. Note that A is uniformly distributed in an unit circle with B at

the centre. The density function of X 4s, the distance between A and B is given by


2.r, O < r< 1
fx, (X= 10, otherwise. (l


Similarly, node C is also uniformly distributed within the transmission range of B, and

hence the pdf of XBc is the same as that of XAB. Node D is in the transmission range of

C but not in the transmission range of B. Hence, it is uniformly distributed in the shaded

region of Figure 5-:3. The joint conditional distribution of XCD and XBD given XBc can

he derived in a similar fashion and is given by (refer to Figure A-1)



Fxc'D,XBD (Y, |XIXc = .r) = -Ata.)(A-2)


where Al(1, y, r) is given by (5-4). The conditional joint density function is given by



1 4yz O < r,~7 y < 1


fXDB (,XXB ) 0, otherwise.


(A-3)

Since A is uniformly distributed in a unit circle with B at the center, the conditional

distribution of X,4D, the distance between nodes A and D is given by


-1 Atl (1, 8,), S + 1 > X,
Fx4D (s|XBD = = = (A-4)
0, otherwise.






























Figure A-1. Circle-circle intersection for analysis.


and the pdf is given by

2s COS-1 s2+z'-1 ,,
fXAD (S|XBD = X) x2z (A5
0, otherwise.

Note that XAD is conditionally independent of XCD, XBc given XBD. Hence


fxAD (S|XCD = X, XBc = y, XBD = X) = fXAD (S|XBD = z). (A-6)


The joint distribution of XAD and XCD is giVen by



fxADXCD 8 XD 9 )XDXD(,z)fax)zd. (A-7)










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BIOGRAPHICAL SKETCH

Surendra Boppana received the B.Tech. degree in electronics and communication

engineering in 2003 from the Indian Institute of Technology (IIT), Guwahati, India, and

the M.S. degree in electrical and computer engineering in 2005 from the University of

Florida, Gainesville. He is currently pursuing his PhD degree. Fr-om M e- 2006 until

January 2007 he was with the Communications Circuit Lab, Intel Corporation, Hillsboro,

Oregon. His research interests include wireless communications, information theory, and

cro ;-lbver design.





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OVERLAPPEDTRANSMISSIONINWIRELESSNETWORKS By SURENDRABOPPANA ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2008 1

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c 2008SurendraBoppana 2

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Tomyparents. 3

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ACKNOWLEDGMENTS MystayattheUniversityofFloridahasbeenaveryenrichingexperience.Afew peoplehavemadeatremendousimpactonmylife,personallyandprofessionally.My sincerestthanksgotomyadvisorDr.JohnM.Shea,whoseguidance,expertise,and professionalismwereinstrumentalinmygrowthasaresearcher.Ithoroughlyenjoyed workingwithhim. IthankDr.Wong,Dr.Fang,Dr.McNairandDr.Presnellfortheirguidance, suggestionsandinterestinmywork.IthankmyfriendswhomademystayinGainesville enjoyable.SpecialthankstoSarvaandDebdeepforthelivelydiscussionswehad,andfor makingmylifeatWINGthatmuchmoreinteresting. Lastly,Idedicatethisworktomyparents,UshaandNagabhushanam,whohavebeen aconstantsourceofinspirationinmylife. 4

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TABLEOFCONTENTS page ACKNOWLEDGMENTS.................................4 LISTOFTABLES.....................................8 LISTOFFIGURES....................................9 ABSTRACT........................................12 CHAPTER 1INTRODUCTION..................................14 1.1CellularNetworks................................14 1.2AdHocNetworks................................15 1.3DissertationOutline..............................16 2OVERLAPPEDTRANSMISSIONINCELLULARNETWORKS........18 2.1Introduction...................................18 2.2SystemDescription...............................21 2.3MaximizingtheUserCapacity.........................25 2.4UserCapacityunderAveragePowerConstraint...............27 2.4.1CellularNetworkwithoutBC.....................27 2.4.2CellularNetworkemployingBC....................29 2.4.3CellularNetworkemployingGWBESequences............31 2.5UserCapacityunderTotalPowerConstraint.................32 2.6Summary....................................34 3USERCAPACITYOFDOWNLINKCELLULARNETWORKS........35 3.1Introduction...................................35 3.2SystemDescription...............................36 3.3UserCapacityofTDMASystem........................36 3.3.1SystemDescription...........................36 3.3.2AsymptoticUserCapacityofTDMASystem.............38 3.4UserCapacityofDPCSystem.........................40 3.4.1SystemDescription...........................40 3.4.2AsymptoticUserCapacityofDPCSystem..............42 3.5ResultsandDiscussion.............................43 3.5.1UserCapacityinExponentialPath-LossChannel,noFading....43 3.5.2UserCapacityinExponentialPath-LossChannelwithFading...46 3.6Summary....................................47 5

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4PERFORMANCECOMPARISONOFOPTIMALANDSUBOPTIMALDOWNLINK CHANNEL-SHARINGSCHEMES.........................49 4.1Introduction...................................49 4.2SystemModel..................................50 4.3AsymptoticAnalysisforRequiredMinimumSNRperMS..........52 4.3.1BroadcastingovertheWholeBand..................52 4.3.2FixedFrequencyDivisionMultiplexing................54 4.3.3Two-LevelBroadcasting........................54 4.3.4Three-LevelBroadcasting........................55 4.3.5OptimalFrequencyDivisionMultiplexing...............56 4.4Results......................................57 4.5Summary....................................63 5OVERLAPPEDTRANSMISSIONINWIRELESSADHOCNETWORKS...65 5.1Introduction...................................65 5.2Motivation....................................68 5.3OverlappedTransmissioninWirelessAdHocNetworks...........71 5.3.1SystemModel..............................71 5.3.2InterferenceduetoSecondaryTransmission..............73 5.3.3ProbabilityofSecondaryTransmission................76 5.4Summary....................................80 6THEOVERLAPPEDCARRIERSENSEMULTIPLEACCESSPROTOCOL.82 6.1Introduction...................................82 6.2TheDesignofOCSMAProtocol........................82 6.2.1PrimaryHandshaking..........................82 6.2.2SecondaryHandshaking.........................85 6.2.3PrimaryTransmission..........................88 6.2.4SecondaryTransmission.........................88 6.2.5DataAcknowledgments.........................89 6.3DesignConsiderations.............................90 6.3.1Cross-LayerInteraction.........................90 6.3.2ComplexityoftheProtocol.......................90 6.3.3ReducedOverhead...........................91 6.4SimulationResults...............................91 6.5Summary....................................101 7IMPACTOFOVERLAPPEDTRANSMISSIONONTHEPERFORMANCE OFTCPINADHOCNETWORKS........................102 7.1Introduction...................................102 7.2InteractionbetweenTCPandOCSMA....................103 7.2.1ImpactofTCPCongestionWindowSize...............104 7.2.2ImpactofCollisionsonTCPThroughput...............109 6

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7.2.3FairnessIssuesandMediumContention................111 7.3OCSMAwithLookAheadCapabilityOCSMA LA............116 7.3.1OCSMA LAProtocolDescription...................117 7.3.2SimulationResults...........................120 7.4Summary....................................123 8CONCLUSIONANDDIRECTIONSFORFUTUREWORK...........124 8.1Conclusion....................................124 8.2DirectionsforFutureWork...........................125 APPENDIX ADERIVATIONOFTHEJOINTPDFOF X AD ;X CD ...............126 REFERENCES.......................................128 BIOGRAPHICALSKETCH................................134 7

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LISTOFTABLES Table page 6-1NS2simulationsetup.................................92 6-2ComparisonofeventsattheMAClevelinaten-nodelinearnetworkwithpacket size400B........................................94 6-3ComparisonofeventsattheMAClevelinaten-nodelinearnetworkwithpacket size1800B.......................................95 7-1SimulationsetupforevaluatingtheimpactofOCSMAonTCPperformance...104 7-2EventsattheMAClevelinaten-nodelinearnetworkunderOCSMAprotocol..106 7-3PerformancecomparisonofOCSMAandOCSMA DA...............111 7-4MAC-leveleventsinaten-nodelinearnetworkunderOCSMA LA........121 8

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LISTOFFIGURES Figure page 2-1Powerdisparitiesinacellularnetwork........................22 2-2Pairingstrategiesinasix-nodecellularnetwork...................24 2-3UsercapacityofsystemsemployingBCandGWBEsequencesunderaverage powerconstraintandinniteuserassumption. N =10, =10dB, =0 : 05...32 2-4AverageusercapacityofsystemsemployingBCandGWBEsequenceswithxed userpopulationandtotalpowerconstraint. N =10, 0 =10dB, =4......33 3-1UsercapacitiesofTDMAandDPCinanexponentialpath-losschannel.....44 3-2EciencyofTDMAcomparedtoDPCinanexponentialpath-losschannel....45 3-3UsercapacitiesofTDMAandDPCinanexponentialpath-losschannelwith fading.........................................47 3-4EciencyofTDMAcomparedtoDPCinaexponentialpath-losschannelwith fading..........................................48 4-1Broadcastingoverthewholebandfor =2and D =50forvariousservice factors, ........................................58 4-2Two-levelBCfor =2and D =50forvariousservicefactors, .........58 4-3Three-levelBCfor =2and D =50forvariousservicefactors, ........59 4-4OptimalFDMfor =2and D =50forvariousservicefactors, ........59 4-5FixedFDMfor =2and D =50forvariousservicefactors, ..........60 4-6Comparisonofalltheschemesfor =2, D =50and =0 : 8...........61 4-7Comparisonofalltheschemesfor =4, D =50and =0 : 8...........62 4-8Ratiosof S 1 fortheFDMschemesandthesuboptimalBCschemestothatfor broadcastingoverwholebandfor =2, D =50and =0 : 8............63 5-1Four-nodelinearnetworkwithconventionalscheduling...............68 5-2Four-nodelinearnetworkwithoverlappedtransmissions..............69 5-3Adhocnetworkwithoverlappedtransmission....................72 5-4Distributionofsignal-to-interferenceratio, .....................75 5-5Probabilityofndingasecondarytransmitter....................78 5-6Upperboundonprobabilityofreceptionbynode B ................79 9

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5-7Upperboundontheprobabilityofasuccessfulsecondarytransmission, p S ...80 6-1TypicalframeexchangesinOCSMAprotocol....................83 6-2TimelineoftheOCSMAprotocol...........................84 6-3FrameformatsoftheOCSMAprotocol.......................85 6-4Ten-nodelinearnetwork................................92 6-5Throughputcomparisoninaten-nodelinearnetworkwithTCPtrac......93 6-6Throughputcomparisoninaten-nodelinearnetworkwithCBRtrac......96 6-7ThroughputcomparisoninlinearnetworkwithmultipleCBRows........96 6-8Eectofvaryingthenumberofnodesinalinearnetworkonthethroughput gainofOCSMAandOCSMA RO..........................97 6-9Binary-treenetwork..................................98 6-10ThroughputgainofOCSMAandOCSMA ROinatreenetwork.........99 6-11Throughputgaininarandomnetworkwithmobility................100 7-1Ten-nodelinearnetworkunderOCSMA.......................104 7-2End-to-endthroughputcomparisoninaten-nodelinearnetworkwithTCPtrac.105 7-3MAC-levelperformancecomparisonofOCSMAandIEEE802.11inaten-node linearnetwork.....................................107 7-4Transmittercongestionwindowevolutioninaten-nodelinearnetwork......108 7-5EectofshortandlongretrycountsonthroughputgainsofOCSMAandOCSMA RO inaten-nodelinearnetwork..............................110 7-6Networkswithmultipleows.............................112 7-7Throughputcomparisoninanetworkwithmultipleparallelows.........113 7-8Throughputcomparisoninanetworkwithmultiplelinearows..........115 7-9Ten-nodelinearnetworkunderOCSMA LA.....................117 7-10FrameformatsoftheOCSMA LAprotocol.....................118 7-11ThroughputcomparisonofOCSMA,OCSMA LAandIEEE802.11inaten-node linearnetwork.....................................120 7-12ThroughputcomparisonofOCSMA LAandIEEE802.11inaten-nodelinear networkwithCBRtraic...............................122 10

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A-1Circle-circleintersectionforanalysis.........................127 11

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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy OVERLAPPEDTRANSMISSIONINWIRELESSNETWORKS By SurendraBoppana August2008 Chair:JohnM.Shea Major:ElectricalandComputerEngineering Inwirelessnetworks,interferenceisoneofthemajorimpairmentsthatdeteriorates theperformanceofasystem.Conventionalchannel-sharingschemessuchasTDMA, FDMA,CDMA,etc,orthogonalizethechannelresourcesamonguserstominimize interference.However,information-theoreticresultsindicatethatorthogonalizationof thechannelresourcesisnotthemostecientwaytotransmittomultipleusers.We usetheterm overlappedtransmission todescribenon-orthogonaltransmissionschemes becausetheseschemesallocatethesamechannelresourcestomorethanoneuser,thus overlappingtheirtransmissions.Weconductedaninvestigationintothepotentialbenets ofoverlappedtransmissionsaswellaspracticalapproachestooverlappedtransmissionin bothcellularandadhocwirelessnetworks. Werstanalyzedthepotentialofoverlappedtransmissionstoimprovetheperformance ofwirelesscellularnetworks.Weconsideredtheuseofcooperativebroadcastingtechniques inthedownlinkofacellularnetworktosupportadditionaluserscomparedtoasystem thatorthogonalizesthechannelresourcesamongtheusers,suchasTDMA,FDMA, CDMA,etc.Weevaluatedtheperformancegainsofcooperativebroadcastingtechniques intermsofnumberofusersthatcanbesupportedbythebasestationinacellular networkwhenthenumberofusersinthesystemisnite.Wealsoevaluatedtheuser capacityofacooperativebroadcastingsystem,whenthenumberofusersinthesystemis 12

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large.Wecomparedtheperformanceoftheoptimalbroadcastingtoseveraloptimaland suboptimalforward-linkchannel-sharingschemes. Next,westudiedtheuseofoverlappedtransmissioninadhocnetworkstoimprove thespatialre-useandthroughputofthenetwork.Weshowedhowmultihoproutingcan resultinmobileradioshavingknowledgeofinterferingsignalsduringthereceptionofa transmission.Wethendemonstratedhowthisknowledgecanbeexploitedtoschedule additionaltransmissionsbyperforminginterferencecancellationatthephysicallayer.We evaluatedtheperformancelimitsofemployingoverlappedtransmissionsinwirelessad hocnetworkswithrandomlydistributednodes.WedevelopedaMACprotocolthattakes advantageoftheknowledgeoftheinterferingsignalstoscheduleadditionaltransmissions, therebyincreasingthespatialre-useandthroughputofthenetwork.Weevaluatedthe performanceofthisMACprotocolinavarietyofnetworkscenariosandcomparedtothat ofIEEE802.11MACprotocol.Wealsoanalyzedtheimpactofoverlappedtransmissions ontheperformanceofTransmissionControlProtocolTCPinwirelessadhocnetworks. 13

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CHAPTER1 INTRODUCTION Withrecentadvancementsinwirelesstechnologies,wirelessnetworkshaveemergedto playanimportantroleinourday-to-daycommunications.Theyprovidegreaterexibility, mobility,and,whenusedinadhocconguration,doawaywiththenecessityofany infrastructurefortheirdeployment.Theyarebeingincreasinglyusedinapplications suchastacticalcommunications,environmentalmonitoring,andcommercialdata communications.Unlikewirelinecommunications,allthenodesinawirelessnetwork sharethesamephysicalmedium,whichresultsinchallengesspecictowirelessnetworks. Interferenceisoneofthemostchallengingimpairmentsthatexistinawirelessenvironment. Duetothebroadcastnatureofthewirelesschannel,simultaneoustransmissionsbyradios mayresultininterferenceatthereceivingradios.Severalchannel-sharingschemes havebeendevelopedanddeployedbasedonthecongurationofthewirelessnetwork infrastructureoradhoc. 1.1CellularNetworks Inacellularnetwork,thetransmissionsarecoordinatedbythebasestationBS. ThechannelresourcesareallocatedbytheBStothosemobileusersthateithertransmit datatotheBSorreceivedatafromtheBS.Channel-sharingschemessuchastime-division multipleaccessTDMA,frequency-divisionmultipleaccessFDMA,code-division multipleaccessCDMA,etc.,areemployedtoaccomplishtheallocationofchannel resources.Theseschemesorthogonalizethechannelresourcessuchthatthereisminimal interferenceamongthetransmissions.However,itiswellknownthatorthogonalizingthe systemresources[1]isnottheoptimalapproachforsimultaneoustransmissiontomultiple users. Thefocusof[1]isatypicalbroadcastchannel,suchasthedownlinkofacellular network,withtheBSandeachofthemobilestationsMSsequippedwithsingle antennas.Whenthesignalateachreceiveriscorruptedonlybythermalnoiseinthe 14

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receiverfront-end,thisistheclassicalsingle-inputsingle-outputSISOGaussian broadcastchannelGBC,whichhasbeenextensivelystudiedintheliterature.The SISOGBCbelongstotheclassofdegradedbroadcastchannels,anditscapacityregion iswellknown.ThecapacityoftheGBCcanbeachievedbyeithersuperpositioncoding SPC[1,2]ordirtypapercodingDPC[3{6].Severalpracticalschemeshavebeen proposedbasedonSPC[7,8]andDPC[9,10]thatexploitthespatialdiversityincellular networksthatachieveimprovedperformance. Intherstpartofthisdissertation,weanalyzedtheperformanceofoverlapped transmissionincellularnetworks.Wedeneoverlappedtransmissionsasthoseadditional transmissionswhicharearesultofBSemployingcooperativebroadcastingtechniques comparedtoacellularnetworkemployingconventionalchannel-sharingschemessuch asTDMA,FDMA,CDMA,etc.Weevaluatedtheperformancegainofcooperative broadcastingintermsofthenumberofusersthatcanbesupportedbyaBSalsosee[11, 12],andcomparedtheperformanceofbroadcastingtoseveraloptimalandsub-optimal channel-sharingschemesalsosee[13]. 1.2AdHocNetworks Inwirelessadhocnetworks,MediumAccessControlMACprotocolssuchasthe IEEE802.11MACprotocol[14]aredesignedtocoordinatetransmissionsamongnodes suchthatthereisminimuminterferenceatthereceivingnodes.However,thestrategies employedbytheseMACprotocols,suchasthepopularRTS/CTSstrategyusedinthe distributedcoordinationfunctionDCFoftheIEEE802.11MACprotocol,resultin inecientutilizationofthechannelresources.Forasurveyonthecurrentresearchonthe designofMACprotocols,pleasereferto[15]andreferencestherein. MultiuserdetectionMUDinwirelessnetworkshasbeenproposedbyseveral authors[16{21]asameanstoincreasethespatialre-useinwirelessnetworksbyincreasing thenumberofsimultaneoustransmissionsinthenetwork.However,inmostcases,the nodesmightnothavesucientprocessingpowertoperformcomplexMUDschemes.The 15

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complexityoftheMUDschemescouldbesignicantlysimpliedandtheperformance enhancediftheinterferingsignalwerecompletelyknownatthereceiver.Inwireless adhocnetworks,theinterferingsignalmaybeknownatthereceiverduetomultihop routing.WeintroducedtheideaofemployingMUDschemeswithknown-interference cancellationinmultihopnetworkstoincreasethenumberofsimultaneoustransmissions in[22].Asimilarideathatemploysnetworkcodingatthephysicallayertoincrease simultaneoustransmissionsinwirelessadhocnetworkswasrecentlyproposedin[23, 24];thesenetworkcodingpapersconsiderthephysical-layeraspectsofemployingsuch overlappedtransmissionschemes,butdonotaddresstheMAClevelimplications.In thesecondpartofthisdissertation,weintroducedoverlappedtransmissionschemes foradhocnetworksbasedoncancellationofknowninterference.Weanalyzedsomeof thefundamentallimitsonemployingoverlappedtransmissioninadhocnetworksalso see[22,25].WedesignedaMACprotocolwhichexploitsthisfeaturetoimprovethe throughputandspatialre-useinwirelessnetworksalsosee[26].Theperformanceofthe resultantOCSMAprotocolisevaluatedinavarietyofnetworkscenariosanditsimpacton theperformanceofTCPowsisinvestigatedalsosee[27]. 1.3DissertationOutline Therestofthedissertationisorganizedasfollows.InChapter2,weintroducedthe notionofoverlappedtransmissionincellularnetworks.Weinvestigatedtheperformance ofacellularnetworkemployingcooperativebroadcastingandcomparedittothatofa systememployingGeneralizedWelchBoundEqualityGWBEsequences.InChapter3, wedenedtheusercapacityofacellularnetwork.Weevaluatedtheusercapacityof systemsemployingdirtypapercodingDPCandTDMA,andcomparedtheperformance ofasystememployingDPCtothatofasystememployingTDMA.Theperformance ofoptimalandsuboptimalforward-linkchannel-sharingschemesincellularnetworks arecomparedinChapter4.InChapter5,weintroducedthenotionofoverlapped transmissioninwirelessadhocnetworks.Weinvestigatedsomelimitsonemploying 16

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overlappedtransmissioninanadhocnetwork.InChapter6,wedevelopedtheOverlapped CarrierSenseMultipleAccessOCSMAprotocoltocoordinatetransmissionssothat knowledgeoftheinterferingsignalsinthenetworkcanbeexploitedtoscheduleoverlapped transmissionsinthenetwork.TheperformanceoftheOCSMAprotocolundervarious networktopologiesisevaluatedusingNetworkSimulatorns2,andiscomparedtothat ofasystememployingtheIEEE802.11MACprotocol.TheinteractionbetweenOCSMA andTCPisinvestigatedinChapter7,whereweevaluatedtheimpactofoverlapped transmissionsontheperformanceonTCPowsinavarietyofnetworkscenarios.The dissertationisconcludedandfutureresearchdirectionsarediscussedinChapter8. 17

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CHAPTER2 OVERLAPPEDTRANSMISSIONINCELLULARNETWORKS 2.1Introduction In[1],Coverintroducedthebroadcastchannelseealso[28,29]anddemonstrated thatitismoreecienttosimultaneouslytransmittomultipleusersthantotime-share orotherwiseuseorthogonaldivisionofthechannelresourcesamongusers.Considera standardtwo-userdegradedGaussianbroadcastchanneldenedby y 1 = h 1 x + n 1 y 2 = h 2 x + n 2 {1 where x isthesignaltransmittedbythesender, y 1 and y 2 arethesignalsreceivedby user1anduser2,respectively, n 1 and n 2 arei.i.d. N ; 1, h 1 and h 2 arethechannel gainsofusers1and2,respectivelywith j h 1 j 2 j h 2 j 2 .Thesenderhasatotalpower constraintof P .Thecapacityregionofthischannelcanbeobtainedbytwodierent codingtechniques.In[1],CoverproposedtheuseofsuperpositioncodingSPCand successivedecodingtoachievebetterperformancethanorthogonaldivisionofthechannel andfoundtheachievablerateregion.Thetransmittergeneratestwocodebooks,onewith power aP atrate R 1 ,andanothercodebookwithpower )]TJ/F50 11.9552 Tf 12.337 0 Td [(a P atrate R 2 ,where P is thetotalpoweravailableatthetransmitter,and a 2 [0 ; 1].User1,whichhasthebetter channel,decodesuser2'scodewordrst,subtractsthisfromthereceivedsignal,andthen decodesitscodeword.Therateregionisgivenby [ a 2 [0 ; 1] 8 > < > : 0 R 1 log+ a j h 1 j 2 P 0 R 2 log 1+ )]TJ/F25 7.9701 Tf 6.587 0 Td [(a j h 2 j 2 P 1+ a j h 2 j 2 P : {2 Bergmans[2]showedthatthisrateregionisthecapacityregionforGaussianbroadcast channels.Thesecondtechniqueisbasedonthecodingforchannelswithknown interference[3{6].Thetransmitterrstgeneratesthecodewordforuser2withpower 18

PAGE 19

aP .Oncethecodewordisgenerated,thetransmitterhasnon-causalinformationabout theinterferencethatthiscodecausesatuser1.Hencetherate[3,4] R 1 =max p u;x j s f I U ; Y )]TJ/F50 11.9552 Tf 11.955 0 Td [(I U ; S g {3 isachievableforuser1,where S N ; )]TJ/F50 11.9552 Tf 13.178 0 Td [(a j h 1 j 2 P .FromCosta[5],weknow thatbyletting U = X 1 + S ,andappropriatelychoosing R 1 in2{3becomes log+ a j h 1 j 2 P ,whichisthebestpossiblerateforuser1.However,thecodewordsof user1causeinterferenceatuser2.Hence,theachievableratesatuser2aregivenby R 2 log 1+ )]TJ/F50 11.9552 Tf 11.955 0 Td [(a j h 2 j 2 P 1+ a j h 2 j 2 P : {4 BroadcaststrategiesfortemporalfadingchannelswereintroducedbyShamaiin[30], andextendedtomultiple-userandmultiple-inputmultiple-outputMIMOchannels in[31{33].Asummaryofinformation-theoreticworkfocusedoncellularcommunications isgivenin[34].PracticalschemesbasedonSPCwereproposedbyPursleyandShea[7,8], whichexploitspatialdierencesamongreceiversandimprovethethroughputinwireless networks. Inthischapter,weevaluatedtheuseofinformation-theoreticbroadcastingBC techniquessuchasSPCandDPCinacellularCDMAcommunicationsystemthat employsorthogonalspreadingsequencesandpowercontrol.Insuchsystems,orthogonal spreadingcodesareusedfordierentusers'signals.Powercontrolisappliedtominimize multipathinterferencetousersinthatcellandtominimizeinterferencetousersin adjacentcells.Ideally,eachuserseesthesamesignal-to-noiseratioSNRforthesignalon theirdesignatedspreadingcode.However,ifauserdespreadsanotheruser'ssignal,power controlmayresultinvastlydierentSNRs.BCmayoersomesignicantadvantages insuchscenariosbysimultaneouslytransmittingmessagestomultipleusersonasingle spreadingcode.AlthoughthefocusofthischapterisonacellularCDMAnetwork,the 19

PAGE 20

ideaspresentedherecanbeappliedtootherchannel-sharingschemessuchasFMDA, TDMA,etc. Inthiswork,weuseanabstractmodelofaCDMAsysteminwhichtherequired transmitpowersaredeterminedaccordingtoShannoncapacityorthecapacityregion oftheadditivewhiteGaussiannoiseAWGNbroadcastchannel.Asin[35],ourgoalis toassessthenumberofusersthatcanbesupportedatsometargetrateunderapower constraint. WecomparetheusercapacityofasystememployingBCtothatofasystem employingGWBEsequenceswiththesamepowerconstraint.Theuseofgeneralized WelchboundequalityGWBEsequencestoaccommodatemoreusersthantheprocessing gainofacellularsystemwasconsideredin[36]seealso[37]forasynchronousAWGN channelwithlinearMMSEreceivers.Thedesignofspreadingsequencestomaximize usercapacityforaCDMAforwardlinkinafadingchannelwasconsideredin[38].The asynchronousCDMAsystemwasaddressedin[39].Iterativeconstructionoftheoptimum sequencesthatmaximizetheusercapacitywithminimumtotaltransmittedpowerwas suggestedin[40].In[36],itisshownthatforaCDMAcellularsysteminwhicheachuser isassignedauniquespreadingcodeandanMMSEreceiverisemployed,theusercapacity K foracommontargetSNRof ,islimitedby K
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2.2SystemDescription Weconsideracellularsystemthatusesorthogonalspreadingandpowercontrolon theforwardlink,whichistypicallyseenincommercialsystems,suchasIS-95,WCDMA andCDMA2000[41].ConsidertheBSatthecenterofacircularareaofcoverage. Withoutlossofgenerality,weassumethatthecircularregionhasunitradiusandthe BSisatposition ; 0.Theusersareuniformlydistributedintheareaofcoverage.Let D i denotethedistancefromtheBStomobileuser M i .Theprobabilitydensityfunction pdfof D i isgivenby f D i d = 8 > < > : 2 d; 0 d 1 0 ; otherwise : {5 Anotherquantityweshallbereferringtolateris U i ,thesquareofthedistancefromthe BStothemobileuser M i .Itiseasytoseethat U i isuniformlydistributedin[0,1].We assumethatthethermalnoise,multiple-accessinterferenceandadjacent-cellinterference canbemodeledasasingleadditivewhiteGaussiannoiseAWGNsourcewithtwosided powerspectraldensity N 0 2 [42].Theassumptionisreasonablesincetheadjacent-cell interferenceishighestatthecellboundariesandmultiple-accessinterferenceishighest intheinteriorofthecell.Let W bethebandwidtheachuserseesafterdespreadingthe receivedsignaland N denotethenumberoforthogonalchannelsinthesystem. Powercontrolisusedtoensurethateachmobileuserreceivessucientpowerto achievethedesiredqualityofservicewhileminimizingtheinterferencetoothermobiles. Weconsiderthecaseinwhich perfect powercontrolisusedtomaintainaconstant signal-to-noiseratioSNRateachmobileuserreceivinginformationfromtheBS.In suchascenario,itisoftenpossibletoidentify pairs ofuserssuchthatoneoftheusers receivesamuchhigherpowerthanthetargetpowerlevelwhenthatuserdemodulates theotheruser'ssignal.Figure2-1depictssuchascenario,inwhichpowercontrolis usedtoachievethesamereceivedpowerateachofthemobileusers M 1 ;M 2 and M 3 Anexponentialpathlossmodelwithouttheeectsoffadingandshadowingisassumed 21

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Figure2-1.Powerdisparitiesinacellularnetwork. forthesakeofexposition.Inthegure,theabscissadenotesthedistanceofthemobile usersfromtheBS,andtheordinatedenotesthepowerofthesignalsintendedforeach user.TheusersareindexedinincreasingorderoftheirdistancefromtheBS.Itcanbe seenfromthegurethatwhentheBStransmitsinformationto M 3 ,maintainingthe targetSNRlevel,theSNRseenbyboth M 1 and M 2 ismuchgreaterthantheirtarget SNRlevelsbyamounts A + B and C respectively.Similarly,whentheBStransmits informationto M 2 M 1 receivesanadditional A dBofpoweraboveitstargetSNRlevel. Thisimpliesthat M 1 hassucientSNRtodecodemessagesintendedforboth M 2 and M 3 and M 2 hassucientSNRtodecodethemessagesintendedfor M 3 .Thepowerdisparities atusers M 1 M 2 and M 3 suggestthatinformationfor M 2 and M 1 canbeincludedin thetransmissionto M 3 throughtheuseofBC.Similarly,wecanincludeinformation for M 1 whiletransmittinginformationto M 2 .ThedottedlineinFigure2-1indicates BStransmittinginformationto M 2 whiletransmittingto M 3 atthetargetSNRlevel byemployingBC.SuchadditionaltransmissionsthatoccurduetotheBSemploying cooperativebroadcastingstrategiesaretermedas overlappedtransmissions Wecanexploitsuchdisparitiestoincreasetheusercapacityofthesystemby employingBC[1,3{6,28,29].Moreover,weshowthatthisadditionalsystemcapacity 22

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comesatverylittleexpensetotheperformanceofthenetwork.Inourbroadcasting strategy,theBSusestwo-levelsuperimposedcodestotransmitto pairs ofuserswhichare allocatedthesamespreadingsequence.Thebroadcastcodesarecomposedofinformation attwodierentratesdesignedfortwodierentSNRrequirementsfortheiraccurate reception.ThemessagewiththelowerSNRrequirementforitsaccuratereception isknownasthe basicmessage ,andthemessagewithhigherSNRrequirementforits accuratereceptionisknownasthe additionalmessage .Theusercapacityofsuchasystem isdependentonthenumberofsuitablepairsthatexistandalsoonwhichuserspair. Toanalyzetheperformanceofsuchasystem,weindexthemobileusersindecreasing orderoftheirchannelgains.Wedenea pairingstrategy f i asaone-to-onefunction whichassociates/pairsuser M i withtheuser M f i ;f i >i for1 i N .Thismeans thatusers M i and M f i sharethesamespreadingcode,and M i pairs with M f i torecover anadditionalstreamofinformationthatissuperimposedonthemessagefor M f i Note that M i hasabetterchannelthan M f i .Theconstraintonthedomainof i indicatesthat themaximumnumberofpairsusingourtwo-levelBCisequaltothenumberoforthogonal channelsavailable.Heretheone-to-oneconditionimpliesthatnotwouserspairwiththe sameuser.Thisrestrictionisrequiredbyouruseoftwo-levelBC.Thefactthat f i isa functionrestrictseachusertopairwithatmostoneuser.Althoughtheserequirements arenotnecessaryfromatheoreticalstandpoint,theyrepresentascenariothatisofmore practicalinterest.TwosuchexamplesofpairingstrategiesaredepictedinFigure2-2for asix-nodecellularnetwork.Assumethattheusersareindexedinthedecreasingorderof theirchannelgains.Forexample,user M 1 hasabetterchannelthan M 2 M 2 hasabetter channelthan M 3 ,andsoon.Thepairingstrategy f i = i +3,indicatesthatuser M i and user M i +3 sharethesamespreadingsequence,anduser M i recoversanadditionalmessage ontopofthetransmissionforuser M i +3 Notethatuser M i hasabetterchannelthan user M i +3 .Underthepairingstrategy f i =7 )]TJ/F50 11.9552 Tf 12.434 0 Td [(i ,users M i and M 7 )]TJ/F25 7.9701 Tf 6.586 0 Td [(i sharethesame 23

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Figure2-2.Pairingstrategiesinasix-nodecellularnetwork. spreadingsequence,anduser M i recoversanadditionalmessagefromthetransmissionfor user M 7 )]TJ/F25 7.9701 Tf 6.586 0 Td [(i AnexponentialpathlossmodelwithRayleighatfadingisassumed,wherethepower P r ,receivedbyuser M r ,isrelatedtothetransmittedpower P t by P r = K p d )]TJ/F25 7.9701 Tf 6.587 0 Td [( r j h r j 2 | {z } z r P t ; {6 where K p isaconstant, d r isthedistanceofthemobileuserfromtheBS, isthepath lossexponent,and j h r j isthemagnitudeofthefadingattheuser M r ,whichisassumedto beconstantovermanysymbols.Theinformationrates R bm and R am ofthebasicandthe additionalmessagesundertwo-levelBCaregivenby[29] R bm = W log 2 1+ )]TJ/F50 11.9552 Tf 11.955 0 Td [(a K p z b P t aK p z b P t + N 0 W ; {7 R am = W log 2 1+ aK p z a P t N 0 W ; {8 24

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where P t isthepowertransmittedbytheBS, z a and z b arethechannelgainsofusers receivingthebasicandadditionalmessages,respectively,and0 a 1isfractionofthe powerallocatedforthetransmissionoftheadditionalmessage.Underanaveragepower constraint,thetransmissionofanadditionalmessagewhilemaintainingthesametarget SNRattheuserreceivingthebasicmessageresultsinanincreaseofthetotaltransmit powerbytheBS.Inthecontextofacellularnetwork,thisadditionaltransmitpower willresultinincreasedinterferencetousersinadjacentcellsandtousersinthecurrent cellfrommulti-path.Henceourfocusisonincreasingthecapacityofthesystemwhile maintainingthesameaveragetransmitpowerattheBS.Suchathroughputgaincanbe achievedbydecreasingtheinformationrateorthetargetSNRoftheusers.Forthesake ofsimplicity,henceforthweassumethatthetargetSNRsofboththeadditionalandthe basicmessagesaresame. 2.3MaximizingtheUserCapacity Inthissection,wederivedanoptimumpairingstrategyforBCthatminimizesthe totalpowertransmittedbytheBSforagivenusercapacityweareinterestedinthecase wheretheusercapacityisgreaterthanthenumberoforthogonalchannels.Firstweneed thefollowingresulttoconstructapairingstrategythatmaximizestheusercapacity. Theorem2.1. Consideracellularnetworkwith K usersand N orthogonalchannelssuch that Nz 2 Let P 1 and P 2 bethepowerstransmittedbythebasestationtotheusers M 1 and M 2 25

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respectively,throughtwoorthogonalchannels,suchthatatargetSNRof ismaintained attheusers.Hencewehave = K p z 1 P 1 N 0 W = K p z 2 P 2 N 0 W .Notethat P 2 >P 1 .Inorderforthese userstopairusingatwo-levelbroadcastcodewithonechannelsuchthatboth M 1 and M 2 haveatargetSNRof ,thereshouldexistapairof a;P satisfyingthefollowing constraints. aZ 1 P N 0 W = ; {9 )]TJ/F50 11.9552 Tf 11.955 0 Td [(a Z 2 P aZ 2 P + N 0 W = ; {10 0 a 1 ; {11 0 P P 1 + P 2 ; {12 where Z i = K p z i ;i =1 ; 2, N 0 = 2isthetwosidednoisepowerspectraldensityofthe AWGNchannel,and W istheeectivebandwidthseenbyeachuserafterdespreadingthe orthogonalcode.Constraints2{9and2{10statethattheSNRsofbasicandadditional messagesshouldsatisfythetargetSNRrequirement.Weshowthatnosuchpair a;P existsthatsatisfytheaboveconstraints.From2{9wehave a = N 0 W Z 1 P a = P 1 P = Z 1 P 1 N 0 W {13 Substituting2{13in2{10, Z 2 P )]TJ/F50 11.9552 Tf 11.955 0 Td [(P 1 P 1 Z 2 + N 0 W = Z 2 P )]TJ/F50 11.9552 Tf 11.955 0 Td [(P 1 = P 1 Z 2 + N 0 W Z 2 P )]TJ/F50 11.9552 Tf 11.955 0 Td [(P 1 = Z 2 P 1 + P 2 = Z 2 P 2 N 0 W P )]TJ/F50 11.9552 Tf 11.955 0 Td [(P 1 = P 1 + P 2 P = P 1 + + P 2 >P 1 + P 2 26

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whichviolatesconstraint2{12. Corollary2.1.1. TheminimumadditionalpowerrequiredforBCtoapairofusers havingthesamespreadingsequenceis P i ,where isthetargetSNRand P i isthepower requiredbytheBStomaintainaconstantSNRof attheuser M i withbetterchannel gainandwithoutemployingBC. Apairingstrategythatminimizesthetotalpowertransmittedforagivennumberofpairs k N is f i = i + N; 1 i k: {14 Notethat,eventhoughthechoiceoftheoptimumpairingstrategyisnotunique,the minimumtotaltransmittedpowerisunique. 2.4UserCapacityunderAveragePowerConstraint Inthissection,wecomparedtheusercapacityofasystememployingBCtothatof asystememployingGWBEsequencesunderthesameaveragetotalpowerconstraint. Sinceourfocusisonincreasingthecapacityofacellularnetworkwithoutincreasingthe totaltransmitpower,wederivetheaveragepowerconstraintfromacellularsystemthat supports N usersthrough N orthogonalchannels. 2.4.1CellularNetworkwithoutBC Consideracellularsystemwithinniteuserpopulationand N orthogonalchannels supporting N users 1 .Weassumethatalltheusersareuniformlydistributedinthe circularareaofcoverageandhaveatargetSNRrequirementof andamaximumoutage probabilityof .Let z denotetheinstantaneouschannelgainbetweentheBSandtheuser 1 Bypopulationwemeanthenumberofmobileradiosrequestingserviceandbyusers wemeantheactualnumberofmobileradioswhicharesupportedbytheBS. 27

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M .Thedistributionofthechannelgain z cf.2{6isgivenby F Z z = F Z z = d )]TJ/F24 7.9701 Tf 6.586 0 Td [(2 j h j 2 =1+ e )]TJ/F25 7.9701 Tf 6.587 0 Td [(z )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 z ;z 0 : {15 AnoutageeventoccursiftheinstantaneousSNRattheuserfallsbelow .Theprobability ofoutageisgivenby Pr K p zP t N 0 W Pr z N 0 W K p P t 1+ e )]TJ/F25 7.9701 Tf 6.587 0 Td [(Z 0 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 Z 0 ;Z 0 = N 0 W K p P t : {16 Let Z denotethemaximumvalueofthechannelgainwhichresultsinanoutageevent. Whenanoutageoccurs,theBSdoesn'ttransmittothatparticularusersinceperfect powercontrolisassumed,theBShasinformationaboutthechannelgainsofalltheusers. Sinceweareassuminganinniteuserpopulation,itisalwayspossibletond N users withchannelgains z Z ,suchthattheyaresupportedbytheBS.Underthisconditional distributionofthechannelgainsi.e. F z z j z Z ,theaveragepowertransmittedbythe BS,suchthatatargetSNRof ismaintainedatauserisgivenby E f P T Z g = E N 0 W K p z j z Z {17 = C 1+ Z 2 \0500 ;Z )]TJ/F50 11.9552 Tf 11.955 0 Td [(e )]TJ/F25 7.9701 Tf 6.586 0 Td [(Z + Z 2 Z )]TJ/F50 11.9552 Tf 11.956 0 Td [(e )]TJ/F25 7.9701 Tf 6.586 0 Td [(Z # ; where C = N 0 W K p )]TJ/F24 7.9701 Tf 6.586 0 Td [(1 and\050 : istheincompletegammafunctiongivenby \050 a;z = Z 1 z t a )]TJ/F24 7.9701 Tf 6.586 0 Td [(1 e )]TJ/F25 7.9701 Tf 6.587 0 Td [(t dt: {18 SincetheBStransmitsto N users,theaveragetotaltransmittedpowerisgivenby N E f P T Z g 28

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2.4.2CellularNetworkemployingBC ConsiderthecellularnetworkemployingBCofSection2.2.Weassumethatthereis aninniteuserpopulation,andlet K;N K 2 N denotethenumberofusersservedin atransmissiondurationweagainassumethatitisalwayspossibletond K userswith channelsgainsgreaterthan Z ,suchthattheyareservedbythebasestation.Inthis section,weassumethatthenumberofusersservedbytheBSisconstantacrossallthe symboldurations.Hence,inanetworkwith K usersuserssupportedbytheBSand N orthogonalchannels,thetotalpower P bc T transmittedbytheBSunderthepairingstrategy of2{14isgivenby P bc T = 0 N 0 W K p K X k =1 1 z k + 0 K )]TJ/F25 7.9701 Tf 6.587 0 Td [(N X k =1 1 z k ;z 1 > >z K = P nbc T + P bc T ; {19 where P nbc T = 0 N 0 W K p K X k =1 1 z k ; P bc T = 0 2 N 0 W K p K )]TJ/F25 7.9701 Tf 6.586 0 Td [(N X k =1 1 z k ; and 0 isthecommontargetSNRofalltheusers,notnecessarilyequalto .Weare awareofthefactthatanincreaseintheusercapacityunderthesameaveragepower constraintwouldresultinthedecreaseofthetargetSNR.Theterm P nbc T canbe interpretedasthetotalpowerrequiredtotransmitto K usersusing K orthogonal channelsand P bc T canbeinterpretedastheincreaseinthetransmittedpowerdue toemployingBCtosupportthese K usersover N orthogonalchannelsreferto Corollary2.1.1.Theexpectedvalueof P nbc T isgivenby 29

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E f P nbc T 0 g = 0 N 0 W K p K X k =1 E 1 z k j z k Z = K 0 N 0 W K p E 1 z j z Z = K 0 N 0 W K p K p N 0 W E f P T Z g = K 0 E f P T Z g {20 where E f P T Z g isgivenby2{17.Similarly,theexpectedvalueof P bc T isgivenby E f P bc T 0 g = 0 2 N 0 W K p K )]TJ/F25 7.9701 Tf 6.586 0 Td [(N X k =1 E 1 z k ;z 1 >z 2 > >z K : {21 Thedistributionof p k = z k )]TJ/F24 7.9701 Tf 6.587 0 Td [(1 canbeevaluatedfromtheprinciplesoforderstatistics.Let P = Z )]TJ/F24 7.9701 Tf 6.587 0 Td [(1 .Theconditionaldensityof p i ; 1 i K isgivenby[43,44] f p i p j p P = K i )]TJ/F15 11.9552 Tf 11.955 0 Td [(1! K )]TJ/F50 11.9552 Tf 11.955 0 Td [(i h p 1 )]TJ/F50 11.9552 Tf 11.955 0 Td [(e )]TJ/F18 5.9776 Tf 7.875 3.259 Td [(1 p i i )]TJ/F24 7.9701 Tf 6.587 0 Td [(1 F p P K h F p P )]TJ/F73 11.9552 Tf 11.955 13.27 Td [( p 1 )]TJ/F50 11.9552 Tf 11.955 0 Td [(e )]TJ/F18 5.9776 Tf 7.876 3.258 Td [(1 p i K )]TJ/F25 7.9701 Tf 6.586 0 Td [(i 1 )]TJ/F50 11.9552 Tf 11.955 0 Td [(e )]TJ/F18 5.9776 Tf 7.876 3.258 Td [(1 p 1+ 1 p ; {22 where F p P isgivenby F p P = P )]TJ/F50 11.9552 Tf 11.955 0 Td [(e )]TJ/F18 5.9776 Tf 10.446 3.258 Td [(1 P : {23 Hencetheexpectedvalueof P bc T is E P bc T 0 = 0 2 N 0 W K p K )]TJ/F25 7.9701 Tf 6.586 0 Td [(N X k =1 Z P 0 p k f p k P dp k ; {24 where f p k p j p P ; 1 k K isgivenby2{22.Theexpectedvalueof P bc T isthesum oftheexpectedvaluesof P nbc T and P bc T E P bc T 0 = E P T nbc 0 + E P bc T 0 : {25 30

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2.4.3CellularNetworkemployingGWBESequences Consideracellularsystemwithinniteuserpopulationand K g >N supportedusers suchthateachuserisassociatedwithauniqueGWBEsignaturesequence[45]weassume thatitisalwayspossibletond K g userswithchannelsgainsgreaterthan Z ,suchthat theyareservedbytheBS.LetthetargetSNRofalltheusersbe 0 .Assumingthatall theorthogonalchannelsareequallyoccupiedbytheusers,thetotaltransmittedpowerby theBSinasymboldurationisgivenby[38] P g T = Ng 0 N 0 W=K p N )]TJ/F50 11.9552 Tf 11.955 0 Td [(Kg 0 K g X k =1 1 z k ; {26 where g 0 = 0 1+ 0 istheeectivebandwidthofeachuserand K g
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GWBEsequencesremainsconstantat10fortargetSNRsrangingfrom10dBto7dB. ThemaximumnumberofusersthatcanbesupportedusingGWBEsequencesisgiven by K g
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Figure2-4.AverageusercapacityofsystemsemployingBCandGWBEsequenceswith xeduserpopulationandtotalpowerconstraint. N =10, 0 =10dB, =4. averagedoveralltransmissiondurationsofboththesystemsunderthesametotalpower constraint.Wearbitrarilychoosethetotalpowerconstraintpersymboldurationequalto theaveragepowerconstraintconsideredpreviouslycf.2{17.TheresultsinFigure2-4 showtheaverageusercapacityofsystemsemployingBCandGWBEsequencesfor =4, numberoforthogonalchannels N =10, K p =10 )]TJ/F24 7.9701 Tf 6.586 0 Td [(2 N 0 =10 )]TJ/F24 7.9701 Tf 6.587 0 Td [(10 W =10 6 Hz,and 0 = =10dB.Wedonotimposeanyoutageconstraintinthiscase.Itcanbenoted thatthereisnogainintheusercapacityofthesystememployingGWBEsequences maximumusercapacityis10inthisscenario.However,theaverageusercapacityofthe systememployingBCincreasesnon-linearlywithincreasinguserpopulationandreaches thetheoreticmaximumof2 N whentheuserpopulationisabout5timesthenumberof orthogonalchannelsavailable.Withsucientlylargepopulation,itisalwayspossibleto nd2 N userswithchannelgainswhichsatisfythetotalpowerconstraintunderBC.With xeduserpopulationandtotalpowerconstraint,anincreaseinaverageusercapacityis possiblewithBCwithoutanydegradationinthetargetSNR. 33

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2.6Summary Inthischapter,weevaluatedtheperformanceofBCinincreasingtheusercapacityof theforwardlinkofCDMAcellularsystems.Thedisparitiesthatexistinanetworkwith powercontrolwereexploitedtosuperimposeinformationtouserswithbetterchannel conditions.WehavecomparedtheperformanceofsuchasystememployingBCtothatof asystememployingGWBEsequencesunderbothaverage-andxed-powerconstraints. Theresultsindicatethatonanaverage,20%increaseinthecapacityispossiblefor =4 underanaveragepowerconstraintbyemployingBCatadegradationof1dBinthetarget SNR.Withaxedpowerconstraint,theincreaseintheusercapacityisfargreaterthan thatofasystememployingGWBEsequences.Inthenextchapter,weevaluatedthe usercapacityofacellularnetworkemployingbroadcastingandcomparedittotheuser capacityofacellularnetworkemployingTDMA. 34

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CHAPTER3 USERCAPACITYOFDOWNLINKCELLULARNETWORKS 3.1Introduction AswehaveseeninChapter2,cooperativebroadcastingtechniquessuchasSPC andDPCcanbeusedtosimultaneouslytransmittomultipleusers,whicharemore ecientthantime-sharingorotherwiseuseorthogonaldivisionofthechannelresources amongusers.Inthischapter,weinvestigatetheperformanceofinformation-theoretic broadcastingBCwhenalltheuserssharetheentirechannelresources.Unlike orthogonalizationschemesortwo-levelbroadcastingschemesofChapter2,underBC, theBSusestheentirechannelresourcestotransmitsimultaneouslytoalltheusersin thesystem.WefocusontheuseofDPC,whichhasbeenshowntoachievethecapacity ofMIMOGaussianbroadcastchannels[46].Asnotedearlier,DPCisoneofthecoding schemesthatcanachievethecapacityofascalarGaussianbroadcastchannel.However, DPCisacomplicatedschemethathasyettobeimplementedinpracticalsystems.Many presentdaysystemsusetime-divisionmultipleaccessTDMA,inwhichthebasestation supportsseveralusersbytransmittingtoonlyoneuseratatime.Theperformancegains ofDPCoverTDMAinaMIMOGaussianbroadcastchannelintermsofsum-ratecapacity wererstevaluatedin[47].Viswanathan etal. [48]haveconsideredtheperformancegain ofDPCoverTDMAintermsofdownlinkusercapacityinaMIMOcellularnetwork. Simulationresultsin[48]suggestthattheperformancegainofDPCoverTDMAisnot signicantforsystememployingsingleantennasateachradio.However,noanalytical resultswereprovided.Inthischapter,weevaluatethedownlinkusercapacityofa single-cellcommunicationsystemunderTDMAandDPCandanalyzetheperformance gainsofDPCoverTDMAwhenthenumberofusersinthecellislarge. Therestofthechapterisorganizedasfollows.Section3.2describesthesystem modelofthecellularnetworkemployedinevaluatingtheusercapacitiesunderTDMA andDPC.InSection3.3,weevaluatedtheusercapacityofacellularnetworkemploying 35

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TDMA,andinSection3.4,weevaluatedtheusercapacityofacellularnetworkemploying DPC.Section3.5evaluatesthegainofDPCoverTDMAunderseveralnetworkscenarios. ThechapterisconcludedinSection3.6. 3.2SystemDescription ConsiderascalarGaussianbroadcastchannelwith N receiversandsingleantennas atthetransmitterandateachofthereceivers.Thisisrepresentativeoftheforwardlink ofasinglecellofacellularcommunicationnetwork.Let x denotethecomplexbaseband transmittedsignaland h k ; 1 k N ,denotethechannelgainfromthetransmitterto user/receiver k .Thecomplexbasebandchanneloutputatuser k y k is y k = h k x k + n k ; 1 k N; {1 where n k N ;N 0 ; 8 k ,iscircularlysymmetriccomplexGaussiannoise.The transmitter/basestationissubjecttoatotalpowerconstraintof P tot andalltheusers haveacommontargetdaterate R 0 .Weassumethatthechannelgainsareperfectly knownatthetransmitterandthereceivers.Thetotalbandwidthofthesystemisassumed tobe W Hz. Inthischapter,wecharacterizedtheusercapacityofTDMAandDPCinascalar Gaussianbroadcastchannel.Wedenethe usercapacity tobetheexpectednumberof usersthatcanbesupportedbythebasestationunderatotaltransmitpowerconstraint, andacommontargetdatarateattheusers.Theusercapacityofcellularsystems employingDPCandTDMAareanalyzedusinganinformation-theoreticframework,and theperformanceisevaluatedforlargeuserpopulations. 3.3UserCapacityofTDMASystem 3.3.1SystemDescription WeconsideraTDMAsysteminwhichthebasestationservesonlyoneuserpertime slotusingtheentiretransmitpower P tot availabletoit.If h k denotesthecomplexchannel 36

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gainofuser k ,thereceivedpower P k isgivenby P k = K p j h k j 2 P tot ; {2 where P tot isthetotaltransmitpoweravailableatthebasestationand K p isaconstant. Timeisdividedinto frames ,andeachframeisdividedintotimeslots,notnecessarily ofequalduration,duringwhichthebasestationtransmitstodierentusersbasedon theirchannelgains.Thechannelgainsofalltheusersareindependentandidentically distributedwithacontinuousandstrictlyincreasingdistributionfunction.Althoughthe channelsgainsarerandomlydistributed,theyareassumedtobeconstantthroughoutthe durationofaframe,andareuncorrelatedacrosstheframes. Let z 1 ;z 2 ;:::z N z 1 z 2 z N denotetheorderedsquared-channel-magnitudes i.e., z k = j h k j 2 ofthemobileusersinthecellularnetwork,and R 0 denotetheircommon targetinformationrate.Thechannelcapacityofuser k is[29] C k = W log 2 1+ K p z k P tot N 0 W : {3 Toachievethetargetrateof R 0 ,thebasestationhastotransmittouser k forafraction oftime R 0 =C k .Hencetheusercapacity K TDMA ofthissystemisgivenby K TDMA = N X k =1 k Pr k X i =1 R 0 C i 1 ; k +1 X i =1 R 0 C i > 1 = N X k =1 k Pr k X i =1 T i T 0 ; k +1 X i =1 T i >T 0 ; where T i = 1 log 2 1+ K p z i P tot N 0 W ; {4 T 0 = W=R 0 ,andwiththeconventionthat Pr N X i =1 T i T 0 ; N +1 X i =1 T i >T 0 =Pr N X i =1 T i T 0 : {5 37

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Proposition3.1. Considerasingle-cellofacellularnetworkemployingTDMAwithtotal transmitpower P tot ,commontargetinformationrate R 0 attheusers,andapopulationof N users.Thenthedownlinkusercapacity K TDMA isgivenby K TDMA = N X k =1 Pr k X i =1 T i T 0 ;T 1 T 2 T N : {6 where T i saregivenby3{4. Proof. For N =2,wehavefrom3{4 K TDMA =Pr T 1 T 0 ;T 1 + T 2 >T 0 +2Pr T 1 + T 2 T 0 =Pr T 1 T 0 ;T 1 + T 2 >T 0 + Pr T 1 T 0 ;T 1 + T 2 T 0 +Pr T 1 + T 2 T 0 =Pr T 1 T 0 +Pr T 1 + T 2 T 0 For N> 2,3{6followsfrominduction. 3.3.2AsymptoticUserCapacityofTDMASystem WecanndtheasymptoticusercapacityofacellularsystememployingTDMAby invokingatheoremonthedistributionofthetrimmedmeanoforderedrandomvariables. Tothatend,weintroducethefollowingnotation.Let M k = 1 k k X i =1 T k ;T 1 T 2 T N {7 = 1 d k N e)-222(d k N e d k N e X i = d k N e +1 T i ; k =0 ; k = k N denotethetrimmedmeanoftheorderedrandomvariables T 1 ;T 2 ; T N withcontinuous andmonotonicallyincreasingparentdistribution F T t [49],where d : e denotestheceiling function.Let l k and u k denotethe k thand k thpercentilesoftheparentdistribution 38

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F T t i.e, l k = F )]TJ/F24 7.9701 Tf 6.587 0 Td [(1 T k and u k = F )]TJ/F24 7.9701 Tf 6.586 0 Td [(1 T k : Further,dene G k x = 8 > > > > < > > > > : 0 ;x
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where M k ; k ; k aregivenby3{7,3{9,and3{10,respectively,and : denotesthe unitnormaldistributionfunction. 3.4UserCapacityofDPCSystem 3.4.1SystemDescription InacellularsystemthatemploystheDPCmultipleaccessscheme,thebasestation encodestheusers'signalsinasequentialmanner.Bydoingso,whenthetransmitter encodesauser'ssignal,thesignalstobetransmittedtoallthepreviouslyencodedusers arefullyknownatthetransmitter.TheDPCtechniqueensuresthattheuserbeing presentlyencodeddoesn'tsueranyinterferencefromthepreviouslyencodedusers.The usersareencodedinorderofincreasingchannelgains,whichensuresthatDPCachieves thesum-ratecapacityofthescalarGaussianbroadcastchannel. WhenthebasestationusesDPC,ittransmitstoeachoftheselectedusersforthe entiredurationoftheframe.Thusthetargetrate R 0 canbetranslatedtoatargetSNRof 0 =2 R 0 W )]TJ/F15 11.9552 Tf 11.546 0 Td [(1.Weconsiderthechannelmodeldescribedin3{2.Thefollowingproposition givestheusercapacityofacellularsystememployingDPC. Proposition3.2. ConsideracellularnetworkemployingDPCwithtotaltransmitpower P tot ,commontargetSNRof 0 anduserpopulation N .Assumingthattheusersare orderedindecreasingorderofchannelmagnitudes z i ; 1 i N ,theusercapacity K DPC is givenby K DPC = N X k =1 Pr N 0 W 0 K p k X i =1 + 0 k )]TJ/F25 7.9701 Tf 6.586 0 Td [(i z i P tot {12 Proof. WhenDPCisemployedatthetransmitter,theinformationoftheuserwiththe bestchannelgain z 1 isencodedlastandhencehedoesn'tseeinterferencefromanyof thepreviouslyencodedusers.Since 0 isthetargetSNR,thepowerrequiredtotransmit totherstuser P 1 withthebestchannelgainisgivenby 0 = z 1 K p P 1 N 0 W P 1 = N 0 W 0 K p 1 z 1 : 40

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Similarly,user2withchannelgain z 2 seesinterferenceonlyfromuser1'ssignal.The powerrequiredtotransmittouser2, P 2 tomaintainatargetSNRof 0 isgivenby[29] 0 = z 2 K p P 2 N 0 W + z 2 K p P 1 P 2 = N 0 W 0 K p 1 z 2 + 0 P 1 = N 0 W 0 K p 0 z 1 + 1 z 2 : Inductively,itcanbeshownthatthepowerrequiredtotransmittouser k P k maintaining atargetSNRof 0 atthereceiverisgivenby P k = N 0 W 0 K p k )]TJ/F24 7.9701 Tf 6.586 0 Td [(1 X i =1 0 + 0 k )]TJ/F24 7.9701 Tf 6.587 0 Td [(1 )]TJ/F25 7.9701 Tf 6.587 0 Td [(i z i + 1 z k # : {13 Sincethetotaltransmitpoweravailableatthebasestationis P tot ,theusercapacityofa cellularsystememployingDPCis K DPC = N X k =1 k Pr k X i =1 P i P tot ; k +1 X i =1 P i >P tot {14 withtheconventionthat Pr N X i =1 P i P tot ; N +1 X i =1 P i >P tot =Pr N X i =1 P i P tot : ByappealingtothetechniqueusedinProposition3.1,theusercapacityofDPCsystem canbeexpressedas K DPC = N X k =1 Pr k X i =1 P i P tot = N X k =1 Pr N 0 W 0 K p k X i =1 i )]TJ/F24 7.9701 Tf 6.587 0 Td [(1 X j =1 0 + 0 i )]TJ/F24 7.9701 Tf 6.586 0 Td [(1 )]TJ/F25 7.9701 Tf 6.587 0 Td [(j z j + 1 z i # P tot = N X k =1 Pr k X i =1 + 0 k )]TJ/F25 7.9701 Tf 6.586 0 Td [(i z i P 0 tot ; {15 where P 0 tot = P tot K p N 0 W 0 )]TJ/F24 7.9701 Tf 6.586 0 Td [(1 41

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3.4.2AsymptoticUserCapacityofDPCSystem WeuseasimilarapproachtoSection3.4.2tondaclosedformexpressionforthe usercapacityofDPCsystemwhentheuserpopulationtendstoinnity.Tothatend,we introducethefollowingnotation.Let X k = 1 N k X i =1 + 0 k )]TJ/F25 7.9701 Tf 6.587 0 Td [(i z i ;z 1 >z 2 > z N {16 = 1 N N X i =1 J k i N +1 p i {17 where p i = z )]TJ/F24 7.9701 Tf 6.586 0 Td [(1 i ,and J k u ; 0 < > : + 0 k )]TJ/F25 7.9701 Tf 6.586 0 Td [(u N +1 ; 0
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where L X denotesthedistributionoftherandomvariableX. Proof. Referto[50]. Althoughthetheoremhasnotbeenprovenforweightfunction, J k u thatvaries with k ,weapplythetheoremtogetanapproximationonthedistributionof X k UsingTheorem3.2,theasymptoticusercapacityofaDPCsystemcanbewrittenas K DPC = N X k =1 Pr k X i =1 + 0 k )]TJ/F25 7.9701 Tf 6.587 0 Td [(i p i P 0 tot = N X k =1 Pr X k P 0 tot N N X k =1 p N P 0 tot )]TJ/F50 11.9552 Tf 11.955 0 Td [(N k J k ;F P N k J k ;F P ;N 1 ; where X k J k k ,and 2 k aregivenby3{16,3{18,3{19,and3{20,respectively,and : istheunitnormaldistributionfunction. 3.5ResultsandDiscussion InordertocomparetheusercapacitiesofTDMAandDPCsystems,wedenethe TDMAeciency, as = K TDMA K DPC ; {21 where K TDMA and K DPC aregivenby3{11and3{21,respectively.Weanalyzethe performanceofTDMAandDPCsystemsinanexponentialpath-losschannel,withand withoutfading. 3.5.1UserCapacityinExponentialPath-LossChannel,noFading Inanexponentialpath-losschannelwithoutfading,thepowerreceivedbyuser k P k isrelatedtothetransmittedpower P t by P k = K p D )]TJ/F25 7.9701 Tf 6.587 0 Td [( i P t {22 where D i isthedistancebetweenthebasestationandtheuser k isthepath-loss exponent,and K p isaconstant.Further,ifweassumethattheusers'locationsare 43

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independentanduniformlydistributedinacircularareaofunitradiuswiththebase stationatthecenter,thedensityfunctionfor D i is f D i d = 8 > < > : 2 d; 0 d 1 0 ; otherwise : {23 Underthischannelassumption,itiseasytoseethatthechannelmagnitudes z i arerelated to D i as z i = D )]TJ/F25 7.9701 Tf 6.587 0 Td [( i andthattheirparentdistributionisgivenby F Z z = z )]TJ/F18 5.9776 Tf 5.756 0 Td [(2 ; 0
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Figure3-2.EciencyofTDMAcomparedtoDPCinanexponentialpath-losschannel. respectively.TheresultsinFigure3-1illustratetheusercapacitiesofTDMAandDPC systemsforuserpopulation N> 100,targetSNR 0 =0,5dB,totaltransmitpower P tot =2 40 ,thebandwidthofthesystem W =10 6 Hz,noisedensity N 0 =10 )]TJ/F24 7.9701 Tf 6.586 0 Td [(10 and K p =10 )]TJ/F24 7.9701 Tf 6.586 0 Td [(2 .Notethat R 0 = W log 2 + 0 : Thesimulatedresultsdashedlines areprovidedalongsidetheanalyticalresultssolidlines,anditcanbeseenthatthe analyticalresultsareingoodagreementwiththesimulatedresults.Notethattheuser capacitiesofboththeTDMAandDPCsystemsincreasewithanincreaseinthepath-loss exponent .Thisisbecauselargervaluesof providegreaterdisparityinchannelgains, whichTDMAandDPCcantakeadvantagetoincreasethesystemcapacity. Therelativeeciency ofTDMAincomparisontoDPCisplottedforseveral dierenttargetSNRs 0 andfor P tot =2 40 inFigure3-2.Itcanbeseenthatforall thethreetargetSNRs 0 shown, isabove0 : 93for =2,andabove0 : 89for =4. ThisindicatesthatthegaininusercapacityachievedbyemployingDPCisatmost12% comparedtotheusercapacityofaTDMAsysteminthisscenario.Alsonotethatan increaseinthepath-lossexponentdecreasestheTDMAeciency,sinceasthedisparity 45

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inthechannelgainsincreases,DPCmoreecientlyexploitsthechanneldisparitiesto increasetheusercapacity. 3.5.2UserCapacityinExponentialPath-LossChannelwithFading Sinceclosedformexpressionsforusercapacitiesinafadingchannelforanygeneral path-lossexponentdonotexist,inthissection,weonlyconsideranexponentialpath-loss modelwithRayleighfadingwherethepath-lossexponent =2.Assumingthattheusers areuniformlydistributedinacircularareaofunitradius,andthebasestationisatthe centerofthecoveragearea,thechannelmagnitudes z i canbeexpressedas z i = D )]TJ/F25 7.9701 Tf 6.586 0 Td [( i r 2 i ; where D i isthedistanceofuser i fromthebasestationreferto3{23and r i isthe magnitudeoffadingexperiencedbyuser i ,whichisRayleighdistributed.Assumingthat thefadingexperiencedbytheusersisi.i.d.,thedistributionfunction F Z z ofthechannel gainscanbeexpressedas F Z z =1+ e )]TJ/F25 7.9701 Tf 6.587 0 Td [(z )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 z ;z> 0 : {26 However,sincetherstandsecondordermomentsof z arenotnite,theconditions ofTheorem3.1andTheorem3.2arenotsatised,andclosedformexpressionsfortheuser capacityofTDMAandDPCsystemscannotbeevaluateddirectly.Henceweconsiderthe truncateddistribution F 0 Z z = 8 > < > : 0 ;z
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transmissionfromthebasestation.TheasymptoticusercapacitiesofTDMAandDPC canbeevaluatedfromtheparentdistributionof F 0 Z z givenin3{27. Figure3-3.UsercapacitiesofTDMAandDPCinanexponentialpath-losschannelwith fading. TheresultsinFigure3-3showtheusercapacitiesofsystemsemployingTDMAand DPCinafadingchannelwithpath-lossexponent =2,forthreedierenttargetSNRs 0 ,totaltransmitpower P tot =2 40 and =0 : 05.Itcanbeseenfromtheplotsthatthe analyticalresultssolidlinesareingoodagreementwiththesimulatedresultsdashed lines.TheTDMAeciency forthreedierenttargetSNRs 0 isplottedinFigure3-4. ItcanbeseenthatTDMAeciencyisgreaterthan0 : 93forallthethreeSNRs.Hencethe gainofDPCoverTDMAintermsofusercapacityisatmost8%forthisscenario.Thus DPCprovideslittlegaininusercapacityincomparisontoTDMAforthisscenario. 3.6Summary Inthischapter,wederivedclosedformexpressionsfortheusercapacityofsingle-cell networksemployingTDMAandDPCschemesforlargeuserpopulationsunderatotal 47

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Figure3-4.EciencyofTDMAcomparedtoDPCinaexponentialpath-losschannelwith fading. transmitpowerconstraint.Inexponentialpath-losschannelswithandwithoutfading, ourresultsindicatethatTDMAisgenerallyatleast89%asecientasDPC.Theresults inthischaptercorroboratetheexistingndingsontheperformancegainofDPCover TDMA[13,47,48].Itwasshownin[48],thatDPCprovidesverylittlegainoverTDMA intermsofusercapacityinascalarGaussianbroadcastchannel.Theresultsreported in[13]indicatethatcooperativebroadcastingprovidessignicantgainsoverTDMA onlywhentherequiredspectraleciency,andtheservicefactorarehigh.Thusforthe downlinkofcellularsystemsthatemploysingleantennasatthebasestationandmobile users,theincreaseinusercapacityprovidedbyusingbroadcastingtechniqueslikesDPC insteadofTDMAmaynotosettheincreaseincomplexityassociatedwiththeformer. Inthenextchapter,theperformancegainsofbroadcastingtechniquessuchasSPC andBCinacellularsystemarefurtherinvestigatedbycomparingseveraloptimaland suboptimalforward-linkchannel-sharingschemesinavarietyofnetworkscenarios. 48

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CHAPTER4 PERFORMANCECOMPARISONOFOPTIMALANDSUBOPTIMALDOWNLINK CHANNEL-SHARINGSCHEMES 4.1Introduction TheresultsinChapter3indicatethatbroadcastingtechniquessuchasDPCandSPC maynotprovidesubstantialgainsoversimplerschemessuchasTDMAinthedownlink ofacellularnetwork.Inthepresentchapter,theperformancegainsofBCarefurther investigatedbycomparingvariousoptimalandsuboptimalchannel-sharingschemesfor Gaussianbroadcastchannelsinthedownlink/forward-linkunderanequal-rateconstraint. Intherecentpasttherehasbeensomerelatedworkreported,namely[12,47,48],that compareddirtypapercodingDPCtotime-divisionmultipleaccessTDMAforthe Gaussianbroadcastchannel.In[48],theauthorsconsideralgorithmsfororderingusers inacellularsystemusingDPCandprovidesimulationresultsonthenumberofusers thatcanbesupportedwithmultiple-inputmultiple-outputMIMOtransmissionunder anequal-rateconstraint.DPCandTDMAschemesarecomparedin[47]onthebasisof thesum-ratecapacityinsteadofanequal-rateconstraintforMIMOGaussianbroadcast channels,anditisshownthattheDPCgainovertheTDMAsum-ratecapacityis upperboundedbytheminimumofthenumberoftransmitantennasandthenumber ofreceivers.In[12],theauthorsprovideanalyticalapproximationsfortheusercapacity underanequal-rateconstraintforsingle-inputsingle-outputSISOtransmissionasthe userpopulationbecomeslarge. Thepresentworkdiersfrompreviousworkinthatweprovideatrueasymptotic analysisofthevariousschemesintermsoftherequiredminimumsignal-to-noiseratio SNRpermobilestationMSatagivenbandwidtheciency.Analyticalresultsare providedforthefollowingschemes:optimalfrequencydivisionmultiplexingFDMwith optimalallocationoffrequencyandpower,xedFDMwithequalbandwidthallocation, BCoverthewholeband,two-levelBCinconjunctionwithxedFDM,andthree-levelBC inconjunctionwithxedFDM.Weperformtheanalysisunderasymptoticconditions, 49

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i.e.,asthenumberofMSsinthesystemandthetotalbandwidthgoestoinnity.The resultsobtainedshowthatBCschemesprovidesignicantperformanceadvantageonly undercertainscenarios.Wealsoobservethatitissucienttousethree-levelBCto achieveperformanceveryclosetothebestperformanceguaranteedbybroadcastingover theentirebandforexample,theasymptoticminimumSNRperMSislessthan1 : 15 timesthatforbroadcastingoverthewholebandataspectraleciencyof5 : 5bits/s/Hz. ThisisincontrasttoFDM,forwhichtherequiredasymptoticminimumSNRperMSis about2 : 55timesthatforbroadcastingoverthewholebandataspectraleciencyof5 : 5 bits/s/Hz.Inthefollowingsection,thesystemmodelisintroduced,andinSection4.3the analysisofthedierentchannel-sharingschemesarepresented.Theresultsarediscussed inSection4.4,andthechapterisconcludedinSection4.5. 4.2SystemModel ConsidertheforwardlinkfromthebasestationBSto M mobilestationsMSs ofaninfrastructurenetwork.Assumethatafrequencybandof W Hzisavailableforthe BStosendinformationtothe M MSs.Assuminganexponentialpath-lossmodelwith Rayleighatfading,for i =1 ; 2 ; ;M ,thepower P ri receivedbythe i thMS,isrelated tothetransmittedpower P i ,by P ri = K p d i =d )]TJ/F25 7.9701 Tf 6.586 0 Td [( j h i j 2 | {z } Z i P i ; {1 where K p isaconstant, d istheclose-indistanceforthesystem, d i d isthedistance betweenthe i thMSandtheBS, isthepath-lossexponent,and j h i j isthemagnitudeof thefadingattheMS,whichisassumedtobeconstantovermanysymbols.Weassume anannularregionofcoveragewithalldistancesfromtheBStoanMSnormalizedby theclose-indistance.Thus,wehaveanannularregionwithaninnerradius d 0 =1and anouterradius D .Tostatisticallycharacterizethechannelgainfactors Z i 's,weassume thatalltheMSsareuniformlydistributedinthisannularareaofcoveragewiththeBS atthecenter.WithindependentblockRayleighfadingwithsecondmoment2 2 ,it 50

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canbeshownthat,forthespecialcases 1 ofpath-lossexponent =2and =4,the channelgainsareindependentandidenticallydistributedi.i.d.randomvariableswith thecumulativedistributionfunctionscdfs: F Z z =1 )]TJ/F15 11.9552 Tf 29.476 8.088 Td [(2 2 z D 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 : e )]TJ/F20 5.9776 Tf 12.034 3.259 Td [(z 2 2 )]TJ/F50 11.9552 Tf 11.955 0 Td [(e )]TJ/F20 5.9776 Tf 7.782 3.259 Td [(D 2 z 2 2 ;z 0{2 and F Z z =1 )]TJ/F15 11.9552 Tf 27.845 8.088 Td [(1 D 2 )]TJ/F15 11.9552 Tf 11.956 0 Td [(1 r 2 2 z : erf D 2 r z 2 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(erf r z 2 2 ;z 0{3 respectively. ItisalsoassumedthattheBShasperfectinformationaboutthechannelgains Z i saythroughaseparatefeedbackchannelfromeachMS,and,withoutlossof generality,weorderthegainsindescendingorder,i.e., Z 1 Z 2 Z M .Under perfectpowercontrolfortheRayleighfadingmodel,itcanbeshownthatitisnotpossible totransmittoeveryMSwhilemaintainingnitetransmissionpowerperMSbecause E [1 =Z i ]isunbounded.Toavoidthismodelingproblem,weassumethatthesystemdoes nottransmittoasetof overfaded MSscf.[38]whosechannelgainsaresuchthat Z i
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interval.Notethatwehave0 < 1.Inaddition,werequirethateachservicedMS hastobesupportedatanequalrateof R nats/s.The spectraleciency ofthesystem isdenedastheratio = KR W intermsofnats/s/Hzthatcanbesupportedoverthe band.WeassumethatthechannelfromtheBStoeachMSiscorruptedbyAWGNwitha two-sidednoisepowerspectraldensityof N 0 = 2.Let P t bethetotalpowertransmittedby theBStosupportthetransmissiontothe K MSs,whenpossible. Wequantifytheperformanceofachannel-sharingschemebytheminimumSNRper MSrequiredtoachieveatargetrateof R nats/sateachofthe K MSs.Moreprecisely, theminimumSNRperMSisdenedby S K =min P t N 0 KR : {4 Belowwepresentanasymptoticanalysisunderwhichthevaluesof W M and K allapproachinnitywhilemaintainingaxedservicefactor andspectraleciency ThevarioustransmissionapproachesmentionedinSection4.1arecomparedintermsof theasymptoticminimumSNRperMS,i.e. S 1 =lim K !1 S K .Notethatthisasymptotic considerationisnotunreasonableasthevaluesof W M and K areusuallyquitelargein practicalwidebandinfrastructurenetworks. 4.3AsymptoticAnalysisforRequiredMinimumSNRperMS Inthissection,theasymptoticanalysisofdierentapproachesarepresentedtowards achievingthegoalsmentionedintheprevioussection.Theveschemesstudiedinthis chapterare:broadcastingoverthewholeband,xedFDM,two-levelBC,three-levelBC andoptimalFDM. 4.3.1BroadcastingovertheWholeBand Underthisscheme,theBStransmitstothe K MSsusing K -levelBCandusingthe entireavailablebandwidth.For i =1 ; 2 ; ;K ,let0
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i =1 ; 2 ; ;K W log 1+ Z i P t a i N 0 W + Z i P t P j
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nitesecondmoment.Hence,usingtheresultin[51,Example1],itcanbeshownthat lim K !1 1 K K X i =1 e )]TJ/F25 7.9701 Tf 6.587 0 Td [(i=K Z i = Z 1 ~ F )]TJ/F18 5.9776 Tf 5.756 0 Td [(1 )]TJ/F25 7.9701 Tf 6.587 0 Td [( ; z 0 1 z exp f)]TJ/F50 11.9552 Tf 15.276 0 Td [( )]TJ/F15 11.9552 Tf 14.606 3.022 Td [(~ F z ; z 0 = g d ~ F z ; z 0 w.p.1 : {12 Asaconsequence,theasymptoticminimumSNRperMSforbroadcastingisgivenby S 1 = e )]TJ/F20 5.9776 Tf 7.782 3.693 Td [( )]TJ/F25 7.9701 Tf 6.586 0 Td [( Z 1 ~ F )]TJ/F18 5.9776 Tf 5.756 0 Td [(1 )]TJ/F25 7.9701 Tf 6.587 0 Td [( ; z 0 exp f ~ F z ; z 0 = g z d ~ F z ; z 0 w.p.1 : {13 4.3.2FixedFrequencyDivisionMultiplexing Inthisscheme,the K bestnon-overfadedusersareservedusingaxedallocationof bandwidth,witheveryuserbeingallocatedanequalshareofthetotalbandwidth,viz. W=K Hz. 2 Forthisscheme,wehave S K = 1 K K X i =1 e )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 1 Z i ; {14 andasbefore,using[51,Example1]wecanshowthatintheasymptoticcase, S 1 = e )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 Z 1 ~ F )]TJ/F18 5.9776 Tf 5.756 0 Td [(1 )]TJ/F25 7.9701 Tf 6.586 0 Td [( ; z 0 1 z d ~ F z ; z 0 : {15 4.3.3Two-LevelBroadcasting Weconsidertwo-levelBCinconjunctionwithxedFDMallocation.Theentire bandwidth W isdividedinto L = d K 2 e equalsub-bandsandtwo-levelBCisusedto supportapairofusersovereachsuchsub-band. Foratypicalpairofusers,sayusers i and j with Z i Z j ,wehave W L log 1+ aZ i p t L N 0 W R; {16 2 Here,wenotethattheperformanceofthexedtimedivisionmultiplexingTDM schemewouldbeidenticaltothatofthexedFDMschemeasprovedin[28]. 54

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and W L log 1+ )]TJ/F50 11.9552 Tf 11.955 0 Td [(a Z j p t L N 0 W + aZ j p t L R; {17 where p t isthetotalpowerexpendedinsupportingthetwousersovertheparticular sub-band.Itcanbeeasilyshown[11]thatachoiceof0 a 1existsifandonlyif p t P i + P j + e LR W )]TJ/F15 11.9552 Tf 11.956 0 Td [(1 P i {18 where P n = e LR=W )]TJ/F24 7.9701 Tf 6.586 0 Td [(1 N 0 W LZ n isthepowerrequiredifabandwidthof W=L Hzisavailable exclusivelyforuser n withoutBC. Therefore,theminimumSNRperMSrequiredtosupportthebest K non-overfadedusers is S K =min P t N 0 KR = 1 N 0 KR K X i =1 P i + L X i =1 e LR=W )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 P i # = e LR W )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 L K X i =1 1 Z i + e LR W )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 2 L L X i =1 1 Z i : {19 Notingthat1 =Z 1 1 =Z 2 1 =Z M areorderstatisticsof M i.i.d.random variablesdistributedaccordingto1 )]TJ/F15 11.9552 Tf 14.684 3.022 Td [(~ F =z for0 z 1 =z 0 andinvokingtheresultin [51,Example1],weobtain S 1 = 2 e = 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 Z 1 ~ F )]TJ/F18 5.9776 Tf 5.756 0 Td [(1 )]TJ/F25 7.9701 Tf 6.586 0 Td [( ; z 0 1 z d ~ F z ; z 0 + e = 2 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 Z 1 ~ F )]TJ/F18 5.9776 Tf 5.756 0 Td [(1 )]TJ/F20 5.9776 Tf 7.812 3.259 Td [( 2 ; z 0 1 z d ~ F z ; z 0 # : {20 4.3.4Three-LevelBroadcasting Weconsiderthethree-levelBCinconjunctionwithxedFDMallocation.Theentire bandwidth W isdividedinto L = d K 3 e equalsub-bandsandthree-levelBCisusedto supportthreeusersovereachsuchsub-band. 55

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Followingthesamemannerasfortwo-levelBC,weget S 1 = 3 e = 3 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 Z 1 ~ F )]TJ/F18 5.9776 Tf 5.756 0 Td [(1 )]TJ/F25 7.9701 Tf 6.586 0 Td [( ; z 0 1 z d ~ F z ; z 0 + e = 3 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 Z ~ F )]TJ/F18 5.9776 Tf 5.756 0 Td [(1 )]TJ/F20 5.9776 Tf 7.813 3.259 Td [( 3 ; z 0 ~ F )]TJ/F18 5.9776 Tf 5.756 0 Td [(1 )]TJ/F18 5.9776 Tf 7.782 3.258 Td [(2 3 ; z 0 1 z d ~ F z ; z 0 + e 2 = 3 )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 Z 1 ~ F )]TJ/F18 5.9776 Tf 5.756 0 Td [(1 )]TJ/F20 5.9776 Tf 7.813 3.258 Td [( 3 ; z 0 1 z d ~ F z ; z 0 # : {21 4.3.5OptimalFrequencyDivisionMultiplexing Inthisscheme,theBSoptimizestheSNRperMSbyoptimalallocationofpowerand bandwidthtoeachofthe K MSsaccordingtotheirchannelgainssuchthateachuseris providedwithadatarateof R nats/s/Hz.Wehave,for i =1 ; 2 ; ;K c i W K log 1+ KZ i P i N 0 c i W R; {22 where c i =K and P i arethethefractionoftotalbandwidthandthetransmittedpowerfor the i thMS,respectively.Thus, 1 K P K i =1 c i =1and P t = P K i =1 P i .Fromtheaboveandthe denitionof S K itcanbeseenthat S K =min 1 K K X i =1 c i Z i e c i )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 =min 1 K K X i =1 g c i Z i ; {23 where g x = x e =x )]TJ/F15 11.9552 Tf 11.955 0 Td [(1. Thus,theproblemreducestondingthe c i 'sthatminimizetherighthandsideof 4{23subjecttotheconstraint 1 K P K i =1 c i =1.Thisstandardoptimizationproblemcan besolvedusingLagrangemultipliers.Writingthefunctionalas J c 1 ;c 2 ; ;c K = 1 K K X i =1 g c i Z i + 1 K K X i =1 c i )]TJ/F15 11.9552 Tf 11.955 0 Td [(1 {24 56

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anddierentiatingwithrespectto c i ,wehave @J @c i = 1 K g 0 c i Z i + K =0 = g 0 c i = )]TJ/F50 11.9552 Tf 9.299 0 Td [(Z i {25 where g 0 x = e x )]TJ/F25 7.9701 Tf 13.151 5.256 Td [( x )]TJ/F15 11.9552 Tf 11.956 0 Td [(1isthederivativeofthefunction g x Welet h denotetheinversefunctionof g 0 .Now, h )]TJ/F50 11.9552 Tf 9.298 0 Td [(Z i isacontinuousfunction, decreasingin > 0,andtherebyitcanbeshownthatthereexists K suchthat 1 K K X i =1 h )]TJ/F50 11.9552 Tf 9.298 0 Td [( K Z i =1and c i = h )]TJ/F50 11.9552 Tf 9.299 0 Td [( K Z i : {26 Intheasymptoticcase,as K M and W gotoinnity,itcanbeprovedusingtheresultin [51,Example1]that lim K !1 1 K K X i =1 h )]TJ/F50 11.9552 Tf 9.299 0 Td [(Z i = 1 Z 1 ~ F )]TJ/F18 5.9776 Tf 5.756 0 Td [(1 )]TJ/F25 7.9701 Tf 6.587 0 Td [( ; z 0 h )]TJ/F50 11.9552 Tf 9.298 0 Td [(z d ~ F z ; z 0 w.p.1 : {27 Asaresultof4{27, 1 =lim K !1 K canbeobtainedbyequatingtherightsideof 4{27to1andsolvingfor 1 Finally,usingtheaboveandtheresultin[51,Example1]onemoretime,weget S 1 = 1 Z 1 ~ F )]TJ/F18 5.9776 Tf 5.757 0 Td [(1 )]TJ/F25 7.9701 Tf 6.587 0 Td [( ; z 0 g [ h )]TJ/F50 11.9552 Tf 9.299 0 Td [( 1 z ] z d ~ F z ; z 0 w.p.1 : {28 4.4Results Usingtheexpressionsderivedintheprevioussection,wecomputetheasymptotic minimumSNRperMS S 1 requiredforeachoftheschemesdescribedbefore.The coverageareafortheBSistheannularregionwithaninnerradiusof d 0 =1andanouter radiusof D ,withalldistancesbeingnormalizedbytheclose-indistanceofthecell,which 57

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Figure4-1.Broadcastingoverthewholebandfor =2and D =50forvariousservice factors, Figure4-2.Two-levelBCfor =2and D =50forvariousservicefactors, istypically100mor1kmforoutdoorenvironments.Asthesizeofmacro-cellstypically rangefrom1kmto30km,typicalvaluesfor D canrangebetween10to300.Amobile stationisconsideredoverfadedifitschannelgainfallsbelow z 0 = F )]TJ/F24 7.9701 Tf 6.586 0 Td [(1 Z : 05;i.e.,whenthe servicefactorisunity =1,theoutageprobabilityis0 : 05.Westudythevariationof S 1 withspectraleciency andtheservicefactor asparameters.Thepath-lossexponents 58

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Figure4-3.Three-levelBCfor =2and D =50forvariousservicefactors, Figure4-4.OptimalFDMfor =2and D =50forvariousservicefactors, consideredare =2and =4.WechoosetheRayleighfadingsecondmomentequalto1 sothatthefadingprocessneitheraddsnorsubtractspower. 59

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Figure4-5.FixedFDMfor =2and D =50forvariousservicefactors, Figure4-1throughFigure4-5showtheperformanceofdierentschemesforthe path-lossexponent =2,andouterradiusofcoverage, D =50,withspectraleciency fortheservicefactor .Figure4-1,Figure4-2,andFigure4-3showtheperformanceof applyingbroadcastingoverthewholeband,two-levelBCandthree-levelBC,respectively. TheseguresdemonstratethattheasymptoticminimumSNRperMSrequiredfor three-levelBCexceedsthatfortheoptimalmethodofbroadcastingoverthewholeband bynotmorethan10%forlowandmoderatelyhighvaluesofthespectraleciency 3 : 5bits/s/Hz.Ontheotherhand,two-levelBCperformsalittleworse,with S 1 within10%andbetween10%to20%morethanthatfortheoptimalmethodwhen 2 : 5bits/s/Hzand2 : 5bits/s/Hz << 4 : 0bits/s/Hz,respectively. 3 Wefurther notethatforalltheschemes,theincreasein S 1 withincreasing becomesmorerapid 3 Notethat S 1 hasnotbeenplottedindBsothattheactualrateofchangeof S 1 with canbeobserveddirectlyfromthegures. 60

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Figure4-6.Comparisonofalltheschemesfor =2, D =50and =0 : 8. forhighervaluesof ;i.e.,whentheservicefactorislow,theeectofanincreaseinthe spectraleciencyonthe S 1 valueislow.Thisisbecause,whentheservicefactoris lower,theBSenjoysmorefreedominchoosingthebest K outof M usersandtherebycan maintainacomparativelylow S 1 ,evenforhighvaluesofspectraleciencybecauseofthe benetsofmulti-userdiversity. Figure4-4andFigure4-5showtheperformanceofoptimalFDMandxedFDM, respectively.Thedegradationintheperformanceforthesuboptimalmethodofxed FDMwhencomparedtooptimalFDMisverysimilartothatforthecaseofthetwo-level BCandbroadcastingoverthewholeband.Forexample,foraservicefactorof0 : 8, S 1 forxedFDMisabout20%morethanthatfortheoptimalFDMschemeat =4 : 0 bits/s/Hz. InFigure4-6andFigure4-7,weshowtheperformancecomparisonofthedierent schemeswhentheservicefactoris0 : 8.Forexample,inFigure4-6,when =3 : 0bits/s/Hz wehave S 1 forbroadcastingoverthewholeband,three-levelBCandtwo-levelBCat 61

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Figure4-7.Comparisonofalltheschemesfor =4, D =50and =0 : 8. 1893 : 8,2027 : 5and2194 : 76,respectively,whereasforoptimalFDMandxedFDMthese valuesare2729 : 5and3150 : 62,respectively.Thedierencesintheperformanceforthe dierentmethodswidenwithanincreasein .Thus,for =2,at =6 : 0bits/s/Hz,we have S 1 at5108 : 1and6031 : 4forbroadcastingoverthewholebandandthree-levelBC, respectively,while11212 : 1and14177 : 8foroptimalFDMandxedFDM,respectively. Wenotethatfordierentvaluesofthepath-lossexponent ,althoughthevaluesof S 1 change,theshapesofthecurvesarealmostunaltered. Finally,inFigure4-8weplot,asafunctionof ,theratioof S 1 fordierentschemes tothatforbroadcastingoverthewholeband.Ithasbeenobservedthatthisplotdoes notsignicantlyvaryfordierentvaluesof D or .Fromthisgure,weobservethatfor 5 : 5bits/s/Hz, S 1 forthree-levelBCiswithin1 : 15timesthatofbroadcastingoverthe wholeband,whereasevenforoptimalFDM, S 1 ismorethantwicethatforbroadcasting overthewholebandathighspectraleciencies.Thus,fromtheseresultsweconclude thattheperformancesobtainedfromtwo-orthree-levelBCschemesaremuchcloserto 62

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Figure4-8.Ratiosof S 1 fortheFDMschemesandthesuboptimalBCschemestothatfor broadcastingoverwholebandfor =2, D =50and =0 : 8. thatforoptimalbroadcastingoverthewholebandthanfortheothertwoFDMschemes, especiallyatmoderateandhighspectraleciencies. 4.5Summary Inthischapter,wecomparedtheperformanceofvariousforward-linkchannel-sharing schemeswiththeconsiderationofbothpath-lossandfading,underanequal-rate constraint,intermsoftheasymptoticminimumSNRperMS.Wefoundthatthe suboptimalmethodofthree-levelBCwithxedFDMallocationrequiresanasymptotic minimumSNRperMSthatiswithin1 : 15timesthatoftheoptimalmethodofbroadcasting overthewholebandwhenthespectraleciencyisbelow5.5bits/s/Hz.Ontheother hand,xedFDMorevenoptimalFDMperformmuchworse,exceptforverylowspectral eciencies.Theseresultsmotivatetheuseofpracticalmethodsliketwo-orthree-level BCinmultibandoperationinsteadoftheoptimalbutpracticallydicultschemes likebroadcastingoverthewholebandoroptimalFDM.Moreover,thefactthatthe performancedegradationfromusingthesuboptimalthree-levelBCmethodislessthan 15%evenforhighvaluesofspectraleciencymotivatestheuseofthree-levelBCnotonly 63

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forthetraditionalcellularnetworksbutalsoforsystemsthatoperateinthehighspectral eciencyregions. Inthefollowingchapters,theproblemofchannel-sharinginwirelessadhocnetworks isconsidered,wherewefocusonthedesign,developmentandanalysisofmedium accesscontrolMACprotocolsthatimprovetheperformanceofwirelessnetworks. WedevelopedaMACprotocol,andthroughanalysisandnetworksimulations,evaluated itsimpactonthethroughputofthenetworkanditsinteractionwithotherlayers. 64

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CHAPTER5 OVERLAPPEDTRANSMISSIONINWIRELESSADHOCNETWORKS 5.1Introduction InwirelessadhocnetworksWANetsthatdonotemploycode-divisionmultiple access,medium-accesscontrolMACprotocols,suchasIEEE802.11[52],areusedto allocatethechannelresourcestospecictransmittersandreceiverssoastominimize theinterferenceinthenetwork.Traditionally,thedesignoftheMACprotocoliscarried outindependentlyofthephysical-layerdesign,assumingasimplisticcollisionchannel model.Inthesemodels,apacketissuccessfullyreceivedbyanodeiftherearenoother transmissionsinitsinterferencerange.TheseMACprotocolsscheduletransmissionssuch thatthecollisionsinthenetworkareminimized. MultiuserdetectionMUD[17,18,20,21,53,54]inwirelessnetworkshasbeen proposedasameanstoincreasespatialre-usebyincreasingthenumberofsimultaneous transmissionsinthenetwork.MUDtechniquesareemployedatthephysicallayerPHY torecoverinformationfromcollidingpacketsatthereceiver.Thesesignalprocessing techniquesusedatthePHYenableanodetoreceivepacketsinthepresenceofother transmissionsinitscommunicationrange.ThismultipacketreceptionMPRcapabilityof thenodesatthePHYleadstogreaterspatialre-useinthenetwork.MACprotocolswere proposedin[19,21]thattakeadvantageoftheMPRcapabilitiesofthePHYtoincrease thespatialre-useinnetworkstoprovidehigh-throughputinheavytracandlowdelayin lighttrac. Inmostcases,mobileradiosdonothavesucientprocessingpowertoperform complexMUDschemes.Recentworkonthetransportcapacityofwirelessnetworks[55] indicatesthatinthelow-attenuationregime,multi-stagerelayingusingcancellation ofknowninterferenceisorderoptimal.Here,theinterferenceisknownfromtheuse ofmultihoprouting.Usinginterferencecancellationforonlyknowninterferencemay signicantlyimprovenetworkperformanceatareasonablecomplexity. 65

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ToexplainhowaninterferingsignalmaybeknowninmultihoproutinginaWANet, considerafour-nodelinearnetworkconsistingofnodesA,B,CandD,whereAtransmits apackettoDusingmultihoprouting.Inaslottedcommunicationsystememployinga conventionalMACprotocol,atypicalsequenceoftransmissionsforapacketwouldbe 1:A B ; 2:B C ; 3:C D ; wherethenotation1:A BindicatesthatnodeAtransmitsapackettonodeBintime slot1,etc.UnderconventionalMACprotocols,inthetimeslotwhenCforwardsapacket toD,AisnotallowedtotransmittoBsinceC'stransmissionwillcauseinterferenceat B.HoweverwhenaMPR-basedMACprotocolisemployed,simultaneoustransmissionsof A BandC Darepossible,sinceMUDtechniquescanbeemployedatBtorecoverthe packettransmittedbyA.NotethatthepackettransmittedbyCtoDisthesamepacket thatBforwardedtoCinanearliertimeslotignoringthedierencesintheheaders.If BweretoretainacopyofthepacketthatitforwardedtoC,Bwouldhaveinformation regardingtheinterferingtransmission.ThisgreatlyreducesthecomplexityoftheMUD algorithmsemployedatthePHYtorecoverthepackettransmittedbyA.Thisexampleis revisitedinSection5.2. Theideaofemployingthistypeofknown-interferencecancellationICtechnique toincreasesimultaneoustransmissionsinWANetswasrstanalyzedin[22].In[22], knowledgeoftheinterferingsignalisassumedatboththetransmitterandthereceiver, andthereceiverperformsMUD/ICtorecoveradditionalmessages.Limitationson schedulingsuchsimultaneoustransmissionswereanalyzedandaMACprotocolthat supportssuchsimultaneoustransmissionswasproposed. Theideaofemployingnetworkcodingtoincreasespatialre-useandthroughputin WANetshasrecentlyreceivedconsiderableattentionfromtheresearchcommunity[56{66]. Atransmittingnodeexploitsthebroadcastnatureofthephysicalmediumalongwith theknowledgeoftheinterferingmessagesatthereceivingnodestocombine/encode 66

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multipleindependentmessagesatthenetworklayerandtransmittoseveralnodes. Anodereceivingtheencodedmessageusestheknowledgeoftheotherinterfering messagesavailableatthenetworklayertorecoverthemessageintendedforit.Practical channel-sharingschemesthatsupportnetworkcodinginWANetswereproposed in[57,60,64,66]. Ourapproachissimilartosomenetworkcodingapproachestoincreasesimultaneous transmissionsinWANets[23,24,67,68].Inphysical-layernetworkcoding[24],relay nodesmayreceivesignalsconsistingofseveralsimultaneoustransmissions.Thesesignals aredecoded,re-encodedandrelayedontotheirnaldestinations.Thedestination,which hastheknowledgeoftheotherinterferingsignals,mitigatestheinterferenceandrecovers theintendedtransmission.However,thisapproachrequiresperfectsynchronization amongthosetransmissionsthatinterfereatarelaynode.Analternativestrategycalled analognetworkcoding[67]doesnotrequiretheintermediaterelaynodestodecode thesignal.Whenarelaynodereceivesasignalconsistingofinterferingtransmissions, thenodeampliesthesignalandbroadcastsit.Onlypacket-levelsynchronizationis necessarybetweentheinterferingtransmissions.Theintendeddestinationsleveragethe informationtheyhaveabouttheinterferingtransmissionstomitigatethem,andrecover theintendedtransmission.TheseapproachesaresimilartotheideaofemployingMUD withknown-interferencecancellation.Theseworksanalyzethephysical-layeraspects involved,butdonotaddresstheMAC-layerimplicationsofemployingsuchsimultaneous transmissionschemesinadhocnetworks. Inthischapter,weanalyzedsomeofthefundamentallimitsonperformingoverlapped transmissionsinaWANet.Ouranalysisprovidesanunderstandingoftheperformance gainsofsuchtransmissions,andaninsightintothePHYandMACinteractionrequired forschedulingsuchtransmissions.InChapter6,wedesignedaMACprotocolbasedon theIEEE802.11MACprotocolthatexploitsthisfeaturetoimprovethespatialre-useand throughputinwirelessnetworks. 67

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Figure5-1.Four-nodelinearnetworkwithconventionalscheduling. Therestofthechapterisorganizedasfollows.Section5.2introducestheideaof employingoverlappedtransmissioninalinearnetwork.InSection5.3,somelimitson performingoverlappedtransmissionsinwirelessnetworksareevaluated.Thechapteris concludedinSection5.4. 5.2Motivation Inthissection,theideaofoverlappedtransmissionsinafour-nodelinearnetworkis illustrated,whichisshowninFigure5-1.Weassumethatthenodescancommunicate onlywiththeadjacentnodesandoperateinhalf-duplexmode.NodeAtransmits packetstonodeDthroughmultihoprouting.Atypicaltransmissionsequenceundera conventionalschedulingschemeisdepictedinFigure5-1,inwhichittakesthreetime slotsforapacketfromAtoreachD.Thescheduledtransmissionsinagiventimeslot aremarkedbysoliddirectedarrowsalongwiththepacketidentiers,andtheinterference causedbythesetransmissionsaremarkedbydashedarrows.Undertypicalcarrier-sense multipleaccessprotocolswithcollisionavoidanceCSMA/CA,whenpacket m 1 isbeing forwardedbyCintimeslot t 3 ,Acannottransmitthemessage m 2 sinceC'stransmission willcauseinterferenceatB. 68

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Figure5-2.Four-nodelinearnetworkwithoverlappedtransmissions. Thethroughputofthisnetworkcanbeimprovedbyemployingsimultaneous transmissionsasdescribedbelow.Weobservethatinthetimeslot t 3 ,Cforwardsthe packet m 1 thatitreceivedfromBintheearliertimeslot t 2 .IfBweretoretainacopy ofthemessage m 1 locally,itknowsthemessagebeingtransmittedby C intimeslot t 3 assumingthatlink-layerencryptionisnotusedandanydierencesintheheadersare ignored.IfAisallowedtotransmitthemessage m 2 inthetimeslot t 3 ,Bcanusethe storedinformationregarding m 1 tomitigatetheinterferencecausedbyC'stransmission. Wecallthisadditionaltransmissionthatresultsduetotheinterferencemitigationof known-interferenceas overlappedtransmission Aschedulingschemeemployingtheideaofoverlappedtransmissionforthefour-node linearnetworkisdepictedinFigure5-2.Underthisschedulingscheme,apacketis transmittedfromAtoBbyemployingoverlappedtransmissionduringthetimeslot thatCforwardsapackettoD.SincethetransmissionofthepacketfromAtoBdid notinvolvetheallocationofaseparatetimeslotforitstransmission,apacketrequires onaverageonlytwotimeslotstobetransmittedfromAtoD.Thesetwotimeslotsare requiredfortheschedulingoftransmissionsfromBtoC,andCtoD,respectively.The performancegainofthisschedulingschemecanbemeasuredintermsoftransmission eciency,whichisdenedastheratioofthetimetakenforthetransmissionof M packets 69

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underconventionalschedulingschemeandtheschedulingschemeemployingoverlapped transmissions.Thetransmissioneciency)]TJ/F24 7.9701 Tf 226.606 -1.793 Td [(4 ofthisschemeisgivenby )]TJ/F24 7.9701 Tf 7.314 -1.793 Td [(4 = 3 M 2 M )]TJ/F15 11.9552 Tf 11.955 0 Td [(1+3 ; 3 2 ;M 1 ; {1 where M isthetotalnumberofpacketstransmittedbyA.Notethatunderconventional scheduling,ittakesthreetimeslotsforeverypacketfromAtoreachD.However,using theschedulingschemeemployingoverlappedtransmissions,ittakestwotimeslotson averageforapacketfromAtoreachD 1 Similarly,inan N N 4nodelinearnetwork,thetransmissioneciency)]TJ/F25 7.9701 Tf 268.617 -1.794 Td [(N canbe showntobe )]TJ/F25 7.9701 Tf 7.314 -1.793 Td [(N = N )]TJ/F15 11.9552 Tf 11.955 0 Td [(1+3 M )]TJ/F15 11.9552 Tf 11.956 0 Td [(1 N )]TJ/F15 11.9552 Tf 11.955 0 Td [(1+2 M )]TJ/F15 11.9552 Tf 11.956 0 Td [(1 ; 3 2 ;M 1 : {2 Weobservethatthecentralizedschedulingschemethatemploysoverlappedtransmissions hasthepotentialtoimprovetheeciencyofalinearnetworkbyuptoapproximately 50%overtheconventionalscheme.InSection5.3,welookatsomeofthelimitations ofemployingoverlappedtransmissionsinWANets.Sincethefocusofthisworkison developingaMACprotocolforoverlappedtransmission,thePHYaspectsoftheprotocol arenotevaluatedhere. Weidentifyatransmissionbetweentwonodesasa primarytransmission ifthe transmissionisnotpredicatedontheuseofnon-causalknowledgeoftheinterfering signalsduringthattransmissioninterval.Forexample,inthenetworkofFigure5-2, thetransmissionofmessage m 1 fromCtoDintimeslot t 3 isthe primarytransmission andthenodesCandDarecalledthe primarytransmitter andthe primaryreceiver respectively.Similarly,atransmissionbetweentwonodesisa secondarytransmission ifat leastoneofthenodeshasnon-causalinformationabouttheprimarytransmissionsinthe 1 Therstpacketrequiresthreetimeslots. 70

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presenttransmissionintervalandperformsMUD/ICtomitigatetheinterference.Inthe networkofFigure5-2,thetransmissionofthemessage m 2 fromnodeAtoBintimeslot t 3 forwhichBperformsMUD/ICtomitigatetheinterferencefromC'stransmissionisthe secondarytransmission ,andthenodesAandBarecalledthe secondarytransmitter and the secondaryreceiver ,respectively 2 5.3OverlappedTransmissioninWirelessAdHocNetworks Inthissection,somefundamentallimitsonperformingoverlappedtransmissionina wirelessnetworkareanalyzed.Thepurposeoftheanalysisistoprovideinsightsintothe typesofscenariosinwhichoverlappedtransmissionmaybeappropriate,andthedesignof aMACprotocoltoecientlyutilizethesimulcastingcapability. 5.3.1SystemModel Considerrstawirelessadhocnetworkwithnodesdistributedaccordingtoa two-dimensionalhomogeneousPoissonpointprocesswithdensity nodesperunit area.Eachnodeisequippedwithatransceiverandcommunicateswithothernodesin half-duplexmode.Weassumethateachnodehasaninnitepacketbuer,andeach radioretainscopiesofthepacketsitforwardsunlessthatpacketistransmittedtoits naldestinationoruntilthatpackethasbeenforwardedonbyoneofitsneighbors.To investigatesomeoftheissuesthatwilllimittheperformanceofoverlappedtransmission, weanalyzetheuseofoverlappedtransmissioninasystemusingslottedcommunications. Inthismodel,eachnodetransmitsinagiventimeslotwithprobability p .Thisassumption isonlytofacilitatetheanalysisofoverlappedtransmissionsinadhocnetworksin Section5.3.However,nosuchassumptionismadeduringthedevelopmentoftheMAC protocolinChapter6.Wealsoassumethatthesecondarytransmitterisinformedofthe 2 Thetermsprimary"andsecondary"arealsousedinthecognitiveradioliterature toclassifyusersaccordingtotheirregulatorystatus,andshouldnotbeconfusedwith theterminologyemployedhere,inwhichusersareclassiedaccordingtotheirrolesinan overlappedtransmission. 71

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correspondingprimarytransmissionandthattheoverlappedtransmissionissynchronized withitscorrespondingprimarytransmission.Thereceivedpower P r inthefareldcan beexpressedas P r = K p d )]TJ/F25 7.9701 Tf 6.587 0 Td [( r P t ; {3 where P t isthetransmittedpower, d r isthedistancebetweenthetransmitterandthe receiver, K p isaconstant,and isthepath-lossexponent.Intheabsenceofinterference, weassumethatatransmissionatthemaximumpowerlevelwillbereceivedcorrectlyif andonlyiftheintendedreceiveriswithinadistanceofoneunitfromthetransmitter. Wealsoassumethatthereissomeinterferencerange,whichistypicallylargerthanthe transmissionrange.Nodeswithintheinterferencerangebutoutsidethetransmission rangeofatransmittercandetectthepresenceofatransmissionbutwillnotbeableto correctlydecodethepacketbeingtransmitted. Figure5-3.Adhocnetworkwithoverlappedtransmission. Inthissection,weconsidersomelimitationsontheabilitytoutilizeoverlapped transmissionstoimprovethethroughputinawirelessadhocnetwork.Theselimitations comefromthefollowingtwosources: Interferenceduetosecondarytransmission: Sincethesecondaryreceiverhas non-causalknowledgeoftheprimarytransmission,itcanmitigatetheinterference duetotheprimarytransmitterandrecovertheintendedmessage.However,the secondarytransmissioncausesinterference,possiblytoseveralprimarytransmissions. 72

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InSection5.3.2,weevaluatedtheamountofinterferencethatasecondary transmissionmaycauseattheprimaryreceiver,andsuggesthowthisinterference canbecontrolledbyadaptingthepowerlevelofthesecondarytransmissiontomeet speciedsignal-to-interferenceratioSIRandoutagerequirementsorbycareful selectionofthesecondarytransmitter. Probabilityofsecondarytransmission: Overlappedtransmissionsdependonthe availabilityofsuitablesecondarytransmittersandthesuccessfulreceptionofthe messagesatthesecondaryreceiver. TheanalyticalresultsinSection5.3.2andSection5.3.3arebasedonthenetwork showninFigure5-3,whichcanbeconsideredtobeapartofalargernetwork.NodesA andCareinthetransmissionrangeofB,andBtransmitspacketstoDthroughCby employingmultihoprouting.HenceDisinthetransmissionrangeofC,butnotinthe transmissionrangeofB.ThisparticularregionisshowninFigure5-3withdashedlines. WealsoassumethatAhaspacketsforB.ThenetworkofFigure5-3isusedtosimplify theanalysis,yetillustratetheimportantaspectsofoverlappedtransmission. 5.3.2InterferenceduetoSecondaryTransmission ConsiderrsttheadhocnetworkofFigure5-3,andthetimeslotduringwhichnode CforwardstoDapacketthatithasreceivedfromBinanearliertransmission.The transmissionfromCtoDisaprimarytransmission,andapossiblesecondarytransmission isfromnodeAtonodeB.WeassumethatbothnodesAandBareinformedofC's transmissiontoD.NodeAisallowedtotransmitonlyifitisnotinthetransmissionrange ofD.ThisrestrictiononA'stransmissionreducestheamountofinterferenceatD,butit isstillnon-negligible.However,Aisallowedtotransmitevenifitisinthetransmission rangeofC.WealsoassumethatBcanperformperfectinterferencecancelationofC's transmissionandrecoverthepackettransmittedbyA.However,A'stransmissioncauses interferenceatnodeD.Inordertoanalyzetheimpactofthesecondarytransmissionat 73

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theprimaryreceiver,weevaluatetheSignal-to-InterferenceRatioSIRatnodeD.We assumethatthesecondarytransmissionistheonlysourceofinterferenceatD. Forconciseness,weintroducethefollowingnotation.Let X ij betherandomvariable denotingthedistancebetweenthenodes i and j .Also,let A l r 1 ;r 2 ;d denotetheareaof thelensformedbytheintersectionoftwocirclesofradii r 1 and r 2 withcentersseparated byadistance d .Mathematically, A l r 1 ;r 2 ;d = r 2 1 cos )]TJ/F24 7.9701 Tf 6.586 0 Td [(1 r 2 1 + d 2 )]TJ/F50 11.9552 Tf 11.955 0 Td [(r 2 2 2 r 1 d + r 2 2 cos )]TJ/F24 7.9701 Tf 6.586 0 Td [(1 r 2 2 + d 2 )]TJ/F50 11.9552 Tf 11.955 0 Td [(r 2 1 2 r 2 d )]TJ/F15 11.9552 Tf 9.299 0 Td [(0 : 5 h p r 1 + r 2 + d r 1 + r 2 )]TJ/F50 11.9552 Tf 11.955 0 Td [(d r 1 )]TJ/F50 11.9552 Tf 11.955 0 Td [(r 2 + d )]TJ/F50 11.9552 Tf 9.299 0 Td [(r 1 + r 2 + d i : {4 Let denotetheratioofthedistancesbetweennodesCandD,andAandDrespectively. Mathematically, = X CD X AD ;X CD < 1 ;X AD > 1 : {5 Theconstraint X CD < 1indicatesthatDisinthetransmissionrangeofCandthe constraint X AD > 1reectsthefactthatthesecondarytransmitterAisallowedto transmitonlyifitisnotinthetransmissionrangeofD.Hencewehave < 1.Inan exponentialpath-losschannelwithoutfading,theratio ofthepowersoftheprimary transmissiontothesecondarytransmissionatnodeDcanbeexpressedas = X CD X AD )]TJ/F25 7.9701 Tf 6.587 0 Td [( = )]TJ/F25 7.9701 Tf 6.587 0 Td [( ;< 1 : {6 Thedensityof canbeexpressedas f r = Z s> 1 sf X AD ;X CD s;rs ds; {7 where f X AD ;X CD s;y isthejointprobabilitydensityfunctionpdfof X AD and X CD Thejointpdfof X AD and X CD isevaluatedinAppendixAandisgivenbyA{7.The 74

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truncateddistributionof isgivenby f r j r< 1= 8 > < > : f r R 1 0 f r dr ; 0 < 1 ; 0 ; otherwise : {8 Thenfrom5{6and5{8,thepdfofSINR ,is f )]TJ/F15 11.9552 Tf 5.787 1.794 Td [( = 1 )]TJ/F24 7.9701 Tf 6.587 0 Td [(1 )]TJ/F18 5.9776 Tf 8.36 3.258 Td [(1 f )]TJ/F18 5.9776 Tf 8.36 3.258 Td [(1 j )]TJ/F18 5.9776 Tf 8.36 3.258 Td [(1 < 1 ; {9 where isthepath-lossexponent. Figure5-4.Distributionofsignal-to-interferenceratio, Thedistributionfunction F )]TJ/F15 11.9552 Tf 5.787 1.794 Td [( ofSIRatD, ,forpath-lossexponent =2 ; 4 arenumericallycomputedandplottedinFigure5-4.Let 0 denotetheminimumSIR requirementforthesuccessfulreceptionofamessage.Anoutageeventoccurswhen < 0 .Let denotetheoutageprobability,Pr 0 = .Sincetheradiolocations arerandom,itmaynotbepossibletoachieve =0foraparticular 0 .Forexample,let =4, =0 : 05and 0 =12dB.ThisSIRrequirementroughlytranslatestoavalueof =0 : 5.FromFigure5-4,wehavefor =0 : 05,SIRof F )]TJ/F24 7.9701 Tf 6.587 0 Td [(1 )]TJ/F15 11.9552 Tf 12.945 3.241 Td [( =4dB,whichislessthan 75

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therequiredSIR.Theinterferencecausedbythesecondarytransmissioncanbecontrolled byusingthelocationinformationofthenodesinchoosingthesecondarytransmitter. AnotherwaytomeetthetargetSIRrequirementwithoutincreasingtheinterferenceto othernodesistoreducethepowerofthesecondarytransmission. 5.3.3ProbabilityofSecondaryTransmission Inthissection,theconditionalprobabilityofasecondarytransmissiongiventhat thereisaprimarytransmissionthatpermitsasecondarytransmissionisevaluated.With respecttothenetworkofFigure5-3,giventhatCsuccessfullyforwardsB'spackettoD, weevaluatetheprobabilityofasuccessfulsecondarytransmissionfromnodeAtoB.The probabilityofasuccessfulsecondarytransmissiondependsonthefollowingfactors. 1. Availabilityofasecondarytransmitter arbitrarilycallednodeAhere:Allthe nodesthatareinthetransmissionrangeofthesecondaryreceivernodeB,but notinthetransmissionrangeoftheprimaryreceivernodeDareidentiedas potentialsecondarytransmitters.Oneofthemisarbitrarilychosenasthethe secondarytransmitter.Wenotethatidenticationofasecondarytransmitter doesnotguaranteeasuccessfulsecondarytransmission.Inthisanalysis,wedo notaddresstheissueofhowasecondarytransmitterischosen,butinvestigatethe factorsthatlimittheavailabilityofasecondarytransmitter. 2. Availabilityofpacketsatthesecondaryreceiver :Inordertosimplifytheanalysis, weassumethatasecondarytransmitteralwayshaspacketsforthecorresponding receiver. 3. Schedulingasecondarytransmission :Weassumethat,onceasecondarytransmitter isidentied,ittransmitsapackettothesecondaryreceiver,independentofthestate ofthemedium.Thisassumptionresultsinanupperboundontheprobabilityof schedulingasecondarytransmissioninatimeslot,asthesecondarytransmission maynotbepossibleifitwillinterferewithotherprimarytransmissions. 76

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4. Successfulreceptionoftheoverlappeddataatthesecondaryreceiver :Thesecondary receivercansuccessfullyreceivethemessageprovidedthatnonodeinitsinterference rangewiththeexceptionoftheprimarytransmittertransmits.Wedonotconsider theeectofothersecondarytransmissionsatthissecondaryreceiver,againyielding anupperboundonthenumberofsuccessfuloverlappedtransmissionsthatcanoccur inanadhocnetwork. UsingtheexamplenetworkofFigure5-3,weevaluatetheprobabilityofasuccessful secondarytransmissionfromAtoBwhileCforwardstoDthepacketithasreceivedfrom Binanearliertransmission.Basedontheabovediscussion,theprobabilityofasuccessful secondarytransmission,p S canbeboundedby p S p F p TjF ; {10 where F denotestheeventthatthereisasuitablesecondarytransmitterdenotedasAin ourexamplenetwork,and T denotestheeventthatthesecondaryreceiverdenotedas Binourexamplenetworksuccessfullyreceivesthepackettransmittedbythesecondary transmitter. Theprobabilityoftheevent F isequivalenttondinganon-transmittingnodethatis inthetransmissionrangeofB,butnotinthetransmissionrangeofD.Thisregion A F z isgivenby A F z = )-222(A l ; 1 ;z ; 1
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Figure5-5.Probabilityofndingasecondarytransmitter. ndingasecondarytransmitterisgivenby p F = Z z 1 X n =0 A F z n e )]TJ/F25 7.9701 Tf 6.587 0 Td [( A F z n )]TJ/F50 11.9552 Tf 11.955 0 Td [(p n f X BD z dz =1 )]TJ/F73 11.9552 Tf 11.955 16.273 Td [(Z z e )]TJ/F25 7.9701 Tf 6.587 0 Td [( A F z )]TJ/F25 7.9701 Tf 6.586 0 Td [(p f X BD z dz; {13 where p istheprobabilityoftransmissionbyanodeinatimeslot.Theprobabilityp F ofndingasecondarytransmitterisshowninFigure5-5forthreedierentnodedensities, .Itcanbeseenthatforagivenprobabilityoftransmissioninatimeslot,theprobability ofndingasecondaryreceiverincreaseswithanincreaseinthenodedensity.Alsonote thatforstableoperationofthenetwork,theprobabilityoftransmission p ,shouldbeless thantheaveragenumberofnodesintheinterferencerangeofanode.Forinstance,ifwe assumethattheinterferencerangeistwicethetransmissionrange,wehave p )]TJ/F24 7.9701 Tf 6.587 0 Td [(1 where isthenodedensity,andtheinterferencerangeofanodeisassumedtobe2units. With p = )]TJ/F24 7.9701 Tf 6.587 0 Td [(1 ,p F is0.51,0.74and0.85for =1 ; 2 ; and3,respectively. 78

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Figure5-6.Upperboundonprobabilityofreceptionbynode B TheprobabilityofsuccessfulreceptionatBofthesecondarytransmissionfromA, p TjF ,canbeupperboundedbytheprobabilitythatnoprimarytransmissionsoccur inthenon-overlappinginterferenceregionsofBandD.Undertheassumptionthatthe interferencerangeistwicethetransmissionrange,theareaofthisregionisgivenby A I z =4 )-222(A l ; 2 ;z ; {14 where A l r 1 ;r 2 ;d isgivenby5{4.Usingthesameapproachasin5{13, p TjF canbe boundedby p TjF Z z e )]TJ/F25 7.9701 Tf 6.586 0 Td [( A I z p f X BD z dz: {15 TheprobabilityofreceptionbynodeBwasnumericallyevaluatedandthepdfisplotted inFigure5-6forthreedierentnodedensities, ,andpath-lossexponent, =4.Asthe nodedensityincreases,theprobabilityofreceptiondecreases,whichisduetotheincrease intheinterferencearoundnodeB.Foranadhocnetworkwithprobabilityoftransmission 79

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p = )]TJ/F24 7.9701 Tf 6.587 0 Td [(1 ,theprobabilityofnodeBreceivingA'smessageis0.53forallthenode densities Figure5-7.Upperboundontheprobabilityofasuccessfulsecondarytransmission, p S Theupperboundontheprobabilityofsuccessfulsecondarytransmission p S cf. 5{10isshowninFig.5-7forseveralvaluesofnodedensiy .Whentheprobability oftransmission, p = )]TJ/F24 7.9701 Tf 6.586 0 Td [(1 ,thevalueoftheupperboundis0.27,0.39,and0.41for =1 ; 2 ; and3,respectively.For p = )]TJ/F24 7.9701 Tf 6.587 0 Td [(1 ,thevalueoftheupperboundis0.37,0.54, and0.61for =1 ; 2 ; and3,respectively. 5.4Summary Inthischapter,weproposedtheideaofoverlappedtransmissiontoenhancethe spatialre-useandthroughputofwirelessnetworks.Bytakingadvantageof apriori knowledgeoftheinterferingpacket,thereceivercanemployasimpliedICschemeto receiveapacketinthepresenceofinterference.Weanalyzedsomeofthefactorsthatlimit theuseofoverlappedtransmissionsinanadhocnetwork.Theanalysisshowsthatthere isahighprobabilityofsuccessfulsecondarytransmissiongiventhatthereisaprimary 80

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transmissioninatimeslot.Althoughthissecondarytransmissioncausesinterference toseveralprimarytransmissions,thisinterferencecanbeminimizedbyeitherselecting secondarytransmissionsthatareoutsideoftheprimaryreceiver'sinterferencerange,orby reducingthepowerofthesecondarytransmission.Inthefollowingchapters,wedeveloped aMACprotocolthatsupportsoverlappedtransmissionandevaluateditsperformance undervariousnetworkscenarios. 81

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CHAPTER6 THEOVERLAPPEDCARRIERSENSEMULTIPLEACCESSPROTOCOL 6.1Introduction Inthischapter,wedeveloptheOverlappedCarrierSenseMultipleAccessOCSMA protocol,whichisbasedontheIEEE802.11MACprotocol.TheOCSMAprotocol supportsoverlappedtransmissioninadhocnetworksandexploitsknowledgeofthe interferingtransmissionstoscheduleadditionaltransmissions,whichimprovethespatial re-useandthroughputinwirelessadhocnetworks. Theorganizationofthechapterisasfollows.Section6.2describestheOCSMA protocol.ThedesignissuesoftheprotocolareconsideredinSection6.3,andSection6.4 providesperformanceevaluationoftheprotocol.ThechapterisconcludedinSection6.5. 6.2TheDesignofOCSMAProtocol TheOCSMAprotocolisbasedonthedistributedcoordinatedfunctionDCF modeoftheIEEE802.11MACprotocol[52,Section9.2].Unlessstatedexplicitly,the terminologyusedinthefollowingsectionscorrespondswiththatintheIEEE802.11 standard. ThedesignoftheOCSMAprotocolisbestdescribedwiththeexamplenetwork ofFigure6-1a.Thetimelineoftheprotocolfortheexamplenetworkisshown inFigure6-2,andtheframeformatsareshowninFigure6-3.Theoperationofthe protocolcanbedividedintovephasesasfollows: 6.2.1PrimaryHandshaking ThisphaseoftheOCSMAprotocolissimilartotheRTS/CTSexchangeoftheIEEE 802.11protocol.Whenanodehasdatatotransmittoanothernodeinitstransmission range,itinitiatesthehandshakebysendingaRequestToSendRTSframe.Thenode thatreceivestheRTSsendsaClearToSendCTSframeifitsensesthemediumto befree.Thenodeinitiatingthehandshakeisthe primarytransmitter andthenode 82

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aAdhocnetwork bRTS cCTS dPTS eRTT fCTT gDATA hODATA iACK1 jACK2 Figure6-1.TypicalframeexchangesinOCSMAprotocol. thatrespondstotheRTSisthe primaryreceiver .Alltheothernodesthatreceivethe handshakesettheirtransmitallocationvectorsTAVforthedurationofthetransmission. ThetransmitallocationvectorissimilartothenetworkallocationvectorNAVdened 83

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Figure6-2.TimelineoftheOCSMAprotocol. intheIEEE802.11standard[52,Section9.2.5.4],withafewsignicantdierencesas describedbelow. EachnodeisequippedwithatransmitallocationmatrixTAXthatisresponsible forthevirtualcarriersensemechanism.TheTAXisanarrayofseveralTAVs.Nodes receivingavalidframethatisnotdestinedforthemupdatetheirTAVwiththe informationintheDuration/IDeld.UnliketheNAVvectorofIEEE802.11,theTAX allocatesaTAVforeachvalidframenotaddressedtothereceivingnodeitreceives, evenifthenewTAVvalueisnotgreaterthananyofthecurrentTAVs.ThustheTAX maintainsanarrayofTAVsforeachframethatitreceives.Themediumisconsidered busyifanyoftheTAVsisset.TheTAVsalsostoreinformationregardingthetransmitter andreceiveroftheframe,ifthatinformationisavailable.TheimplementationoftheTAX greatlysimpliesthedesignofOCSMAprotocol,asdiscussedinlatersections.Another importantdistinctionbetweenNAVandTAVisthatanodecantransmiteveniftheTAV ofanodeisset.Theconditionsunderwhichthisispossiblearediscussedlater. ConsidertheWANetinFigure6-1a,whereatsomepointoftime,nodeCintendsto forwardapackettoDthatithasreceivedfromBinanearliertransmission.Ctransmits anRTStoD,andDrespondswithaCTS,asshowninFigure6-1bandFigure6-1c, 84

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respectively.TheframeformatsoftheRTSandCTSrefertoFigure6-3inOCSMAare thesameasintheIEEE802.11protocol[52,Section7.2.1]. Figure6-3.FrameformatsoftheOCSMAprotocol. 6.2.2SecondaryHandshaking ThesecondaryhandshakingcanbethoughtofasasecondaryRTS/CTSexchange todeterminethepossibilityofperformingoverlappedtransmissionwiththeprimary transmission.UponreceiptoftheCTS,theprimarytransmittersendsaPrepareToSend PTSframetothenodefromwhichitreceivedthepresentDATAframeinanearlier transmission.Ifthedataislocallygenerated,noPTSissent,andtransmissionofthe DATAframestartsafteradurationofSIFS[52,Section9.2.5].IfthePTSissent,the 85

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primarytransmitterdefersthetransmissionoftheDATAframeuntilthecompletionof thesecondaryhandshaking. ContinuingourexampleusingFigure6-1a,afterthecompletionoftheRTS/CTS exchangebetweenCandD,nodeCsendsaPTStoB.ThePTSframeformatisshown inFigure6-3.TheformatissimilartotheformatofanRTSframeexceptforthe additionaleldsDAandPID.TheDestinationAddressDAeldcontainstheaddressof theprimaryreceiver,andthePacketIDPIDeldcontainstheuniqueIDoftheDATA framethatisbeingtransmittedtotheprimaryreceiver.ThenodereceivingthePTS frameiscalledthe secondaryreceiver .Beingasecondaryreceiverimpliesthatthepresent nodehasinformationregardingtheprimarytransmissionandiscapableofreceivingan overlappedtransmission. UponreceiptofthePTS,thesecondaryreceiverensuresthatitsTAVissetonlyby theprimarytransmitter.NotethattheTAVsstoreinformationregardingthetransmitter andthereceiverofanyvalidframeitreceivesthatisnotaddressedtothereceivingnode. Thisistoensurethattherearenoothertransmissionsoccurringintherangeofthe secondarytransmitterexceptfortheprimarytransmission.Ifthisistrue,itidentiesa suitablepartnerforsecondarytransmissionasdescribedbelow. Oncethesecondaryreceiveridentiesthemediumtobefreeexceptfortheprimary transmission,itgeneratesalistofpotentialpartners.Thenodesareidentiedbasedon thefollowingcriteria: 1.Thenodeshouldnotcauseexcessiveinterferencetotheprimarytransmission.In thischapter,weconsideronlyoneofthetwoapproachesdescribedinSection5.3.2, inwhichthesecondaryreceiverknowsthelocationsoftheneighboringnodesand usesthisinformationtoidentifypotentialcandidatesforthesecondarytransmitter. 2.Thenodeshouldhavetransmittedaframetothesecondaryreceiverinanearlier timeslot.Theinformationregardingreceiptofframesfromalltheothernodesis maintainedinacacheattheMAClevel. 86

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Thesecondconditionisbasedontheheuristicthatifanodehastransmittedaframe tothesecondaryreceiverinanearliertimeslot,itisverylikelythattheremightbemore framesdestinedforthesecondaryreceiver.Thisensuresthatthereisagreaterprobability ofsecondarytransmissionforanyparticularpartner.Anodeischosenrandomly 1 from thepotentialcandidatestobethe secondarytransmitter ThesecondaryreceiversendsaRequesttoTransmitRTTframetotheselected secondarytransmitter.TheformatoftheRTTissimilartotheformatoftheRTSexcept thatitalsocontainsanadditionaleld,PrimaryAddressPA,whichcontainstheaddress oftheprimarytransmitter.Thesecondarytransmittercomparestheaddressofthe primarytransmitteragainstthetransmitterinfooftheTAVsifitisavailable,andall theTAVsthataresetbytheprimarytransmitterarereset.ThisensuresthattheTAV ofthesecondarytransmitterisnotsetbyeithertheRTSorthePTSsentbytheprimary transmitter.Ifitndsthemediumtobefreeandhasasuitablepackettotransmit, itrespondswithaCleartoTransmitCTTframewhoseformatisthesameasthe CTSFigure6-3.TransmissionofCTTimpliesthatthesecondarytransmitteriscapable oftransmittingoverlappeddatawithoutcausinginterferencetoanyofthetransmissions includingtheprimarytransmissioninitscommunicationrange. IntheexamplenetworkofFigure6-1a,whenBreceivesthePTSfromC,itensures thatitsTAVissetonlybyC'stransmissionofRTStoDrefertotheTAV0settingof BshowninFigure6-2.SinceBisnotinthetransmissionrangeofD,itwillbeable todetectD'stransmissionofCTSbutwillnotbeabletodecodeit.Thiswouldcause B'sTAV1tobesettoadurationofExtendedInterFrameSpacingEIFS[52,Section 9.2.3.5],butitwouldexpirebeforethePTSframeisreceivedrefertoTAV1settingof BinFigure6-2.Basedontheselectioncriteriaforchoosingapartner,assumenodeB 1 Usingotherapproaches,suchasroundrobinscheduling,mayincreasetheprobability ofchoosinganodewithapacketforthesecondaryreceiver. 87

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choosesnodeAtosendtheRTT.WhenAreceivestheRTT,itensuresthatitsTAVis notsetrefertotheTAVsettingsofAinFigure6-2.Ifitsensesthemediumtobefree, itrespondswithaCTTframe.Inthepresentexample,ifweassumethatAisinthe interferencerangeofCitcansenseC'stransmissionbutnotdecodeit,itwouldhaveset itsTAVwhenCtransmitsPTStoBtoadurationofEIFS,whichwouldhaveexpired bythetimeAreceivestheRTTframe. 6.2.3PrimaryTransmission Atimerattheprimarytransmitterissettoexpireinsynchronouswiththe completionofthesecondaryhandshaking.NotethatitsTAVtimerwillnotbesetduring secondaryhandshakingrefertotheTAVsettingsofnodeCinFigure6-2.Wenote thatthisdiersfromthetypicalNAVimplementationofIEEE802.11protocol.When thetimerexpires,ittransmitsitsDATAframetotheprimaryreceiver.Intheexample networkofFigure6-1a,uponcompletionofthesecondaryhandshaking,Cstartsthe primarytransmissiontoD,asshowninFigure6-1g.TheframeformatoftheDATA framerefertoFigure6-3isthesameasintheIEEE802.11protocol[52,Section7.2.2]. 6.2.4SecondaryTransmission Thesecondarytransmitterstartsitsoverlappedtransmission 0 secondsafterthe commencementoftheprimarytransmissionrefertoFigure6-2.This overlappeddelay 0 isdesignedtoallowthesecondaryreceivertoacquirethetimingandphaseoftheprimary transmission,whichgreatlysimpliestheinterferencecancellationICmechanismat thePHY.Itdoesnotensureperfectsymbolorphasesynchronizationoftheprimaryand secondarytransmissionsatthesecondaryreceiver.Theformatoftheoverlappeddata ODATAframeisthesameastheDATAframe.Thesecondaryreceivercancelsthe interferenceandrecoverstheoverlappeddata.ThisphaseisillustratedinFigure6-1h, whichdepictsnodeBreceivinganODATAframewhilecancelingouttheinterference causedbyC'stransmissionprimarytransmission.Notethatthesecondarytransmission isallowedtoterminate 1 secondsaftertheendoftheprimarytransmission. 88

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6.2.5DataAcknowledgments IftheDATAandODATAframesaresuccessfullyreceived,theprimaryand secondarytransmittersacknowledgetheirsuccessfulreceptionasshowninFigure6-1i andFigure6-1j,respectively.TheformatoftheACKframesarethesameasinthe IEEE802.11protocol[52,Section7.2.1.3]. Howthenodesthencontendforchannelaccessisanimportantdesignconsideration thatsignicantlyaectstheperformanceofOCSMA.Considerrsttheprimaryand secondaryreceivers.IftheDATAandODATApacketsweresuccessful,bothofthese nodeshavepacketstotransmitandwillcontendforchannelaccess.Iftheprimaryreceiver sendsanRTSbeforethesecondaryreceiver,thenitwillbecometheprimarytransmitter forthatpacket,andthesecondaryreceiverfromthepreviousoverlappedtransmission willhavetheappropriatepackettoactasasecondarytransmitterforanoverlapped transmission.However,ifthesecondaryreceivergainsaccesstothechannelbeforethe primaryreceiver,thenanoverlappedtransmissionwilldependontheavailabilityof appropriatepacketsfurtherbackinthenetwork.Thebehavioroftheprimaryreceiveris similartothatofasuccessfulreceiverinIEEE802.11protocol[52,Section9.2.4,Section 9.2.5.1].Togivethesecondaryreceiverahighprobabilityofchoosingtodeferlongerthan theprimaryreceiver,itwillchoosearandombackovalueinawindowthatistwicethe sizeofthecurrentcontentionwindow,onceitsensesthechanneltobeidle. Next,considerthereceptionofacknowledgmentsattheprimaryandsecondary transmitters.UponreceptionofACK,theprimarytransmitterresetsitcontentionwindow parameterasintheIEEE802.11[52,Section9.2.5.5]protocol.Ifithasapacketto transmit,thechannelaccessmechanismisthesameasthemechanismintheIEEE802.11 protocol.However,thesecondarytransmitterdoesnotresetitscontentionwindow.This ensuresthat,withhighprobability,thesecondarytransmitterdoesnotcontendwith theprimarytransmitterforchannelaccess.Thecontentionwindowparameterofthe secondarytransmitterisresetwhenitreceivesanACKforanyDATAframeandnotan 89

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ODATAframethatittransmitslater.Weobservedthat,innetworkswithlinearows, thisdesignleadstoagreaterprobabilityofoverlappedtransmission. 6.3DesignConsiderations Inthissection,wediscussvariousdesignissuesconcerningtheOCSMAprotocol.In particular,wecompareandcontrasttheOCSMAprotocolwiththeIEEE802.11MAC protocol,onwhichitisbased. 6.3.1Cross-LayerInteraction ThedesignofOCSMAprotocolinvolvesagreaterlevelofcross-layerinteraction comparedtotheIEEE802.11protocol.Forinstance,whenanodereceivesanRTT, theMACneedstointeractwiththehigherlayerstodetermineifapacketofsuitable lengthcanbesenttothesecondaryreceiver.Itisalsopossiblethatapacketmight needfragmentationsuchthatthetransmissionofoverlappeddataisterminatedwithin 1 secondsoftheterminationoftheprimarytransmissionrefertothetimelineofthe protocolinFigure6-2.Similarly,whenthesecondaryreceiverreceivesaCTT,theMAC needstoindicatetothePHYlayerthatinterferencemitigationwillbeneededtorecover theoverlappedtransmission.Cross-layerinteractionisalsoneededatthesecondary transmitterwhenidentifyingpotentialpartnersforoverlappedtransmission. 6.3.2ComplexityoftheProtocol TheOCSMAprotocolinvolvesgreatercomputationalcomplexitythantheIEEE 802.11protocol.ThisisaresultofemployingMUDatthePHYandalsoincreased bookkeepingattheMAClevel.However,theincreaseinthecomputationalcomplexity attheMAClevelisminimal,andwebelievethatthedesignoftheprotocolcangreatly reducethecomputationalcomplexityatthePHYlayerincomparisontootherMUD approaches.WealsonotethattheprotocoloverheadofOCSMAismorethanthatof IEEE802.11becauseofanincreaseinthenumberofcontrolframes.However,asthe resultsinSection6.4indicate,thisoverheadbecomesnegligibleasthesizeoftheDATA frameincreases. 90

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6.3.3ReducedOverhead Thedesignoftheprotocolandtheframeformatsaretoalargeextentcompatible withtheexisting802.11frameformats.HencetheycanbeintegratedwithexistingIEEE 802.11-basedwirelessnetworkswithminimalchanges.TheoverheadoftheOCSMA protocolcanbereducedconsiderablyifnosuchconformityisrequired.Forinstancethe CTTpacketcanbeeliminatedwithoutasignicantpenaltyonthethroughput.The eliminationofCTTpacketresultsinreducedprotocoloverheadbutincreasesthepower consumptionatthePHYofthesecondaryreceiversinceinterferencecancelationhas tobeturnedonmoreoften.Inaddition,theDAandPAeldsofthePTSandRTT frames,respectively,canbeeliminatedwithoutanysignicantperformancepenalty refertoFigure6-3.WecallthisprotocoltheOCSMAprotocolwithreducedoverhead OCSMA RO.Theperformanceofthisreduced-overheadprotocolissimulatedinthe nextsection.ThePTScanalsobeeliminatedbyincludingtheinformationofthePTS frameintheRTS.Inthiscase,theRTSformatwillbemuchdierentfromtheformatof RTSoftheIEEE802.11protocol.However,wedidnotobserveanysignicantchangein thethroughputwiththismodication.Finally,theframeformatsofalltheframescan bemodiedtoreducetheoverhead,althoughwedidnotevaluatesuchapproachesinthis work. 6.4SimulationResults WeevaluatedtheperformanceoftheOCSMAprotocolunderdierentnetwork topologiesandtracconditionsusingNetworkSimulatorns2[69].Sinceweevaluate onlytheperformanceoftheMACprotocol,weassumeperfectinterferencecancellationat thePHYandthattheODATApacketcanberecoveredwheneverthereisanoverlapped transmissionwiththecorrespondingprimarytransmissionbeingtheonlysourceof interference.Thesimulationsarebasedonthe1MbpsDSSSmodecf.[52,Section 15]ofIEEE802.11;exceptwherespecied,theparametersaregiveninTable6-1. Theoverlappeddelay 0 of240 scorrespondstoabout30bytesofdata,whichis 91

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slightlylargerthanthesumofthelengthsofPLCPheaderandPLCPpreamble bytes[52,Section15.2.2].Forothersystemparameters,thedefaultvaluesofthe802.11 implementationinns2areused.Henceforth,werefertoaMACservicedataunitMSDU asaframe,andatransportlayerserviceunitTSDUasapacket. Table6-1.NS2simulationsetup. Parameter Defaultvalue Datarate 1Mbps Simulationduration 4000s Warmuptime 400s Routingprotocol AODV Channelmodel Tworaypropagation RTSThreshold 150Bytes Transmissionradius 250m Carrier-sensingradiusInterferencerange 550m IFQlength 100 OverlappedDelay 0 240 s 1 240 s STARetryLimitsShort,Long ,4 Figure6-4.Ten-nodelinearnetwork. WerstevaluatetheOCSMAprotocolinaxedten-nodelinearnetworkasshown inFigure7-1,withthesourceandthedestinationlocatedateitherendofthenetwork. Thenodesareplacedatregularintervalsof200m.Thistranslatestotheadjacentnodes beinginthecommunicationrangeofeachother,andnodestwohopsapartbeinginthe interferencerangeofeachother.Thetransmissionpowerofthesecondarytransmission 92

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isthesameasthatoftheprimarytransmission.ThetracmodelisbasedonFTP simulatedapplication",inwhichtheTCPqueueisneverempty.TCPisusedfor owcontrol,withamaximumwindowsizeof32.Theend-to-endthroughputsofthe networkundertheOCSMA,OCSMA RO,andIEEE802.11MACprotocolsareshown inFigure6-5. Figure6-5.Throughputcomparisoninaten-nodelinearnetworkwithTCPtrac. WeobservethatthethroughputoftheIEEE802.11MACprotocolincreasesuntil thedatapacketlengthreaches1000bytes,beyondwhichitstartsdecreasing.However, thethroughputofbothOCSMAandOCSMA ROincreaseuntilthepacketlengthreaches 1400bytes,beyondwhichthethroughputdecreases.TheOCSMAprotocolprovides throughputgainsof4%to39%overtherangeofpacketlengthsshowninFigure6-5.The maximumthroughputunderOCSMAisachievedforapacketlengthof1400bytes,at whichpointitprovides21%throughputgainoverIEEE802.11.Similarly,thereduced overheadversionofOCSMAOCSMA ROprovidesthroughputgainsof11-40%overthe packetlengthssimulated,andprovidesathroughputgainof28%overIEEE802.11fora packetlengthof1400bytes. 93

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TheMAC-leveleventsacrossthenetworkforallthreeprotocolsaretabulated inTable6-2andTable6-3fordatapacketlengthsof400and1800bytes,respectively.The averagerateofRTSframesreceivedforOCSMAandOCSMA ROishigherthantherate ofRTSframesreceivedinthecaseofIEEE802.11.Weobservethattheproportionofthe averagerateofreceptionofPTStothatofRTSisveryhigh,indicatingthatthereisa veryhighprobabilityofanoverlappedtransmissionfromtheperspectiveoftheprimary transmitter.However,theratioofthereceptionofCTTtothatofRTTissignicantly low,whichindicatesthattheactualnumberofODATAtransmissionsissignicantlyless thanthepotentialnumberofoverlappedtransmissions.Thismightbeduetothelackof suitablepacketsatthesecondarytransmitterorthemediumbeingperceivedasbusyby thesecondarytransmitter.ToinvestigatethereasonforthelowCTTtoRTTratio,we createdaNoPackettoTransmitNPTframe.ThesecondaryreceivertransmitsanNPT inresponsetoanRTTifitndsthemediumtobefreebutdoesn'thaveasuitableframe forthesecondaryreceiver.TheNPTframewasintroducedonlyforsimulationpurposes, andisnotapartoftheOCSMAprotocol.Wedidnotobserveanyadverseeectonthe systemthroughputfromtheinclusionoftheNPTframe. Table6-2.ComparisonofeventsattheMAClevelinaten-nodelinearnetworkwith packetsize400B. Receivedframe IEEE802.11 OCSMA OCSMA RO type Events/s Events/s Events/s RTS 161.8 193.6 201.0 CTS 136.2 127.9 140.0 PTS 110.8 105.8 RTT 79.1 78.9 CTT 22.8 NPT 41.8 DATA 134.0 117.0 127 ODATA 22.8 22.7 Collision 9.3 15.5 10.1 94

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Table6-3.ComparisonofeventsattheMAClevelinaten-nodelinearnetworkwith packetsize1800B. Receivedframe IEEE802.11 OCSMA OCSMA RO type Events/s Events/s Events/s RTS 36.0 59.5 61.0 CTS 32.4 39.5 41.5 PTS 34.4 36.0 RTT 26.0 28.0 CTT 6.7 NPT 16.4 DATA 32.3 39.0 41 ODATA 6.7 7.1 Collision 0.7 3.2 3.2 AscanbeseeninTable6-2andTable6-3,theratioofCTTtoNPTisabout54%, and41%forpacketlengthsof400bytesand1800bytes,respectively.Thisindicatesthat thefullpotentialoftheoverlappedtransmissionsisnotrealizedduetolackofsuitable packets.TheratioofoverlappeddataODATApacketsreceivedtothatofdataDATA packetsis19.5%and17.9%forOCSMAandOCSMA RO,respectively,forapacket sizeof400bytes.Theratiois17.9%and17.3%,respectively,whenthepacketsizeis increasedto1800bytes.Itisalsoworthnotingthattheaveragenumberofcollisionsat theMAClevelinthecaseofboththeOCSMAprotocolsishigherthanthatoftheIEEE 802.11protocol.Weobservedthatthesecollisionsaremainlyduetothecontrolframes duringthesecondaryhandshakingRTTandCTTcausingcollisionsinthevicinityofthe secondarytransmitter.However,thesecollisionsareosetbytheincreaseinthroughput duetooverlappedtransmissions.TheinteractionbetweenTCPandOCSMAisthoroughly investigatedinChapter7. Thethroughputoftheten-nodelinearnetworkofFigure7-1withconstantbitrate CBRtracisshowninFigure6-6forseveralpacketarrivalrates.Thepacketsize is1000bytes.Weobservethatthethroughputofallthreeprotocolsisthesameuntil thepacketarrivalratereaches20packets/s.Asthepacketrateincreases,thereisa dramaticfallintherateofpacketsdeliveredbyIEEE802.11.However,underOCSMA 95

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Figure6-6.Throughputcomparisoninaten-nodelinearnetworkwithCBRtrac. andOCSMA RO,thedeclineinthethroughputismoregradual,andthethroughputgains providedbyOCSMAprotocolsoverIEEE802.11aresignicant. Figure6-7.ThroughputcomparisoninlinearnetworkwithmultipleCBRows. 96

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Next,weconsidertheeectofmultiple-owsinalinearnetwork.Threesourcesand threedestinationsareplacedateitherendofaten-nodelinearnetwork,andthetrac typeisCBR.ThethroughputgainsofOCSMAandOCSMA ROover802.11withCBR tracandmultiplesowsinalinearnetworkareshowninFigure6-7.Thepacketarrival rateindicatesthecommonrateatwhichpacketsarriveateachofthesources.Itcanbe observedthateveninthepresenceofmultipleows,OCSMAandOCSMA ROprovide signicantgainsoverIEEE802.11inaten-nodelinearnetwork. Figure6-8.Eectofvaryingthenumberofnodesinalinearnetworkonthethroughput gainofOCSMAandOCSMA RO. Next,wevarythenumberofnodesinthelinearnetwork.FTPsimulatedapplication" tracwithTCPcongestioncontrolwassimulated.TheTCPpacketsizeis1400bytes, andthecongestionwindowsizeis32.Theend-to-endthroughputgainsoftheOCSMA andOCSMA ROprotocolsoverIEEE802.11areshowninFigure6-8asafunctionof thenumberofnodesinthelinearnetwork.ItcanbeseenthatOCSMAandOCSMA RO providemaximumthroughputgainsof72%and77%,respectively,whenthenetwork consistsofsixnodes.Thegaindecreaseswithanincreaseinthenumberofnodesinthe 97

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network.Inathirty-nodenetwork,thethroughputgainsofOCSMAandOCSMA RO are16%and10%,respectively.ForaxedTCPcongestionwindowsize,underOCSMA andOCSMA RO,weobservedthat,asthesizeofthelinearnetworkincreases,theratio ofODATAtoDATAframesdecreasesandthecollisionrateincreases.Whenthesizeof thenetworkislarge,wenoticedthatthefullpotentialofoverlappedtransmissionsisnot realizedduetothelackofavailabilityofpacketsatsecondarytransmitters.Increasing theCWsizeincreasestheprobabilityofoverlappedtransmission,butdoesn'tcompletely eliminatethe packetstarvation issue.InChapter7,theinteractionbetweenOCSMAand TCPinadhocnetworksisanalyzedandtheOCSMAprotocolismodiedtoimprovethe performanceofTCPows. Figure6-9.Binary-treenetwork. WealsoevaluatedthethroughputgainsofOCSMAandOCSMA ROoverIEEE 802.11inabinary-treenetworkshowninFigure6-9.Thelocationofthenodesaregiven inparanthesis.Inthistopology,eachnodeofthetreenetworkhasexactlytwochildren, andtherootlocatedat,580transmitsindependentmessagestoeachoftheleaf nodes.ThetractypeisCBR,andthepacketsmeantforeachoftheleafnodesarriveat 98

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thesourcewithsamerate.TherestofthesimulationparametersaregiveninTable6-1. TheperformancegainsofOCSMAandOCSMA ROinabinarytreenetworkwithadepth offourisshowninFigure6-10.Itcanbeobservedthatforpacketarrivalratesgreater than3,OCSMAandOCSMA ROprovideatleast35%throughputgainovertheIEEE 802.11protocol. Figure6-10.ThroughputgainofOCSMAandOCSMA ROinatreenetwork. Wenextconsiderarandomtopologywith50nodesdistributedina1500m 1500m square.Thisscenariocorrespondstoanaveragenodedensityoffournodesinacircleof radiusequaltothetransmissionrangeofanodesetto250m.Themobilitymodelchosen istherandomwaypointmodel,whichisthedefaultmodelinns2.Thenodesmovewith aspeedthatisuniformlydistributedintheinterval[0 ; max speed],whereweconsider dierentvaluesofmax speed.TwentyTCPconnectionswererandomlygeneratedwith packetsize1400bytes,andtherestofthesystemparametersaregiveninTable6-1.The throughputgainsofOCSMAandOCSMA ROoverIEEE802.11areaveragedover500 instantiationsoftherandomnetwork.TheperformancegainofOCSMAprotocolsover 99

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Figure6-11.Throughputgaininarandomnetworkwithmobility. IEEE802.11asafunctionofthemaximumspeedofthenodesinthenetworkisshown inFigure6-11.WeobservethatthethroughputgainsoftheOCSMAprotocolsdecreaseas themobilityinthenetworkincreases.Whenthereisnomobilityinthenetwork,OCSMA providesanaveragethroughputgainofabout13%withastandarddeviationof11%.The highstandarddeviationindicatesthatincertainscenarios,OCSMAprovidessignicant gainsoverIEEE802.11.Similarly,OCSMA ROprovidesanaveragethroughputgain of17%withastandarddeviationof12%.Underhighmobilitymax speed=20m/s, OCSMAandOCSMA ROprovideaveragethroughputgainsof5%standarddeviation= 5%and7%standarddeviation=5%,respectively.Theresultsindicatethat,ingeneral, thethroughputgainfromoverlappedtransmissionsissmallwhenthereishighmobilityin thenetwork.However,incertainscenarios,OCSMAprovidessignicantgainoverIEEE 802.11. 100

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6.5Summary WedevelopedtheOCSMAprotocolbasedontheIEEE802.11MACprotocolto supportoverlappedtransmissionsinawirelessnetwork.Networksimulationsemploying OCSMAprotocolanditsreducedoverheadvariant,OCSMA RO,showthatthe end-to-endthroughputcanbeimprovedbyasmuchas77%overtheIEEE802.11protocol inalinearnetworkwithTCPtrac.UnderCBRtrac,OCSMAandOCSMA ROare morerobusttothetracloadandmultipleowsthantheIEEE802.11protocol.Ina randomnetworkwith50nodesand20TCPconnections,theOCSMAandOCSMA RO protocolsprovideanaveragethroughputgainof13%and17%,respectively,whenthereis nomobilityinthenetwork.ThethroughputgainoftheOCSMAprotocolsdecreasewith anincreaseinthemobilityinthenetwork.Althoughtheaveragegainprovidedbythe OCSMAprotocolsinhighmobilityconditionsisonly5%to7%,thethroughputgainin certainscenarioscanbemuchhigher. 101

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CHAPTER7 IMPACTOFOVERLAPPEDTRANSMISSIONONTHEPERFORMANCEOFTCPIN ADHOCNETWORKS 7.1Introduction Inthepreviouschapter,wedevelopedtheOCSMAprotocolandcomparedits performancetotheIEEE802.11MACprotocolinavarietyofnetworkscenariosusing ns2.Inthischapter,theperformanceofOCSMAisfurtherinvestigatedwithanemphasis onitsimpactonnetworksthatemployTransmissionControlProtocolTCP.Inwireless networks,congestioncontrolmechanismsareemployedinconjunctionwithMACprotocols toprovidereliableandecientend-to-endservice. TheinteractionsbetweentheTCPandMACprotocols,likeIEEE802.11,inwireless adhocnetworkshavebeenwellinvestigatedbytheresearchcommunitysee[70{76]and thereferencestherein.Inwirelessnetworks,TCPsuersfrompoorbandwidthutilization andnetworkunfairness.Thisisprimarilyduetotheuniquecharacteristicsofthewireless environmentsuchashalf-duplexlinks,channelnoise,andmobility. ToalleviatetheissuesassociatedwithTCPinwirelessnetworks,severalschemeshave beenproposedcf.[76{78].Theseschemesaimtoachievebettercross-layerinteraction betweentheMACandtransportlayersbyeithermodifyingtheMAClevelbehavioror thecongestioncontrolmechanismatthetransportlayer.Forasurveyoftheworkon improvingTCPperformanceinwirelessnetworks,referto[76]. Inthepresentchapter,theinteractionbetweenTCPandOCSMAisinvestigatedin multihopnetworkswithlinearows.Throughnetworksimulations,westudytheimpactof overlappedtransmissiononthebehaviorofTCPows.Thefocusisonidentifyingfactors attheMACandtransportlayersthatimpacttheperformanceofthenetwork.The resultsshowthatwhenTCPisusedforcongestioncontrol,OCSMAprovidessignicant performanceadvantagesovertheIEEE802.11MACprotocolinseveralscenariosof interest. 102

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Therestofthechapterisorganizedasfollows.TheinteractionbetweenTCPand OCSMAinavarietyofnetworkscenariosisinvestigatedinSection7.2.InSection7.3,we modifytheOCSMAprotocoltoincreasethethroughputofTCPowsinlinearnetworks. Throughnetworksimulations,weshowthatthemodiedOCSMAprotocolimprovesthe performanceofbothTCPandUDPtracinlinearnetworks.Thechapterisconcluded inSection7.4. 7.2InteractionbetweenTCPandOCSMA Inthissection,thecross-layerinteractionbetweenTCPandOCSMAisinvestigated. Wepresentresultsfromns2simulationsforavarietyofscenariosandstudytheinteraction betweenthetwolayers.WecompareandcontrasttheOCSMAprotocolwiththeIEEE 802.11MACprotocol.Inthefollowingsections,werefertoaMACservicedataunit MSDUasaframe,andatransportlayerserviceunitTSDUasapacket.AMAClevel acknowledgmentisdenotedbyacapitalizedACK,whileatransportlayeracknowledgment isrepresentedbyanitalicized ack Werstconsideraten-nodelinearnetwork,asdepictedinFigure7-1.Node1is thesource,andnode10isthedestination.Thenodesareplacedatregularintervalsof 200m.Thecommunicationradiusis250m,andthesensingrangeis550m.Inthelinear networkofFigure7-1,thetransmissionrangesofnodes3and9aredenotedbysolid circles,andtheirrespectivesensingrangesaredenotedbydashedcircles.Thedefault valuesofsimulationparametersaresummarizedinTable7-1. 103

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Figure7-1.Ten-nodelinearnetworkunderOCSMA. Table7-1.SimulationsetupforevaluatingtheimpactofOCSMAonTCPperformance. Parameter Value Datarate 1Mbps CongestionControl TCPReno Simulationduration 2000s Warm-uptime 200s Routingprotocol AODV Channelmodel Tworaypropagation RTSThreshold 150Bytes Transmissionradius 250m Carrier-sensingradiusInterferencerange 550m IFQlength 100 OverlappedDelay 0 240 s STARetryLimitsShort,Long ,4 TCPpacketsize 1400Bytes Applicationtype FTPsimulatedapplication" 7.2.1ImpactofTCPCongestionWindowSize Inthissubsection,weevaluatedtheimpactoftheTCPcongestionwindowCWsize ontheend-to-endthroughputofthenetwork.Inns2,theCWparameterrepresentsthe receiveradvertisedwindowsize,anddenesthemaximumnumberofpacketstobesentat everyround-trip-time.TCPisdesignedtoadjusttheowbasedontheCWsizeandthe congestioninthenetwork.Inthefollowingsections,unlessotherwisestated,CWrefersto thereceiver'sadvertisedCW. 104

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Figure7-2.End-to-endthroughputcomparisoninaten-nodelinearnetworkwithTCP trac. Theend-to-endthroughputundertheOCSMA,OCSMA ROandIEEE802.11MAC protocolsintheten-nodelinearnetworkofFigure7-1asafunctionTCPCWsizeare showninFigure7-2.InthecaseofIEEE802.11,thethroughputofthenetworkincreases withanincreaseinCWsizeuntiltheCWsizeis4,beyondwhichitdecreases.This behaviorofTCPthroughputunderIEEE802.11hasbeenreportedintheliterature[78, 79],whereitwasnotedthattheoptimumperformanceisachievedwhentheCWsizeof TCPisafractionusually1/4ofthenumberofnodesinthelinearnetwork. However,thebehaviorofOCSMAprotocolsisquitedierentfromthatoftheIEEE 802.11protocol.TheTCPthroughputunderOCSMAandOCSMA ROincreaseswith anincreaseinCWsize,andthethroughputsaturatesforCWsizesgreaterthan14.This behaviorofOCSMAcanbebetterunderstoodbyanalyzingthelinkthroughput. ThelinkthroughputMAClevelunderOCSMAandIEEE802.11areshown inFigure7-3a.TheleftordinatescaleisforDATAframes,andtherightordinateis forODATAtransmission.NotethatunderOCSMA,bothDATAandODATAframes 105

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contributetothelinkthroughput.TheDATAandODATAlossrateforOCSMAand IEEE802.11areplottedinFigure7-3b. WeobservethatthelinkthroughputunderIEEE802.11mimicstheend-to-end throughputcurveofFigure7-2.NotethattherateatwhichDATAframesaredropped duetocollisionsincreasesastheCWsizeincreasesasshowninFigure7-3b.Inthecase ofOCSMA,boththeDATAandODATAreceptionrateincreaseswithanincreaseinthe CWsize,andsaturatesforCWsizesgreaterthan14.IncreasingtheCWsizeincreases thenumberofframesavailableforoverlappedtransmissioninthenetwork.Notethatthe DATAreceptionrateunderOCSMAislessthantheDATAreceptionrateunderIEEE 802.11.However,thecombinationofDATAandODATAframesinOCSMAprovidesa greaterend-to-endthroughputoverIEEE802.11.Althoughthecollisionrateinthethe caseofOCSMAisveryhigh,theabilitytoperformoverlappedtransmissionsosetsthese collisionstoprovidehighthroughputevenwhenCWsizeishigh. Table7-2.EventsattheMAClevelinaten-nodelinearnetworkunderOCSMAprotocol. Frame CW=1 CW=2 CW=4 CW=8 CW=16 type Events/s Events/s Events/s Events/s Events/s RTS 63.8 84.9 155.4 182.4 190.0 CTS 63.8 76.3 103.2 106.6 107.1 PTS 49.6 59.3 78.9 80.1 79.6 RTT 49.6 52.0 58.6 57.8 56.6 CTT 0 11.2 11.5 18.3 21.5 NPT 49.6 38.4 38.5 28.7 23.4 DATA 63.8 72.8 94.1 96.0 95.8 ODATA 0 11.2 11.5 18.3 21.5 COLL 0 3.4 7.8 8.7 8.8 WefurtherinvestigatethebehaviorofOCSMAbyanalyzingtheMAC-levelevents 1 acrossthenetwork.TheMAC-leveleventsunderOCSMAaretabulatedinTable7-2for 1 Inthisscenario,eventscorrespondtoeitherreceptionofaframeoracollision 106

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aLinkthroughputinaten-nodelinearnetwork bFrame-droprateinaten-nodelinearnetwork Figure7-3.MAC-levelperformancecomparisonofOCSMAandIEEE802.11inaten-node linearnetwork. severalvaluesofCWsize.WeseethattheaveragerateofRTSframesreceivedincreases astheCWsizeincreases.WealsonotethatthereceptionofRTTframesincreases indicatingthattheopportunitytoperformoverlappedtransmissionsasperceivedby thesecondaryreceiverincreases.However,theratioofthereceptionofCTTtothatof RTTissignicantlylowerthanone,whichindicatesthattheactualnumberofODATA transmissionsissignicantlylessthanthepotentialnumberofoverlappedtransmissions. 107

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TheNPTframewasintroducedinSection6.4duringthesimulationstoinvestigatethe reasonforthelowrateofoverlappedtransmissionsinthesystem.Itisnotapartofthe OCSMAprotocol,andwedidnotobserveanyadverseeectonthesystemthroughput duetoitsinclusion.InTable7-2,wenotethattheratioofNPTtoRTTisveryhigh indicatingthatalotofopportunitiesofoverlappedtransmissionsaremissedbecauseofa lackofsuitableframesforoverlappedtransmissionatthesecondarytransmitters.Wenote thatthenumberofoverlappedtransmissionsincreaseswithanincreaseintheCWsize; yet,thefullpotentialofoverlappedtransmissionsisnotrealized.Forinstance,foraCW sizeof16,theratioofCTT/NPT+CTTisonly48%.Thisismainlyduetothelackof interactionbetweenOCSMAandTCPasexplainedbelow. Figure7-4.Transmittercongestionwindowevolutioninaten-nodelinearnetwork. ConsiderthenetworkofFigure7-1andassumethatTCPisoperatingincongestion avoidancephaseandthequeueatnode1isempty.Whenthesourcereceivesan ack packetforaTCPpacketthatittransmittedtonode9,itpushesapacketmostofthe timetotheinterfacequeueattheMAClevel.TheMACofnode1transmitsthisDATA frame"tonode2,whichitforwardstonode3,andsoon.Whennode3forwardsthis 108

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frametonode4,thereisapossibilityofanoverlappedtransmissionbetweennodes1and 2.However,thisispossibleonlyifthetransportlayeratnode1receivesanew ack fora TCPpacketthatittransmittedearlier.WeobservedthatwhenthereceiverCWsizeis small,theprobabilityofthishappeningisverysmall,andtheopportunityforoverlapped transmissionsarewastedeverytimeaTCPpacketisforwardedalongthelinearnetwork duringthecongestionavoidancephase.WhentheCWsizeincreases,thecollisionsin thenetworkincrease,andthereisahighprobabilitythatanodeisinbackostate, whichindicatesthatitsqueueisnon-empty.Thisincreasestheprobabilityofoverlapped transmission.TheresultsinFigure7-4plottheevolutionofthesourcecontention window. 2 NotethatwhentheCWsizeislow,TCPisinthecongestionavoidancephase, whichimpliesthattheprobabilityoftransmittingonepacketuponreceptionofanACK isveryhigh.AstheCWsizeincreases,TCPexperiencesfaststartphasesquiteoften, 3 whichimpliesthattheTCPatnode1releasesmultiplepacketsquiteofteninresponseto an ack packet.Thisincreasestheprobabilityofoverlappedtransmissioninthesystem. However,thiscannotcompletelyeliminate packetstarvation inanoverlappedtransmission. TheobservationmaderegardingOCSMAapplytotheOCSMA ROprotocoltoo,theonly dierencebeingthatthereisnoCTTframeinOCSMA RO. 7.2.2ImpactofCollisionsonTCPThroughput Intheprevioussectioncf.Table7-2,weobservedthatthecollisionrateunder OCSMAprotocolsisveryhigh.Thisisduetoanincreaseinthenumberofcontrolframes inOCSMAcomparedtoIEEE802.11.Inthissection,weconsiderstrategiesthatnegate theimpactofthehighercollisionrateinOCSMAandincreasetheTCPthroughput. 2 Theactualnumberofpacketstransmittedbythesourceisminimumofthe transmitterandreceiverCWs. 3 TheTCPvariantTCP-Renoisusedforcongestioncontrol. 109

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Figure7-5.EectofshortandlongretrycountsonthroughputgainsofOCSMAand OCSMA ROinaten-nodelinearnetwork. First,weanalyzetheimpactoftheSTAShortRetryCountSSRC,andSTA LongRetryCountSLRClimits[52,Section9.2.5.3]onthethroughputofOCSMA andOCSMA RO.TheresultsinFigure7-5showthethroughputgainsofOCSMAand OCSMA ROoverIEEE802.11forvariousvaluesoftheSSRCandSLRClimits.TheTCP windowsizeis32andthepacketsizeis1400bytes.ThevaluesoftheSLRCandSSRC limitsusedareshowninparenthesis.WeobservethatthethroughputgainofOCSMA andOCSMA ROincreasemonotonicallywithanincreaseintheSSRCandSLRClimits. TheincreaseincollisionsinthecaseofOCSMAprotocolsareosetbytheincreasein theSSRCandSLRClimits.WeobservethatwhenSSRCandSLRCare20and10, respectively,thethroughputgainofOCSMAoverIEEE802.11is31%.Forthesevaluesof retrylimits,thereducedoverheadvariantOCSMA RO,providesathroughputgainof34% overIEEE802.11. Next,weconsiderthestrategyofsendingone ack permultiplereceivedpackets,i.e. delayedack .Thedestinationnodetransmitsone ack fortwoconsecutivepacketsreceived. Thischangesthegranularityatthetransmittingnode.Foreach ack thatthetransmitter 110

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receives,TCPsendsmultiplepacketstotheinterfacequeue.Weexpectthisstrategyto decreasethenumberofcollisionsinthesystemduetofewer ack sbeingtransmitted,and increasethenumberofoverlappedtransmissions. Table7-3.PerformancecomparisonofOCSMAandOCSMA DA. Frame OCSMA OCSMA DA OCSMA OCSMA DA Type CW=2 CW=2 CW=16 CW=16 TPUT 9.3 9.7 13.0 15.1 RTS 84.9 66.3 190.1 196.1 CTS 76.3 65.8 107.1 112.1 PTS 59.3 51.6 79.6 84.6 RTT 52.0 51.3 56.6 61.7 CTT 11.2 18.1 21.5 30.0 NPT 49.6 32.0 23.4 18.0 DATA 63.8 65.1 95.8 105.4 ODATA 11.2 18.1 21.5 30.0 COLL 3.4 0.0 8.8 5.4 Theend-to-endthroughputandtheMACleveleventsunderOCSMAandOCSMA withdelayedack OCSMA DAaretabulatedinTable7-3.WhentheCWsizeis2,the end-to-endthroughputTPUTunderOCSMAandOCSMA DAarethesame.However, thenumberofcollisionsinthecaseofOCSMA DAismuchlowerthaninthecaseof OCSMA.Notethatthenumberofoverlappedtransmissionsaregreaterinthecaseof OCSMA DA.WhentheCWsizeis16,OCSMA DAprovides16%throughputgainover OCSMA.Alsonotetheincreaseinoverlappedtransmissionsandreductionincollisionsin thecaseofOCSMA DA. 7.2.3FairnessIssuesandMediumContention Inthissubsection,weinvestigatedtheinter-owcontentionissueswhenTCPis usedinconjunctionwithOCSMA.Mediumcontentionisamajorsourceofunfairnessin multihopadhocnetworks.Dierentowsmayexperiencedierentcongestionissues,and theresourcesallocatedtothemmaybedierent.Starvationisanothermajorproblem whichresultsduetothegreedinessofTCPows.Inordertoevaluatetheseissuesinthe 111

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aNetworkwithparallelows bNetworkwithintersectingows Figure7-6.Networkswithmultipleows. contextofOCSMA,weconsiderthetwonetworktopologiesillustratedinFigure7-6a andFigure7-6b.Figure7-6ashowsanetworkwiththreeparallelowseachtraversing throughsixnodes.Theadjacentnodesinaowareplacedatadistanceof200m,andthe adjacentowsareseparatedbyadistanceof400m. TheresultsinFigure7-7plotthethroughputevolutionofeachofthethreeows undertheOCSMAandIEEE802.11MACprotocols.WechoseaTCPCWsizeof2for eachoftheows.TheTCPpacketsizeis1400bytes,andtheshortandlongretrylimits are20and10,respectively.WeobservedthataCWsizeof2gavethebestperformance underbothOCSMAandIEEE802.11.Weobservethatunder802.11,ows1and3 112

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Figure7-7.Throughputcomparisoninanetworkwithmultipleparallelows. havenon-zerothroughputatalltimes,whereasthethroughputofow2iszero.The nodesofow2experienceinterferencefromboththeows1and3,whichresultsinzero throughputforow2.Thisistheclassicstarvationproblemencounteredinmultihop networksthatarisesbecauseofthegreedinessofTCPows. However,underOCSMA,thethroughputofow2isnon-zero,butstilllowerthan thatofows1and3.Sinceow2experiencesinterferencefromnodesinow1and3,it isnotsurprisingthatthethroughputofow2islowerthanthatofows1and3.The non-zerothroughputofow2underOCSMAisprimarilyduetotheeectofincreased collisions,andtheabilitytoperformoverlappedtransmission.Sincethecollisionrate underOCSMAisveryhigh,nodesincludingthenodesinows1and3spendmoretime inbacko,whichprovidesagreaterchancefornodesinow2tocompeteandsucceedin accessingthechannel.Ontheotherhand,theincreaseincollisionsacrossalltheowsis osettoalargeextentbyanincreaseinspatialre-useduetooverlaptransmissions.For instance,inFigure7-7,notethethroughputsofows1and3underOCSMAaresimilar althoughlowertothecaseofIEEE802.11. 113

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WecomparethefairnessofIEEE802.11andOCSMAbyemployingJain'sfairness index[80].Jain'sfairnessindexisdenedas f x 1 ;x 2 ; ;x n = P n i =1 x i 2 n P n i = x 2 i ; {1 where x 1 ;x 2 ; ;x n aretheowthroughputsofeachofthe n ows,respectively.Using Jain'sfairnessindexcf.7{1,andevaluatingtheaveragethroughputofeachofthe threeowsoverasimulationdurationof1800scf.Table7-1,wehavewithIEEE802.11, f 802 : 11 x 1 ;x 2 ;x 3 =0 : 67 ; {2 andwithOCSMA f OCSMA x 1 ;x 2 ;x 3 =0 : 89 : {3 Thecloserthefairnessindexistounity,thegreaterthefairnessinthenetwork.The fairnessindexof0.67inthecaseofIEEE802.11isduetothechannelresourcesbeing equallydividedbetweentwoowsow1andow3,andthethirdowow2is completelydeprivedofthechannelresources.However,wenotethatinthecaseof OCSMA,ow2hasnon-zerothroughput,whichisreectedbyahighervalueoffairness index. Next,wesimulatethenetworkofFigure7-6b,andevaluatethethroughputofeach theowsunderOCSMAandIEEE802.11.TheTCPCWsizeis2thisprovidedthe bestperformanceforbothOCSMAandIEEE802.11.TCPpacketsizeis1400bytes, andtheretrylimitsare,10.Thethroughputevolutionofeachofthetwoowsunder OCSMAandIEEE802.11MACprotocolsaredepictedinFigure7-8.InthecaseofIEEE 802.11,weseethatatanypointoftime,oneoftheowscapturestheresources,whilethe otherowiscompletelydeprivedofthechannelresources.Thisexempliesthegreediness ofTCPows.However,inthecaseofOCSMA,wenotethatthechannelresourcesare moreevenlydistributedamongboththeows,andthethroughputoftheowsissimilar 114

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Figure7-8.Throughputcomparisoninanetworkwithmultiplelinearows. duringtheentireobservationinterval.WeobservedthesametrendevenwhentheCW sizeisincreased.ThisindicatesthatOCSMAintroducesacertainamountoffairnessin situationsinvolvinginter-owcontention. Toevaluateshort-termfairness,werstcomputedtheaveragethroughputofeach owoverconsecutivewindowsof10s.Jain'sfairnessindexwascomputedforeach10s window,andtheaveragefairnessoverallthewindowswascomputed.Thefairnessindices underIEEE802.11andOCSMAare f 802 : 11 =0 : 50 ; {4 and f OCSMA =0 : 99 ; {5 respectively.Afairnessindexof0.5underIEEE802.11indicatesthatoneoftheows iscompletelydeprivedofthechannelresources.However,underOCSMA,thefairness indexisveryclosetounity,indicatingafairallocationofthechannelresources.Next,we 115

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evaluatethelong-termfairnessbycalculatingtheaveragethroughputofeachoftheows overasimulationdurationof1800s.ThefairnessindicesunderIEEE802.11andOCSMA are f 802 : 11 =0 : 98 ; {6 and f OCSMA =0 : 99 ; {7 respectively.NotethatwhileIEEE802.11providesonlylong-termfairness,OCSMA providesbothlong-termandshort-termfairness. 7.3OCSMAwithLookAheadCapabilityOCSMA LA Intheprevioussections,weanalyzedtheimpactofOCSMAontheperformanceof TCPowsinwirelessnetworks.ThesimulationresultssuggestthatOCSMAprovides betterend-to-endthroughputandfairnessoverIEEE802.11protocol.Basedonnetwork simulations,weidentiedparametersthatimpacttheperformanceofthenetwork. However,thediscussionsofSection7.2suggestthatthefullpotentialofoverlapped transmissionsisnotrealized.Weattributedthisto packetstarvation ,andlackof interactionbetweenthetwolayers.Inthissection,wemodifytheOCSMAprotocolto addresstheissueof packetstarvation Motivatedbytheworkin[81],weintroducetheconceptofLookAhead.Uponthe completionofanoverlappedtransmission,boththeprimaryandsecondaryreceivers contendforthechannelaccess.TheOCSMAprotocolwasdesignedtoallowforthe secondaryreceivertobackoforagreaterdurationandallowfortheprimaryreceiver tohaveagreaterchanceforchannelaccesspleaserefertoSection6.2.5formore details.However,thisdesigndoesn'talwaysguaranteetheoccurrenceofanoverlapped transmission.Innetworkswithlinearows,theprobabilityofanoverlappedtransmission canbeincreasedbyensuringthattheprimaryreceiverofthecurrentoverlapped transmission always getsaccesstothechannelbeforethesecondaryreceiver.Thisis accomplishedwiththehelpoftheLookAheadfeature,asexplainedbelow. 116

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7.3.1OCSMA LAProtocolDescription Figure7-9.Ten-nodelinearnetworkunderOCSMA LA. SinceOCSMA LAisbasedonOCSMAprotocol,wehighlightonlythedierences betweenthetwoprotocols.WewillusetheexamplenetworkofFigure7-9todescribe thedesignofOCSMA LAprotocol.ForacompletedescriptionofOCSMAprotocol,refer toSection6.2.ThedierencesbetweenOCSMAandOCSMA LAareduringthe primary transmission and acknowledgment phases,asdescribedbelow. InthenetworkofFigure7-9,assumethatnode3'stransmissiontonode4isthe primarytransmission ,andnode1'stransmissiontonode2isthe secondarytransmission AfterthecompletionofthesecondaryhandshakingphaserefertoFigure6-1d,Figure6-1e, andFigure6-1f,node3commencesthetransmissionoftheDATAframetonode4. UponsuccessfulreceptionoftheDATAframe,node4acknowledgesitwithamodied ACK,theAKMAcKModiedframe.TheframeformatoftheAKMframeisshown inFigure7-10.TheAKMframe,inadditiontotheReceiverAddressRAeld,contains theadditionaleldsTA,NAandNFD.TheTransmitterAddressTAeldcontainsthe addressofthenodetransmittingtheAKMframe.TheNextAddressNAeldcontains theaddressofthenodeforwhichthepresentnodethenodetransmittingtheAKMhas aDATAframe,andtheNextFrameDurationNFDcontainsthedurationinformationof theDATAframe.Continuingwithourexample,uponsuccessfulreceptionoftheDATA frame,node4usesthecontentsoftherstavailableDATAframeinitsqueuetoll theelds,NAandNFD.Ifnode4doesnothaveaDATAframeinitsqueue,andifthe presentframeistobeforwardedonbyD,itgeneratestherequiredinfobeforesendingit tothehigherlayersasfollows. 117

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Figure7-10.FrameformatsoftheOCSMA LAprotocol. Whennode4receivestheDATAframe,beforeforwardingittothehigherlayers,the MAClayerusesinformationcontainedintheframetodeterminethenexthopreceiverof thisframe.WeassumethattheMAClayerhasaccesstotheroutingtables.TheMAC 118

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addressofthereceiveriscopiedintotheNAeldoftheAKMframe,whoseformatis showninFigure7-10. ContinuingwiththeexamplenetworkofFigure7-9,oncenode4receivestheDATA frame,andassumingthatthereisaframealreadyinthequeuefornode5,itappropriately setstheNAandNFDeldsandtransmitstheAKMframe.WhentheAKMframeis receivedbytheprimarytransmitter,node3,itresetsitsretrylimits,andperformsbacko justlikeinthecaseofthereceptionofanACKframe.Whenthenexthopreceiver, node5receivestheAKMframe,itwaitsforadurationequaltothetransmissionofan ACKframetoallowfornode2'stransmissionofACKtonode1,andtransmitsaCTS frameifthemediumisfree.Notethattheinformationnecessaryforupdatingtheelds RAandDurationoftheCTSframerefertoFigure7-10areavailablethroughtheTA andNFDeldsoftheAKMframerefertoFigure7-10.Whennode3receivesthe CTSframe,itensuresthatthisframeisinresponsetoeitheranRTSframeoranAKM frame.Ifthisistrue,itproceedswiththesecondaryhandshakingphaseoftheOCSMA protocolrefertoSection6.2. Sincethenexthopreceivernode5inthepresentexamplerequestsfortheDATA frameevenbeforethesecondaryandprimaryreceivershaveachancetocontendforthe channelaccess,thesecondaryreceiver,node3hasthesuitableframeforanoverlapped transmissionwhennode4transmitstheDATAframetonode5.Onceanoverlapped transmissionoccursinthelinearnetwork,withhighprobability,thecapabilitytoperform overlappedtransmissionisretaineduntiltheDATA/ODATAframesreachthedestination. Forinstance,intheexamplenetworkofFigure7-9,whennode4transmitsaDATAframe inresponsetotheCTSsentbynode5whichrespondstoanAKMframesentbynode4, node3hasasuitableframeforanoverlappedtransmission,andinthenexttransmission durationwhennode5transmitstheDATAframeinresponsetotheCTSsentbynode6, node4wouldhaveasuitableframetheODATAframethatitreceivedfromnode3for anoverlappedtransmission,andsoon.Theprobabilityofoverlappedtransmissionishigh 119

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onlywhenthecollisionsinthenetworkarelow.Whenthecollisionrateincreases,there isahighprobabilitythattheprimarydatatransmissionmightnotbesuccessful,which aectstheperformancegainoftheLookAheadvariant. Figure7-11.ThroughputcomparisonofOCSMA,OCSMA LAandIEEE802.11ina ten-nodelinearnetwork. 7.3.2SimulationResults Inthissubsection,theperformanceofOCSMA LAisevaluatedusingns2,and comparedtothatofOCSMAandIEEE802.11.Therstscenarioweconsideristhe ten-nodelinearnetworkofFigure7-1.Theparametersusedforthesimulationare tabulatedinTable7-1.Weemploythedelayedack versionofTCPRenodescribed inSection7.2.2.TheresultsinFigure7-11comparetheend-to-endthroughputofthe OCSMA,OCSMA LA,andIEEE802.11protocolsasafunctionoftheTCPCWsizealso seeFigure7-2.WenotethatthethroughputofthenetworkunderIEEE802.11increases untiltheCWsizeequals5,beyondwhichitdecreases.ThethroughputsunderOCSMA andOCSMA LAincreasewithanincreaseinCWsize,andthethroughputssaturatefor 120

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CWsizesgreaterthan14.ForCWsizegreaterthan20,wenotethatOCSMAprovidesa throughputgainof30%overIEEE802.11,whileOCSMA LAprovidesathroughputgain of39%overIEEE802.11. Table7-4.MAC-leveleventsinaten-nodelinearnetworkunderOCSMA LA. Frame OCSMA LA OCSMA LA OCSMA LA OCSMA LA OCSMA LA Type CW=2 CW=4 CW=8 CW=16 CW=32 TPUT 11.54 13.7 15.1 15.7 15.71 RTS 19.0 55.5 103.8 118.6 119.6 CTS 71.9 97.6 115.3 115.7 116.2 PTS 58.2 80.0 88.8 74.3 74.6 RTT 57.2 73.5 76.4 74.0 74.9 CTT 38.0 31.8 30.7 36 37.2 NPT 15.7 31.0 32.5 23.0 20.0 DATA 65.9 91.1 103.5 103.3 104.2 ODATA 38.0 34.0 30.7 36.0 37.2 COLL 0.0 6.6 12.4 14.4 15.4 TheMAC-leveleventsunderOCSMAandOCSMA LAaretabulatedinTable7-4for threedierentvaluesofCWsize.NotethatthecongestioncontrolalgorithmisTCPwith delayedack .NotethatunderOCSMA LA,thenumberofCTSframesreceivedcanbe greaterthanthenumberofRTSframesreceived.ACTSistransmittedeitherinresponse toanRTSoranAKM.WenotethatwhenCWsizeis2,theratioofCTT/CTT+NPT is71%,andDATAlossduetocollisionsiszero.AstheCWsizeincreases,theend-to-end throughputunderOCSMA LAincreases;however,thenumberofoverlappedtransmissions ratioofCTTtoCTT+NPTdecreasesuntilaCWsizeof8,andthenincreases.This behaviorisincontrasttothebehaviorofOCSMA.WenotedthatwhentheCWsize increases,theincreaseinthenumberofpacketsatthenodesasevidencedbytheincrease inthenumberofRTSframesdecreasestheeectivenessoftheLookAheadcapability ofOCSMA LA,asothertransmissionsinthenetworkmaycollidewiththeprimary transmissioninitiatedbyanAKMframe.However,beyondacertainCWsize,theincrease 121

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Figure7-12.ThroughputcomparisonofOCSMA LAandIEEE802.11inaten-nodelinear networkwithCBRtraic. inthecollisionrateinthenetworkcausesmostofthenodestobeinbackostate,which ensuresthattherearemorepacketsavailableforoverlappedtransmission. TheOCSMA LAprotocolisdesignedtoaddresstheissueofpacketstarvationin TCPows.However,weexpecttheLookAheadfeatureofOCSMA LAtobenetUDP tracalso.WeevaluatetheperformanceofOCSMA LAinaten-nodelinearnetworkwith CBRtrac.TheresultsinFigure7-12comparetheend-to-endthroughputofaten-node linearnetworkunderOCSMA LAandIEEE802.11withCBRtracasfunctionofpacket arrivalrateatthesource,node1alsoseeFigure6-7.Thepacketsizeis1400bytes,and theshortandlongretrylimitsare20and10,respectively.WenotethatOCSMA LA hasahigherthroughputthanIEEE802.11,andwhenthepacketarrivalrateincreases beyond22packets/s,thedegradationinthethroughputismoregradualcomparedto IEEE802.11.Forpacketarrivalratesgreaterthan22packets/s,OCSMA LAprovidesat least98%gainoverIEEE802.11protocol. 122

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7.4Summary Inthischapter,weinvestigatedtheimpactofoverlappedtransmissionsonthe throughputofTCPinmultihopnetworkswithlinearows.Throughnetworksimulations, weanalyzedtheinteractionsbetweenOCSMAandTCPprotocols.Weidentiedsome ofthekeyparametersattheMACandtransportlayersthatimpacttheperformanceof thesystem.Bymodifyingtheseparameters,weshowedthatOCSMAcanimprovethe performanceofTCPowsinavarietyofnetworkscenariosandismoreecientthan IEEE802.11inaddressingfairnessandmediumcontentionissuesassociatedwithTCP ows.Later,wemodiedtheOCSMAprotocoltoaddresstheissueofpacketstarvation inTCPows.WeevaluatedtheperformanceoftheresultantOCSMA LAprotocolin linearnetworks.Throughnetworksimulations,wedemonstratedthatOCSMA LAcan signicantlyimprovethethroughputofbothTCPandUDPtracinwirelessadhoc networks. 123

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CHAPTER8 CONCLUSIONANDDIRECTIONSFORFUTUREWORK 8.1Conclusion Inthiswork,westudiedtheuseofoverlappedtransmissionstoimprovethespatial re-useandthroughputinwirelessnetworks.InCDMA-basedcellularnetworks,the basestationcanexploitthespatialdiversityalongwithcooperativebroadcasting techniquestoscheduleadditionaltransmissionsinthesystem.Theresultsindicate thatsuchoverlappedtransmissionscanleadtosignicantgaininusercapacityovera conventionalCDMAsystem.Wealsoevaluatedtheusercapacityofacellularnetwork employingDPCasabroadcastingtechniquewhentheuserpopulationislarge,and comparedittothatofasystememployingTDMA.Theresultsindicatethatunderlow spectral-eciencyrequirement,thegaininusercapacitybyemployingDPCoverTDMA isverymodest,atmost12%forthesystemparametersthatweconsidered.Thisisnot verysurprisingconsideringthefactthatrecentresearchinthisareahasshownthatin asingle-inputsingle-outSISOdegradedGaussianbroadcastchannel,DPCprovides signicantgainsoverTDMonlywhenthereislimitedmulti-userdiversityandthe spectraleciencyrequirementoftheusersisveryhigh[13,47,48].Next,weevaluated theperformanceofoptimalandsub-optimalforward-linkchannel-sharingschemes.We observedthatunderhighspectral-ecienyregime,thereisasignicantperformancegain inemployingcooperativebroadcastingoverconventionalchannel-sharingschemes,and thatcomputationallysimplerschemesliketwo-andthree-levelbroadcastingtechniques provideperformanceclosetotheoptimalscheme. Inwirelessadhocnetworks,overlappedtransmissionshavethepotentialto signicantlyimprovethespatialre-useandthethroughputofthenetwork.Wehave analyzedsomeofthelimitsonperformingoverlappedtransmissionsinadhocnetworks. WedevelopedtheOCSMAMACprotocol,thatexploitstheknowledgeoftheinterfering signalsalongwithMUD/ICcapabilitiesofthePHYtoscheduleoverlappedtransmissions 124

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inthenetwork.Networksimulationsindicatedthatsystemswithlinearowsshow asignicantthroughputimprovementwithOCSMAoverconventionalIEEE802.11 protocol.Innetworkswithrandomtopologyandmobility,OCSMAstillprovides considerablethroughputgainoverconventionalMACprotocolslikeIEEE802.11.Wealso investigatedtheinteractionbetweenOCSMAandTCP,andthroughnetworksimulations wedemonstratedthesuperiorityofOCSMAoverconventionalMACprotocolslikeIEEE 802.11inaddressingthefairnessandmediumcontentionissuesassociatedwithTCPin wirelessadhocnetworks.WemodiedtheOCSMAprotocoltoincreasetheprobabilityof overlappedtransmissionunderTCPows.Throughnetworksimulations,wedemonstrated thattheresultantOCSMA LAprotocolimprovestheperformanceofbothTCPandUDP owsinwirelessadhocnetworks. 8.2DirectionsforFutureWork ThedevelopmentandperformanceevaluationoftheOCSMAMACprotocolwere carriedoutassumingthatthephysicallayercanperformperfectinterferencecancellation. Clearly,thisisnotthecaseinreality.Theperformanceofoverlappedtransmissionat thephysicallayercanbeevaluatedbymodelingthesystemoffournodesinvolvedinthe transmissionasaninterferencechannel.Sincetheprimaryreceiverisnoteectedbythe secondarytransmitter,wecanfurtherreducethesystemtoa`Z'-intererencechannel[82]. Sincethesecondaryreceiverisawareoftheinterferenceduetoprimarytransmission, itwouldbereasonabletoassumethatthesecondarytransmitterhaspartialinformation regardingtheinterference.Insuchascenario,itwouldbeinterestingtolookatstrategies thatthesecondarytransmittercanusetoimprovetheperformanceoftheMUD/IC schemesatthesecondaryreceiver. Inthiswork,weevaluatedtheimpactofoverlappedtransmissionsontheperformance ofTCPinwirelessnetworks.Itwouldbeinterestingtoinvestigatetheinteractionbetween OCSMAandroutingprotocolsinwirelessadhocnetworks. 125

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APPENDIXA DERIVATIONOFTHEJOINTPDFOF X AD ;X CD Considerthefour-nodenetworkofFigure5-3.Inordertoevaluatethejoint distributionof X AD and X CD ,werstlookattherelativepositionsofnodesAandD withrespecttonodeB.NotethatAisuniformlydistributedinanunitcirclewithBat thecentre.Thedensityfunctionof X AB ,thedistancebetweenAandBisgivenby f X AB x = 8 > > < > > : 2 x; 0 x 1 0 ; otherwise. A{1 Similarly,nodeCisalsouniformlydistributedwithinthetransmissionrangeofB,and hencethepdfof X BC isthesameasthatof X AB .NodeDisinthetransmissionrangeof CbutnotinthetransmissionrangeofB.Hence,itisuniformlydistributedintheshaded regionofFigure5-3.Thejointconditionaldistributionof X CD and X BD given X BC can bederivedinasimilarfashionandisgivenbyrefertoFigureA-1 F X CD ;X BD y;z j X BC = x = 8 > < > : y 2 A l ;y;x A l ; 1 ;x ;z>x + y A l z;y;x A l ;y;x A l ; 1 ;x ;z > > > < > > > > : 1 A l ; 1 ;x 4 yz p x + y + z x + y )]TJ/F25 7.9701 Tf 6.587 0 Td [(z x )]TJ/F25 7.9701 Tf 6.586 0 Td [(y + z )]TJ/F25 7.9701 Tf 6.586 0 Td [(x + y + z ; 0 x;y 1 ; 1 < > : 1 A l ;s;z ;s +1 >z; 0 ; otherwise : A{4 126

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FigureA-1.Circle-circleintersectionforanalysis. andthepdfisgivenby f X AD s j X BD = z = 8 > < > : 2 s cos )]TJ/F24 7.9701 Tf 6.586 0 Td [(1 s 2 + z 2 )]TJ/F24 7.9701 Tf 6.586 0 Td [(1 2 sz ;s +1 >z; 0 ; otherwise : A{5 Notethat X AD isconditionallyindependentof X CD X BC given X BD .Hence f X AD s j X CD = x;X BC = y;X BD = z = f X AD s j X BD = z : A{6 Thejointdistributionof X AD and X CD isgivenby f X AD X CD s;y = Z x Z z f X AD s j x;y;z f X CD ;X BD y;z j x f BC x dzdx: A{7 127

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BIOGRAPHICALSKETCH SurendraBoppanareceivedtheB.Tech.degreeinelectronicsandcommunication engineeringin2003fromtheIndianInstituteofTechnologyIIT,Guwahati,India;and theM.S.degreeinelectricalandcomputerengineeringin2005fromtheUniversityof Florida,Gainesville.HeiscurrentlypursuinghisPhDdegree.FromMay2006until January2007hewaswiththeCommunicationsCircuitLab,IntelCorporation,Hillsboro, Oregon.Hisresearchinterestsincludewirelesscommunications,informationtheory,and cross-layerdesign. 134


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