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,
sII_~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!11! .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 Nuetworks
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 PathLoss C'I .Ill., I
:3.5.2 User Capacity in Exponential PathLoss C'I .Ill., I
no Fadingf
with Fading
:3.6 Suninary
4 PERFORMANCE COMPARISON OF OPTIMAL AND SUBOPTIMAL DOWNLINK(
CHANNELSHARING 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 TwoLevel Broadcasting . ..... .. .. 54
4.3.4 ThreeLevel 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 CrossL .vri 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
61 NS2 simulation setup. ......... . .. 92
62 Comparison of events at the MAC level in a tennode linear network with packet
size 400B. .. .......... ........... 94
63 Comparison of events at the MAC level in a tennode linear network with packet
size 1800B. ......... ... .. 95
71 Simulation setup for evaluating the impact of OCSMA on TCP performance. .104
72 Events at the MAC level in a tennode linear network under OCSMA protocol. 106
73 Performance comparison of OCSMA and OCSMA_DA. ... .. .. 111
74 MAClevel events in a tennode linear network under OCSMA_LA. .. .. .. 121
LIST OF FIGURES
Figure page
21 Power disparities in a cellular network. . ..... 22
22 Pairingf strategies in a sixnode cellular network. .... .. 24
23 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
24 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
:31 User capacities of TDMA and DPC in an exponential pathloss channel. .. 44
:32 Efficiency of TDMA compared to DPC in an exponential pathloss channel. .. 45
:33 User capacities of TDMA and DPC in an exponential pathloss channel with
fading. ............... .. .. 47
:34 Efficiency of TDMA compared to DPC in a exponential pathloss channel with
fadingf ............ .......... ... 48
41 Broadcastingf over the whole hand for n~ = 2 and D = 50 for various service
factors, 6. ......... .... . 58
42 Twolevel BC for n~ = 2 and D = 50 for various service factors, 6. .. .. .. 58
4:3 Threelevel BC for n~ = 2 and D = 50 for various service factors, 6. .. .. .. 59
44 Optimal FDM for n~ = 2 and D = 50 for various service factors, 6. .. .. .. 59
45 Fixed FDM for n~ = 2 and D = 50 for various service factors, 6. .. .. .. .. 60
46 Comparison of all the schemes for n~ = 2, D = 50 and 6 = 0.8. .. .. .. .. 61
47 Comparison of all the schemes for n~ = 4, D = 50 and 6 = 0.8. .. .. .. .. 62
48 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
51 Fournode linear network with conventional scheduling. ... .. .. 68
52 Fournode linear network with overlapped transmissions. .. .. .. 69
5:3 Ad hoc network with overlapped transmission. ..... .. 72
54 Distribution of signaltointerference ratio, y. ..... .... 75
55 Probability of finding a secondary transmitter. ..... .. 78
56 IUpper bound on probability of reception by node B. .. .. .. 79
57 Upper bound on the probability of a successful secondary transmission, p(S). ..
61 Typical frame exchanges in OCSMA protocol. ..........
62 Timeline of the OCSMA protocol. ..........
63 Frame formats of the OCSMA protocol. ..........
64 Tennode linear network. ..........
65 Throughput comparison in a tennode linear network with TCP traffic. .....
66 Throughput comparison in a tennode linear network with CBR traffic. .....
67 Throughput comparison in linear network with multiple CBR flows. .......
68 Effect of varying the number of nodes in a linear network on the throughput
gain of OCSMA and OCSMA_RO. ..........
69 Binarytree network. ..........
610 Throughput gain of OCSMA and OCSMA_RO in a tree network. ........
611 Throughput gain in a random network with mobility. ..........
71 Tennode linear network under OCSMA. ..........
72 Endtoend throughput comparison in a tennode linear network with TCP traffic.
73 MAClevel performance comparison of OCSMA and IEEE 802.11 in a tennode
linear network. ..........
74 Transmitter congestion window evolution in a tennode linear network. .....
75 Effect of short and long retry counts on throughput gains of OCSMA and OCSM~
in a tennode linear network. ...........
76 Networks with multiple flows. ..........
77 Throughput comparison in a network with multiple parallel flows. ........
78 Throughput comparison in a network with multiple linear flows. .........
79 Tennode linear network under OCSMA_LA. ..........
710 Frame formats of the OCSMA_LA protocol. ..........
711 Throughput comparison of OCSMA, OCSMA_LA and IEEE 802.11 in a tennode
linear network. ..........
712 Throughput comparison of OCSMA_LA and IEEE 802.11 in a tennode 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
A1 Circlecircle 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 channelsharing schemes such as TDMA,
FDMA, CDMA, etc, orthogonalize the channel resources among users to minimize
interference. However, informationtheoretic 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 nonorthogonal 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 forwardlink channelsharing schemes.
Next, we studied the use of overlapped transmission in ad hoc networks to improve
the spatial reuse 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 reuse 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~itod~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 channelsharing schemes
have been developed and deploic 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 timedivision
multiple access (TDMA), frequea s lidivision multiple access (FDMA), codedivision
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 frontend, this is the classical singleinput singleoutput (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) [36]. 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 channelsharing 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 suboptimal
channelsharing 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 [1621] as a means to increase the spatial reuse 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 knowninterference
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 physicall 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 reuse 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 forwardlink channelsharing 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 timeshare
or otherwise use orthogonal division of the channel resources among users. Consider a
standard twouser degraded Gaussian broadcast channel defined by
yri = ix + ni
y2 2 ha2n (21)
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 h12 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\(22)
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 [36]. The transmitter first generates the codeword for user 2 with power
aP. Once the codeword is generated, the transmitter has noncausal information about
the interference that this code causes at user 1. Hence the rate [3, 4]
R1 = max {I(U; Y) I(U; S)} (23)
is achievable for user 1, where S ~ #1(0, (1 a)hl2P). From Costa [5], we know
that by letting U = X1 + PS, and appropriately choosing P, R1 in (23) becomes
log(1 + alhl2P), 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 multipleuser and multipleinput multipleoutput (jl\!llO) channels
in [3133]. A summary of informationtheoretic 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 informationtheoretic 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 signaltonoise 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 channelsharing 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 ialchronous 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 IS95, 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, multipleaccess interference and .ll11 Il:entcell 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.:entc~ell
interference is highest at the cell boundaries and multipleaccess 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
signaltonoise 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 21 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 21. 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 21 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, 36, 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 twolevel 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 onetoone 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 twolevel BC is equal to the number of orthogonal
channels available. Here the onetoone condition implies that no two users pair with the
same user. This restriction is required by our use of twolevel 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 22 for
a sixnode 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 22. Pairing strategies in a sixnode 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,
(26)
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 twolevel BC are given by [29]
(1 a)K ObPt
a~pxbPt 0 ~W
aK ~ P,
Rbm
Rn,
(27)
(28)
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 multipath. 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 twolevel 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 twolevel 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 twolevel 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 twolevel 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
(29)
(210)
(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 (29) and (210) 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 (29) we have
Z1P
4 a = (. 7
Z P,
) ~
(213)
Substituting (213) in (210),
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 (212).
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. (26)) is given by
Fz (x) = Fz (x = d2 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
ezo 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 ahli 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 (217)
[ 1 + Zarn2,(0, eZ,,) ezp (1 + Z,,)
where C' = yiNoWT(KI>)l and r(.) is the incomplete gamma function given by
F~, ) tl tdt. (218)
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 (214) is given by
I (K KN l X
=P,"bc aC, (219)
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"( ')}
(220)
where E {PT(Z,)} is given by (217). Similarly, the expected value of Abc iS giVen by
E {A Abfe ,l 7/2 0E, zl > z2 > K. (221)
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
(222)
where F,(P,) is givn b
F,(P,) = P,(1 e ep).
Hence, the expected value,, of A~e is
(223)
KN~i p~
E {APfe q,)
(224)
where f,,(plp < P,), 1 < k < K is given by (222). The expected value of Pfe is the sum
of the expected values of Pu"bc and APfe
(225)
([1 i1
p l~i 1aii ( en Ki
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 ahliw 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 (226)
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,} (227)
where E{(PT(Z,)} is given by (217).
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 23 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 nonbroadcasting system y = 10 dB, PSD of the AWGN channel NVo = 1 x 1010
bandwidth W = 1 x 106 Hz, and K(,= 1 x 102
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
twolevel BC with little degradation in the target SNR.
14.5
Sa=4, BC
e a=2, BC
ea=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 23. 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 24. 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. (217)). The results in Figure 24
show the average user capacity of systems employing BC and GWBE sequences for a~ = 4,
number of orthogonal channels NV = 10, K, = 102, 0V = 1010, 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 nonlinearly 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 alrws 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 fixedpower 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 timesharing or otherwise use orthogonal division of the channel resources
among users. In this chapter, we investigate the performance of informationtheoretic
broadcasting (BC) when all the users share the entire channel resources. Unlike
orthogonalization schemes or twolevel 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 timedivision 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 sumrate 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
singlecell 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 emploie 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, (31)
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 informationtheoretic 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, (32)
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 squaredchannelmagnitudes
(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 =,(34)
To = W/Ro, and with the convention that
i= 1 N+i= 1 ) P ,,i= 13
Proposition 3.1. Consider a singlecell 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. (36)
where Tis are given by (34).
Proof. For NV = 2, we have from (34)
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, (36) 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)(39)
and
o =i" Z2dGk (X) p ~. (310)
The following theorem from [49] states that if FT(t) is continuous almost everywhere and
strctl inresin an { xdFT(x) < 00, the .Iiph.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) + 1I3)
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 .Iimptotic 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 sumrate 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. Atn ;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 k1 x0 70 k1
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 (314)
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~i1 +07 1
=~ Pr i (1 + o)i Ptot, (315)
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 (320)
The following theorem from [50] states that, under very general conditions, the linear
combination of ordered random variables .imptotically (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 .imptotic user capacity of a DPC system can be written as
KDPCi= y0 kifi 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 (316),31) 31) and (320), 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 (321)
where KDMA istedand DC e gitwen t bys (311)n and (31) resper ,ctivey We panalyzeth
Ianexponent a i al posanthloss 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 (34) 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 ^
(325)
20 200 400 600 800 1000 1200 1400 1600
Node population (N)
Figure 31. User capacities of TDMA and DPC in an exponential pathloss channel.
The .Iimpllicl~ 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 32. Efficiency of TDMA compared to DPC in an exponential pathloss channel.
respectively. The results in Figure 31 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 = 1010 and
K, = 102. 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 pathloss
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 32. 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 pathloss 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 PathLoss Channel with Fading
Since closed form expressions for user capacities in a fading channel for any general
pathloss exponent do not exist, in this section, we only consider an exponential pathloss
model with Rayleigh fading where the pathloss 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 (323)) 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. (326)
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) = (327)
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 overfaded and nonc; ., Jral..l based on their channel
conditions in a particular frame. The truncation on the distribution function indicates
that only the nonoverfaded 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 37)
~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 33. User capacities of TDMA and DPC in an exponential pathloss channel with
fading.
The results in Figure 33 show the user capacities of systems employing TDMA and
DPC in a fadingf channel with pathloss 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 34.
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 singlecell
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 :34. Efficiency of TDMA compared to DPC in a exponential pathloss channel with
fading.
transmit power constraint. In exponential pathloss 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 forwardlink channelsharing schemes in a variety of network scenarios.
CHAPTER 4
PERFORMANCE COMPARISON OF OPTIMAL AND SUBOPTIMAL DOWNLINK(
CHANNELSHARING 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 channelsharing schemes for
Gaussian broadcast channels in the downlink/forwardlink under an equalrate constraint.
In the recent past there has been some related work reported, namely [12, 47, 48], that
compared dirty paper coding (DPC) to timedivision 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 multipleinput multipleoutput (j\! [MO) transmission under
an equalrate constraint. DPC and TDMA schemes are compared in [47] on the basis of
the sumrate capacity (instead of an equalrate constraint) for MIMO Gaussian broadcast
channels, and it is shown that the DPC gain (over the TDMA sumrate 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 equalrate constraint for singleinput singleoutput (SISO) transmission as the
user population becomes large.
The present work differs from previous work in that we provide a true .Iiinidlli'lc
analysis of the various schemes in terms of the required minimum signaltonoise 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, twolevel BC in conjunction with fixed FDM, and threelevel BC
in conjunction with fixed FDM. We perform the analysis under .Iimisind 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 threelevel BC to
achieve performance very close to the best performance guaranteed by broadcasting over
the entire band (for example, the .Iiintlllnd 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 .Iimptotic 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 channelsharing 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 pathloss 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 closein distance for the system, di(> d) is the distance
between the ith MS and the BS, a~ is the pathloss 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 closein 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 pathloss 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~ (42)
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 viewpoint. 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 n1onor; [:./..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
twosided 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 channelsharing 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 44)
NoK R
Below we present an .liinjull'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 iini d ul ic minimum SNR per MS, i.e. So, = limK>o SK. Note that this .I iini 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 .Iin 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, twolevel BC, threelevel BC
and optimal FDM.
4.3.1 Broadcasting over the Whole Band
Under this scheme, the BS transmits to the K MSs using Klevel 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 CK1 as = 1. Then for
i= 1,2,  ,K,
W log 1l +vw zpa > R. (45)
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
> ~(46)
NVoR P Z1
For the case of two users, K = 2, p = 2R/W and from equation (45) we obtain,
(e /* 1)
at Pt > No oW (47)
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 KPi/K
> (6/ 10)
NVoKR P Z,
i= 1
Hence, using the definition of SK in (44),
eP 60/K P/ Kt 6Pi/KZ.
SK 41
Clearly, as K approaches infinity, B in (411) approaches P. To investigate the .Ioind 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{p1Fz o)'d~;z)w .1
K>oo K1 i=] Zi p(S ~;zo 6
(412)
As a consequence, the .Iiinidlli'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. (413)
6 p1(1S;zo)
4.3.2 Fixed Frequency Division Multiplexing
In this scheme, the K best nonoverfaded 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 = ( )414)
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). (415)
P6 p1(1S;zo)
4.3.3 TwoLevel Broadcasting
We consider twolevel BC in conjunction with fixed FDM allocation. The entire
bandwidth W is divided into L = [K1 equa~l Subbands andr twolevel BC; is used to
support a pair of users over each such subband.
For a typical pair of users, ;?i users i and j with Zi > Zj, we have
lo 1 + > R (416)
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
subband. 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
(417)
(418)
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 nonoverfaded 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(419)
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
(420)
4.3.4 ThreeLevel Broadcasting
We consider the threelevel BC in conjunction with fixed FDM allocation. The entire
bandwidth W is divided into L = [K~ equa~l Subbaindsi a~nd threelevel BC is usedr to
support three users over each such subband.
2(eP/2 00 ~o
ps p(1S;zo)
Following the same manner as for twolevel BC, we get
3(e#/3 ) 0011 ;o
So F, zo +(e3 0o)
ps p1(1S;zo) 1~z~ (d31F(1Z;o X;zo )1
+t(e2i'/3l )
J 1(1 ;zo) Ii; ]
(421)
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 (422)
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 PK1C adl Pt L= E Pi. From the above and the
definition of SK it can be seen that
OSSK min 1 :'~~ I)
i= 1
= mm i~ (423)
i= 1
where g(x) = x(ePl" 1).
Thus, the problem reduces to findings the ce's that minimize the right hand side of
(423) subjct to th~e constrain~t ( C,K1 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 (424)
and differentiating with respect to ci, we have
8 J 1 g' (ci) A
8ci K Zi IK
s '(ce) = AZe
(425)
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
(426)
In the .Iiinpind 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.
(427)
As a result of (427), A,, = limK>o XK can be obtained by equating the right side o
(427) 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 .Iimptotic
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 closein distance of the cell, which
0 7000
S6000  =0 4
z e 8=0 6
S 5000  =
4000 a2a~nd D=50
~3000
S2 3 4 5 6
Spectral Efficiency, (3 (bits/s/Hz)
Figure 41. 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 42. Twolevel 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 macrocells 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 pathloss 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
a81 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 43. Threelevel 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 44. 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 45. Fixed FDM for a~ = 2 and D = 50 for various service factors, 6.
Figure 41 through Figure 45 show the performance of different schemes for the
pathloss exponent a~ = 2, and outer radius of coverage, D = 50, with spectral efficiency
Sfor the service factor 6. Figure 41, Figure 42, and Figure 43 show the performance of
applying broadcasting over the whole band, twolevel BC and threelevel BC, respectively.
These figures demonstrate that the .eimpi ndic'l minimum SNR per MS required for
threelevel 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, twolevel 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 ETwolevel BC
eThreelevel 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 46. 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 niultiuser diversity.
Figure 44 and Figure 45 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 twolevel
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 46 and Figure 47, we show the performance comparison of the different
schemes when the service factor is 0.8. For example, in Figure 46, when /9 = 3.0 bits/s/Hz
we have S, for broadcasting over the whole hand, threelevel BC and twolevel BC at
 Fixed FDM
(n16 II Optimal FDM
ll Twolevel SPC
g 9 Threelevel 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 47. 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 threelevel BC,
respectively, while 11212.1 and 14177.8 for optimal FDM and fixed FDM, respectively.
We note that for different values of the pathloss exponent c0, although the values of S,
change, the shapes of the curves are almost unaltered.
Finally, in Figure 48 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 threelevel 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 threelevel BC schemes are much closer to
~2.6
Fixed FDM
2. El Optimal FDM
S8 Twolevel SPC
o 2.2C e Threelevel 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 48. 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 forwardlink channelsharing
schemes with the consideration of both pathloss and f ..111, under an equalrate
constraint, in terms of the .Iiini!!lle'~ minimum SNR per MS. We found that the
suboptimal method of threelevel 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 threelevel
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 threelevel BC method is less than
1'.even for high values of spectral efficiency motivates the use of threelevel 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 channelsharing 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 codedivision multiple
access, mediumaccess 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 physical1.,;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 reuse by increasing the number of simultaneous
transmissions in the network. AllD techniques are emploiu 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 reuse in the network. MAC protocols were
proposed in [19, 21] that take advantage of the MPR capabilities of the PHY to increase
the spatial reuse in networks to provide highthroughput 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 lowattenuation regime, multistage 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 fournode 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 MPRbased 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 knowninterference 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 reuse and throughput in
WANets has recently received considerable attention from the research community [5666].
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 11sc 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
channelsharing 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 physical1.,:r network coding [24], relay
nodes may receive signals consisting of several simultaneous transmissions. These signals
are decoded, reencoded 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 packetlevel 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 knowninterference cancellation. These works analyze the physical111< v aspects
involved, but do not address the MAC1.,: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 reuse and
throughput in wireless networks.
ABCD
ABCD
***
ABC
t!ABCD
e 
~ ABCD
Figure 51. Fournode 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 fournode linear network is
illustrated, which is shown in Figure 51. We assume that the nodes can communicate
only with the .Il11 Il:ent nodes and operate in halfduplex mode. Node A transmits
packets to node D through multihop routing. A typical transmission sequence under a
conventional scheduling scheme is depicted in Figure 51, 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 carriersense
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 52. Fournode 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 linkr1 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
knowninterference as overlapped transmission.
A scheduling scheme employing the idea of overlapped transmission for the fournode
linear network is depicted in Figure 52. 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, (51)
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. (52)
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 noncausal knowledge of the interfering
signals during that transmission interval. For example, in the network of Figure 52,
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 noncausal 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 52, 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
twodimensional homogeneous Poisson point process with density A nodes per unit
area. Each node is equipped with a transceiver and communicates with other nodes in
halfduplex 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,, (53)
where P, is the transmitted power, dr is the distance between the transmitter and the
receiver, KI is a constant, and a~ is the pathloss 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 53. 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
noncausal 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 signaltointerference 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 53, 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 53, 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 nonnegligible. 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 SignaltoInterference 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 o1 r7 d2 ~~+ro1 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 pathloss 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. (56)
The density of p can be expressed as
f,,(r)= sfACD(,r>s (57)
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 (A7). The
truncated distribution of p is given by
(58)
Then front (56) and (58), the pdf of SINR y, is
fr(r) =1 ,q d <1,
(59)
where nr is the pathloss 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 54. Distribution of signaltointerference ratio, y.
The distribution function Fr (y) of SIR at D, y, for pathloss exponent n~ = 2, 4
are numerically computed and plotted in Figure 54. 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. From Figure 54, 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 53, 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 ahrlw 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 53, 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(TFT), (510)
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 nontransmitting 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, (511)
where Al(TI, T2, d) is given by (54) 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 (A3) and (A1), 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 55. Probability of finding a secondary transmitter.
finding a secondary transmitter is given by
0(XAFy(z))neXAA(z)
p(F) = n! (1 ") fxBxDx
zn=0
= 1 eAp~z(1p /XD (zdz,(513)
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 55 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~~~ eaeoa
0 0.05 0.1 0.15 0.2
Probability of transmission in a time slot (p)
Figure 56. Upper bound on probability of receipt y oeB
The probability of successful reception at B of the secondary transmission from A,
p(TFT), can be upper bounded by the probability that no primary transmissions occur
in the nonoverlapping 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), (514)
where Al(rl, r2, d) is giVen by (54). Using the same approach as in (513), p(TFT) can be
bounded by
p(TFT) < euzllz)pfxBD (z)dz. (515)
The probability of reception by node B was numerically evaluated and the pdf is plotted
in Figure 56 for three different node densities, A, and pathloss 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 57. 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.
(510)) is shown in Fig. 57 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 reuse 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
reuse 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 61(a). The timeline of the protocol for the example network is shown
in Figure 62, and the frame formats are shown in Figure 63. 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 61. 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 62. 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 61(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 61(b) and Figure 61(c),
respectively. The frame formats of the RTS and CTS (refer to Figure 63) 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 02312 4
CF01Duaio/ dAddressddes Address3 Squnc Address41 Frame Bodyl FCS
DATA/ODATA Frame
Octets: 2 2 6 4
C olDurationl RA FCS
ACK Frame
Figure 63. 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 61(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 63. 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 63). 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 61(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 62). 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 62). 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 62). 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 62). 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 61(a), upon completion of the secondary 1. .141 11:;0s, C starts the
primary transmission to D, as shown in Figure 61(g). The frame format of the DATA
frame (refer to Figure 63) 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 62). 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 61(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 61(i)
and Figure 61(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 CrossLayer 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 62). 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
802.11hased 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 63). We call this protocol the OCSMA protocol with reduced overhead
(OCSMA_RO). The performance of this reducedoverhead 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 61.
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 61. 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
Carriersensing radius (Interference range) 550 ni
IFQ length 100
Overlapped Delay ao 240 ps
a, 240 ps
STA Retry Limits (Short, Long) (7,4)
*y *
:1 2 3 4 5
e **
~7 8 9 10
Figure 64. Tennode linear network.
We first evaluate the OCSMA protocol in a fixed tennode linear network as shown
in Figure 71, 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 Ilent 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 endtoend throughputs of the
network under the OCSMA, OCSMA_RO, and IEEE 802.11 MAC protocols are shown
in Figure 65.
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 65. Throughput comparison in a tennode 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 65. 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 MAClevel events across the network for all three protocols are tabulated
in Table 62 and Table 63 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 62. Comparison of events at the MAC level in a tennode 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 tennode 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 62 and Table 63, 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 tennode linear network of Figure 71 with constant hit rate
(CBR) traffic is shown in Figure 66 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 66. Througfhput comparison in a tennode 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 67. Throughput comparison in linear network with multiple CBR flows.
Next, we consider the effect of multipleflows in a linear network. Three sources and
three destinations are placed at either end of a tennode 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 67. 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 tennode linear network.
1.0
1.7
1.6
a. x OCSMA
0e OCSMA RO
1.2
1.1
5 10 15 20 25 30
Number of nodes in the linear network
Figure 68. 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 endtoend throughput gains of the OCSMA
and OCSMA_RO protocols over IEEE 802.11 are shown in Figulre 68 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 thirtynode 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 69. Binarytree network.
We also evaluated the throughput gains of OCSMA and OCSMA_RO over IEEE
802.11 in a hinarytree network shown in Figure 69. 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 61.
The performance gains of OCSMA and OCSMA_RO in a binary tree network with a depth
of four is shown in Figure 610. 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 610. 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 61. 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 611. 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 611. 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
endtoend 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 emploio I in conjunction with MAC protocols
to provide reliable and efficient endtoend 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 [7076] 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 halfduplex links, channel noise, and mobility.
To alleviate the issues associated with TCP in wireless networks, several schemes have
been proposed (cf. [7678]). 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 tennode linear network, as depicted in Figure 71. 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 71, 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 71.
Table 71. 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
Warntup time 200 s
Routing protocol ADDV
CI. ill. I mdelTwo ray propagation
RTS Threshold 150 Bytes
Transmission radius 250 ni
Carriersensing radius (Interference range) 550 ni
IFQ length 100
Overlapped Delay ao 240 ps
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 endtoend 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 roundtriptinle. 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 71. Tennode linear network under OCSMA.
S 12
10 0
o xOCSMA
F IFOCSMA RO
S9~1 0 IEEE 802.11
5 10 15 20 25 30
TCP Congestion Window Size (packets)
Figure 72. Endtoend throughput comparison in a tennode linear network with TCP
traffic .
The endtoend throughput under the OCSMA, OCSMA_RO and IEEE 802.11 MAC
protocols in the tennode linear network of Figure 71 as a function TCP CW size are
shown in Figure 72. 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 73(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 endtoend
throughput curve of Figure 72. 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 endtoend 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 72. Events at the MAC level in a tennode 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 MAClevel events
across the network. The MAClevel events under OCSMA are tabulated in Table 72 for
1 In this scenario, events correspond to either reception of a frame or a collision
eOCSMA, DATA
Y80
2 4 6 8 10 12 14 16 18
TCP Congestion Window size (packets)
(a) Link throughput in a tennode linear network
6 OCSMA
# IEEE 802.11
~t5
L4
O 01
3 ogsinWndwsz pces
o b rmrprt na eoelna ewr
(b)ea Frmdo rt i enndelnernewr
802.11 in a tennode
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 72, 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 74. Transmitter congestion window evolution in a tennode linear network.
Consider the network of Figure 71 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 nonempty. This increases the probability of overlapped
transmission. The results in Figure 74 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 72), 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 TCPReno 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 75. Effect of short and long retry counts on throughput gains of OCSMA and
OCSMA_RO in a tennode 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 75 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. I1ack. 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 endtoend throughput and the MAC level events under OCSMA and OCSMA
with d.l 1 i, I1ack (OCSMA_DA) are tabulated in Table 7:3. When the CW size is 2, the
endtoend 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 interflow 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 76. Networks with multiple flows.
context of OCSMA, we consider the two network topologies illustrated in Figure 76(a)
and Figure 76(b). Figure 76(a) shows a network with three parallel flows each traversing
through six nodes. The .Il11 Ilent nodes in a flow are placed at a distance of 200 m, and the
.Il1i Ilent flows are separated by a distance of 400 m.
The results in Figure 77 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 4OCSMA, flow3
12
104
0 10 20 30 40 50 60 70 80 90 100
Time (s)
Figure 77. Throughput comparison in a network with multiple parallel flows.
have nonzero 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 nonzero, 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
nonzero 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 reuse due to overlap transmissions. For
instance, in Figure 77, 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. (71)), and evaluating the average throughput of each of the
three flows over a simulation duration of 1800 s (cf. Table 71), we have with IEEE 802.11,
f802.11 1l, 2a, 3) = 0.67, (72)
and with OCSMA
fOCSM/Axl 1a 2 3) = 0.89. (73)
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 nonzero throughput, which is reflected by a higher value of fairness
index.
Next, we simulate the network of Figure 76(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 78. 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 78. 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 interflow contention.
To evaluate shortternt 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, (74)
and
focum4r = 0.99, (75)
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 longterm 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, (76)
and
focsM/A = 0.99, (77)
respectively. Note that while IEEE 802.11 provides only longterm fairness, OCSMA
provides both longterm and shortterm 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 endtoend 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 ahrlas 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 79. Tennode 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 79 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 79, 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 61(d), Figure 61(e),
and Figure 61(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 710. 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 lIwris 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 02312 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 710. 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 710.
Continuing with the example network of Figure 79, 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 710) are available through the TA
and NFD fields of the AK(M frame (refer to Figure 710). 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 79, 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 711. Throughput comparison of OCSMA, OCSMA_LA and IEEE 802.11 in a
tennode 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
tennode linear network of Figure 71. The parameters used for the simulation are
tabulated in Table 71. We employ the de 1li Ilack version of TCP Reno described
in Section 7.2.2. The results in Figure 711 compare the endtoend throughput of the
OCSMA, OCSMA_LA, and IEEE 802.11 protocols as a function of the TCP CW size (also
see Figure 72). 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 74. MAClevel events in a tennode 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 MAClevel events under OCSMA and OCSMA_LA are tabulated in Table 74 for
three different values of CW size. Note that the congestion control algorithm is TCP with
d.1 0. .1ack. 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 endtoend
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 atxOCSMA 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 712. Throughput comparison of OCSMA_LA and IEEE 802.11 in a tennode 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 tennode linear network with
CBR traffic. The results in Figure 712 compare the endtoend throughput of a tennode
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 67). 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
reuse and throughput in wireless networks. In CDMAhased 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
spectralefficiency 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 singleinput singleout (SISO) degraded Gaussian broadcast channel, DPC provides
significant gains over TDM only when there is limited multiuser diversity and the
spectral efficiency requirement of the users is very high [13, 47, 48]. Next, we evaluated
the performance of optimal and suboptimal forwardlink channelsharing schemes. We
observed that under high spectralefficieny regime, there is a significant performance gain
in employing cooperative broadcasting over conventional channelsharing schemes, and
that computationally simpler schemes like two and threelevel broadcasting techniques
provide performance close to the optimal scheme.
In wireless ad hoc networks, overlapped transmissions have the potential to
significantly improve the spatial reuse 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 fournode 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 A1)
Fxc'D,XBD (Y, XIXc = .r) = Ata.)(A2)
where Al(1, y, r) is given by (54). The conditional joint density function is given by
1 4yz O < r,~7 y < 1
fXDB (,XXB ) 0, otherwise.
(A3)
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 (sXBD = = = (A4)
0, otherwise.
Figure A1. Circlecircle intersection for analysis.
and the pdf is given by
2s COS1 s2+z'1 ,,
fXAD (SXBD = X) x2z (A5
0, otherwise.
Note that XAD is conditionally independent of XCD, XBc given XBD. Hence
fxAD (SXCD = X, XBc = y, XBD = X) = fXAD (SXBD = z). (A6)
The joint distribution of XAD and XCD is giVen by
fxADXCD 8 XD 9 )XDXD(,z)fax)zd. (A7)
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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. From 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.
PAGE 1
OVERLAPPEDTRANSMISSIONINWIRELESSNETWORKS By SURENDRABOPPANA ADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOL OFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENT OFTHEREQUIREMENTSFORTHEDEGREEOF DOCTOROFPHILOSOPHY UNIVERSITYOFFLORIDA 2008 1
PAGE 2
c 2008SurendraBoppana 2
PAGE 3
Tomyparents. 3
PAGE 4
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
PAGE 5
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 3.5.1UserCapacityinExponentialPathLossChannel,noFading....43 3.5.2UserCapacityinExponentialPathLossChannelwithFading...46 3.6Summary....................................47 5
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4PERFORMANCECOMPARISONOFOPTIMALANDSUBOPTIMALDOWNLINK CHANNELSHARINGSCHEMES.........................49 4.1Introduction...................................49 4.2SystemModel..................................50 4.3AsymptoticAnalysisforRequiredMinimumSNRperMS..........52 4.3.1BroadcastingovertheWholeBand..................52 4.3.2FixedFrequencyDivisionMultiplexing................54 4.3.3TwoLevelBroadcasting........................54 4.3.4ThreeLevelBroadcasting........................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 6.3.1CrossLayerInteraction.........................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
PAGE 7
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
PAGE 8
LISTOFTABLES Table page 61NS2simulationsetup.................................92 62ComparisonofeventsattheMAClevelinatennodelinearnetworkwithpacket size400B........................................94 63ComparisonofeventsattheMAClevelinatennodelinearnetworkwithpacket size1800B.......................................95 71SimulationsetupforevaluatingtheimpactofOCSMAonTCPperformance...104 72EventsattheMAClevelinatennodelinearnetworkunderOCSMAprotocol..106 73PerformancecomparisonofOCSMAandOCSMA DA...............111 74MACleveleventsinatennodelinearnetworkunderOCSMA LA........121 8
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LISTOFFIGURES Figure page 21Powerdisparitiesinacellularnetwork........................22 22Pairingstrategiesinasixnodecellularnetwork...................24 23UsercapacityofsystemsemployingBCandGWBEsequencesunderaverage powerconstraintandinniteuserassumption. N =10, =10dB, =0 : 05...32 24AverageusercapacityofsystemsemployingBCandGWBEsequenceswithxed userpopulationandtotalpowerconstraint. N =10, 0 =10dB, =4......33 31UsercapacitiesofTDMAandDPCinanexponentialpathlosschannel.....44 32EciencyofTDMAcomparedtoDPCinanexponentialpathlosschannel....45 33UsercapacitiesofTDMAandDPCinanexponentialpathlosschannelwith fading.........................................47 34EciencyofTDMAcomparedtoDPCinaexponentialpathlosschannelwith fading..........................................48 41Broadcastingoverthewholebandfor =2and D =50forvariousservice factors, ........................................58 42TwolevelBCfor =2and D =50forvariousservicefactors, .........58 43ThreelevelBCfor =2and D =50forvariousservicefactors, ........59 44OptimalFDMfor =2and D =50forvariousservicefactors, ........59 45FixedFDMfor =2and D =50forvariousservicefactors, ..........60 46Comparisonofalltheschemesfor =2, D =50and =0 : 8...........61 47Comparisonofalltheschemesfor =4, D =50and =0 : 8...........62 48Ratiosof S 1 fortheFDMschemesandthesuboptimalBCschemestothatfor broadcastingoverwholebandfor =2, D =50and =0 : 8............63 51Fournodelinearnetworkwithconventionalscheduling...............68 52Fournodelinearnetworkwithoverlappedtransmissions..............69 53Adhocnetworkwithoverlappedtransmission....................72 54Distributionofsignaltointerferenceratio, .....................75 55Probabilityofndingasecondarytransmitter....................78 56Upperboundonprobabilityofreceptionbynode B ................79 9
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57Upperboundontheprobabilityofasuccessfulsecondarytransmission, p S ...80 61TypicalframeexchangesinOCSMAprotocol....................83 62TimelineoftheOCSMAprotocol...........................84 63FrameformatsoftheOCSMAprotocol.......................85 64Tennodelinearnetwork................................92 65ThroughputcomparisoninatennodelinearnetworkwithTCPtrac......93 66ThroughputcomparisoninatennodelinearnetworkwithCBRtrac......96 67ThroughputcomparisoninlinearnetworkwithmultipleCBRows........96 68Eectofvaryingthenumberofnodesinalinearnetworkonthethroughput gainofOCSMAandOCSMA RO..........................97 69Binarytreenetwork..................................98 610ThroughputgainofOCSMAandOCSMA ROinatreenetwork.........99 611Throughputgaininarandomnetworkwithmobility................100 71TennodelinearnetworkunderOCSMA.......................104 72EndtoendthroughputcomparisoninatennodelinearnetworkwithTCPtrac.105 73MAClevelperformancecomparisonofOCSMAandIEEE802.11inatennode linearnetwork.....................................107 74Transmittercongestionwindowevolutioninatennodelinearnetwork......108 75EectofshortandlongretrycountsonthroughputgainsofOCSMAandOCSMA RO inatennodelinearnetwork..............................110 76Networkswithmultipleows.............................112 77Throughputcomparisoninanetworkwithmultipleparallelows.........113 78Throughputcomparisoninanetworkwithmultiplelinearows..........115 79TennodelinearnetworkunderOCSMA LA.....................117 710FrameformatsoftheOCSMA LAprotocol.....................118 711ThroughputcomparisonofOCSMA,OCSMA LAandIEEE802.11inatennode linearnetwork.....................................120 712ThroughputcomparisonofOCSMA LAandIEEE802.11inatennodelinear networkwithCBRtraic...............................122 10
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A1Circlecircleintersectionforanalysis.........................127 11
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AbstractofDissertationPresentedtotheGraduateSchool oftheUniversityofFloridainPartialFulllmentofthe RequirementsfortheDegreeofDoctorofPhilosophy OVERLAPPEDTRANSMISSIONINWIRELESSNETWORKS By SurendraBoppana August2008 Chair:JohnM.Shea Major:ElectricalandComputerEngineering Inwirelessnetworks,interferenceisoneofthemajorimpairmentsthatdeteriorates theperformanceofasystem.ConventionalchannelsharingschemessuchasTDMA, FDMA,CDMA,etc,orthogonalizethechannelresourcesamonguserstominimize interference.However,informationtheoreticresultsindicatethatorthogonalizationof thechannelresourcesisnotthemostecientwaytotransmittomultipleusers.We usetheterm overlappedtransmission todescribenonorthogonaltransmissionschemes 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 suboptimalforwardlinkchannelsharingschemes. Next,westudiedtheuseofoverlappedtransmissioninadhocnetworkstoimprove thespatialreuseandthroughputofthenetwork.Weshowedhowmultihoproutingcan resultinmobileradioshavingknowledgeofinterferingsignalsduringthereceptionofa transmission.Wethendemonstratedhowthisknowledgecanbeexploitedtoschedule additionaltransmissionsbyperforminginterferencecancellationatthephysicallayer.We evaluatedtheperformancelimitsofemployingoverlappedtransmissionsinwirelessad hocnetworkswithrandomlydistributednodes.WedevelopedaMACprotocolthattakes advantageoftheknowledgeoftheinterferingsignalstoscheduleadditionaltransmissions, therebyincreasingthespatialreuseandthroughputofthenetwork.Weevaluatedthe performanceofthisMACprotocolinavarietyofnetworkscenariosandcomparedtothat ofIEEE802.11MACprotocol.Wealsoanalyzedtheimpactofoverlappedtransmissions ontheperformanceofTransmissionControlProtocolTCPinwirelessadhocnetworks. 13
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CHAPTER1 INTRODUCTION Withrecentadvancementsinwirelesstechnologies,wirelessnetworkshaveemergedto playanimportantroleinourdaytodaycommunications.Theyprovidegreaterexibility, mobility,and,whenusedinadhocconguration,doawaywiththenecessityofany infrastructurefortheirdeployment.Theyarebeingincreasinglyusedinapplications suchastacticalcommunications,environmentalmonitoring,andcommercialdata communications.Unlikewirelinecommunications,allthenodesinawirelessnetwork sharethesamephysicalmedium,whichresultsinchallengesspecictowirelessnetworks. Interferenceisoneofthemostchallengingimpairmentsthatexistinawirelessenvironment. Duetothebroadcastnatureofthewirelesschannel,simultaneoustransmissionsbyradios mayresultininterferenceatthereceivingradios.Severalchannelsharingschemes havebeendevelopedanddeployedbasedonthecongurationofthewirelessnetwork infrastructureoradhoc. 1.1CellularNetworks Inacellularnetwork,thetransmissionsarecoordinatedbythebasestationBS. ThechannelresourcesareallocatedbytheBStothosemobileusersthateithertransmit datatotheBSorreceivedatafromtheBS.Channelsharingschemessuchastimedivision multipleaccessTDMA,frequencydivisionmultipleaccessFDMA,codedivision 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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receiverfrontend,thisistheclassicalsingleinputsingleoutputSISOGaussian 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 comparedtoacellularnetworkemployingconventionalchannelsharingschemessuch asTDMA,FDMA,CDMA,etc.Weevaluatedtheperformancegainofcooperative broadcastingintermsofthenumberofusersthatcanbesupportedbyaBSalsosee[11, 12],andcomparedtheperformanceofbroadcastingtoseveraloptimalandsuboptimal channelsharingschemesalsosee[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]asameanstoincreasethespatialreuseinwirelessnetworksbyincreasing thenumberofsimultaneoustransmissionsinthenetwork.However,inmostcases,the nodesmightnothavesucientprocessingpowertoperformcomplexMUDschemes.The 15
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complexityoftheMUDschemescouldbesignicantlysimpliedandtheperformance enhancediftheinterferingsignalwerecompletelyknownatthereceiver.Inwireless adhocnetworks,theinterferingsignalmaybeknownatthereceiverduetomultihop routing.WeintroducedtheideaofemployingMUDschemeswithknowninterference cancellationinmultihopnetworkstoincreasethenumberofsimultaneoustransmissions in[22].Asimilarideathatemploysnetworkcodingatthephysicallayertoincrease simultaneoustransmissionsinwirelessadhocnetworkswasrecentlyproposedin[23, 24];thesenetworkcodingpapersconsiderthephysicallayeraspectsofemployingsuch overlappedtransmissionschemes,butdonotaddresstheMAClevelimplications.In thesecondpartofthisdissertation,weintroducedoverlappedtransmissionschemes foradhocnetworksbasedoncancellationofknowninterference.Weanalyzedsomeof thefundamentallimitsonemployingoverlappedtransmissioninadhocnetworksalso see[22,25].WedesignedaMACprotocolwhichexploitsthisfeaturetoimprovethe throughputandspatialreuseinwirelessnetworksalsosee[26].Theperformanceofthe resultantOCSMAprotocolisevaluatedinavarietyofnetworkscenariosanditsimpacton theperformanceofTCPowsisinvestigatedalsosee[27]. 1.3DissertationOutline Therestofthedissertationisorganizedasfollows.InChapter2,weintroducedthe notionofoverlappedtransmissionincellularnetworks.Weinvestigatedtheperformance ofacellularnetworkemployingcooperativebroadcastingandcomparedittothatofa systememployingGeneralizedWelchBoundEqualityGWBEsequences.InChapter3, wedenedtheusercapacityofacellularnetwork.Weevaluatedtheusercapacityof systemsemployingdirtypapercodingDPCandTDMA,andcomparedtheperformance ofasystememployingDPCtothatofasystememployingTDMA.Theperformance ofoptimalandsuboptimalforwardlinkchannelsharingschemesincellularnetworks 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 thatitismoreecienttosimultaneouslytransmittomultipleusersthantotimeshare orotherwiseuseorthogonaldivisionofthechannelresourcesamongusers.Considera standardtwouserdegradedGaussianbroadcastchanneldenedby 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
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aP .Oncethecodewordisgenerated,thetransmitterhasnoncausalinformationabout 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], andextendedtomultipleuserandmultipleinputmultipleoutputMIMOchannels in[31{33].Asummaryofinformationtheoreticworkfocusedoncellularcommunications isgivenin[34].PracticalschemesbasedonSPCwereproposedbyPursleyandShea[7,8], whichexploitspatialdierencesamongreceiversandimprovethethroughputinwireless networks. Inthischapter,weevaluatedtheuseofinformationtheoreticbroadcastingBC techniquessuchasSPCandDPCinacellularCDMAcommunicationsystemthat employsorthogonalspreadingsequencesandpowercontrol.Insuchsystems,orthogonal spreadingcodesareusedfordierentusers'signals.Powercontrolisappliedtominimize multipathinterferencetousersinthatcellandtominimizeinterferencetousersin adjacentcells.Ideally,eachuserseesthesamesignaltonoiseratioSNRforthesignalon theirdesignatedspreadingcode.However,ifauserdespreadsanotheruser'ssignal,power controlmayresultinvastlydierentSNRs.BCmayoersomesignicantadvantages insuchscenariosbysimultaneouslytransmittingmessagestomultipleusersonasingle spreadingcode.AlthoughthefocusofthischapterisonacellularCDMAnetwork,the 19
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ideaspresentedherecanbeappliedtootherchannelsharingschemessuchasFMDA, 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,suchasIS95,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,multipleaccessinterferenceandadjacentcellinterference canbemodeledasasingleadditivewhiteGaussiannoiseAWGNsourcewithtwosided powerspectraldensity N 0 2 [42].Theassumptionisreasonablesincetheadjacentcell interferenceishighestatthecellboundariesandmultipleaccessinterferenceishighest intheinteriorofthecell.Let W bethebandwidtheachuserseesafterdespreadingthe receivedsignaland N denotethenumberoforthogonalchannelsinthesystem. Powercontrolisusedtoensurethateachmobileuserreceivessucientpowerto achievethedesiredqualityofservicewhileminimizingtheinterferencetoothermobiles. Weconsiderthecaseinwhich perfect powercontrolisusedtomaintainaconstant signaltonoiseratioSNRateachmobileuserreceivinginformationfromtheBS.In suchascenario,itisoftenpossibletoidentify pairs ofuserssuchthatoneoftheusers receivesamuchhigherpowerthanthetargetpowerlevelwhenthatuserdemodulates theotheruser'ssignal.Figure21depictssuchascenario,inwhichpowercontrolis usedtoachievethesamereceivedpowerateachofthemobileusers M 1 ;M 2 and M 3 Anexponentialpathlossmodelwithouttheeectsoffadingandshadowingisassumed 21
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Figure21.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 .ThedottedlineinFigure21indicates 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,theBSusestwolevelsuperimposedcodestotransmitto pairs ofuserswhichare allocatedthesamespreadingsequence.Thebroadcastcodesarecomposedofinformation attwodierentratesdesignedfortwodierentSNRrequirementsfortheiraccurate reception.ThemessagewiththelowerSNRrequirementforitsaccuratereception isknownasthe basicmessage ,andthemessagewithhigherSNRrequirementforits accuratereceptionisknownasthe additionalmessage .Theusercapacityofsuchasystem isdependentonthenumberofsuitablepairsthatexistandalsoonwhichuserspair. Toanalyzetheperformanceofsuchasystem,weindexthemobileusersindecreasing orderoftheirchannelgains.Wedenea pairingstrategy f i asaonetoonefunction 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 themaximumnumberofpairsusingourtwolevelBCisequaltothenumberoforthogonal channelsavailable.Heretheonetooneconditionimpliesthatnotwouserspairwiththe sameuser.ThisrestrictionisrequiredbyouruseoftwolevelBC.Thefactthat f i isa functionrestrictseachusertopairwithatmostoneuser.Althoughtheserequirements arenotnecessaryfromatheoreticalstandpoint,theyrepresentascenariothatisofmore practicalinterest.TwosuchexamplesofpairingstrategiesaredepictedinFigure22for asixnodecellularnetwork.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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Figure22.Pairingstrategiesinasixnodecellularnetwork. 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 additionalmessagesundertwolevelBCaregivenby[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 cellfrommultipath.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 userstopairusingatwolevelbroadcastcodewithonechannelsuchthatboth 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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Figure24.AverageusercapacityofsystemsemployingBCandGWBEsequenceswith xeduserpopulationandtotalpowerconstraint. N =10, 0 =10dB, =4. averagedoveralltransmissiondurationsofboththesystemsunderthesametotalpower constraint.Wearbitrarilychoosethetotalpowerconstraintpersymboldurationequalto theaveragepowerconstraintconsideredpreviouslycf.2{17.TheresultsinFigure24 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 systememployingBCincreasesnonlinearlywithincreasinguserpopulationandreaches 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 asystememployingGWBEsequencesunderbothaverageandxedpowerconstraints. 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 ecientthantimesharingorotherwiseuseorthogonaldivisionofthechannelresources amongusers.Inthischapter,weinvestigatetheperformanceofinformationtheoretic broadcastingBCwhenalltheuserssharetheentirechannelresources.Unlike orthogonalizationschemesortwolevelbroadcastingschemesofChapter2,underBC, theBSusestheentirechannelresourcestotransmitsimultaneouslytoalltheusersin thesystem.WefocusontheuseofDPC,whichhasbeenshowntoachievethecapacity ofMIMOGaussianbroadcastchannels[46].Asnotedearlier,DPCisoneofthecoding schemesthatcanachievethecapacityofascalarGaussianbroadcastchannel.However, DPCisacomplicatedschemethathasyettobeimplementedinpracticalsystems.Many presentdaysystemsusetimedivisionmultipleaccessTDMA,inwhichthebasestation supportsseveralusersbytransmittingtoonlyoneuseratatime.Theperformancegains ofDPCoverTDMAinaMIMOGaussianbroadcastchannelintermsofsumratecapacity wererstevaluatedin[47].Viswanathan etal. [48]haveconsideredtheperformancegain ofDPCoverTDMAintermsofdownlinkusercapacityinaMIMOcellularnetwork. Simulationresultsin[48]suggestthattheperformancegainofDPCoverTDMAisnot signicantforsystememployingsingleantennasateachradio.However,noanalytical resultswereprovided.Inthischapter,weevaluatethedownlinkusercapacityofa singlecellcommunicationsystemunderTDMAandDPCandanalyzetheperformance 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 employingDPCandTDMAareanalyzedusinganinformationtheoreticframework,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 denotetheorderedsquaredchannelmagnitudes 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. ConsiderasinglecellofacellularnetworkemployingTDMAwithtotal 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 thesumratecapacityofthescalarGaussianbroadcastchannel. 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 performanceofTDMAandDPCsystemsinanexponentialpathlosschannel,withand withoutfading. 3.5.1UserCapacityinExponentialPathLossChannel,noFading Inanexponentialpathlosschannelwithoutfading,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 isthepathloss 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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Figure32.EciencyofTDMAcomparedtoDPCinanexponentialpathlosschannel. respectively.TheresultsinFigure31illustratetheusercapacitiesofTDMAandDPC 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 capacitiesofboththeTDMAandDPCsystemsincreasewithanincreaseinthepathloss exponent .Thisisbecauselargervaluesof providegreaterdisparityinchannelgains, whichTDMAandDPCcantakeadvantagetoincreasethesystemcapacity. Therelativeeciency ofTDMAincomparisontoDPCisplottedforseveral dierenttargetSNRs 0 andfor P tot =2 40 inFigure32.Itcanbeseenthatforall thethreetargetSNRs 0 shown, isabove0 : 93for =2,andabove0 : 89for =4. ThisindicatesthatthegaininusercapacityachievedbyemployingDPCisatmost12% comparedtotheusercapacityofaTDMAsysteminthisscenario.Alsonotethatan increaseinthepathlossexponentdecreasestheTDMAeciency,sinceasthedisparity 45
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inthechannelgainsincreases,DPCmoreecientlyexploitsthechanneldisparitiesto increasetheusercapacity. 3.5.2UserCapacityinExponentialPathLossChannelwithFading Sinceclosedformexpressionsforusercapacitiesinafadingchannelforanygeneral pathlossexponentdonotexist,inthissection,weonlyconsideranexponentialpathloss modelwithRayleighfadingwherethepathlossexponent =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. Figure33.UsercapacitiesofTDMAandDPCinanexponentialpathlosschannelwith fading. TheresultsinFigure33showtheusercapacitiesofsystemsemployingTDMAand DPCinafadingchannelwithpathlossexponent =2,forthreedierenttargetSNRs 0 ,totaltransmitpower P tot =2 40 and =0 : 05.Itcanbeseenfromtheplotsthatthe analyticalresultssolidlinesareingoodagreementwiththesimulatedresultsdashed lines.TheTDMAeciency forthreedierenttargetSNRs 0 isplottedinFigure34. ItcanbeseenthatTDMAeciencyisgreaterthan0 : 93forallthethreeSNRs.Hencethe gainofDPCoverTDMAintermsofusercapacityisatmost8%forthisscenario.Thus DPCprovideslittlegaininusercapacityincomparisontoTDMAforthisscenario. 3.6Summary Inthischapter,wederivedclosedformexpressionsfortheusercapacityofsinglecell networksemployingTDMAandDPCschemesforlargeuserpopulationsunderatotal 47
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Figure34.EciencyofTDMAcomparedtoDPCinaexponentialpathlosschannelwith fading. transmitpowerconstraint.Inexponentialpathlosschannelswithandwithoutfading, 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 suboptimalforwardlinkchannelsharingschemesinavarietyofnetworkscenarios. 48
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CHAPTER4 PERFORMANCECOMPARISONOFOPTIMALANDSUBOPTIMALDOWNLINK CHANNELSHARINGSCHEMES 4.1Introduction TheresultsinChapter3indicatethatbroadcastingtechniquessuchasDPCandSPC maynotprovidesubstantialgainsoversimplerschemessuchasTDMAinthedownlink ofacellularnetwork.Inthepresentchapter,theperformancegainsofBCarefurther investigatedbycomparingvariousoptimalandsuboptimalchannelsharingschemesfor Gaussianbroadcastchannelsinthedownlink/forwardlinkunderanequalrateconstraint. Intherecentpasttherehasbeensomerelatedworkreported,namely[12,47,48],that compareddirtypapercodingDPCtotimedivisionmultipleaccessTDMAforthe Gaussianbroadcastchannel.In[48],theauthorsconsideralgorithmsfororderingusers inacellularsystemusingDPCandprovidesimulationresultsonthenumberofusers thatcanbesupportedwithmultipleinputmultipleoutputMIMOtransmissionunder anequalrateconstraint.DPCandTDMAschemesarecomparedin[47]onthebasisof thesumratecapacityinsteadofanequalrateconstraintforMIMOGaussianbroadcast channels,anditisshownthattheDPCgainovertheTDMAsumratecapacityis upperboundedbytheminimumofthenumberoftransmitantennasandthenumber ofreceivers.In[12],theauthorsprovideanalyticalapproximationsfortheusercapacity underanequalrateconstraintforsingleinputsingleoutputSISOtransmissionasthe userpopulationbecomeslarge. Thepresentworkdiersfrompreviousworkinthatweprovideatrueasymptotic analysisofthevariousschemesintermsoftherequiredminimumsignaltonoiseratio SNRpermobilestationMSatagivenbandwidtheciency.Analyticalresultsare providedforthefollowingschemes:optimalfrequencydivisionmultiplexingFDMwith optimalallocationoffrequencyandpower,xedFDMwithequalbandwidthallocation, BCoverthewholeband,twolevelBCinconjunctionwithxedFDM,andthreelevelBC inconjunctionwithxedFDM.Weperformtheanalysisunderasymptoticconditions, 49
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i.e.,asthenumberofMSsinthesystemandthetotalbandwidthgoestoinnity.The resultsobtainedshowthatBCschemesprovidesignicantperformanceadvantageonly undercertainscenarios.WealsoobservethatitissucienttousethreelevelBCto achieveperformanceveryclosetothebestperformanceguaranteedbybroadcastingover theentirebandforexample,theasymptoticminimumSNRperMSislessthan1 : 15 timesthatforbroadcastingoverthewholebandataspectraleciencyof5 : 5bits/s/Hz. ThisisincontrasttoFDM,forwhichtherequiredasymptoticminimumSNRperMSis about2 : 55timesthatforbroadcastingoverthewholebandataspectraleciencyof5 : 5 bits/s/Hz.Inthefollowingsection,thesystemmodelisintroduced,andinSection4.3the analysisofthedierentchannelsharingschemesarepresented.Theresultsarediscussed inSection4.4,andthechapterisconcludedinSection4.5. 4.2SystemModel ConsidertheforwardlinkfromthebasestationBSto M mobilestationsMSs ofaninfrastructurenetwork.Assumethatafrequencybandof W Hzisavailableforthe BStosendinformationtothe M MSs.Assuminganexponentialpathlossmodelwith 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 isthecloseindistanceforthesystem, d i d isthedistance betweenthe i thMSandtheBS, isthepathlossexponent,and j h i j isthemagnitudeof thefadingattheMS,whichisassumedtobeconstantovermanysymbols.Weassume anannularregionofcoveragewithalldistancesfromtheBStoanMSnormalizedby thecloseindistance.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 ofpathlossexponent =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 twosidednoisepowerspectraldensityof N 0 = 2.Let P t bethetotalpowertransmittedby theBStosupportthetransmissiontothe K MSs,whenpossible. WequantifytheperformanceofachannelsharingschemebytheminimumSNRper 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,twolevelBC,threelevelBC 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 bestnonoverfadedusersareservedusingaxedallocationof 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 4.3.3TwoLevelBroadcasting WeconsidertwolevelBCinconjunctionwithxedFDMallocation.Theentire bandwidth W isdividedinto L = d K 2 e equalsubbandsandtwolevelBCisusedto supportapairofusersovereachsuchsubband. 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 subband.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 nonoverfadedusers 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 4.3.4ThreeLevelBroadcasting WeconsiderthethreelevelBCinconjunctionwithxedFDMallocation.Theentire bandwidth W isdividedinto L = d K 3 e equalsubbandsandthreelevelBCisusedto supportthreeusersovereachsuchsubband. 55
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FollowingthesamemannerasfortwolevelBC,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 ,withalldistancesbeingnormalizedbythecloseindistanceofthecell,which 57
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Figure41.Broadcastingoverthewholebandfor =2and D =50forvariousservice factors, Figure42.TwolevelBCfor =2and D =50forvariousservicefactors, istypically100mor1kmforoutdoorenvironments.Asthesizeofmacrocellstypically 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.Thepathlossexponents 58
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Figure43.ThreelevelBCfor =2and D =50forvariousservicefactors, Figure44.OptimalFDMfor =2and D =50forvariousservicefactors, consideredare =2and =4.WechoosetheRayleighfadingsecondmomentequalto1 sothatthefadingprocessneitheraddsnorsubtractspower. 59
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Figure45.FixedFDMfor =2and D =50forvariousservicefactors, Figure41throughFigure45showtheperformanceofdierentschemesforthe pathlossexponent =2,andouterradiusofcoverage, D =50,withspectraleciency fortheservicefactor .Figure41,Figure42,andFigure43showtheperformanceof applyingbroadcastingoverthewholeband,twolevelBCandthreelevelBC,respectively. TheseguresdemonstratethattheasymptoticminimumSNRperMSrequiredfor threelevelBCexceedsthatfortheoptimalmethodofbroadcastingoverthewholeband bynotmorethan10%forlowandmoderatelyhighvaluesofthespectraleciency 3 : 5bits/s/Hz.Ontheotherhand,twolevelBCperformsalittleworse,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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Figure46.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 benetsofmultiuserdiversity. Figure44andFigure45showtheperformanceofoptimalFDMandxedFDM, respectively.Thedegradationintheperformanceforthesuboptimalmethodofxed FDMwhencomparedtooptimalFDMisverysimilartothatforthecaseofthetwolevel BCandbroadcastingoverthewholeband.Forexample,foraservicefactorof0 : 8, S 1 forxedFDMisabout20%morethanthatfortheoptimalFDMschemeat =4 : 0 bits/s/Hz. InFigure46andFigure47,weshowtheperformancecomparisonofthedierent schemeswhentheservicefactoris0 : 8.Forexample,inFigure46,when =3 : 0bits/s/Hz wehave S 1 forbroadcastingoverthewholeband,threelevelBCandtwolevelBCat 61
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Figure47.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 : 4forbroadcastingoverthewholebandandthreelevelBC, respectively,while11212 : 1and14177 : 8foroptimalFDMandxedFDM,respectively. Wenotethatfordierentvaluesofthepathlossexponent ,althoughthevaluesof S 1 change,theshapesofthecurvesarealmostunaltered. Finally,inFigure48weplot,asafunctionof ,theratioof S 1 fordierentschemes tothatforbroadcastingoverthewholeband.Ithasbeenobservedthatthisplotdoes notsignicantlyvaryfordierentvaluesof D or .Fromthisgure,weobservethatfor 5 : 5bits/s/Hz, S 1 forthreelevelBCiswithin1 : 15timesthatofbroadcastingoverthe wholeband,whereasevenforoptimalFDM, S 1 ismorethantwicethatforbroadcasting overthewholebandathighspectraleciencies.Thus,fromtheseresultsweconclude thattheperformancesobtainedfromtwoorthreelevelBCschemesaremuchcloserto 62
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Figure48.Ratiosof S 1 fortheFDMschemesandthesuboptimalBCschemestothatfor broadcastingoverwholebandfor =2, D =50and =0 : 8. thatforoptimalbroadcastingoverthewholebandthanfortheothertwoFDMschemes, especiallyatmoderateandhighspectraleciencies. 4.5Summary Inthischapter,wecomparedtheperformanceofvariousforwardlinkchannelsharing schemeswiththeconsiderationofbothpathlossandfading,underanequalrate constraint,intermsoftheasymptoticminimumSNRperMS.Wefoundthatthe suboptimalmethodofthreelevelBCwithxedFDMallocationrequiresanasymptotic minimumSNRperMSthatiswithin1 : 15timesthatoftheoptimalmethodofbroadcasting overthewholebandwhenthespectraleciencyisbelow5.5bits/s/Hz.Ontheother hand,xedFDMorevenoptimalFDMperformmuchworse,exceptforverylowspectral eciencies.Theseresultsmotivatetheuseofpracticalmethodsliketwoorthreelevel BCinmultibandoperationinsteadoftheoptimalbutpracticallydicultschemes likebroadcastingoverthewholebandoroptimalFDM.Moreover,thefactthatthe performancedegradationfromusingthesuboptimalthreelevelBCmethodislessthan 15%evenforhighvaluesofspectraleciencymotivatestheuseofthreelevelBCnotonly 63
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forthetraditionalcellularnetworksbutalsoforsystemsthatoperateinthehighspectral eciencyregions. Inthefollowingchapters,theproblemofchannelsharinginwirelessadhocnetworks isconsidered,wherewefocusonthedesign,developmentandanalysisofmedium accesscontrolMACprotocolsthatimprovetheperformanceofwirelessnetworks. WedevelopedaMACprotocol,andthroughanalysisandnetworksimulations,evaluated itsimpactonthethroughputofthenetworkanditsinteractionwithotherlayers. 64
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CHAPTER5 OVERLAPPEDTRANSMISSIONINWIRELESSADHOCNETWORKS 5.1Introduction InwirelessadhocnetworksWANetsthatdonotemploycodedivisionmultiple access,mediumaccesscontrolMACprotocols,suchasIEEE802.11[52],areusedto allocatethechannelresourcestospecictransmittersandreceiverssoastominimize theinterferenceinthenetwork.Traditionally,thedesignoftheMACprotocoliscarried outindependentlyofthephysicallayerdesign,assumingasimplisticcollisionchannel model.Inthesemodels,apacketissuccessfullyreceivedbyanodeiftherearenoother transmissionsinitsinterferencerange.TheseMACprotocolsscheduletransmissionssuch thatthecollisionsinthenetworkareminimized. MultiuserdetectionMUD[17,18,20,21,53,54]inwirelessnetworkshasbeen proposedasameanstoincreasespatialreusebyincreasingthenumberofsimultaneous transmissionsinthenetwork.MUDtechniquesareemployedatthephysicallayerPHY torecoverinformationfromcollidingpacketsatthereceiver.Thesesignalprocessing techniquesusedatthePHYenableanodetoreceivepacketsinthepresenceofother transmissionsinitscommunicationrange.ThismultipacketreceptionMPRcapabilityof thenodesatthePHYleadstogreaterspatialreuseinthenetwork.MACprotocolswere proposedin[19,21]thattakeadvantageoftheMPRcapabilitiesofthePHYtoincrease thespatialreuseinnetworkstoprovidehighthroughputinheavytracandlowdelayin lighttrac. Inmostcases,mobileradiosdonothavesucientprocessingpowertoperform complexMUDschemes.Recentworkonthetransportcapacityofwirelessnetworks[55] indicatesthatinthelowattenuationregime,multistagerelayingusingcancellation ofknowninterferenceisorderoptimal.Here,theinterferenceisknownfromtheuse ofmultihoprouting.Usinginterferencecancellationforonlyknowninterferencemay signicantlyimprovenetworkperformanceatareasonablecomplexity. 65
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ToexplainhowaninterferingsignalmaybeknowninmultihoproutinginaWANet, considerafournodelinearnetworkconsistingofnodesA,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.HoweverwhenaMPRbasedMACprotocolisemployed,simultaneoustransmissionsof A BandC Darepossible,sinceMUDtechniquescanbeemployedatBtorecoverthe packettransmittedbyA.NotethatthepackettransmittedbyCtoDisthesamepacket thatBforwardedtoCinanearliertimeslotignoringthedierencesintheheaders.If BweretoretainacopyofthepacketthatitforwardedtoC,Bwouldhaveinformation regardingtheinterferingtransmission.ThisgreatlyreducesthecomplexityoftheMUD algorithmsemployedatthePHYtorecoverthepackettransmittedbyA.Thisexampleis revisitedinSection5.2. TheideaofemployingthistypeofknowninterferencecancellationICtechnique toincreasesimultaneoustransmissionsinWANetswasrstanalyzedin[22].In[22], knowledgeoftheinterferingsignalisassumedatboththetransmitterandthereceiver, andthereceiverperformsMUD/ICtorecoveradditionalmessages.Limitationson schedulingsuchsimultaneoustransmissionswereanalyzedandaMACprotocolthat supportssuchsimultaneoustransmissionswasproposed. Theideaofemployingnetworkcodingtoincreasespatialreuseandthroughputin WANetshasrecentlyreceivedconsiderableattentionfromtheresearchcommunity[56{66]. Atransmittingnodeexploitsthebroadcastnatureofthephysicalmediumalongwith theknowledgeoftheinterferingmessagesatthereceivingnodestocombine/encode 66
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multipleindependentmessagesatthenetworklayerandtransmittoseveralnodes. Anodereceivingtheencodedmessageusestheknowledgeoftheotherinterfering messagesavailableatthenetworklayertorecoverthemessageintendedforit.Practical channelsharingschemesthatsupportnetworkcodinginWANetswereproposed in[57,60,64,66]. Ourapproachissimilartosomenetworkcodingapproachestoincreasesimultaneous transmissionsinWANets[23,24,67,68].Inphysicallayernetworkcoding[24],relay nodesmayreceivesignalsconsistingofseveralsimultaneoustransmissions.Thesesignals aredecoded,reencodedandrelayedontotheirnaldestinations.Thedestination,which hastheknowledgeoftheotherinterferingsignals,mitigatestheinterferenceandrecovers theintendedtransmission.However,thisapproachrequiresperfectsynchronization amongthosetransmissionsthatinterfereatarelaynode.Analternativestrategycalled analognetworkcoding[67]doesnotrequiretheintermediaterelaynodestodecode thesignal.Whenarelaynodereceivesasignalconsistingofinterferingtransmissions, thenodeampliesthesignalandbroadcastsit.Onlypacketlevelsynchronizationis necessarybetweentheinterferingtransmissions.Theintendeddestinationsleveragethe informationtheyhaveabouttheinterferingtransmissionstomitigatethem,andrecover theintendedtransmission.TheseapproachesaresimilartotheideaofemployingMUD withknowninterferencecancellation.Theseworksanalyzethephysicallayeraspects involved,butdonotaddresstheMAClayerimplicationsofemployingsuchsimultaneous transmissionschemesinadhocnetworks. Inthischapter,weanalyzedsomeofthefundamentallimitsonperformingoverlapped transmissionsinaWANet.Ouranalysisprovidesanunderstandingoftheperformance gainsofsuchtransmissions,andaninsightintothePHYandMACinteractionrequired forschedulingsuchtransmissions.InChapter6,wedesignedaMACprotocolbasedon theIEEE802.11MACprotocolthatexploitsthisfeaturetoimprovethespatialreuseand throughputinwirelessnetworks. 67
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Figure51.Fournodelinearnetworkwithconventionalscheduling. Therestofthechapterisorganizedasfollows.Section5.2introducestheideaof employingoverlappedtransmissioninalinearnetwork.InSection5.3,somelimitson performingoverlappedtransmissionsinwirelessnetworksareevaluated.Thechapteris concludedinSection5.4. 5.2Motivation Inthissection,theideaofoverlappedtransmissionsinafournodelinearnetworkis illustrated,whichisshowninFigure51.Weassumethatthenodescancommunicate onlywiththeadjacentnodesandoperateinhalfduplexmode.NodeAtransmits packetstonodeDthroughmultihoprouting.Atypicaltransmissionsequenceundera conventionalschedulingschemeisdepictedinFigure51,inwhichittakesthreetime slotsforapacketfromAtoreachD.Thescheduledtransmissionsinagiventimeslot aremarkedbysoliddirectedarrowsalongwiththepacketidentiers,andtheinterference causedbythesetransmissionsaremarkedbydashedarrows.Undertypicalcarriersense multipleaccessprotocolswithcollisionavoidanceCSMA/CA,whenpacket m 1 isbeing forwardedbyCintimeslot t 3 ,Acannottransmitthemessage m 2 sinceC'stransmission willcauseinterferenceatB. 68
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Figure52.Fournodelinearnetworkwithoverlappedtransmissions. Thethroughputofthisnetworkcanbeimprovedbyemployingsimultaneous transmissionsasdescribedbelow.Weobservethatinthetimeslot t 3 ,Cforwardsthe packet m 1 thatitreceivedfromBintheearliertimeslot t 2 .IfBweretoretainacopy ofthemessage m 1 locally,itknowsthemessagebeingtransmittedby C intimeslot t 3 assumingthatlinklayerencryptionisnotusedandanydierencesintheheadersare ignored.IfAisallowedtotransmitthemessage m 2 inthetimeslot t 3 ,Bcanusethe storedinformationregarding m 1 tomitigatetheinterferencecausedbyC'stransmission. Wecallthisadditionaltransmissionthatresultsduetotheinterferencemitigationof knowninterferenceas overlappedtransmission Aschedulingschemeemployingtheideaofoverlappedtransmissionforthefournode linearnetworkisdepictedinFigure52.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 transmissionisnotpredicatedontheuseofnoncausalknowledgeoftheinterfering signalsduringthattransmissioninterval.Forexample,inthenetworkofFigure52, thetransmissionofmessage m 1 fromCtoDintimeslot t 3 isthe primarytransmission andthenodesCandDarecalledthe primarytransmitter andthe primaryreceiver respectively.Similarly,atransmissionbetweentwonodesisa secondarytransmission ifat leastoneofthenodeshasnoncausalinformationabouttheprimarytransmissionsinthe 1 Therstpacketrequiresthreetimeslots. 70
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presenttransmissionintervalandperformsMUD/ICtomitigatetheinterference.Inthe networkofFigure52,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 twodimensionalhomogeneousPoissonpointprocesswithdensity nodesperunit area.Eachnodeisequippedwithatransceiverandcommunicateswithothernodesin halfduplexmode.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 isthepathlossexponent.Intheabsenceofinterference, weassumethatatransmissionatthemaximumpowerlevelwillbereceivedcorrectlyif andonlyiftheintendedreceiveriswithinadistanceofoneunitfromthetransmitter. Wealsoassumethatthereissomeinterferencerange,whichistypicallylargerthanthe transmissionrange.Nodeswithintheinterferencerangebutoutsidethetransmission rangeofatransmittercandetectthepresenceofatransmissionbutwillnotbeableto correctlydecodethepacketbeingtransmitted. Figure53.Adhocnetworkwithoverlappedtransmission. Inthissection,weconsidersomelimitationsontheabilitytoutilizeoverlapped transmissionstoimprovethethroughputinawirelessadhocnetwork.Theselimitations comefromthefollowingtwosources: Interferenceduetosecondarytransmission: Sincethesecondaryreceiverhas noncausalknowledgeoftheprimarytransmission,itcanmitigatetheinterference duetotheprimarytransmitterandrecovertheintendedmessage.However,the secondarytransmissioncausesinterference,possiblytoseveralprimarytransmissions. 72
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InSection5.3.2,weevaluatedtheamountofinterferencethatasecondary transmissionmaycauseattheprimaryreceiver,andsuggesthowthisinterference canbecontrolledbyadaptingthepowerlevelofthesecondarytransmissiontomeet speciedsignaltointerferenceratioSIRandoutagerequirementsorbycareful selectionofthesecondarytransmitter. Probabilityofsecondarytransmission: Overlappedtransmissionsdependonthe availabilityofsuitablesecondarytransmittersandthesuccessfulreceptionofthe messagesatthesecondaryreceiver. TheanalyticalresultsinSection5.3.2andSection5.3.3arebasedonthenetwork showninFigure53,whichcanbeconsideredtobeapartofalargernetwork.NodesA andCareinthetransmissionrangeofB,andBtransmitspacketstoDthroughCby employingmultihoprouting.HenceDisinthetransmissionrangeofC,butnotinthe transmissionrangeofB.ThisparticularregionisshowninFigure53withdashedlines. WealsoassumethatAhaspacketsforB.ThenetworkofFigure53isusedtosimplify theanalysis,yetillustratetheimportantaspectsofoverlappedtransmission. 5.3.2InterferenceduetoSecondaryTransmission ConsiderrsttheadhocnetworkofFigure53,andthetimeslotduringwhichnode CforwardstoDapacketthatithasreceivedfromBinanearliertransmission.The transmissionfromCtoDisaprimarytransmission,andapossiblesecondarytransmission isfromnodeAtonodeB.WeassumethatbothnodesAandBareinformedofC's transmissiontoD.NodeAisallowedtotransmitonlyifitisnotinthetransmissionrange ofD.ThisrestrictiononA'stransmissionreducestheamountofinterferenceatD,butit isstillnonnegligible.However,Aisallowedtotransmitevenifitisinthetransmission rangeofC.WealsoassumethatBcanperformperfectinterferencecancelationofC's transmissionandrecoverthepackettransmittedbyA.However,A'stransmissioncauses interferenceatnodeD.Inordertoanalyzetheimpactofthesecondarytransmissionat 73
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theprimaryreceiver,weevaluatetheSignaltoInterferenceRatioSIRatnodeD.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 exponentialpathlosschannelwithoutfading,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 isthepathlossexponent. Figure54.Distributionofsignaltointerferenceratio, Thedistributionfunction F )]TJ/F15 11.9552 Tf 5.787 1.794 Td [( ofSIRatD, ,forpathlossexponent =2 ; 4 arenumericallycomputedandplottedinFigure54.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.FromFigure54,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 respecttothenetworkofFigure53,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. UsingtheexamplenetworkofFigure53,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 isequivalenttondinganontransmittingnodethatis inthetransmissionrangeofB,butnotinthetransmissionrangeofD.Thisregion A F z isgivenby A F z = )222(A l ; 1 ;z ; 1
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Figure55.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 ofndingasecondarytransmitterisshowninFigure55forthreedierentnodedensities, .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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Figure56.Upperboundonprobabilityofreceptionbynode B TheprobabilityofsuccessfulreceptionatBofthesecondarytransmissionfromA, p TjF ,canbeupperboundedbytheprobabilitythatnoprimarytransmissionsoccur inthenonoverlappinginterferenceregionsofBandD.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 inFigure56forthreedierentnodedensities, ,andpathlossexponent, =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 Figure57.Upperboundontheprobabilityofasuccessfulsecondarytransmission, p S Theupperboundontheprobabilityofsuccessfulsecondarytransmission p S cf. 5{10isshowninFig.57forseveralvaluesofnodedensiy .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 spatialreuseandthroughputofwirelessnetworks.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 reuseandthroughputinwirelessadhocnetworks. 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 ofFigure61a.Thetimelineoftheprotocolfortheexamplenetworkisshown inFigure62,andtheframeformatsareshowninFigure63.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 Figure61.TypicalframeexchangesinOCSMAprotocol. thatrespondstotheRTSisthe primaryreceiver .Alltheothernodesthatreceivethe handshakesettheirtransmitallocationvectorsTAVforthedurationofthetransmission. ThetransmitallocationvectorissimilartothenetworkallocationvectorNAVdened 83
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Figure62.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. ConsidertheWANetinFigure61a,whereatsomepointoftime,nodeCintendsto forwardapackettoDthatithasreceivedfromBinanearliertransmission.Ctransmits anRTStoD,andDrespondswithaCTS,asshowninFigure61bandFigure61c, 84
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respectively.TheframeformatsoftheRTSandCTSrefertoFigure63inOCSMAare thesameasintheIEEE802.11protocol[52,Section7.2.1]. Figure63.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. ContinuingourexampleusingFigure61a,afterthecompletionoftheRTS/CTS exchangebetweenCandD,nodeCsendsaPTStoB.ThePTSframeformatisshown inFigure63.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 CTSFigure63.TransmissionofCTTimpliesthatthesecondarytransmitteriscapable oftransmittingoverlappeddatawithoutcausinginterferencetoanyofthetransmissions includingtheprimarytransmissioninitscommunicationrange. IntheexamplenetworkofFigure61a,whenBreceivesthePTSfromC,itensures thatitsTAVissetonlybyC'stransmissionofRTStoDrefertotheTAV0settingof BshowninFigure62.SinceBisnotinthetransmissionrangeofD,itwillbeable todetectD'stransmissionofCTSbutwillnotbeabletodecodeit.Thiswouldcause B'sTAV1tobesettoadurationofExtendedInterFrameSpacingEIFS[52,Section 9.2.3.5],butitwouldexpirebeforethePTSframeisreceivedrefertoTAV1settingof BinFigure62.Basedontheselectioncriteriaforchoosingapartner,assumenodeB 1 Usingotherapproaches,suchasroundrobinscheduling,mayincreasetheprobability ofchoosinganodewithapacketforthesecondaryreceiver. 87
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choosesnodeAtosendtheRTT.WhenAreceivestheRTT,itensuresthatitsTAVis notsetrefertotheTAVsettingsofAinFigure62.Ifitsensesthemediumtobefree, itrespondswithaCTTframe.Inthepresentexample,ifweassumethatAisinthe interferencerangeofCitcansenseC'stransmissionbutnotdecodeit,itwouldhaveset itsTAVwhenCtransmitsPTStoBtoadurationofEIFS,whichwouldhaveexpired bythetimeAreceivestheRTTframe. 6.2.3PrimaryTransmission Atimerattheprimarytransmitterissettoexpireinsynchronouswiththe completionofthesecondaryhandshaking.NotethatitsTAVtimerwillnotbesetduring secondaryhandshakingrefertotheTAVsettingsofnodeCinFigure62.Wenote thatthisdiersfromthetypicalNAVimplementationofIEEE802.11protocol.When thetimerexpires,ittransmitsitsDATAframetotheprimaryreceiver.Intheexample networkofFigure61a,uponcompletionofthesecondaryhandshaking,Cstartsthe primarytransmissiontoD,asshowninFigure61g.TheframeformatoftheDATA framerefertoFigure63isthesameasintheIEEE802.11protocol[52,Section7.2.2]. 6.2.4SecondaryTransmission Thesecondarytransmitterstartsitsoverlappedtransmission 0 secondsafterthe commencementoftheprimarytransmissionrefertoFigure62.This overlappeddelay 0 isdesignedtoallowthesecondaryreceivertoacquirethetimingandphaseoftheprimary transmission,whichgreatlysimpliestheinterferencecancellationICmechanismat thePHY.Itdoesnotensureperfectsymbolorphasesynchronizationoftheprimaryand secondarytransmissionsatthesecondaryreceiver.Theformatoftheoverlappeddata ODATAframeisthesameastheDATAframe.Thesecondaryreceivercancelsthe interferenceandrecoverstheoverlappeddata.ThisphaseisillustratedinFigure61h, whichdepictsnodeBreceivinganODATAframewhilecancelingouttheinterference causedbyC'stransmissionprimarytransmission.Notethatthesecondarytransmission isallowedtoterminate 1 secondsaftertheendoftheprimarytransmission. 88
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6.2.5DataAcknowledgments IftheDATAandODATAframesaresuccessfullyreceived,theprimaryand secondarytransmittersacknowledgetheirsuccessfulreceptionasshowninFigure61i andFigure61j,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. 6.3.1CrossLayerInteraction ThedesignofOCSMAprotocolinvolvesagreaterlevelofcrosslayerinteraction comparedtotheIEEE802.11protocol.Forinstance,whenanodereceivesanRTT, theMACneedstointeractwiththehigherlayerstodetermineifapacketofsuitable lengthcanbesenttothesecondaryreceiver.Itisalsopossiblethatapacketmight needfragmentationsuchthatthetransmissionofoverlappeddataisterminatedwithin 1 secondsoftheterminationoftheprimarytransmissionrefertothetimelineofthe protocolinFigure62.Similarly,whenthesecondaryreceiverreceivesaCTT,theMAC needstoindicatetothePHYlayerthatinterferencemitigationwillbeneededtorecover theoverlappedtransmission.Crosslayerinteractionisalsoneededatthesecondary 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 802.11basedwirelessnetworkswithminimalchanges.TheoverheadoftheOCSMA protocolcanbereducedconsiderablyifnosuchconformityisrequired.Forinstancethe CTTpacketcanbeeliminatedwithoutasignicantpenaltyonthethroughput.The eliminationofCTTpacketresultsinreducedprotocoloverheadbutincreasesthepower consumptionatthePHYofthesecondaryreceiversinceinterferencecancelationhas tobeturnedonmoreoften.Inaddition,theDAandPAeldsofthePTSandRTT frames,respectively,canbeeliminatedwithoutanysignicantperformancepenalty refertoFigure63.WecallthisprotocoltheOCSMAprotocolwithreducedoverhead OCSMA RO.Theperformanceofthisreducedoverheadprotocolissimulatedinthe 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,theparametersaregiveninTable61. Theoverlappeddelay 0 of240 scorrespondstoabout30bytesofdata,whichis 91
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slightlylargerthanthesumofthelengthsofPLCPheaderandPLCPpreamble bytes[52,Section15.2.2].Forothersystemparameters,thedefaultvaluesofthe802.11 implementationinns2areused.Henceforth,werefertoaMACservicedataunitMSDU asaframe,andatransportlayerserviceunitTSDUasapacket. Table61.NS2simulationsetup. Parameter Defaultvalue Datarate 1Mbps Simulationduration 4000s Warmuptime 400s Routingprotocol AODV Channelmodel Tworaypropagation RTSThreshold 150Bytes Transmissionradius 250m CarriersensingradiusInterferencerange 550m IFQlength 100 OverlappedDelay 0 240 s 1 240 s STARetryLimitsShort,Long ,4 Figure64.Tennodelinearnetwork. WerstevaluatetheOCSMAprotocolinaxedtennodelinearnetworkasshown inFigure71,withthesourceandthedestinationlocatedateitherendofthenetwork. Thenodesareplacedatregularintervalsof200m.Thistranslatestotheadjacentnodes beinginthecommunicationrangeofeachother,andnodestwohopsapartbeinginthe interferencerangeofeachother.Thetransmissionpowerofthesecondarytransmission 92
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isthesameasthatoftheprimarytransmission.ThetracmodelisbasedonFTP simulatedapplication",inwhichtheTCPqueueisneverempty.TCPisusedfor owcontrol,withamaximumwindowsizeof32.Theendtoendthroughputsofthe networkundertheOCSMA,OCSMA RO,andIEEE802.11MACprotocolsareshown inFigure65. Figure65.ThroughputcomparisoninatennodelinearnetworkwithTCPtrac. WeobservethatthethroughputoftheIEEE802.11MACprotocolincreasesuntil thedatapacketlengthreaches1000bytes,beyondwhichitstartsdecreasing.However, thethroughputofbothOCSMAandOCSMA ROincreaseuntilthepacketlengthreaches 1400bytes,beyondwhichthethroughputdecreases.TheOCSMAprotocolprovides throughputgainsof4%to39%overtherangeofpacketlengthsshowninFigure65.The maximumthroughputunderOCSMAisachievedforapacketlengthof1400bytes,at whichpointitprovides21%throughputgainoverIEEE802.11.Similarly,thereduced overheadversionofOCSMAOCSMA ROprovidesthroughputgainsof1140%overthe packetlengthssimulated,andprovidesathroughputgainof28%overIEEE802.11fora packetlengthof1400bytes. 93
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TheMACleveleventsacrossthenetworkforallthreeprotocolsaretabulated inTable62andTable63fordatapacketlengthsof400and1800bytes,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. Table62.ComparisonofeventsattheMAClevelinatennodelinearnetworkwith 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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Table63.ComparisonofeventsattheMAClevelinatennodelinearnetworkwith 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 AscanbeseeninTable62andTable63,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. ThethroughputofthetennodelinearnetworkofFigure71withconstantbitrate CBRtracisshowninFigure66forseveralpacketarrivalrates.Thepacketsize is1000bytes.Weobservethatthethroughputofallthreeprotocolsisthesameuntil thepacketarrivalratereaches20packets/s.Asthepacketrateincreases,thereisa dramaticfallintherateofpacketsdeliveredbyIEEE802.11.However,underOCSMA 95
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Figure66.ThroughputcomparisoninatennodelinearnetworkwithCBRtrac. andOCSMA RO,thedeclineinthethroughputismoregradual,andthethroughputgains providedbyOCSMAprotocolsoverIEEE802.11aresignicant. Figure67.ThroughputcomparisoninlinearnetworkwithmultipleCBRows. 96
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Next,weconsidertheeectofmultipleowsinalinearnetwork.Threesourcesand threedestinationsareplacedateitherendofatennodelinearnetwork,andthetrac typeisCBR.ThethroughputgainsofOCSMAandOCSMA ROover802.11withCBR tracandmultiplesowsinalinearnetworkareshowninFigure67.Thepacketarrival rateindicatesthecommonrateatwhichpacketsarriveateachofthesources.Itcanbe observedthateveninthepresenceofmultipleows,OCSMAandOCSMA ROprovide signicantgainsoverIEEE802.11inatennodelinearnetwork. Figure68.Eectofvaryingthenumberofnodesinalinearnetworkonthethroughput gainofOCSMAandOCSMA RO. Next,wevarythenumberofnodesinthelinearnetwork.FTPsimulatedapplication" tracwithTCPcongestioncontrolwassimulated.TheTCPpacketsizeis1400bytes, andthecongestionwindowsizeis32.TheendtoendthroughputgainsoftheOCSMA andOCSMA ROprotocolsoverIEEE802.11areshowninFigure68asafunctionof thenumberofnodesinthelinearnetwork.ItcanbeseenthatOCSMAandOCSMA RO providemaximumthroughputgainsof72%and77%,respectively,whenthenetwork consistsofsixnodes.Thegaindecreaseswithanincreaseinthenumberofnodesinthe 97
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network.Inathirtynodenetwork,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. Figure69.Binarytreenetwork. WealsoevaluatedthethroughputgainsofOCSMAandOCSMA ROoverIEEE 802.11inabinarytreenetworkshowninFigure69.Thelocationofthenodesaregiven inparanthesis.Inthistopology,eachnodeofthetreenetworkhasexactlytwochildren, andtherootlocatedat,580transmitsindependentmessagestoeachoftheleaf nodes.ThetractypeisCBR,andthepacketsmeantforeachoftheleafnodesarriveat 98
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thesourcewithsamerate.TherestofthesimulationparametersaregiveninTable61. TheperformancegainsofOCSMAandOCSMA ROinabinarytreenetworkwithadepth offourisshowninFigure610.Itcanbeobservedthatforpacketarrivalratesgreater than3,OCSMAandOCSMA ROprovideatleast35%throughputgainovertheIEEE 802.11protocol. Figure610.ThroughputgainofOCSMAandOCSMA ROinatreenetwork. Wenextconsiderarandomtopologywith50nodesdistributedina1500m 1500m square.Thisscenariocorrespondstoanaveragenodedensityoffournodesinacircleof radiusequaltothetransmissionrangeofanodesetto250m.Themobilitymodelchosen istherandomwaypointmodel,whichisthedefaultmodelinns2.Thenodesmovewith aspeedthatisuniformlydistributedintheinterval[0 ; max speed],whereweconsider dierentvaluesofmax speed.TwentyTCPconnectionswererandomlygeneratedwith packetsize1400bytes,andtherestofthesystemparametersaregiveninTable61.The throughputgainsofOCSMAandOCSMA ROoverIEEE802.11areaveragedover500 instantiationsoftherandomnetwork.TheperformancegainofOCSMAprotocolsover 99
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Figure611.Throughputgaininarandomnetworkwithmobility. IEEE802.11asafunctionofthemaximumspeedofthenodesinthenetworkisshown inFigure611.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 endtoendthroughputcanbeimprovedbyasmuchas77%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 toprovidereliableandecientendtoendservice. TheinteractionsbetweentheTCPandMACprotocols,likeIEEE802.11,inwireless adhocnetworkshavebeenwellinvestigatedbytheresearchcommunitysee[70{76]and thereferencestherein.Inwirelessnetworks,TCPsuersfrompoorbandwidthutilization andnetworkunfairness.Thisisprimarilyduetotheuniquecharacteristicsofthewireless environmentsuchashalfduplexlinks,channelnoise,andmobility. ToalleviatetheissuesassociatedwithTCPinwirelessnetworks,severalschemeshave beenproposedcf.[76{78].Theseschemesaimtoachievebettercrosslayerinteraction 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,thecrosslayerinteractionbetweenTCPandOCSMAisinvestigated. Wepresentresultsfromns2simulationsforavarietyofscenariosandstudytheinteraction betweenthetwolayers.WecompareandcontrasttheOCSMAprotocolwiththeIEEE 802.11MACprotocol.Inthefollowingsections,werefertoaMACservicedataunit MSDUasaframe,andatransportlayerserviceunitTSDUasapacket.AMAClevel acknowledgmentisdenotedbyacapitalizedACK,whileatransportlayeracknowledgment isrepresentedbyanitalicized ack Werstconsideratennodelinearnetwork,asdepictedinFigure71.Node1is thesource,andnode10isthedestination.Thenodesareplacedatregularintervalsof 200m.Thecommunicationradiusis250m,andthesensingrangeis550m.Inthelinear networkofFigure71,thetransmissionrangesofnodes3and9aredenotedbysolid circles,andtheirrespectivesensingrangesaredenotedbydashedcircles.Thedefault valuesofsimulationparametersaresummarizedinTable71. 103
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Figure71.TennodelinearnetworkunderOCSMA. Table71.SimulationsetupforevaluatingtheimpactofOCSMAonTCPperformance. Parameter Value Datarate 1Mbps CongestionControl TCPReno Simulationduration 2000s Warmuptime 200s Routingprotocol AODV Channelmodel Tworaypropagation RTSThreshold 150Bytes Transmissionradius 250m CarriersensingradiusInterferencerange 550m IFQlength 100 OverlappedDelay 0 240 s STARetryLimitsShort,Long ,4 TCPpacketsize 1400Bytes Applicationtype FTPsimulatedapplication" 7.2.1ImpactofTCPCongestionWindowSize Inthissubsection,weevaluatedtheimpactoftheTCPcongestionwindowCWsize ontheendtoendthroughputofthenetwork.Inns2,theCWparameterrepresentsthe receiveradvertisedwindowsize,anddenesthemaximumnumberofpacketstobesentat everyroundtriptime.TCPisdesignedtoadjusttheowbasedontheCWsizeandthe congestioninthenetwork.Inthefollowingsections,unlessotherwisestated,CWrefersto thereceiver'sadvertisedCW. 104
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Figure72.EndtoendthroughputcomparisoninatennodelinearnetworkwithTCP trac. TheendtoendthroughputundertheOCSMA,OCSMA ROandIEEE802.11MAC protocolsinthetennodelinearnetworkofFigure71asafunctionTCPCWsizeare showninFigure72.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 inFigure73a.TheleftordinatescaleisforDATAframes,andtherightordinateis forODATAtransmission.NotethatunderOCSMA,bothDATAandODATAframes 105
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contributetothelinkthroughput.TheDATAandODATAlossrateforOCSMAand IEEE802.11areplottedinFigure73b. WeobservethatthelinkthroughputunderIEEE802.11mimicstheendtoend throughputcurveofFigure72.NotethattherateatwhichDATAframesaredropped duetocollisionsincreasesastheCWsizeincreasesasshowninFigure73b.Inthecase ofOCSMA,boththeDATAandODATAreceptionrateincreaseswithanincreaseinthe CWsize,andsaturatesforCWsizesgreaterthan14.IncreasingtheCWsizeincreases thenumberofframesavailableforoverlappedtransmissioninthenetwork.Notethatthe DATAreceptionrateunderOCSMAislessthantheDATAreceptionrateunderIEEE 802.11.However,thecombinationofDATAandODATAframesinOCSMAprovidesa greaterendtoendthroughputoverIEEE802.11.Althoughthecollisionrateinthethe caseofOCSMAisveryhigh,theabilitytoperformoverlappedtransmissionsosetsthese collisionstoprovidehighthroughputevenwhenCWsizeishigh. Table72.EventsattheMAClevelinatennodelinearnetworkunderOCSMAprotocol. 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 WefurtherinvestigatethebehaviorofOCSMAbyanalyzingtheMAClevelevents 1 acrossthenetwork.TheMACleveleventsunderOCSMAaretabulatedinTable72for 1 Inthisscenario,eventscorrespondtoeitherreceptionofaframeoracollision 106
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aLinkthroughputinatennodelinearnetwork bFramedroprateinatennodelinearnetwork Figure73.MAClevelperformancecomparisonofOCSMAandIEEE802.11inatennode linearnetwork. severalvaluesofCWsize.WeseethattheaveragerateofRTSframesreceivedincreases astheCWsizeincreases.WealsonotethatthereceptionofRTTframesincreases indicatingthattheopportunitytoperformoverlappedtransmissionsasperceivedby thesecondaryreceiverincreases.However,theratioofthereceptionofCTTtothatof RTTissignicantlylowerthanone,whichindicatesthattheactualnumberofODATA transmissionsissignicantlylessthanthepotentialnumberofoverlappedtransmissions. 107
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TheNPTframewasintroducedinSection6.4duringthesimulationstoinvestigatethe reasonforthelowrateofoverlappedtransmissionsinthesystem.Itisnotapartofthe OCSMAprotocol,andwedidnotobserveanyadverseeectonthesystemthroughput duetoitsinclusion.InTable72,wenotethattheratioofNPTtoRTTisveryhigh indicatingthatalotofopportunitiesofoverlappedtransmissionsaremissedbecauseofa lackofsuitableframesforoverlappedtransmissionatthesecondarytransmitters.Wenote thatthenumberofoverlappedtransmissionsincreaseswithanincreaseintheCWsize; yet,thefullpotentialofoverlappedtransmissionsisnotrealized.Forinstance,foraCW sizeof16,theratioofCTT/NPT+CTTisonly48%.Thisismainlyduetothelackof interactionbetweenOCSMAandTCPasexplainedbelow. Figure74.Transmittercongestionwindowevolutioninatennodelinearnetwork. ConsiderthenetworkofFigure71andassumethatTCPisoperatingincongestion 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, whichindicatesthatitsqueueisnonempty.Thisincreasestheprobabilityofoverlapped transmission.TheresultsinFigure74plottheevolutionofthesourcecontention 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.Table72,weobservedthatthecollisionrateunder OCSMAprotocolsisveryhigh.Thisisduetoanincreaseinthenumberofcontrolframes inOCSMAcomparedtoIEEE802.11.Inthissection,weconsiderstrategiesthatnegate theimpactofthehighercollisionrateinOCSMAandincreasetheTCPthroughput. 2 Theactualnumberofpacketstransmittedbythesourceisminimumofthe transmitterandreceiverCWs. 3 TheTCPvariantTCPRenoisusedforcongestioncontrol. 109
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Figure75.EectofshortandlongretrycountsonthroughputgainsofOCSMAand OCSMA ROinatennodelinearnetwork. First,weanalyzetheimpactoftheSTAShortRetryCountSSRC,andSTA LongRetryCountSLRClimits[52,Section9.2.5.3]onthethroughputofOCSMA andOCSMA RO.TheresultsinFigure75showthethroughputgainsofOCSMAand 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. Table73.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 TheendtoendthroughputandtheMACleveleventsunderOCSMAandOCSMA withdelayedack OCSMA DAaretabulatedinTable73.WhentheCWsizeis2,the endtoendthroughputTPUTunderOCSMAandOCSMA DAarethesame.However, thenumberofcollisionsinthecaseofOCSMA DAismuchlowerthaninthecaseof OCSMA.Notethatthenumberofoverlappedtransmissionsaregreaterinthecaseof OCSMA DA.WhentheCWsizeis16,OCSMA DAprovides16%throughputgainover OCSMA.Alsonotetheincreaseinoverlappedtransmissionsandreductionincollisionsin thecaseofOCSMA DA. 7.2.3FairnessIssuesandMediumContention Inthissubsection,weinvestigatedtheinterowcontentionissueswhenTCPis usedinconjunctionwithOCSMA.Mediumcontentionisamajorsourceofunfairnessin multihopadhocnetworks.Dierentowsmayexperiencedierentcongestionissues,and theresourcesallocatedtothemmaybedierent.Starvationisanothermajorproblem whichresultsduetothegreedinessofTCPows.Inordertoevaluatetheseissuesinthe 111
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aNetworkwithparallelows bNetworkwithintersectingows Figure76.Networkswithmultipleows. contextofOCSMA,weconsiderthetwonetworktopologiesillustratedinFigure76a andFigure76b.Figure76ashowsanetworkwiththreeparallelowseachtraversing throughsixnodes.Theadjacentnodesinaowareplacedatadistanceof200m,andthe adjacentowsareseparatedbyadistanceof400m. TheresultsinFigure77plotthethroughputevolutionofeachofthethreeows undertheOCSMAandIEEE802.11MACprotocols.WechoseaTCPCWsizeof2for eachoftheows.TheTCPpacketsizeis1400bytes,andtheshortandlongretrylimits are20and10,respectively.WeobservedthataCWsizeof2gavethebestperformance underbothOCSMAandIEEE802.11.Weobservethatunder802.11,ows1and3 112
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Figure77.Throughputcomparisoninanetworkwithmultipleparallelows. havenonzerothroughputatalltimes,whereasthethroughputofow2iszero.The nodesofow2experienceinterferencefromboththeows1and3,whichresultsinzero throughputforow2.Thisistheclassicstarvationproblemencounteredinmultihop networksthatarisesbecauseofthegreedinessofTCPows. However,underOCSMA,thethroughputofow2isnonzero,butstilllowerthan thatofows1and3.Sinceow2experiencesinterferencefromnodesinow1and3,it isnotsurprisingthatthethroughputofow2islowerthanthatofows1and3.The nonzerothroughputofow2underOCSMAisprimarilyduetotheeectofincreased collisions,andtheabilitytoperformoverlappedtransmission.Sincethecollisionrate underOCSMAisveryhigh,nodesincludingthenodesinows1and3spendmoretime inbacko,whichprovidesagreaterchancefornodesinow2tocompeteandsucceedin accessingthechannel.Ontheotherhand,theincreaseincollisionsacrossalltheowsis osettoalargeextentbyanincreaseinspatialreuseduetooverlaptransmissions.For instance,inFigure77,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.Table71,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,ow2hasnonzerothroughput,whichisreectedbyahighervalueoffairness index. Next,wesimulatethenetworkofFigure76b,andevaluatethethroughputofeach theowsunderOCSMAandIEEE802.11.TheTCPCWsizeis2thisprovidedthe bestperformanceforbothOCSMAandIEEE802.11.TCPpacketsizeis1400bytes, andtheretrylimitsare,10.Thethroughputevolutionofeachofthetwoowsunder OCSMAandIEEE802.11MACprotocolsaredepictedinFigure78.InthecaseofIEEE 802.11,weseethatatanypointoftime,oneoftheowscapturestheresources,whilethe otherowiscompletelydeprivedofthechannelresources.Thisexempliesthegreediness ofTCPows.However,inthecaseofOCSMA,wenotethatthechannelresourcesare moreevenlydistributedamongboththeows,andthethroughputoftheowsissimilar 114
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Figure78.Throughputcomparisoninanetworkwithmultiplelinearows. duringtheentireobservationinterval.WeobservedthesametrendevenwhentheCW sizeisincreased.ThisindicatesthatOCSMAintroducesacertainamountoffairnessin situationsinvolvinginterowcontention. Toevaluateshorttermfairness,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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evaluatethelongtermfairnessbycalculatingtheaveragethroughputofeachoftheows overasimulationdurationof1800s.ThefairnessindicesunderIEEE802.11andOCSMA are f 802 : 11 =0 : 98 ; {6 and f OCSMA =0 : 99 ; {7 respectively.NotethatwhileIEEE802.11providesonlylongtermfairness,OCSMA providesbothlongtermandshorttermfairness. 7.3OCSMAwithLookAheadCapabilityOCSMA LA Intheprevioussections,weanalyzedtheimpactofOCSMAontheperformanceof TCPowsinwirelessnetworks.ThesimulationresultssuggestthatOCSMAprovides betterendtoendthroughputandfairnessoverIEEE802.11protocol.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 Figure79.TennodelinearnetworkunderOCSMA LA. SinceOCSMA LAisbasedonOCSMAprotocol,wehighlightonlythedierences betweenthetwoprotocols.WewillusetheexamplenetworkofFigure79todescribe thedesignofOCSMA LAprotocol.ForacompletedescriptionofOCSMAprotocol,refer toSection6.2.ThedierencesbetweenOCSMAandOCSMA LAareduringthe primary transmission and acknowledgment phases,asdescribedbelow. InthenetworkofFigure79,assumethatnode3'stransmissiontonode4isthe primarytransmission ,andnode1'stransmissiontonode2isthe secondarytransmission AfterthecompletionofthesecondaryhandshakingphaserefertoFigure61d,Figure61e, andFigure61f,node3commencesthetransmissionoftheDATAframetonode4. UponsuccessfulreceptionoftheDATAframe,node4acknowledgesitwithamodied ACK,theAKMAcKModiedframe.TheframeformatoftheAKMframeisshown inFigure710.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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Figure710.FrameformatsoftheOCSMA LAprotocol. Whennode4receivestheDATAframe,beforeforwardingittothehigherlayers,the MAClayerusesinformationcontainedintheframetodeterminethenexthopreceiverof thisframe.WeassumethattheMAClayerhasaccesstotheroutingtables.TheMAC 118
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addressofthereceiveriscopiedintotheNAeldoftheAKMframe,whoseformatis showninFigure710. ContinuingwiththeexamplenetworkofFigure79,oncenode4receivestheDATA frame,andassumingthatthereisaframealreadyinthequeuefornode5,itappropriately setstheNAandNFDeldsandtransmitstheAKMframe.WhentheAKMframeis receivedbytheprimarytransmitter,node3,itresetsitsretrylimits,andperformsbacko justlikeinthecaseofthereceptionofanACKframe.Whenthenexthopreceiver, node5receivestheAKMframe,itwaitsforadurationequaltothetransmissionofan ACKframetoallowfornode2'stransmissionofACKtonode1,andtransmitsaCTS frameifthemediumisfree.Notethattheinformationnecessaryforupdatingtheelds RAandDurationoftheCTSframerefertoFigure710areavailablethroughtheTA andNFDeldsoftheAKMframerefertoFigure710.Whennode3receivesthe CTSframe,itensuresthatthisframeisinresponsetoeitheranRTSframeoranAKM frame.Ifthisistrue,itproceedswiththesecondaryhandshakingphaseoftheOCSMA protocolrefertoSection6.2. Sincethenexthopreceivernode5inthepresentexamplerequestsfortheDATA frameevenbeforethesecondaryandprimaryreceivershaveachancetocontendforthe channelaccess,thesecondaryreceiver,node3hasthesuitableframeforanoverlapped transmissionwhennode4transmitstheDATAframetonode5.Onceanoverlapped transmissionoccursinthelinearnetwork,withhighprobability,thecapabilitytoperform overlappedtransmissionisretaineduntiltheDATA/ODATAframesreachthedestination. Forinstance,intheexamplenetworkofFigure79,whennode4transmitsaDATAframe inresponsetotheCTSsentbynode5whichrespondstoanAKMframesentbynode4, node3hasasuitableframeforanoverlappedtransmission,andinthenexttransmission durationwhennode5transmitstheDATAframeinresponsetotheCTSsentbynode6, node4wouldhaveasuitableframetheODATAframethatitreceivedfromnode3for anoverlappedtransmission,andsoon.Theprobabilityofoverlappedtransmissionishigh 119
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onlywhenthecollisionsinthenetworkarelow.Whenthecollisionrateincreases,there isahighprobabilitythattheprimarydatatransmissionmightnotbesuccessful,which aectstheperformancegainoftheLookAheadvariant. Figure711.ThroughputcomparisonofOCSMA,OCSMA LAandIEEE802.11ina tennodelinearnetwork. 7.3.2SimulationResults Inthissubsection,theperformanceofOCSMA LAisevaluatedusingns2,and comparedtothatofOCSMAandIEEE802.11.Therstscenarioweconsideristhe tennodelinearnetworkofFigure71.Theparametersusedforthesimulationare tabulatedinTable71.Weemploythedelayedack versionofTCPRenodescribed inSection7.2.2.TheresultsinFigure711comparetheendtoendthroughputofthe OCSMA,OCSMA LA,andIEEE802.11protocolsasafunctionoftheTCPCWsizealso seeFigure72.WenotethatthethroughputofthenetworkunderIEEE802.11increases untiltheCWsizeequals5,beyondwhichitdecreases.ThethroughputsunderOCSMA andOCSMA LAincreasewithanincreaseinCWsize,andthethroughputssaturatefor 120
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CWsizesgreaterthan14.ForCWsizegreaterthan20,wenotethatOCSMAprovidesa throughputgainof30%overIEEE802.11,whileOCSMA LAprovidesathroughputgain of39%overIEEE802.11. Table74.MACleveleventsinatennodelinearnetworkunderOCSMA 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 TheMACleveleventsunderOCSMAandOCSMA LAaretabulatedinTable74for threedierentvaluesofCWsize.NotethatthecongestioncontrolalgorithmisTCPwith delayedack .NotethatunderOCSMA LA,thenumberofCTSframesreceivedcanbe greaterthanthenumberofRTSframesreceived.ACTSistransmittedeitherinresponse toanRTSoranAKM.WenotethatwhenCWsizeis2,theratioofCTT/CTT+NPT is71%,andDATAlossduetocollisionsiszero.AstheCWsizeincreases,theendtoend 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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Figure712.ThroughputcomparisonofOCSMA LAandIEEE802.11inatennodelinear networkwithCBRtraic. inthecollisionrateinthenetworkcausesmostofthenodestobeinbackostate,which ensuresthattherearemorepacketsavailableforoverlappedtransmission. TheOCSMA LAprotocolisdesignedtoaddresstheissueofpacketstarvationin TCPows.However,weexpecttheLookAheadfeatureofOCSMA LAtobenetUDP tracalso.WeevaluatetheperformanceofOCSMA LAinatennodelinearnetworkwith CBRtrac.TheresultsinFigure712comparetheendtoendthroughputofatennode linearnetworkunderOCSMA LAandIEEE802.11withCBRtracasfunctionofpacket arrivalrateatthesource,node1alsoseeFigure67.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 reuseandthroughputinwirelessnetworks.InCDMAbasedcellularnetworks,the basestationcanexploitthespatialdiversityalongwithcooperativebroadcasting techniquestoscheduleadditionaltransmissionsinthesystem.Theresultsindicate thatsuchoverlappedtransmissionscanleadtosignicantgaininusercapacityovera conventionalCDMAsystem.Wealsoevaluatedtheusercapacityofacellularnetwork employingDPCasabroadcastingtechniquewhentheuserpopulationislarge,and comparedittothatofasystememployingTDMA.Theresultsindicatethatunderlow spectraleciencyrequirement,thegaininusercapacitybyemployingDPCoverTDMA isverymodest,atmost12%forthesystemparametersthatweconsidered.Thisisnot verysurprisingconsideringthefactthatrecentresearchinthisareahasshownthatin asingleinputsingleoutSISOdegradedGaussianbroadcastchannel,DPCprovides signicantgainsoverTDMonlywhenthereislimitedmultiuserdiversityandthe spectraleciencyrequirementoftheusersisveryhigh[13,47,48].Next,weevaluated theperformanceofoptimalandsuboptimalforwardlinkchannelsharingschemes.We observedthatunderhighspectralecienyregime,thereisasignicantperformancegain inemployingcooperativebroadcastingoverconventionalchannelsharingschemes,and thatcomputationallysimplerschemesliketwoandthreelevelbroadcastingtechniques provideperformanceclosetotheoptimalscheme. Inwirelessadhocnetworks,overlappedtransmissionshavethepotentialto signicantlyimprovethespatialreuseandthethroughputofthenetwork.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 ConsiderthefournodenetworkofFigure53.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 regionofFigure53.Thejointconditionaldistributionof X CD and X BD given X BC can bederivedinasimilarfashionandisgivenbyrefertoFigureA1 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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FigureA1.Circlecircleintersectionforanalysis. 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 crosslayerdesign. 134
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