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Direct-sequence code-division multiple-access overlay systems

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Direct-sequence code-division multiple-access overlay systems
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Rainbolt, Brad J, 1972-
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ix, 86 leaves : ill. ; 29 cm.

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Bandwidth ( jstor )
Binary phase shift keying ( jstor )
Code division multiple access ( jstor )
Error rates ( jstor )
Narrowband ( jstor )
Random variables ( jstor )
Receivers ( jstor )
Signals ( jstor )
Simulations ( jstor )
Transmitters ( jstor )
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non-fiction ( marcgt )

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Thesis:
Thesis (Ph. D.)--University of Florida, 1998.
Bibliography:
Includes bibliographical references (leaves 83-85).
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Typescript.
General Note:
Vita.
Statement of Responsibility:
by Brad J. Rainbolt.

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DIRECT-SEQUENCE CODE-DIVISION .MULTIPLE-ACCESS OVERLAY SYSTEMS














BY

BRAD .J. RAINBOLT














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 1998
















I dedicate this work to my parents, Patricia A. and Ronald J. Rainbolt.














ACKI\KNOWLEDGMENTS

I would like to thank Professor Leoni \. Couch II, Professor Ulrich H. Kurzweg, Professor Haniph A. Latcluna, and Prof'essor .Jian Li for serving as members of my committee. I extend special thanks to imy adviser, Professor Scott L. Miller, not only for his time, but also for his expert guidance throughout my studies, as related both to research issues and to professional issues.

I thank my family, my parents Patricia A. and Ronald J. Rainbolt in particular, for their support and encouragement throughout my studies. I also wish to acknowledge all of my friends at the University of Florida and elsewhere, especially my colleagues Ron Smith and Ali Almutairi.

Finally, I acknowledge with gratitude financial support from the Robert C. Pittman Fellowship and from the National Science Foundation.

























111















TABLE OF CONTENTS

page

ACKNOWLEDGMENTS ......... .................. iii

LIST OF ABBREVIATIONS ............................. vi

ABSTRACT ................. ................... viii

CHAPTERS

1 INTRODUCTION ............................ 1

1.1 Code-Division Multil)h-Access ...... .............. 1
1.2 CDMA Overlay ............................ 5
1.3 Overview of the Dissertation . .................. 6

2 NARROWBAND SYSTEM PERFORMANCE IN THE AWGN
CHANNEL ............................. 10

2.1 Effects of Overlay on a Narrowband User .......... 10
2.2 CDMA Transmitter Filtering .................. 15
2.3 Filtering Performance Criteria ................... 16
2.3.1 Gain of the BPSIK System ..................16
2.3.2 Effect on the PSD of the CDMA Signal ........ 17 2.3.3 Effect on the CDMA Code Sequence .......... 17
2.4 Filtering Methods and Results ................ 18
2.4.1 Eigenvector Filtering ................. 18
2.4.2 Null Filtering ....... ............... 20
2.4.3 Butterworth Filtering ................. 20
2.4.4 DFT-Based Filtering .................. 22
2.5 Summary ............. .................. 24

3 MMSE DETECTION OF FILTERED CDMA SIGNALS ...... 25

3.1 The MMSE Reciver ....... . .. ....... .. 25
3.2 MMSE Detection of Filtered CDMA Signals ........ 26 3.3 Simulation Results .... . . ................ 29
3.4 Summnary.......... ............................. 36

4 CDMA OVERLAY IN A CELLULAR. SYSTEM .......... 37

4.1 Characterization of the Cellular Environment ......... 38


iv









4.2 Performance of the Narrowband System ........... 45
4.3 Effects of CDMA Transmitter Notching ........... 47
4.3.1 Same-Link Assigninent . ................ 50
4.3.2 Staggereld-Link Assignment .............. 52
4.4 Simulations and Results . . .. .......... .. 53
4.5 Summary ...... ..... ................ 59

5 CELLULAR OVERLAY IN A FADING CHANNEL ......... 60

5.1 Limits on CDMA Capacity .................. 60
5.2 Limits on Narrowband Campacity. ... ....... ...... 65
5.3 Performance of the CDMA System .............. 71
5.4 Summary....................... ............... 77

6 CONCLUSIONS AND FUTURE WORK< .............. 78

6.1 Conclusions ......... ................. 78
6.2 Future Work ..... ...... ........... 81

REFERENCES ....................... .......... 83

BIOGRAPHICAL SKETCH .. ...... . ..... ............ 86














LIST OF ABBREVIATIONS AWGN: additive white Gaussian noise BPSK: binary phase-shift keying CDF: cumulative distribution function CDMA: code-division multiple-access DFT: discrete Fourier transform DS: direct-sequence FDMA: frequency-division multiple-access FH: frequency-hopped FIR: finite impulse response IEEE: The Institute of Electrical and Electronics Engineers, Inc. IIR: infinite impulse response ISI: inter-symbol interference LMS: least mean-squared LPD: low probability of detection LPI: low probability of intercept MAI: multi-access interference MC-CDMA: multi-carrier code-division nimultiple-access MMSE: minimum mean-squared error MSE: mean-squared error NBI: narrowband interference PDF: probability density function PSD: power spectral density RLS: recursive least-squares


\'i









SNR: signal-to-noise ratio SS: spread-spectrum



















































vii1














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



DIRECT-SEQUENCE CODE-DIVISION MULTIPLE-ACCESS OVERLAY SYSTEMS





Brad .J. Rainbolt

December 1998

Chairman: Dr. Scott L. Miller
Major Department: Electrical and Computer Engineering

In this dissertation, the possibility of code-division multiple-access (CDMA) overlay, that is the simultaneous sharing of a frequency band by a narrowband system and a CDMA system, is investigated. In contrast to the majority of existing studies on overlay, which investigate almost exclusively the degradation experienced by CDMA users as a result of the narrowband users. the results presented here focus specifically on the effects of the overlay on the narrowband system. It is shown that even for CDMA systems operating with a small number of users in comparison to the system capacity in the absence of overlay, the narrow)and system will experience a substantial loss in performance. The use of notch-filtering in the CDMA users' transmitters in order to avoid active narrowband users can alleviate the degradation experienced by the narrowband system. In turn, the effects of the notching on the CDMA system itself are seen to be quite modest.




v111









Overlay has great potential in a situation in which a frequency band which currently provides narrowband cellular service is designated to provide CDMA cellular service in the future. This transition can he made gradually with the implementation of overlay. Such a scenario is investigated in this research and promising results are presented. The use of multi-carrier CDNIA (MC-CDMA) is investigated for this purpose, and is seen to perform quite well. In a fading channel, diversity such as that offered by the use of multiple carriers improves the performance of a system operating at a given power level. In the overlay scenario in particular, there is the additional benefit to overall system performance. in terms of both CDMA and narrowband, that the CDMA users can lower their power in a imulti-carrier scenario and thus can reduce the amount of interference on the narrowband system.

The feasibility of CDMA overlay is bolstered by the results presented in this dissertation, and a strong motivation for its use as a method of transition from narrowband service to CDMA service is argued as well.



























ix














CHAPTER 1
INTRODUCTION

In this chapter, the concept of code-division multiple-access (CDMA) will be presented. The benefits that CDMA offers as well as some of the main works of research in this field will be summarized. This chapter will also introduce CDMA overlay, the focus of this dissertation. which is the sharing of frequency spectrum by a CDMA system and a sparsely-populated narrowband system. An overview of the dissertation will conclude this introductory chapter.


1.1 Code-Division Multiple-Access

CDMA is an emerging technology which employs spread-spectrum (SS) signaling, that is the intentional spreading of a digital signal over a bandwidth that is much greater than its information bandwidth. typically on the order of a 100-fold increase or more. Although spread-spectrumn systems are generally divided into two categories, direct-sequence (DS) and frequency-hopped (FH), depending on the method used to spread the user's bandwidth, this research will only be concerned with direct-sequence spread-spectrum, which is illustrated in Figure 1.1.

In the direct sequence method, a digital signal is multiplied in the transmitter by a periodic waveform of narrow pulses called the spreading code. In the example shown, an unspread binary phase-shift keying (BPSK) signal is shown at baseband as a series of unit-amplitude square pulses of width Ti,, the bit time, and its power spectral density (PSD) has a null bandwidth of 1/Tb. The resulting waveform after spreading also consists of a series of pulses, but the width is reduced to T, = Tb/N, where T, and N are referred to as the c'lilp time and the processing gain, respectively, and N = 7 in this case. The PSD of the spread signal has the same form as that


1






2





-11
(a) (b)



0 Tb 2T1, 3TI, 4T 0 Tb 7/Tb
Time Frequency + c(t)I c(t) + c(t)I + c(t)






0 Tb 2T,, 3T, 4T, o VTb 7/ b
Time Frequency Figure 1.1: Illustration of DS-SS wavefornls and PSDs, 7 chips/bit. (a) Unspread signal waveform; (b) PSD of unspread signal: (c) Spread signal waveform; (d) PSD of spread signal.



of the unspread signal, but has a null bandwidth of 1/T, = N/Tb, which is N times larger than the null bandwidth of the unslpread signal. Also note that since the total power is the same in the two signals, the height of the PSD is reduced.

For many years, spread spectrum has been used in military applications, due mainly to three of its features. First, it has a resistance to jamming, a process in which an adversary transmits an interferei'nc signal, which is usually narrowband, in an attempt to destroy communication. but not to intercept and make sense of it. Spread spectrum also has low probability of intercept (LPI) capability, meaning that it is difficult for an adversary to receive and demodulate the signal without knowing the spreading code. Finally, because the power is spread over such a large bandwidth, the spectral height of the spread-spectrum signal is reduced significantly, possibly to the point where an adversary would not be able to distinguish it from the channel






3

noise and hence would not even know that a communication is taking place. This is referred to as low probability of detection (LPD) capability.

In the past two decades, the research in this area has shifted from military to commercial applications, particularly in the study of CDMA systems, in which many direct-sequence spread-spectrum signals are transmitted in the same bandwidth and the code sequences are used as a means of providing separation between them. When the code sequences have some degree of orthogonality to each other, the job of the receiver is made easier, although exact orthogonality is not necessary, nor is it achievable in asynchronous communication systems. The problem of choosing good code sequences has been studied, and a good sunmmnary of many of the major results is found in Sarwate and Pursley [1].

CDMA is a very promising technology for several reasons. Most importantly, in a cellular scenario, there is the potential for a iany-fold increase in user capacity over traditional frequency-division imultile-access (FDMIA) systems. The cellular scenario will be looked at in detail in Chapters 4 and 3. Another advantage of using CDMA over FDMA is the inherent ability of a wideband signal, such as a CDMA signal, to realize diversity due to the frequency selectivity of the fading channel. An additional attribute of CDMA is the potential for privacy through the unique spreading codes of the different users.

A survey of the receiver structures that have been proposed in the literature begins with the conventional matched filter receiver, which was analyzed by Pursley [2] and by Yao [3] for an additive white Gaussian noise (AWGN) channel. One of the principal shortcomings of this receiver is its susceptibility to the near-far problem, a situation in which one or more users are physically located much closer to the CDMA receiver than is the desired user. and the desired user's signal is thus overwhelmed by this multi-access interference (NIAI). In such an environment, the system must use power control, a process in which the base station, a centralized control center,







4

sends information back to the mobile users, telling them to either raise or lower their transmit powers. With perfect power control. all of the signals are received at the same power level at the base station.

In response to the near-far problem, researchers have developed a large number of receiver structures with varying degrees of complexity and performance. A key feature of these near-far resistant receivers is that they utilize information about the other users' signals, either explicitly or implicitly in their processing. They take advantage of the known form of' the MAI and hence they also are referred to as multi-user detectors. The matched-filter receiver, on the other hand, treats the MAI as white noise which simply increases the therinal noise floor.

The optimum multiple-user detector [4,5] consists of a bank of matched filters and uses a Viterbi algorithm to demodulate the data streams of all of the CDMA users. While it does minimize the probability of bit crror, its complexity increases exponentially with the number of users. rendering it infeasible in practice. The optimum detector is very important, however. because at the time of its inception, common sentiment was that the near-far problem was an inherent shortcoming of CDMA that could not be overcome. The existence of this near-far resistant detector served as motivation for the development of implementable receivers that could outperform the conventional matched-filter receiver.

Because the optimum detector has such a high complexity, and requires a large amount of side information about all of the CDMIA users, several sub-optimum nearfar resistant receivers have been developed which have more manageable complexities. A few noteworthy receivers include the decorrelator [6.,7] and the multistage detector [8]. The minimum mean-squared error (MMSE) receiver [9-15] has received a great deal of attention during the past few years as it also offers near-far resistance and is very simple to implement. The MMSE also has an inherent resistance to narrowband interference (NBI), a feature that is very beneficial in an overlay scenario, which will






5

be discussed in the next section. It will also be seen that the MMSE can reject inter-symbol interference (ISI). A significant portion of the research presented in this dissertation focuses on the MMSE.


1.2 CDMA Overlay

In communication systems, a major design factor involves the limited amount of frequency spectrum that is available. With this as motivation, the overlay of a CDMA system on a frequency buadi that is also populated by narrowband users from another system has been examined b1 Milstein et al. [16]. An actual CDMA overlay system was simulated in this field study, and gave preliminary indications that it is an attainable goal, as both the CDNIA users and the narrowband users were able to communicate reliably. It would be very beneficial if some of the frequency bands which are currently occupied by sparsely-plopulated narrowband systems could increase their overall capacity by adding CDMA technology. Of particular interest is the possibility of implementing overlay in a cellular scenario as a means of gradually phasing-out an existing narrowband cellular system in a frequency band which ultimately will support exclusively a CDMA cellular system. This will be looked at in detail in Chapters 4 and 5.

In theory, the two systems, CDMA and narrowband, can coexist in the same frequency band as a result of their intrinsic properties. Consider first the effect of interference from a CDMA system on a narrowlband system. Using the same idea as that used in low probability of detection systems, CDMA users that are spread will have only a fraction of their power affecting the narrowband system which has a relatively small bandwidth. The effect of the CDMA system on the narrowband system may be tolerable if the processing gain is large enough and if the ratio of CDMA users to processing gain is small enough.

Conversely, when narrowband interference appears at a CDMA receiver, its effect can be lessened to some extent by using various interference rejection techniques






6

that have been thoroughly studied [17-20]. These techniques in general exploit the predictability of the narrowband interference aiid tile unpredictability of the wideband CDMA signals to form an estiniate of the narrowband interference. This estimate is then subtracted off of the received signal. The resulting signal will have a weaker contribution from the narrowband interference, but will also have some distortion on the wideband signals. The net effect of the interference rejection on the CDMA system should be favorable, however.

The design of an overlay system has many important trade-offs. In terms of the CDMA system, the ratio of users to processing gain should be maximized. But increasing this ratio too high might make the narrowband system inoperable. On the other hand, if the bandwidth of the narrowband users is increased too much, the interference rejection techniques employed in the CDMA system become less effective. And if either system operates at an excessive power level, it will render the other system inoperable. These considerations will be examined in detail in subsequent chapters.


1.3 Overview of the Dissertation

The focus of this dissertation will be those issues arising when a CDMA system is overlaid on an existing narrowband system. The material can be divided broadly into three parts. First, overlay in an AWGN channel will be investigated in Chapters 2 and 3. This material will be extended to a cellular system in Chapter 4. Finally, in Chapter 5, the results for the cellular system will be extended to the fading channel, which is a much more realistic model for a \wireless environment. Conclusions and related topics of future research will be looked at in Chapter 6.

Previous research in this area. has focused almost exclusively on the performance improvement of a CDMA system when techniques are applied to reject narrowband interference in the same frequency band. While this problem is certainly applicable and important, an equally and perhaps more important task is to quantify the effect






7

that CDMA overlay has on a typical narrowband system. Because the CDMA is being added to a frequency band that is already established, it seems logical that the operation of the existing narrowalnd system should be given top priority. A careful evaluation of the degradation due to overlay which is experienced by a BPSK user in an AWGN channel is given in Section 2.1. It is shown that the BPSK user can only tolerate the overlay if the loading of the CDMA system is extremely light. In this case, it is questionable as to whether or not it is cost-effective to even design and implement a new CDMA system when the added benefits seem to be very limited.

A technique to alleviate the severe degradation seen by the narrowband system is presented in Section 2.2. By employing a notch filter in the CDMA transmitter, the frequency bands occupied by narrowband users can be avoided, and the effects of the CDMA overlay on the narrowband users will be reduced dramatically. The rationale behind this is that the wideband CDMA signals should still maintain their desirable properties to a large degree if the notch is not too wide. Some criteria to measure the effectiveness of different filtering methods are given in Section 2.3, and are applied to four filtering methods presented in Section 2.4. The narrowband system is found to benefit tremendously from this filtering, even if the CDMA users are received at large near-far ratios. It is found tha.t the narrowband system can tolerate the overlay of a CDMA system that is loaded up to levels far beyond that which the CDMA system itself can realistically handle. A significant conclusion of this dissertation is that the proposed filtering operations arc vital for the realization of CDMA overlay.

Given that CDMA transmitter filtering is necessary in order for the narrowband system to work, the next step is to quantify the effects that the filtering will have on the performance of the CDMA system. This is done in Chapter 3 for the AWGN channel. With filtering added, the problem amounts to more than just receiving a CDMA signal corrupted by MAI and llrrowband noise, which has been studied extensively. The MMSE receiver, first mentioned in Section 1.1, is described in detail






8

in Section 3.1. Performance equations for the NIMSE receiver are presented in Section 3.2. Simulation results are then presented in Section 3.3, both for a receiver which is able to track the ideal WViener solution and for one which uses an adaptive algorithm. The MMSE receiver was compared to a conventional matched filter receiver, and was clearly superior, showing a capacity gain of 8-11 times when using the Wiener solution and 6-8 times when using an adaptive algorithm. It is also important to note that the MMSE receiver using an adaptive algorithnl was able to perform well although it did not even know that the code sequence was filtered, a very attractive feature in this scenario. The results of these simulations, combined with the results on the performance of the narrowband system presented in Chapter 2, present a strong case for the feasibility of CDMA overlay.

The previous results simply demonstrated that overlay can be done if the CDMA users employ transmitter notching. In Chapter 4, a. compelling motivation for overlay is presented, as these results are extended to the cellular scenario, where overlay seems to have the most potential from a commercial point of view. If a frequency bandwidth which supports a narrowband cellular system is designated for conversion to a CDMA cellular system, overlay is an ideal way to make this transition gradually. Over the long term, the number of subscribers still using the narrowband products would shrink while the number of subscribers using the new CDMA products would increase. Conclusions similar to those reache(l in Chapters 2 and 3 will be realized in the cellular case. In Section 4.1. the cellular environment will be characterized. The effects of overlay on the narrowband system will be examined in Section 4.2, and it will be seen again that the narrowband users undergo a large amount of performance degradation as a result of the overlay. In Section 4.3, the idea of notch-filtering the CDMA signals will be applied, and will again provide tremendous benefits to the narrowband system. Simulations and results will be presented in Section 4.4.






9

In Chapter 5, the results of the cellular overlay system presented in Chapter 4, for which an AWGN channel model was used. will be extended to the fading channel, which is a more realistic model for \wireless communication. In a flat-fading channel, the number of CDMA and narrowband users which can be supported simultaneously is very low, as will be shown in Sections 5.1 and 5.2. The effect of the CDMA overlay on the narrowband system is substantial. and can be solved by CDMA transmitter notching once again. However, in order to support a reasonable amount of narrowband users, the CDMA users must do a large amount of notching. A solution to this is to use multi-carrier CDNIA (IC-CDMIA), which has recently become quite popular. The transmission of the CDNIA signal on several carriers, which are spaced in frequency so that the fading on each will be independent, allows for frequency diversity. Thus the CDMA users may transmit at lower powers, and will therefore not require as much notching as in the single-carrier case with a flat-fading channel. It will be seen that overlay is realizable in cellular scenarios, and can provide a very efficient means of transition from narrowband cellular to CDMA cellular.

In Chapter 6, the overall conclusions of this research will be summarized by two major points. First, it is not practical in terms of maximizing user capacity to implement overlay without the use( of transmitter notching in the CDMA signals. Their effect otherwise is too harmful to the narrowband system. Second, there exists great potential for CD.MA overlay as a ineans for the cellular service provided in a given frequency bandwidth to be transitioned gradually from narrowband to CDMA.














CHAPTER 2
NARROWBAND SYSTEM PERFORMANCE IN THE AWGN CHANNEL

In an overlay scenario, it is especially important to make sure that the CDMA system does not degrade the narrowband system's performance to the point of inoperability. One possible situation occurs when a CDMA system is overlaid on a sparsely-populated narrowband systern that is already in operation. The designers of the CDMA system must work around the narrowband system and should not expect the designers of the narrowband system to make significant modifications to their design in order to accommodate the CDMA system. Another situation is one in which the two systems are to be designed jointly. It is the goal of this chapter to quantify the effect of the CDMA system on the performancene of a narrowband user.


2.1 Effects of' Overlay oil a Narrowband User

As mentioned before, little attention has been given to quantifying the effects of CDMA interference on a narrowband user in an overlay scenario. The subject was treated by Davis [21] and it was reported that the CDMA overlay can cause problems for the narrowband users. Results were given by Pickholtz et al. [22] for the case of a single spread-spectrum user and actual measurements were reported in the CDMA overlay field study performed by Milstein et al. [16]. We will demonstrate in this paper exactly how much degradation is caused to a typical narrowband system in such an environment.

Toward this end, consider the performance of a BPSK user operating in an overlay scenario in an AWGN channel. In order to hand-limit the BPSK user's signal, a rootraised cosine pulse shape will be used in tihe, transmitter and in the matched-filter receiver. Assuming equal carrier frequencies for the narrowband and CDMA systems,


10






11

the received signal at the input to the BPSIK matched filter after down-conversion is


r(t) = V2 Eb d,,h(t iT,) + E 2P d,,ick(t iT- 7k) cos(Ok)+ n(t)
i=- 00= 1 i=-co
(2.1)

where Eb is the average energy-per-bit of the BPSI( system, Tb is the bit time for both systems, and db,i and dk,i are the ith data bits of the BPSK user's and the kth CDMA user's data stream, and h(t) is the BPSIK user's root-raised cosine pulse shape, which is normalized so that the integral of h2(t) on (-oo, oo), its energy, is unity. Also, K is the number of' CDMA users. PA. is the average power of the kth CDMA user, ck(t) is the kth user's spreading waveform consisting of unit-amplitude positive and negative pulses of duration T,, the chip time, and N is the processing gain, or the number of chips/bit. The kth CDMA user's delay and phase, Tk and Ok, are taken as constant throughout transmission, as the channel is assumed to be non-fading and stationary. Also. ,(t) is a white Gaussian noise process with spectral height No/2 The jth sample of the output of the matched filter is


Zj = 2d,j + V PAT cos(0k)Ik(j) + Nj (2.2) k=l

where Nj is a zero-mean Gaussian random variable with variance No and the random process Ik(j) associated with the contribution from the kth CDMA user in the jth bit interval is given by


I(j) = dk(j+[!LJ) k..,od(,,,N)h(nmTc Tk) (2.3) m=-LN

and [xJ is the floor function. It is assumed in this expression that h(t) is negligible for Itl > LTb. Thus the interference contribution from each CDMA user is the sum of samples of the root-raised cosine pulse weighted by both a data bit and a spreading chip. It appears that the central limit th'or(emi may be invoked to approximate Ik as a Gaussian process since it is the sun of many random variables. Although this






12



(a) (b)






(c) (d)

_Illlli ll dII II IIIIII I

Figure 2.1: Histograms for CDMA interference caused to a BPSK user. (a) Single CDMA user, BPSK user employing root-raised cosine pulses; (b) Single CDMA user, BPSK user employing square pulses; (c) 3 CDMA users, BPSIK user employing rootraised cosine pulses; (d) 3 CDNMA users, BPSIK user employing square pulses.



approximation does not hold for each individual Ik the total CDMA interference is the sum of K of these terms, and for relatively small values of K, the distribution of the sum of the Ik terms does approach Gaussian. An example is shown in Figure 2.1. The histograms for a single CDMA user's interference contribution are shown for the case when the BPSIK signal uses root-raised cosine pulses, and also for the case when square pulses are used. In both cases, the interference is clearly nonGaussian. However, when the root-raised cosine filter is used, the interference does take on somewhat of a continuum of values concentrated in three areas, in contrast to the discrete 4-valued variable resulting in tihe square pulse case. As a result of this continuum, the sum of only 3 such variables is seen to be well-approximated by a Gaussian distribution, while in the square pulse case, the sum of 3 interference terms is still not close to Gaussian. Using the Gaussian approximation, and the fact that Ik(j) is of zero mean, the decision statistic from equation (2.2) can be rewritten as


Zj = 2bb,j + N 0. 2P,.T, cos' (0k)Var(Ik) + No (2.4)






13

where the notation N(m, a2) is used to denote a Gaussian random variable with mean m and variance a2. The probability of error can then be approximated as



Pe 2 Q 2E, (2.5) S E 2PA.T cos-(O.)Var(Ik) + N0


where the Q-function is defined as

1 u
Q(x) =e -) cdu (2.6)


Equation (2.5) then simplifies to


eA + N k Cos 2(Ok)l/ar(Ik) (2.7)


where Pb = Eb/Tb is the BPSK user's average power. The variance of Ik, with the averaging done only with respect to the data bits, is then found as I. N
l/Var( k) = (h(mT. )) LN
+ hm [(itT, T)h(ni2Tc Tk) (2.8) ml=-L A'


X Ck,mod(m i, ) C('k.niod(i...V)

Because the variance is dependent on the particular code sequence, it may take on a range of values. If the expectation is further takeii over all code sequences, the second term of equation (2.8) drops out, and the variance is equal to the sum of samples of h2(t) spaced at intervals of T_. Because h(t) was normalized such that the integral of h2(t) on (-oo, o) is unity, then this variance can be approximated by invoking






14

the definition of a Rieman sum, which states that

b I
f (x) dx = li a (a + (ba) (2.9)


Thus for sufficiently large N. the variance is approximately 1/T,. Combining this with equation (2.7) gives


Pe1 + cOS2 (0k)1/2 (2.10) Elk= 2E11

The same expression for the probability of error was obtained by Davis [21], and was also derived by Pickholtz et al. [22] for the single-user case, when square pulses are used in the transmitter, and the corresponding matched filter is an integrate-anddump. An approximation for the case of square pulses was also given as [21]


P, mQ +2Ek)] -1/2 (2.11)


This expression is much easier to evaluate than is equation (2.10), which requires a K-dimensional numerical integration over the IK CDMA users' random phases, a very time-consuming process even for a small nnullber of users. The numerical integration was performed, and a plot of the probability of error vs. Eb/No for the BPSK system is shown in Figure 2.2 for the case of 3 CDMA users of equal power ratio, (P/Pb), and a processing gain of 31 chips/bit. The different curves represent different values of (Pl/Pb), and the case of no overlay is shown for reference. The approximation of equation (2.11) is also shown and matches the numerical results pretty well. Although each CDMA signal may have only a small fraction of its energy in the same bandwidth as the BPSK user as a result of the processing gain, that energy obviously has a non-negligible effect. The collective effect of the 3 CDMA users clearly degrades the performance significantly even when they are received at 0 dB, a situation which would require strict power control working cooperatively with both the CDMA system






15

10- 2 . (Pc/Pb)
2 dB

-2 dB

10 6 -6 dB
No overlay -10 dB
10-8 -14 dB
7 8 9 10 11 12 Eb/No (dB)

Figure 2.2: Probability of error, P, of BPSI< user vs. Eb/NO with CDMA overlay of 3 users with 31 chips/bit. Solid curve is for numerical integration, dashed curve is for approximation of equation (2.11).



and the narrowband system. These results cast considerable doubt on the feasibility of CDMA overlay. It may not even be worthwhile to implement a CDMA system with a loading of K/N = 3/31, and these results indicate that this very lightly-loaded system still causes severe degradation to the narrowband system. Obviously, something must be done to lessen the effect of the CDMA interference on the narrowband system, and one such method will be investigated in the next section.


2.2 CDMA Transmitter Filtering

In an effort to improve the previous results, which seem to preclude the chance of CDMA overlay, an idea which was suggested both by Milstein et al. [16] and by Davis [21] will be investigated. The energy from a CDMA signal that does appear in the same bandwidth of a narrowband user apparently requires more attenuation than that which results solely from the irocessiing gain. The attractive properties of a CDMA signal, such as its inherent separation from other CDMA signals as a result of the spreading codes, its inherent separation from narrowband signals as a result of the processing gain, and its robustness to multipath, may not be sacrificed too much if only a small notch is placed in its spectrum. And if the frequency ranges occupied






16

by narrowband signals are notched out. the CDMA signal will effectively avoid the narrowband system.

To perform the notch filtering, the code sequence is altered to a new code sequence, which consists of pulses, most likely square, whose amplitudes are no longer constrained to the values 1. The filtered code sequence is then modulated with the data waveform and converted up to bandpass and transmitted, just as the unfiltered code sequence would be.

Four methods of filtering the code sequence will be examined and will be compared based on three criteria which will be elaborated on in the next section: the gain realized in the BPSK system, the effect on the PSD of the CDMA signal, and the effect on the CDMA code sequence.


2.3 Filtering Performance Criteria

In this section, three criteria will be presented which will measure the effectiveness of a given method of notching at the CDMA transmitter. The gain of the BPSK system, the effect on the PSD of the CDMA signal, and the effect on the CDMA code sequence will now be explained in detail.


2.3.1 Gain of the BPSK System

The probability of error of the BPS system given in equation (2.7) depends on the variance of Ik, given in equation (2.8), which in turn depends on the users' code sequences. As will be seen later, two of the four filtering methods used in this work result in ISI, and hence the expression for Ilk must be modified in those cases to include the appropriate contributions which result from the spillover.

The evaluation of the variance of Ik requires simulation. It is then used in equation (2.7) to get the probability of error. Because the variance is multiplied by the CDMA-to-BPSK power ratio (PA./PI,), if the filtering reduces the variance by a certain multiplicative factor, the power ratio can be increased by the same factor and the






17

performance will be the same as in the unfiltered case. Thus the ratio of the variance without filtering to the variance with filtering should be found, and it will indicate how much additional near-far effect the BPSK system can tolerate. The amount of gain required depends strongly upon environmental factors such as the cell geometry and path-loss exponent [16]. It is conceivable that gains on the order of 50 dB may be required. This could be the case when many CDMA users are present and/or a severe near-far problem results from one or more of these users transmitting from a location much closer to the narrowband receiver than that of the narrowband transmitter. If the CDMA users and the BPSIK user are not power-controlled by the same mechanism, then large near-far ratios are very possible.


2.3.2 Effect on the PSD of' the CDMA Signal

To see how certain filters perform in notching the CDMA signal, consider the PSD of a CDMA user's signal which is given as


IQq ~ A' 2 -2
SI ((f ) c,,e-1 f
T ,=o (2.12) I (. C(f)l


where Q(f) is the Fourier transform of the chip pulse shape, c, is the nth chip, and the number of chips in the spreading sequence is N.i, which may be greater than the processing gain N. From this expression, it is clear that the effects of filtering will appear only in the rightmost magnitude-squared term, IC(f)12 which can be plotted as a function of frequency to show these effects.


2.3.3 Effect on the CDMA Code Sequence

In two of the four filtering methods examined in this dissertation, the output code sequences are of length greater than N, which means that they span more than a single bit. While this spillover greatly alleviates the effect of CDMA interference on






18

the BPSK system by making deep notches in the PSD, it may cause obvious problems in the CDMA receiver. Even if the receiver can handle this ISI, it is obviously desirable to minimize it.


2.4 Filtering Methods and Results

In this section, four filtering methods will be presented and compared based on the three previously described criteria. Simulations were performed in which a BPSK user employed root-raised cosine pulse shapes with a rolloff of a = 0.35. The BPSK user and an interfering CDMA user were assumed to have the same data rate, 1/Tb, with the CDMA user employing a random code sequence of length N = 32 chips/bit, or a filtered version of this sequence, and a delay chosen from a uniform distribution on (0,Tc). Then 10000 trials were run. each of which generated a sample of Ik when filtering was employed and a sample when no filtering was employed. The ratio of sample variances of Ik for the filtered and unfiltered cases was then computed. This gain and a plot of |C(f)12 in equation (2.12) will be presented for each filtering method. A plot of the filtered code sequence will be presented for the two methods in which ISI results.


2.4.1 Eigenvector Filtering

This method was proposed by Davis [21] and will be summarized briefly. The code sequence is clocked through a finite impulse response (FIR) filter with 2M + 1 taps, and the filtered code sequence will be taken from the delayed output. The weights are chosen so as to minimize the effects of the CDMA interference on the BPSK system. For the case when the BPSIK system uses square pulses, not root raised cosine pulses, the variance of the CDMA system's contribution to the BPSK system's matched filter was derived with and without transmitter filtering [21]. The two quantities were found to differ by a multiplicative factor of aBaT, where a is a






19

Table 2.1: Gains in dB for BPSIK system for eigenvector and null filters.

Taps 6 7 8 9 10
Eigenvector 32.8 36.8 35.5 24.0 20.0 Null 9.7 14.9 20.9 15.5 10.6



row vector of tap weights, B is a matrix whose (i, j)th element is given by


B(i,j) = V (2.13) where N is the processing gain and w is the difference of the two systems' carrier frequencies. If the quantity aBaT is minimized, then the effect of the CDMA interference on the BPSK system will also be minimized. This minimization is performed by letting a be the eigenvector of B corresponding to its smallest eigenvalue. Then the quantity aBaT is equal to this eigenvalue.

It will be the convention throughout this dissertation to denote vector and matrix quantities in boldface type.

In Table 2.1, the gains achieved by the eigenvector filter are shown when the number of taps, M, on each side of the center tap varies from 6 to 10, and the processing gain is 32 chips/bit. Although it seems that the gain should increase and eventually level off as the number of taps is increased, the maximum gain is 37 dB, occurring for AM = 7. An explanation for this behavior might be that the eigenvector filter was derived for the case when the BPSIK system uses square pulses, not root raised cosine pulses.

In Figure 2.3, a plot of IC(f)12 for an cigenvector filter with M = 7 and Aw = 27r(0.125) shows that the filter severely distorts the CDMA signal. The desired response should have a deep inull of finite width around the desired frequency, and as little distortion as possible in the passband. This filter does not even have a parameter to control the width of the notch. Although it does provide a pretty sizable gain






20

of 37 dB for the BPSK system, the eigenvector filter does not seem to be a plausible option based on its detrimental effect on the CDMA signal.


2.4.2 Null Filtering

In the second method proposed by Davis [21], the filter puts a spectral null at the BPSK system's carrier frequency. The tap weights a are given as

'o = 1
-2 cos(mAWT,.)
m in = 1, 2,... M (2.14) 2M1 1 +
a= 3/10

and the filtered code sequence is formed again from the delayed output of the FIR filter with tap weights given by a. The gains achieved by the null filter are shown in Table 2.1 for the same values of M as for the eigenvalue filter and also for a processing gain of 32 chips/bit. A maximum gain of 21 dB. significantly lower than that of the eigenvalue filter, occurs for I = 8. and again an explanation for this behavior could be that this filter was derived for the case of square pulses in the BPSK system.

A plot of IC(f)12 for the null filter with 1 = 8 and Aw = 27r(0.125) is also shown in Figure 2.3. Again, the CDMA signal is somewhat distorted, and there is only a minor notch at the desired notched frequency, and no parameter to control this width explicitly. Based on this, the null filtering method does not seem like a plausible option, either.


2.4.3 Butterworth Filtering

We next consider the use of a digital Butterworth notch filter, which is an infinite impulse response (IIR) filter. The response when one period of the code sequence appears at the input lasts forever in theory. although it is negligible beyond a few bits. Nonetheless, the filtered code sequence will spill over into other bit intervals, resulting in ISI. To form the output code sequence, the unfiltered code sequence, which is one bit long and has N chips, is padded with several bits of zeros and clocked into the IIR






21




S(a)
S

10-5


0
-o)



10-5
0 (b)




S
iO- I

10-5




0! (d)

10-5
C'4i




100
S i i (e)




1 i I l l i
10-5




0 0.25 0.5 Digital frequency

Figure 2.3: PSDs for notch-filtered signals. Processing gain is 32 chips/bit. (a) Eigenvector filter, MI = 7 taps on each side: (b) Null filter, M = 8 taps on each side; (c) Butterworth filter. 8th order. 3-dB BW 1/32; (d) DFT-based filtering, no zero-padding; (e) DFT-based filtering, zero-pLadded to 8 bits. Solid curves are for unfiltered, dashed curves are for filtered.






22

Table 2.2: Gains in (11dB for B3PSI systeni for Butterworth filter.

BW 1/N 1.25/_N 1.5/AN
Gain (dB) 50.5 67.9 80.5








> One bit -1 > One bit
0 Tb 2T, 3T, 3.5Tb 4.5Tb
(a) (b) Figure 2.4: Real part of filtered code sequences. Processing gain is 32 chips/bit. (a) Butterworth filter, 8th order, 3-dB BW 1/32; (b) DFT-based filtering, zero-padded to 8 bits.


filter. The gains realized by the But.terworth filter are shown in Table 2.2 for an 8th order filter with 3-dB bandwidths of 1/.N, 1.25/N. and 1.5/N. The plot of IC(f)12 in Figure 2.3 for a bandwidth of 1/N shows that the notch is very pronounced and that the signal in the passband is not distorted. As shown in Figure 2.4, also for a filter of bandwidth 1/N, the code sequence continues well beyond one bit time, but is negligible beyond about 2 bits.

When a receiver is used that can handle sequences with spillover, the Butterworth filter seems like a very good option. It gives the BPSK system a large gain without distorting the CDMA signal's frequency response and without causing excessive spillover.


2.4.4 DFT-Based Filtering

Another way to filter the code sequence is to use a Discrete Fourier Transform (DFT), which provides a representation of the code sequence in the frequency domain. Because the inverse DFT is the sum of discrete frequency components weighted by the corresponding value of the DFT coefficient, notch filtering of the code signal can






23

Table 2.3: Gains in dB for BPSI( system for DFT-based filter.

Length (bits) 1 2 4 8 16 Gain (dB) 11.2 22.8 31.4 39.2 46.3



be performed by forcing to zero those values of the DFT that correspond to frequencies within the desired notching range and taking an inverse DFT. The frequencies represented are spaced by 1/N in the digital frequency domain, corresponding to a frequency spacing of 1/Tb in the analog domain. Thus if a notch of width 2/Tb is desired, there are three DFT coefficicnts. two surrounding the range and one in the middle of it, which should be set to zero. A plot of |C(f)' is shown in Figure 2.3, in the graph for no zero-padding.

Notice that there are deep nulls, but there are also high peaks between the nulls. When an N-point DFT of the unfiltered code sequence is used, no more resolution is available for notching. However, if the code sequence is padded with zeros so that an N-point DFT with N > N is performed. there will be more resolution. As shown again in Figure 2.3 for the case when the sequence is padded to cover 8 bits, the resulting notch is much deeper.

The DFT-based method was tested for an unpadded sequence and for sequences padded with zeros to cover 2, 4, 8. and 16 bits. The gains are shown in Table 2.3. To achieve a gain comparable to that of the Butterworth filtering method, a sequence padded with zeros up to 16 bits must be used. In Figure 2.4, the code sequence resulting from zero-padding up to 8 bits dies off pretty quickly, with much less spillover than was seen in the Butterworth case. The DFT-based filtering method also seems like a viable filtering method, perhaps in situations where the large gains given to the narrowband system by the Butterworth filtering are not needed. It will be seen later that the DFT-based filtering method is the better choice in terms of performance of the CDMA system.






24

2.5 Summary

It has been shown in this chapter that CDMA overlay has quite a damaging effect on a typical narrowband user. A very good solution is to employ notch-filtering in the CDMA signals to avoid active iiarrowbanid users. For Butterworth notch-filtering and DFT-based notch-filtering, substantial benefits were seen by the narrowband users, while the CDMA signals experienced little distortion in their PSDs and a manageable amount of ISI.














CHAPTER 3
MMSE DETECTION OF FILTERED CDMA SIGNALS

In this chapter, we will focus on how the filtering described in Chapter 2 affects the performance of the CDMA system in an overlay scenario. It will be shown that the MMSE receiver performs very well in this environment.


3.1 The IMMSE Receiver

The MMSE receiver has received significant attention due to many of its features such as near-far resistance to multi-access interference [9-11]. For the case of a single spread-spectrum user in the presence of narrowband noise, it was observed by Pateros and Saulnier [13] that the frequency response of the MMSE filter will adapt such that there is a notch at the location of the narrowband noise, thus providing inherent resistance to this type of interference as well. It. was shown by Poor and Wang [23] that the MMSE outperforms conventional narrowband interference rejection techniques, and that it can simultaneously suppress MAI along with the narrowband interference. It will be seen that the MMSE receiver also has the ability to reject inter-symbol interference. Another feature of the MMISE that is useful in the overlay scenario is its ability to work without previous knowledge of the desired user's spreading code. In fact, it does not even need to know that the code has been filtered.

A block diagram of the MMSE receiver is shown in Figure 3.1. The received signal is passed through a chip-lnatched filter, and the samples are stored until one bit time has passed. The contents of the equalizer are then correlated with the tap weights and compared to the desired output, which is the data bit of the desired user. For an initial training period, a known precanble is sent and thus the desired output is already known at the receiver. After trainingn. the taps should have had time to


25






26

t t = nTc

Tc

N-1 Wo
t =nTb

I C Decision


Adaptive algorithm, update taps error
signal
Training
Sequence

Figure 3.1: Block diagram of the MMSE receiver.



approach the ideal Wiener solution, but will fluctuate around it. Then the receiver uses decision feedback, in which the bit decision is used as the desired output.


3.2 MMSE Detection of Filtered CDMA Signals

The performance of the MMSE receiver in an overlay scenario will now be examined. We will consider a K-user CDMA svsteni. which uses code sequences of length N chips/bit that are filtered to give sequences of length N, which will be greater than N. The kth user's filtered sequence will be denoted as ck = (ck,O, ck,1, ... Ck,l-)T, where ck,n is the nth filtered chip. Then cA. is partitioned into L = [N/N] sequences each of length N, giving ck = (Ck,,C1 .... /,Ck,L-1 (3.1)
Ck.1 = (Ck,IN, CkN+1,. Ck,N+N-1 )T with I = 0,1,..., L 1. The last sequence, c..L-1, may be padded with zeros to make it of length N.

It should be noted that in this application, it is desired to place a notch in the bandpass CDMA signal in order to avoid a frequency range that a narrowband user






27

occupies. If this notch is not to be placed symmetrically about the carrier frequency, as will generally be the case, then the baseband CDMA signal will have a PSD that is not symmetric about zero frequency. Thus the notched code sequence will be complex. For the Butterworth filter, instead of doing a bandstop filtering operation in the appropriate frequency range. the impulse response of a highpass filter with the same bandwidth can be found, and then multiplied by a complex exponential sequence to shift the notch to the appropriate frequency range. For DFT-based filtering, the DFT points represent both positive and negative frequency ranges, and thus only the appropriate one-sided range of coefficients should be set to zero.

The received signal at baseband, denoted as r(t) in Figure 3.1, is given by


r(t) = (E ,.c.(t iTb Tk) exp(jOk) (3.2) +2n(t) exp(-jc,ft) + 2.1(t) exp(-jwct)

where Pk and Ok are the kth user's average power and phase, and dk(i) is the ith data bit of the kth user. Also in this equation, nl(t) is a white Gaussian noise process with spectral height No/2. The noise process resulting from a. narrowband user is given by j(t). Its PSD is modeled as a square pulse centered at an offset of Aw from the CDMA carrier frequency, and having width 2p. where p is a number between 0 and 1, most likely close to 0, that represents the fraction of the bandwidth (null-to-null) that the narrowband user occupies.

The receiver forms a bank of samples by integrating r(t) over chip-length intervals, as shown in Figure 3.1. The vector of matched-filter samples is given by
L-1
u(i) = T exp( 0I )d (i i)cl.I + n(i) + j(i)
1=0 -(3.3) + exp(j0s) [i.(i )fk,l + dk(i 1)gk,l] k=2 I=0






28

The cyclic shifts of the Ith partition of the kth CDMA user's code sequence are given by

fk,l =(1 k)(0, 0,... 0, cA (ki+, . Ck,lN-pk-1)T + 6k(0, 0, . 0, c Ck,/i +,I .. Ck,lN-Pk_2)T (3.4)
gk,t =(1 Sk)(Ck.N,-p.. CO.A-l,.+l1 ... Ck,lN-1, 0,0... O)T

+ 6k(Ck,N-Pl ,k1C.I p .-p. ,Ck,IN-1,0, 0, ... )T where the kth user's delay has been written as 7k = pkTc + 6k with pk an integer in the range (0, 1,... N 1) and rA. a. non-integer in the range (0, 1). Also in equation (3.3), n(i) is an N-length vector of independent complex Gaussian random variables with the real and the imaginary parts independent of each other and each having zero mean and variance o = Y/(2E,/No). The vector j(i) consists of complex narrowband interference samples with the real and imaginary parts independent of each other. The (i,j)th element of the matrix representing the correlation between the real parts of two samples is given by

Rjj(i, j) = Sa(2p7r(i j)) cos((Aw)Te(i j)) (3.5) where Pj is the narrowband user's average power and the same result holds for the imaginary parts of the ith and jth samples. Also in equation 3.5, Sa(x) = sin(x)/x.

Denoting the tap weights as w = (wo, wl, .. ,W -1)T, the output of the tapped delay line is given as Zi = w"u(i), which is generally a complex number. The receiver then compares Zi with the desired output dil(i). The tap weights wo which will minimize the mean-squared error between the two, J = E[IZ d1(i)12], are the solution to the Wiener-Hopf equation

Rwo = p (3.6)


where R = E[u(i)uH(i)] and p = E[dl(i)u(i)] = c1,o are the correlation matrix and steering vector, respectively. The bit decision is made as di(i) =sign(Re(Z})).






29

3.3 Simulation Results

In order to get an idea of how filtering affects the performance of the MMSE receiver, an overlay system was simulated. The CDMA users operated with filtered random sequences and a processing gain of N = 32 chips/bit. The value of Eb/No was fixed at 10 dB. The powers of the interfering CDMA users were chosen from a log-normal distribution with a standard deviation of 1.5 dB, to simulate powercontrol error. The notch-filtering was done using a DFT-based filter with 8 bits of zero-padding. The narrowband users were generated by putting white Gaussian noise through a Butterworth bandpass filter with a, digital 3-dB bandwidth of 0.5/32. Their center frequencies were chosen to fall within the analog frequency range (-0.5/T, < fNB < 0.5/T,), which corresponds to the digital frequency range of (-0.5 < fNB,d < 0.5) as the sampling rate is 1/T,. Their powers (near-far ratios) were chosen from a distribution that results from a situation in which they are uniformly distributed spatially around the CDMA receiver, a path-loss exponent of n = 3 is used, and the maximum near-far ratio is set to 40 dB.

For different numbers of narrowband users, the number of CDMA users was varied to find the maximum number that could be tolerated by the CDMA system. For each simulation, the code sequences, delays, and powers of the CDMA users as well as the frequency locations and powers of' the narrowband users were varied. The criterion chosen was that the blocking probability had to be less than 0.02, where a block was defined as a scenario in which the probability of bit error of the desired CDMA user, Pe,CDMA, was greater than 0.05. So the capacity of the CDMA system for a given number of narrowband users was the maxinmun number of CDMA users that could be present and still satisfy the performance criterion


Pr(Pc,. A > 0.05) < 0.02 (3.7)






30

50


40


S 30
S(b)

2 (a)
0 20


10
(c)

0 2 4 6 8 10
Narrowband users

Figure 3.2: Two-dimensional capacity plot for DFT-based filtering, zero-padded to 8 bits. Processing gain is 32 chips/bit. (a) MMSE receiver, minimizing J = E[IZi di(i)12]; (b) MMSE receiver, minimizing J = E[{Re(Zi dl(i))}2] ; (c) matched filter.


In Figure 3.2, a two-dimensional capacity plot is shown for a system which employs DFT-based filtering, with zero-padding upl to 8 bits. The curve labeled (a) represents possible operating points for the system, in terms of the number of CDMA users and the number of narrowband users that can simultaneously use the frequency band and still satisfy the CDMA system's performance criterion given in equation (3.7).

It should be noted that in this receiver, the blit decision is made by looking only at the real part of the filter output Zi = w" u(i). Hence better results would probably be obtained by choosing an algorithm to minimize J = E[{Re(Zi di(i))}2] as opposed to minimizing J = E[jZ di(i)12]. In this case, the imaginary part of the error can be ignored since it will not be used. With the same equalizer contents as in equation (3.3), the filter output can be written as Zi = (wo,.. + jwo.) (u.(i) + ju(i)) (3.8)






31

where wo,, wo,y, u.,(i), and u,(i) are all real vectors of length N. For the new definition of the error, we have


J = E[{i (i) (wO,u,,,(i) + wTyuy(i))}2] (3.9) Now in choosing the taps to minimize J, it is clear that this is equivalent to a real Wiener filtering problem with 2N taps. The first N taps are filled with uz(i) while the last N taps are filled with u,(i). The \Vicner-Hopf equation given in (3.6) can then be applied, with the understanding that u(i) = [u7'(i), u'(i)]T and wo = -[w o, w ,]T and p = E[di(i)u(i)] are now real vectors of length 2N and R = E[u(i)uT(i)] becomes a 2N x 2N matrix.

The results for this variation of the MMSE receiver are shown in Figure 3.2 as well, in the curve labeled (b). There is clearly an advantage realized over the case of minimizing the square of the absolute error. It is seen that between 1 and 2 additional narrowband users can be tolerated for a fixed number of CDMA users, for operating points at which there are 6 or less narrowband users. If the narrowband users employ spectrally efficient digital modulation at the same signaling rate as the CDMA system, then this range can fit N = 32 users without guard bands. So with 5 narrowband users, the band is about 135: populated, and the system can still support about 20 CDMA users.

The results for the matched filter in which the receiver is matched to the filtered code sequence are also shown in Figure 3.2 for comparison, in the curve labeled (c). Note that there is a substantial performance improvement realized by the MMSE receiver over the matched filter. When there are 8 narrowband users present, the MMSE receiver performs as well as the inatched-filter performs in the case of no overlay.

The performance of the DFT-based filtering method was also compared to the Butterworth filtering method in Figure 3.3. The DFT-based filtering method is clearly






32




40 ':


30 -' DFT-based


Q 20


Butterworth


0 2 4 6 8 Narrowband users

Figure 3.3: Two-dimensional capacity plot for MMSE receiver minimizing J = E[{Re(Zi di(i))}2]. Shown for DFT-based filtering, zero-padded to 8 bits, and Butterworth filter, 8th order, 3-dB BW 1/32. Processing gain is 32 chips/bit. Solid curves are for Wiener solutions, dashed curves are for adaptive solutions for LMS algorithm with step size 0.2/(total input power).



superior, and this can be explained by examining the filtered code sequences in Figure 2.4. The code sequence resulting from the Butterworth filtering had more energy that spilled over into other bit intervals than did the code sequence that used the DFTbased filtering method, which obviously degrades the CDMA system's performance.

Another important issue is the implecltation of these algorithms. The previous results assume that the receiver will be operating at the Wiener solution, and thus are best-case results. In practice, an adaptive algorithm, such as a least mean-squared (LMS) or recursive least-squares (RLS), would be used. Some simulations were performed to take this into account. In Figure 3.3, results are shown for both Butterworth filtering and DFT-bascd filtering, for the case when J = E[{Re(Zi d(i))}2] is minimized. As the LMS algorithm converges slowly, and the fast-converging RLS






33

(a) (b)
1 1



0.8 (3) 0.8



0.6 0.6
0 4 .

0.4 (2) 0.4



0.2 1 1 )Ji 0.2

mill i

0 100 200 0 100 200 Bits Bits

Figure 3.4: Transient behavior of mean-squared error using the RLS algorithm and a training sequence. (1) is for minimizing J = E[{ Re(Zi-dj (i)) }2], (2) is for minimizing J = E[IZi di(i)12], (3) is resulting absolute squared-error under criterion of (1).
(a) 20 CDMA users, 0 narrowband users and 0 notches; (b) 20 CDMA users, 2 narrowband users with near-far ratio of 20 dB. and 2 notches.



algorithm may have stability problems. the training was avoided for now by initializing the tap weights to the Wiener solution and allowing an LMS algorithm to run with a known preamble for many bits. This allows the filter to reach a steady state solution which takes into account the excess mean-squared error which would result from an adaptive algorithm. For a step size of 0.1/tip, where tip is the total input power, almost no difference was seen in comparison to the Wiener solution. For a step size of 0.2/tip, some difference was seen as shown in Figure 3.3. Thus if the filter is trained well, results close to the ideal ones with the Wiener solution can be achieved for a small enough step size.







34

It would also be interesting to observe the transient behavior of the MMSE receiver in the overlay environment, in addition to its steady-state operation reported above. The performance of the RLS algorithm will be looked at for this purpose, as its speed of convergence does not depend on the inlut power as in the case of the LMS algorithm. For 200 trials, the RLS algorithms was run first with 20 CDMA users and without narrowband users and notches, and then with 2 narrowband users and notches added. The squared error was averaged over the 200 trials in Figure 3.4. Both of the previously described IMMSE criteria were used for comparison.

In the first case with no narrowband users or notches, the mean-squared error is seen to converge to a steady-state value in about 150 bits. Notice that there is a significant improvement in the mean squared-error when the receiver minimizes J = E[{Re(Z; di(i))}2] as opposed to J = E[jZj di(i)12], but the required convergence time is about the same. Also notice that in the case when J = E[{Re(Z dl(i))}2] is minimized, the corresponding absolute value of the mean squared-error is very high. As stated before, the square of the real part of the error, which is used in making the bit decision, is minimized at the cost of allowing a large increase in the imaginary part of the error, which will not be used anyway. The same environment was simulated with 2 narrowband users received at a near-far ratio of 20 dB and with the corresponding notches added. The same amount of time, about 150 bits, was required for convergence to a steady-state value, which is seen to be somewhat higher than when no narrowband users are present. It is worth noting that the computational complexity of the two algorithms is the same, as every complex computation that is required for minimizing J = E[IZi di(i)12] requires two real computations in the other case. Thus minimizing J = E[{Re(Zi di(i))}2] offers a substantial improvement in performance with no added complexity or required training time.






35

(a) (b) (c)













I i
iI



0 0.05 0.1 0 0.05 0.1 0 0.05 0.1
Pe Pe Pe

Figure 3.5: Histograms of CDMA probability of bit error, Pe, for overlay system with 42 CDMA users and 1 narrowband user. Processing gain is 32 chips/bit. MMSE receiver minimizes J = E[{Re(Z, dI(i))}2]. DFT-based filtering, zero-padded to 8 bits. Solid curve is for no narrowband signal present, dashed curve is for narrowband signal present with a given narrowband-to-CDMA near-far ratio. (a) Ratio is 0 dB;
(b) Ratio is 20 dB; (c) Ratio is 40 dB.



It is also interesting to look more closely at the ability of the MMSE receiver to inherently reject strong narrowband interference. It was determined previously that when J = E[{Re(Z -di (i))}2] is minimized, 42 CDMA users could share the channel with a single narrowband user. In order to examine the effect of the narrowband noise, a system was simulated with 42 CDMA users with a single notch and a narrowband user with varying levels of power. In each trial, a new set of code sequences, delays, and powers were chosen for the CDMA users and a new frequency location was chosen for the narrowband user, all using the same parameters as in the previous simulations. Then the probability of bit error was found for the CDMA system for narrowband-toCDMA near-far ratios of 0, 20, and 40 dB, and also for the case when the narrowband signal was not present but the notching was still performed.






36

The resulting histograms of the probability of bit error are shown in Figure 3.5 for the three different near-far ratios and each is compared to the case in which no narrowband signal is present. It is seen that when the narrowband signal is received at 0 dB, there is little difference, but the performance does degrade somewhat for the 20 dB case, and degrades significantly for the 40 dB case. Hence it appears that the MMSE receiver is relatively robust to the presence of the narrowband signal, but for large near-far ratios its performance will be degraded. This is consistent with the conclusions reached by Poor and WVang [23], that while the MMSE receiver does outperform conventional narrowband interference rejection schemes, the output signal-to-interference ratio of the hlMMSE receiver will degrade for high-powered narrowband interference. Fortunately, the probability that a narrowband user will have such a large near-far ratio is low, as this would occur only in a small geographic region around the CDMA receiver.


3.4 Summary

In this chapter, we have shown that with the notch-filtering which was determined necessary in Chapter 2, the MMSE receiver can function quite well in an overlay environment. In the simulations performed here, the CDMA system could be loaded up to about 20 users for a processing gain of 32 chips/bit when 5 narrowband users were present, or about 15% of the band was jammed. It offers a substantial performance improvement over a conventional matched-filter receiver. These results, along with those of Chapter 2, are quite encouraging for the prospects of CDMA overlay.














CHAPTER 4
CDMA OVERLAY IN A CELLULAR SYSTEM

We will now extend the ideas of the previous two chapters to the cellular environment, an application for which CDMA overlay has perhaps the most potential for increasing user capacity. Because overlay is feasible only when the existing narrowband system is sparsely-populated, the cellular concept seems quite conducive to overlay, as each cell in a. narrowband system only utilizes a fraction of the system bandwidth, even when fully loaded. A cellular overlay system would be quite beneficial in a situation in which a narrowband cellular system is to be phased out in favor of a CDMA system [24]. With overlay, the transition could be gradual, as a new CDMA product could be introduced while the system still provides support to the existing narrowband products. In this chapter, it will be shown that overlay can be realized in the cellular scenario.

The total system bandwidth of the narrowband system is divided into several frequency groups, each consisting of a number of narrowband channels separated in frequency so as to minimize adjacent-chanuel interference. The groups are assigned to the cells in an intelligent manner which minimizes the co-channel interference, that is interference caused by users in different cells using the same channel. Thus even when fully-loaded, each cell only utilizes a small fraction of the total system bandwidth, as would be necessary for overlay. A CDMA system could be implemented using the same cellular layout, with the CDMA users in each cell spread in frequency over the whole system bandwidth.







37






38

4.1 Characterization of the Cellular Environment

In this section, some aspects of the cellular environment, such as the assignment of users to cells, the power control that is employed, and the interference that users cause to base stations other than their own will be described. We will look at a system with a frequency reuse of 1/7, which means that the total system bandwidth will be divided into seven groups which are then assigned to the cells in a manner which minimizes the co-channel interference. Each group will consist of a number of narrowband channels separated in frequency so as to minimize adjacent-channel interference.

As shown in Figure 4.1, with cell 1 as the cell of interest, effects from users in those cells beyond the two outer layers of cells shown will be considered negligible. The individual cells, numbered 1-19, are also given a letter from A-G which indicates which of the seven channel groups it will use. The coverage areas are shown as circles for simplicity, but in practice and in this research, a user will be assigned to the cell for which the path between the mobile and the base station is least attenuated. This will depend not only on the distance of propagation, but also on log-normal shadowing, which may be severe. So a user often will be assigned to a base station that is not the closest one geographically.

We begin by looking at the received power at a distance d, from a transmitter which may be either CDMA or narrowband. The power is typically modeled by first finding the received power at a close-in reference distance do, denoted Po. Then with n as the path-loss exponent and o, as the standard deviation of the log-normal shadowing, the received power at d,. is given in dB units as [25]

P= P 10 log( +N(0,) (4.1)

= [Po + 10, loglo(do)] + [N(0, ~) 10n loglo(d,)] 9- V~g-Ill~OL~l







39


12(F) I1(G) 10(E)

13(B) 4(D) 3(C) 9(F) d

14(G) 5(E) 1(A) 2(B) 8(D)

15(C) 6(F) 7(G) 19(E)

16(B) 17(D) 18(C) Cell # 1


(a) (b)

Figure 4.1: Illustration of a narrowband cellular system. (a) Cellular layout for threelayer cluster. Cells numbered 1-19. Letter is the cell's channel-group assignment, chosen from A-G; (b) Magnified view of Cell 1.



When comparing the paths to different base stations, it is only necessary to compare the rightmost term in the second line of equation (4.1), that is Gi = [N(0, a,) 10n loglo(di)] (4.2)


where di is the distance from the mobile to the ith base station, normalized such that the cells are of unit radius. Also note that the quantity Gi in equation (4.2) will be referred to as a channel gain, as it is the sum of the path loss and shadowing, but this is not intended to imply that there is an amplification of the signal through the channel. This quantity will be used in comparing different paths on a relative basis only. Without loss of generality, it will be assumed that the user of interest is physically located in cell 1, and at a distance di and angle 01 as shown in Figure 4.1. The rest of the Gi quantities may be found in terms of d and 01 by using the law of cosines. We define the following quantities. also in dB units: I'V = max(G1, G2,..., CG9)
(4.3)
YI = max(GI, G,,... G19)
#/_i






40

The meaning of the random variable 1T' should be clear. And the random variable Y3, for instance, is Y3 = max(G1, GC2, G4 .... G19) with G3 excluded from the argument of the max function. The use of the Yi allows the assignment of a user to the jth cell to be characterized simply by two exhaustive events, namely that the user is in fact assigned to the jth cell, (G- > ")), or is not, (G. < Yj). Certain pieces of information, such as the exact cell to which the user is assigned and the exact number of cells for which the corresponding Gi are greater than Gj, are not contained in the quantity Yj. In the results obtained in this work, this information is not necessary, and the corresponding simplification makes the analysis much more tractable.

These random variables in equation (4.3). which depend implicitly on dl and 01, can be described by using the fact that for fixed values of dl and 01, the rest of the di will also be fixed and the Gi are then independent Gaussian random variables with means of mg,i = -10nloglo(d;) and each with variance 2. It is important to keep in mind that the independence holds only when the di are treated as fixed quantities and not as random variables themselves. The probability density function (PDF) of W can be shown to be

i19 19 exp ( 2



The expressions for the PDFs of the ; are almost identical, with the only change being that the indices of the product and summnnation are adjusted so as not to include the ith term. As shown in Figure 4.2. for a user located at a distance of d = 0.75 and at an angle 01 = 0, and with aj = 8 dB and n = 3, the PDFs of W and Yi can be well-approximated as Gaussian. We can then find, for example, the probability that a user is assigned to the ith cell as



F,i 9
P1 (G i > + 0,92






41

0.1






0.05






0
-15 25 dB

Figure 4.2: Exact PDFs (solid) and Gaussian approximations (dashed) for Y and W, defined in equation (4.3), for a user at d1 = 0.75 and 01 = 0.



where my,i and o ,i are the mean and variance of Y;, which again depend on the user's position, and must be found numerically.

The variables in equations (4.2) and (4.3) can also be used to describe the effect that power control will have on the power levels at which users will be received at a base station. In practice, the transmitted powers of the mobiles assigned to a cell are adjusted so that the received powers of all of those users are the same at the base station. For both narrowband a.nd CDMA systems, the users employ power control as a means of conserving battery life. It is wasteful for a mobile that has a strong path to the base station to transmit as much power as does a user with a severely attenuated path. In CDMA systems only, there is the additional motivation of alleviating the near-far problem amongst a system's own users, so that one strong user does not disrupt communication for all the rest.

Consider again a user located in cell 1 at a position of dl and 01 from Figure 4.1. As mentioned before, the user will be assigned to the ith cell, i = 1,2,... ,19, for which Gi in equation (4.2) is maximum. If the minimum acceptable received power






42

in dB at the base station is 7, the user's transmitted power will be adjusted to 7- W, where W is defined in equation (4.3), so that it will arrive at a power y at its own base station. At a base station to which the user is not assigned, in cell k, the received power is y + (Gk -Yk). Note that it is necessary to know Yk under this condition, that is (Yk > Gk), as it determines the user's transmitted power. But it is not necessary to know which of the base stations other than the kth that the user is assigned to. We must then find the PDF of HA., which is the interference power level at the kth base station relative to those users assigned to the kth base station. Under the condition that the user is not assigned to the kth base station, Hk will always be less than 0 dB.

The PDF of Hk will have a discrete part, which is an impulse at 0 dB, with a weight equal to Pr(G- > Y.), the probability that the user is assigned to the kth cell. It will also have a continuous part. resulting from the event that it is not assigned to the kth cell, and appears as outer-cell interference. To find this part of the PDF, we first find the joint cumulative distribution function (CDF)


Pr(Hk < h, H, < 0) =Q ,k - li(h, 0) (4.6) V ,k + og

The derivative of equation (4.6) with respect to h gives the continuous part of the PDF of Hk, and the complete PDF is


fHk (h),k h)


1 (h (mg,k y,k))2 u(-h) (4.7) + e+ xp 2 +2) (-h)


where u(h) is the unit-step function. The continuous part of this PDF is just a Gaussian PDF that is truncated at h = 0.

The expression in equation (4.7) is dependent on the exact position of the user. This will be useful in some cases, but it would also be helpful to have a PDF for






43

Table 4.1: Composite ,., mY,. and E[Y2] averaged with position.

dB quanttiies m my a + m
Cell 1 6.51 3.07 34.93
Layer 2 -9.03 9.28 151.56
Layer 3 -18.06 9.52 153.86
Over all 3 layers -13.92 9.11 146.88



which the position is somehow averaged out. For instance, it may be necessary to know the PDF of the interference level caused to the cell of interest for a user that is located uniformly in a second-layer cell, without having to know its position and then look up the corresponding values of mnj,; and a, in a table. A true averaging of the PDF in equation (4.7) can be done numerically, with the help of a table of my,i and a2,. values. However, it was observed that a very good approximation may be obtained by first averaging m,,i, m,,;. and the second moment ayi + mi with respect to position over the cell of interest. over a second-layer cell, and over a third-layer cell, and then forming for each an expression similar to equation (4.7), with the averaged parameters substituted appropriately. This approximation to the true averaging was done, and is shown to match pretty well with simulated results, which are shown in Figure 4.3. The average values are shown in Table 4.1.

Then because there are 1, 6, and 12 cells in the 1st, 2nd, and 3rd layers, respectively, the averaging can be further extended to give averages which can be used to characterize the interference caused to cell 1 by a user located uniformly throughout the 3 layers of cells. This also matches the simulation results very well, as shown in Figure 4.3, and the averages with respect to position are also shown in Table 4.1. The approximate PDF is written below for use later:

1 1 (h + 23)2
fHk(h) -_ (h.) + 18exp 2(128) u(-h) (4.8) 19 V27(128) 2(128)

It should be noted that while this function and the others in Figure 4.3 are good approximations, they are not truly valid PDFs as they do not integrate exactly to






44





0.05
2nd layer Cell 1 Po=0.05 Po =0.64



3rd layer (a) Po =0.007 /





0
-60 -40 -20 0 dB
0.05
Averaged over all 3 layers PO = 1/19


// '%, (b)






0
-60 -40 -20 0 dB

Figure 4.3: Histograms and Gaussian approximations for interference caused to base station 1. (a) Interference from a user in cell 1, in a 2nd layer cell, and in a 3rd layer cell. For each, there is also an impulse at h = 0 with a weight of po; (b) Interference from a user located uniformly throughout the 3 layers. There is an impulse at h = 0, with weight po = 1/19.






45

unity, but close to it. The function in equation (4.8), for example, integrates to 1.032. It is simple to generate random variables with PDFs very close to these ones, however, and there is a substantial savings in time in comparison to the task of generating a user's position and shadowing processes to each base station. The approximate PDF of equation (4.8) will also be useful in the next section in investigating the effects of overlay on the existing narrowband system.


4.2 Performance of the Narrowband System

Given the characterization of the mobiles' received powers, the effect that the CDMA overlay has on the narrowband system can now be examined. It would be best if the overlay necessitated as little change as possible for the narrowband system, which is assumed to already be in existence. However, it will cause degradation to some extent, and it is thus necessary to define an acceptable level of degradation, and then to quantify the number of CDMA users for which this level is not exceeded.

We begin by considering the effects of overlay, either in the single- or multi-cell case, on the performance of a single BPSIK user operating in the presence of additive white Gaussian noise of spectral height No/2. The probability of error of the BPSK matched-filter receiver was found in equation (2.7) which will be repeated here with a slight modification.


Pe Q1 cos2() 1 2 (4.9) with Vk = TcVar(Ik), which is a random variable with respect to the CDMA users' codes and delays. As verified by simulation, the 1'. variables can be well-approximated as unit-mean exponential random variables.

Now a criterion must be established to determine if the overlay causes too much degradation to the narrowband user. Such a criterion is described by Milstein et al. [16], which states that if the BPSIK user's probability of error is increased from






46

10-6 to greater than 10-5 as a. result only of the overlay, that is while its signal-tonoise-ratio (SNR) remains constant, then the overlay is excessive. This criterion was employed in conjunction with a convolutional code of rate 7- = 2/3 and a constraint length m = 9. The optimum code has a free distance dfree = 8, as was found through an exhaustive computer search [26]. A tight lower bound for the probability of bit error of the coded system is

1 E
P, > Q 2rdfree (4.10) In 1 NO

The values of 2Eb/No required for this bound to achieve bit error rates of 10-6 and 10-5, denoted SNR6 and SNR5 respectively, are 5.43 dB and 4.27 dB.

In order to apply this to the overlay system, note that the square of the argument of the Q-function in equation (4.9) must be greater than SNR5, and also note that SNR6 = 2Eb/No, to give the necessary condition

1 P_ 1 1
1 cos2(0k)n < = 0.09 (4.11) k= l SR SNR
for which the overlay is not excessive. The number of CDMA users that can satisfy this condition for all but a. specified percentage statistically, say 2%, will be the limit on the CDMA capacity from the narrowband system's perspective. This should not be confused with a different limit. which may or may not be greater than this one, which is the number of users for which the MAI eventually becomes too severe for the CDMA system itself. That limit will be looked at in Section 4.4.

Before the capacity limit defined by equation (4.11) can be found, it is necessary to specify that, in this chapter, it will be assumed that the received powers of the CDMA and narrowband users at their respective assigned base stations are powercontrolled to the same level. The approximate PDF of the received power given in equation (4.8) was used to generate realizations of the CDMA-to-BPSK near far ratio Pk/Pb. Then 10000 different realizations of the sum on the left-hand side of equation






47

(4.11) were formed and compared with the value 0.09 for a fixed value of the number of users K, and for a processing gain N = 32. Then K was varied until the sum was greater than 0.09 for more than 2% of the 10000 realizations. It was found that K = 14 users was the maximum number which could meet the criterion. Note that there are 14 users spread over the three layers, or 19 cells, which is 0.75 users/cell, which is extremely low for a processing gain of 32.

A similar conclusion, that the overlay is excessive even for a lightly-loaded CDMA system, was observed in Chapter 2 for the single-cell case. One way to improve this loading relative to a fixed processing gain is to increase substantially the power level at which the narrowband users arrive at their own base stations. Doing so would not lead to increased co-channel interference amongst the narrowband users, because all the narrowband users in the system would increase their powers equally. It would, however, decrease their battery life, which is inconsistent with the idea that the overlay should require that the narrowband system change as little as possible. Another solution is to employ notch-filtering in the CDMA transmitters to avoid certain narrowband users, as was done in Chapter 2 for the single-cell case. This will be explored in the next section.


4.3 Effects of CDMA Transmitter Notching

In an effort to alleviate the severe degradation caused to the narrowband system as a result of the CDMA overlay, the idea of notching the CDMA signals at their transmitters in order to avoid narrowband users was investigated in Chapter 2 for the single-cell case. The DFT-based filtering method, described in Section 2.4.4, will be employed here in the cellular case.

The use of notching is more involved than in the single-cell case, where the CDMA signals were notched to avoid all of the narrowband users present. In the cellular case, it is very possible that in addition to those narrowband users located near to it physically, a CDMA mobile may have to avoid a narrowband user that is assigned






48

to an adjacent cell or even to a cell that is two layers away. But it obviously cannot notch for all of the narrowband users in the system, as that would likely constitute the entire system bandwidth, nor does it need to. As a result of the shadowing described in Section 4.1, there will be in some cases narrowband users near to the CDMA mobile that are not significantly degraded by the CDMA signal, and hence a notch is not necessary for them. This also holds for a significant percentage of the users that are not near to the CDMA mobile.

The total CDMA interference seen by a narrowband user depends on the CDMA signals' received powers, phases, and on the Vs7 variables according to equation (4.9). When deciding whether or not a notch is necessary, the power can be estimated and the information exchanged between base stations, but the phases and the Vk obviously will be unknown. Hence a specific criterion that will be used is that a CDMA signal must be notched if the power level at which it arrives at the corresponding narrowband receiver relative to the narrowband signal is higher than a given threshold.

From Table 2.3, when the DFT-based filtering method is used with 8 bits of zeropadding, the interference contribution is reduced by about 40 dB. The experiment of Section 4.2 was repeated, that is the number of CDMA users for which the excessive overlay criterion of equation (4.11) could be met was found, with transmitter filtering employed in those users for which the narrowband-to-CDMA power ratio at the narrowband receiver was less than a threshold T, given in dB. The results are shown in Figure 4.4 for T = 7, 9. 11 dB. In contrast to the 0.75 CDMA users/cell that was found in the unfiltered case, it is possible that with T = 9 dB, 19 users/cell can be tolerated by the narrowband system when filtering is employed, a tremendous increase in capacity. As the threshold is raised to T = 11 dB, and hence a CDMA user is more likely to need a notch, the amount of CDMA loading that can be tolerated by the narrowband system increases substantially to 29 users/cell, a level at which the CDMA system itself probably cannot function. And if it is reduced to T = 7 dB, the






49

30



20



S10
10 No notching
0.75 users/cell


0
7 9 11 Notching threshold (dB)

Figure 4.4: Maximum CDMA loading tolerable to narrowband system. Processing gain is 32 chips/bit. CDMA user notched if NB-to-CDMA power ratio is less than the notching threshold.


possible loading drops to 13 users/cell. In the next section, the capacity limit will be looked at based on how much notching the CDMA system can handle.

It should be pointed out that there is a good deal of information that must be exchanged between base stations, such as the received powers of both the CDMA and narrowband users. This combined with possible inaccuracies in estimating the received powers could lead to cases in which the CDMA users need to notch for certain narrowband users, but they do not. To measure this effect, we will declare that the CDMA users miss a necessary notch with probability p,,,. In Figure 4.5, the number of CDMA users/cell that can be tolerated is shown to degrade quite rapidly as Pm increases, which indicates that careful attention must be given to the estimation of the received powers.

Next, the amount of notching that must be done by the CDMA signals will be determined. This brings up an important design issue involving whether or not the






50

30
T= lldB


S20
T = 9 dB



10 T = 7 dB




0 0.01 0.02 Pl = Pr(missed notch)

Figure 4.5: Effects of missing notches on CDMA loading that narrowband system can tolerate. Processing gain is 32 chips/bit. CDMA user notched if NB-to-CDMA power ratio is less than the notching threshold, T = 7, 9, 11 dB.


two systems should use the same frequency band for the forward link, and correspondingly for the reverse link, or if they should be staggered such that one band covers the forward link of one system and the reverse link of the other. These two scenarios will be referred to as the same-link and staggered-link cases, and will be compared now based on the reverse link of the CDMA system.


4.3.1 Same-Link Assignment

In this case, the CDMA mobiles and the narrowband mobiles are transmitting in the same band, and thus the narrowband base station is taken to be the receiver. To determine the required notching, consider again a CDMA user located at a distance dl from the first base station as shown in Figure 4.1. We will find the probability that a CDMA user located at this position must notch for a single narrowband user that is located uniformly within the hexagonal enclosure of the three layers of cells. This will require for i = 1,2, ... ,19, the values of my,i and o,2 which are numerically calculated, as well as the m.q,i, which are easily found using the law of cosines.






51

First we define I = (Received narrowband power) (Received CDMA power), where the received power refers to the power in dB at the base station to which the narrowband user is assigned. A notch will then be required if I < T, with T given in dB. Recall that at this base station, the narrowband user's received power will be a specified value, denoted y. It was stated earlier that the CDMA and narrowband users would be power-controlled to the same level if assigned to the same base station. In that case, I = 0 and there is certainly a notch required.

For a CDMA user that is not assigned to the same cell as the narrowband user, denoted cell k, the conditional PDF of the CIDMA received power at the narrowband user's base station is

exp (h-( m y,k))2
fHk (h(Gk < ) 2(a +,k ) u(-h) (4.12) 27r(a, + c(),k)(Pr(Gk < 1k))

where again nzg,k, ,.k, and T., depend on (11, and Pr(Gk < I) is the probability that the CDMA user is not assigned to the kth cell. The notching probability, p,, is then found as
19
.= [ Pr(I < T, NB to cell k, CDMA to cell k)
k=1 (4.13) + Pr(I < T, NB to cell k, CDMA not to cell k)] which simplifies to

19

PT =T + Q -Q (4.14) The notching probability is plotted in Figure 4.6, as a function of dl, for T = 1,3,... ,15 dB. As expected, it is highest at the edge of the cell, as those users are more likely to be transmitting at a higher power than are those nearer to the base station, as a result of the power control. For a number of narrowband users located throughout the region, that is the density of users/cell multiplied by 19 for






52




T = 11 dE
0.3



S0.2
ST = 7 dB

0.1


T= l dB

0 0.2 0.4 0.6 0.8 1 d,

Figure 4.6: Notching probability as a function of dl for same-link case. Notching thresholds are T = 1, 3,... ,15 dB.


the number of cells, the number of notches required for the CDMA signal is then a binomial random variable with success probability p,,.


4.3.2 Staggered-Link Assignment

In contrast to the previous case, the CDMA mobiles and the narrowband base station are now transmitting in the same band. It is not necessary to perform a detailed analysis in this case. The signal on the narrowband forward link will have a composite gain from the base station's transmitter antenna and the mobile's receiver antenna, while the interference from a CDMA mobile to the narrowband mobile will only be amplified by its own transmit antenna and the narrowband mobile's receiver antenna. Obviously, the base station antennas will be much larger in effective area than will a size-limited mobile antenna. So the narrowband forward-link signal is likely to arrive at the mobile at a much higher level than would the interference from the CDMA mobile. Hence it is possible that notching is not required of the CDMA mobiles in the staggered-link case.






53

The major drawback to this configuration, however, is the severe near-far problem that results at the CDMA base station as it must receive signals from its mobiles in the presence of the signals sent from the narrowband base station, located a short distance away on the same tower, to its own mobiles. It will be seen later that this disadvantage outweighs by far the advantage of needing few, if any, notches in the CDMA mobiles, and that the same-link assignment is the better of the two configurations.


4.4 Simulations and Results

In order to investigate the perforinanice of the CDMA system, an environment similar to that used in the single-cell results of Chapter 3 was constructed, incorporating the cellular layout of Figure 4.1, and log-normal shadowing and power control as described earlier. The CDMA system had a processing gain of N = 32 chips/bit, an Eb/NO value of 10 dB, and used the DFT-based filtering method with 8 bits of zero-padding when filtering was necessary. For a 1/7 frequency reuse system, each cell would have at most 4-5 narrowband users.

In a "brute-force" simulation of the cellular overlay system, the coverage area that must be considered would consist of 6 layers of cells surrounding the center cell of interest. It was observed that a CDMA user might have to notch for a narrowband user that is 2 layers away from its geographic location. And any user could be assigned to a cell at most usually 2 layers away from its geographic location. So a CDMA user in the second layer out might have to notch for a narrowband user in the fourth layer out whose base station could be in the sixth laver out.

The total number of cells in the geographic coverage area multiplied by the density of users/cell gives the total number of users, either CDMA or narrowband, which would then be distributed uniformly about the coverage area. Each user would then be assigned to the cell at which its received power is maximum, and power control would be implemented. After it is determined how much of an increase or decrease






54

in transmitted power from the mobiles is required, the necessary notching for each CDMA mobile would be found by comparing its received power with that of each of the narrowband mobiles assigned to one of the cells within a three-layer cluster of the CDMA mobile's base station. This procedure would obviously require a great deal of simulation time, which can be decreased significantly with some simplifications.

The first simplification results from the observation, which was verified by simulation, that if an interfering CDMA user is left unfiltered, there is no noticeable difference in its effect on the desired CDMA user. The notching probability for a CDMA user depends jointly on its position and its transmitted power. But since it does not need to be known in the simulations, it is sufficient only to know the interferer's received power relative to the desired user, and its position is unimportant. So we can further simplify the simulations by using equation (4.8), which gives the approximate PDF of the received power for a user that is located uniformly throughout a three-layer cluster around the cell of interest, taking into account both cell assignment and power control. This was used to generate the near-far ratios of both the interfering CDMA users and the narrowband users.

For the desired user, it was assigned to the center cell, and based on its position, its notching probability was found from a numerically-evaluated table. The number of notches required was then a binomial random variable dependent on the density of narrowband users. Each CDMA user was given a random code sequence, delay, and phase, and each narrowband user was assigned to a random frequency location. The desired user was demodulated using an MMSE receiver, with the true Wiener solution. As explained in Section 3.3, the best performance is obtained by choosing the tap weights to minimize in expected value the square of the real part of the error as opposed to the square of its absolute value. The system capacity in CDMA users/cell was determined to be the maximum density for which the following blocking criterion






55

was satisfied:


Pr((Pe,CDAA > 0.05) U (#notches > 10)) < 0.02 (4.15)


In this criterion, a CDMA user will be blocked if its bit error rate is too high, or if it needs more than 10 notches. As the sampling rate of the system is 1/Tc, the range in which notching can be done is actually (-0.5/T, < f < 0.5/Te). Any frequency locations outside of this range must be notched in the appropriate location mirrored around 0.5/T,. Thus with a processing gain of 32, there are effectively only 16 notching locations. With more than 60% of the CDMA signal notched out, the user must be dropped.

A two-dimensional capacity plot is shown in Figure 4.7 for the same-link case, with notching thresholds of T = 7, 9, 11 dB. The notching threshold may affect the capacity criterion of equation (4.15) in two ways. First, as more notching becomes necessary, it is more likely that the desired user will have more than 10 notches and will be dropped. Also, it should be more difficult to demodulate the desired user's signal as more notches are added, and hence the probability of error should be higher on average. Notice that when the narrowband system is lightly-loaded, there is little difference in the amount of CDMA loading possible for each threshold. It was observed that when the loading was at most 1.5 narrowband users/cell, no drops occurred as a result of excessive notching. The fact that the threshold had little effect at these loading levels suggests that the notching has a minimal effect on the bit error rate, an idea which later will be investigated further.

As the narrowband loading increases beyond 1.5 users/cell, the system in which a notch is placed if the narrowband-to-CIDMA power ratio is less than T = 11 dB immediately shows the effects of having users dropped as there now are some instances in which the desired user requires more than 10 notches. For the other values T = 7, 9 dB, the effects of dropping users show up for higher values of narrowband loading.






56



20
T = 9 dB

CT = 7 dB

T= 11 dB
U
2.3 NB i 2.8 NB
:3.5 NE


0 1 2 3 4 NB users/cell

Figure 4.7: Capacity plot for same-link case. Processing gain is 32 chips/bit. Eb/No of CDMA system is 10 dB. Notching thresholds are T = 7, 9, 11 dB. For 2.3, 2.8, and 3.5 NB users, respectively, the CDDMA system reaches capacity in terms of those drops which result from needing too many notches.


Notice that the CDMA system is constrained by the fact that for a high enough narrowband loading, the probability that a CDMA user is dropped is greater than 2%, and the criterion of equation (4.15) cannot be satisfied for any amount of CDMA loading. From Figure 4.7, this occurs at 3.5, 2.8, and 2.3 narrowband users/cell respectively for T = 7, 9, 11 dB.

The results of Figure 4.7 characterize the joint capacity limits of the system as dictated by the CDMA system. In conjunction with the limits resulting from considerations of the narrowband system as shown in Figures 4.4 and 4.5, it is clear that the notching threshold T = 9 dB is the best choice, as its limits according to each of the two systems are relatively close. From Figure 4.5, if the probability of missing a notch is 1%, then about 15 CDMA users/cell can be tolerated by the narrowband system. And if the narrowband system is about half-loaded with 2 users/cell, then the CDMA system itself can support about 15 users/cell according to Figure 4.7.






57

This is a significant capacity improvement which would be very useful as mentioned in the transition from a narrowband cellular system to a CDMA cellular system.

It would also be of interest to investigate separately the effects of notching and the effects of narrowband noise on the CDMA system. This was done by comparing results for the staggered-link case, which naturally has a very high level of narrowband interference, and the same-link case explicitly in terms of the number of notches in the desired user and in the number of narrowband users which interfere with the CDMA signal. Recall that these will likely be different as the CDMA mobiles often must notch for narrowband users that are assigned to other cells. Also, although it was stated earlier that notching will not likely be required in the staggered-link case, it will be done here only in an effort to look specifically at the difference in the effects of notching and narrowband noise.

In the capacity plot shown in Figure 4.8, results for the staggered-link case are shown as solid lines while the one dashed line applies to the same-link case. For the staggered-link results, the number of narrowband users assigned to the desired user's cell was held constant at 0, 1, 2, 3. or 4, while the number of notches in the desired user was varied, and the CDMA density was found according to only the bit error rate part of the criterion of equation (4.15). Recall that in this configuration, the signals on the narrowband system's forward link will appear on the CDMA reverse link as interference at a very high near-far ratio. Assuming that the problem can be alleviated to some extent by shielding the two antennas, the near-far ratio was fixed at 20 dB. In going downward from curve to curve, it is seen that the effect of an additional narrowband user is to decrease the CDMA density by about 4 users/cell, which is significant.

For the same-link case, when there are no narrowband users assigned to the desired CDMA user's cell, the capacity curve is the same as in the staggered-link case. The narrowband users that are assigned to the cell will arrive at 0 dB with respect to the






58


0 NB users Same-link 20 4 NB users
1

2
10 '
0 3




0 4 8 12 Notches in desired user

Figure 4.8: CDMA users/cell vs. number of notches in the desired user. Solid line is staggered-link case, with narrowband-to-CDMA near far ratio at CDMA base station of 20 dB, and 0, 1, 2, 3, or 4 narrowband users assigned to cell of interest. Dashed line is same-link case, with 4 narrowband users with near-far ratio of 0 dB assigned to cell of interest. Eb/NO of CDMA system is 10 dB.



CDMA user's power level, as mentioned before. The plot when there are 4 narrowband users assigned to the cell of interest is shown, and the plots for 1, 2, and 3 users will naturally fall between it and the plot for no narrowband users present. It is seen that 4 narrowband users received at a near-far ratio of 0 dB have the effect of decreasing the CDMA capacity by only about 4 users/cell, as compared to a degradation of about 4 CDMA users/cell for each narrowband user in the staggered-link case.

These results are not surprising, but they do give useful insight as to how much effect the narrowband interference has. It is interesting that in all of the curves shown, the CDMA capacity degrades slowly as the number of notches is increased to around 7 or 8, and then degrades more rapidly. Clearly, the presence of narrowband interference has more effect on CDMA capacity than does the notching.






59

4.5 Summary

In this chapter, we have looked at applying CDMA overlay to the cellular case, as narrowband cellular systems by design only use a fraction of the system bandwidth in each cell. The CDMA overlay, if not very lightly-loaded, was shown to have an adverse effect on the existing narrowband system. The use of notch-filtering at the CDMA transmitters to avoid active narrowband users can greatly increase the amount of loading that the narrowband system can tolerate. Simulations showed that while the CDMA signals may at times require a large amount of notching to avoid narrowband users located throughout the cellular coverage region, the performance degradation is not severe. It was observed that the CDMA system is much more sensitive to the presence of strong narrowband interference than it is to notching. It was also found that the CDMA and narrowband users should have their forward links supported by the same frequency band. The results indicate that CDMA overlay is very promising for cellular systems, particularly as a means of transition from a system which exclusively supports narrowband service to one which supports CDMA service but can still meet previous commitments to narrowband subscribers.














CHAPTER 5
CELLULAR OVERLAY IN A FADING CHANNEL

In this chapter, the use of CDMA overlay in a cellular scenario will be extended to the fading channel. As has been the case throughout this research, the overlay will again cause severe problems for the existing narrowband system. The narrowband users also will benefit once again from notch-filtering in the CDMA transmitters. But in a flat fading channel, there is a large amount of notching necessary in order that enough relief is provided to the narrowband system. This places a strict constraint on user capacity in terms of the number of CDMIA and narrowband users which can simultaneously share the spectrum. The use of multi-carrier CDMA, however, allows the CDMA users to realize frequency diversity, and thus they may transmit at lower power levels. This reduces the amount of notching necessary, and provides a substantial improvement in joint user capacity.


5.1 Limits on CDMA Capacity

The idea of multi-carrier CDMA has recently received significant attention as an alternative to traditional single-carrier CDIMA [27]. The transmission of a CDMA signal on two or more disjoint carrier frequencies, with enough frequency spacing so that the fading on each signal is independent, allows for the possibility of frequency diversity, and therefore an increase in user capacity.

In this section, a development of user capacity limits for overlay in the fading channel begins with a quantification of how many CDMA users can be tolerated by the narrowband system before its performance is degraded too severely. We will then look at the resulting improvement due to the CDMA users employing notch-filtering in their transmitters.


60






61

Throughout this chapter, a cellular system identical to the one in Chapter 4, with the addition of fading, will be considered. From Figure 4.1, interference from cells within two outer layers of the center cell of interest will be taken into account. The PDF of the near-far ratio of an interfering user, either CDMA or narrowband, located uniformly throughout the three-layer area, was approximated in equation (4.8) as

1 1 (h + 23)2
fHk(h) I 6(h) + 2(128) xp(- 2(128) )u(-h) (5.1) 19 27(12 2(128)

We will now look at the performance of a BPSIK user received in the presence of overlay in a fading channel. A general multi-carrier CDMA format will be used, where there are Q carriers, and the total power of each CDMA user is divided equally amongst the Q carriers. The identical CDMA signal will be transmitted simultaneously on each carrier. The fading process on each carrier will be taken as frequencynonselective, and independent of the fading processes on other paths. The CDMA bandwidth in the single-carrier case must be smaller than, or on the order of, the coherence bandwidth of the channel in order that the fading be frequency-nonselective. Thus in the realization of multi-carrier CDMA, the carriers must have sufficient frequency spacing between themselves in order for the fading on each carrier to be independent.

It will be assumed that only the particular CDMA signal which overlaps the BPSK signal at bandpass will pass through the BPSK receiver, and thus we will concentrate only on that signal in the equations which follow. The BPSK user employs square pulses of width T, the bit time, and a matched-filter receiver. The complex baseband received signal can be written as
00
r(t) = V 7Pby,(i)d,(i)I((t iTb)/Tb) + 2n(t) exp(-jwt)
i=-OO
S-0 K (5.2) + E1 2PA/Qkk(i)dk(i)ck(t iTb rk) i=-oo k=l






62

where II(t/Tb) is a unit-amplitude square pulse of width Tb, Pb is the BPSK user's average power, Pk is the kth CDMA user's composite average power from all of its carriers, yb(i) and 7k(i) are the BPSIK user's and kth CDMA user's fading process during the ith bit interval, with each a zero-mean complex Gaussian random variable. The kth user's spreading waveform, A.(t), has a period of Tb and consists of unitamplitude square pulses of width QT. where the single-carrier chip-time is T, = Tb/N and N is the composite processing gain. The output of the BPSK user's matched-filter in the ith bit interval is
(i+1)Tb K
Z(i)= 1 T r(t) dt = y(i)dP(i) + Pk (iTb iTb
(5.3)

where Ne(i) and N,(i) are zero-mean Gaussian random variables each with variance r2 = (2Eb/No)-1, Eb is the average energy-per-bit of the BPSIK system, and the term due to interference from the kth CDMA user during the ith bit interval, Ik(i), is
T, Tk
Ik(i) = dk (i 1) C (t) d dk () f Ck (t) dt (5.4) rA. 0

Denoting the nth chip of the kth user's spreading code as ck,,2, and assuming that the per-carrier processing gain N/Q is an integer, we have

Ik(i) Q
S= d(i 1) 6kCkN/Q-pk-1 + 1 Ckj +
=b N/N Qj=NQ-pk (5.5)

dk (i) Ck,j + (1 6k)Ck,N/QPk-1 j=0

where the delay has been written as h. = (p + 6k)QTc with pk an integer in the range (0, 1, . (N/Q) 1) and 5, a non-integer in the range (0, 1). The variance of this term, for fixed codes and delays, and hence with the expectation taken only with respect to the data bits, is itself a random variable. From Section 4.2, it can be






63

verified by simulation that with respect to the codes and delays, the variance can be well-approximated as an exponential random variable.

Assuming coherent detection for the BPSK user, the decision on the ith BPSK data bit is db(i) = sign(Re[Z exp(-jZy,(i))]). Invoking a Gaussian approximation on the CDMA interference contribution, the probability of bit error, conditioned on the BPSK user's fading process ye(i), is



Pr(error/yb(i)) = Q (- Ai 2 (5.6) k= 1


where (Eb/NO)b has been clarified to apply to the BPSK user, not to be confused with the CDMA system, for which (Eb/No)c will be used. Also, Vk is a unit-mean exponential random variable. Note that the probability of bit error for the BPSK user does not depend on the number of carriers used in the multi-carrier CDMA signaling, which checks with intuition. When the number of carriers is doubled, for example, the CDMA users on each carrier are only spread by half of the original processing gain, but in turn, they transmit only half of the power on each carrier.

In order to determine how many CDMA users may be tolerated by the BPSK system before the overlay is excessive, consider the probability of error in the presence of no overlay, conditioned again on the BPSIK user's fading process, which is


Pr(error/ hb(i)) Q ( 2 () b (i)2 (5.7) We denote SNR as the square of the argument of the Q-function of equation (5.7) and SNReff as the same for equation (5.6). Thus with the addition of the overlay, the BPSK user must increase its power by a factor of

SNR r= 1 + 7.(i) cos2(ZC S (i)) Vk (5.8)
SNRIf f ,vo b k= Pb






64

As mentioned before, it should be stipulated that the overlay cause only a minor amount of degradation to the existing narrowband system. For a fixed number of CDMA users, the quantity in equation (5.8) is a random variable depending on the CDMA users' fading processes and near-far ratios (with respect to the BPSK user) and also on the exponentially-distributed 1,. variables. As the criterion here, we will say that the number of CDMA users is excessive if the random variable of equation (5.8) is greater than 3 dB more than 2% of the time. That is, we find the maximum value of K such that


Pr (: A(i) cos(Z b(i)) ) > 1 < 0.02 (5.9)


The capacity limits dictated by equation (5.9) will be found for a system with a composite processing gain of N = 32 chips/bit and with (Eb/No)b = 14 dB for the BPSK system. This choice results from averaging the conditional probability of error of equation (5.7) over the Rayleigh fading process 7b(i), which gives the well-known result

0.25
P 0.5 (5.10)
(Es,/No)b

and choosing (Eb/No)b = 14 dB to get a bit error rate of 0.01 in the absence of overlay.

The maximum number of users K will be found for a range of values of (Eb/No)c. Recall that the results will not depend on the number of carriers used. However, the added frequency diversity resulting from multiple carriers allows for a smaller value of (Eb/No)c in order to achieve the same probability of error with the same number of CDMA users. For a CDMA user which is assigned to one of the cells within three layers of the center cell of interest at random, its near-far ratio in dB, (Pk/Pb), will come from the approximate PDF of equation (5.1), with an adjustment to account for the difference in the values of E,/No for a CDMA and a BPSK user assigned to the same cell.






65

Without the CDMA notching that has been mentioned, the amount of CDMA loading that the narrowband system can tolerate is practically zero. To implement the notching, when a CDMA signal is received such that the BPSK user's received power is less than T dB above that CDMA signal, a. notch is placed in the CDMA signal, and the near-far ratio, with the PDF given by equation (5.1), is then reduced by about 40 dB. This reduction assumes that the code sequences will be filtered when necessary by using the DFT-based filtering from Section 2.4.4, with the filtered code sequences zero-padded to 8 bits.

In Figure 5.1, for a range of values for the notching threshold T and for several values of the difference (E,1/No), (E,/No)c, the amount of CDMA loading tolerable to the BPSK user was found such that the criterion of equation (5.9) was satisfied. As expected, for larger values of (E1/No)b (E,/No), the PDF of (Pk/Pb) tends to shift toward lower values and thus more CDMIA users can be tolerated by the BPSK user. And as the notching threshold T increases, and the CDMA users are therefore more likely to place notches. the BPSIK user also can tolerate more CDMA users. In order to make use of these results we must next investigate how much notching the CDMA system can handle before its signals become too distorted to be received reliably.


5.2 Limits on Narrowband Capacity

In this section, we will look at the effects of notching from the perspective of the CDMA system. As more notches are necessary, there will be a point at which an excessive amount of some of the CDMA signals' spectra must be notched out, and hence many of the CDMA users would have to be dropped. This would occur not only in cases for which the notching threshold T is large, but would also occur when the quantity (Eb/No)b (Ebi/No)c is decreased, or equivalently the value of (Eb/No)c is increased.






66

25
(Eb/NO)b(Eb /)C = 7 dB 5 dB
20
0-3 dB
4 15

10

5


0 "j
5 7 9 11 13 15 17 T (dB)

Figure 5.1: CDMA users/cell tolerable to the BPSK system. CDMA user is notched if BPSK power is less than T dB above CDMA power. Curves are for (Eb/NO)b (Eb/No)c values of 7,5,... ,-3 dB. (E,/No)b and (Eb/No)c represent values after power control at the base station to which the BPSK or CDMA mobile is assigned.


This problem was examined in Section 4.3.1, where a narrowband user was located at random such that it was equally likely to be assigned to any of the cells within two outer layers of a center cell of interest. Then a CDMA user located at a normalized distance 0 < d < 1 from the center cell of interest, must notch for that narrowband user with probability p,,, which is plotted in Figure 4.6. It must be noted however, that in Chapter 4, the narrowband and CDMA users, when assigned to the same base station, were power-controlled so as to arrive at that base station at the same level. In this chapter, that level will be allowed to vary, and hence the quantity T in Figure

4.6 will actually be replaced by T ((E,/No)b (Eb/No)).

We will now look at several different multi-carrier CDMA schemes, and for each the number of narrowband users which can be present so that the CDMA users do not require an excessive amount of notching will be found. A different quantification of how much notching is excessive will be given for each case.






67

Later in this chapter, the performance of the CDMA system employing the MMSE receiver will be investigated. The sampling rate used in the MMSE is 1/QTc, or 1/T, in the single-carrier case. The CDMA signals, with spectrally efficient pulse shapes, will typically be contained within the frequency range (-1/Tc < f < 1/T,). However, the notching can really only be done uniquely within the range (-0.5/T, < f < 0.5/T) as a result of the sampling rate. Each notch within this range, therefore, gives rise to a second notch outside of this range, but still within the range (-1/T, < f < 1/T,). Thus, recalling that the BPSIK and CDMA systems have the same data rate, there are only 16 unique notching locations when the processing gain is 32 chips/bit.

In the single-carrier case, a CDMA user will be dropped if more than half of its signal must be notched, or 8 unique notching locations. The density of narrowband users/cell for which this criterion can be satisfied was found for a range of values of T((Eb/NO)b- (Eb/NO)c), in dB, and the results appear in Figure 5.2. Notice as expected that as T gets larger, and hence more notching is necessary, fewer narrowband users can be present. Also, as ((Eb/No)b (Eb/No)c) gets larger, the CDMA users are less likely to need notches and more narrowband users can be present.

In Figure 5.3, a combination of the results of Figures 5.1 and 5.2 is shown for the single-carrier case. Several two-dimensional capacity curves, each with a constant value of ((Eb/NO)b (Eb/NoT)). were formed by finding the tolerable densities of CDMA users/cell from Figure 5.1 and narrowband users/cell from Figure 5.2 for a given value of the notching threshold T. This was repeated for a range of values of T. As ((Eb/NO)b (Eb/NTO)) gets larger, the CDMA users are less likely to interfere with the BPSK user and are less likely to require notches, and thus more users of each type should be supportable.

It is important to keep in mind that we have not yet considered how much selfinterference the CDMA system can handle, nor the effects of narrowband interference







68


5
Single-carrier
4.
S4 barriers
3

2 carriers
.0 2

8 carriers, n o notching

SI III
4 carriers, no notching

0 2 4 6 8 10 12 14 T- ((Eb/No)b (EbNo),), (dB)

Figure 5.2: Narrowband users/cell tolerable to CDMA system before too much notching is required. Shown are single-carrier and multi-carrier cases. The "no notching" curves represent cases in which a carrier is dropped if even one notch is necessary.




25 25 25
+7 +7: +7 +5 +5
20 20 20

-1 +3 +3
15 15 15--10 .-- :10 10 +1

5 --- 5 5 ---0 1 2 3 4 0 1 2 3 4 0 1 2 3 4
NB users/cell NB users/cell NB users/cell
(a) (b) (c)

Figure 5.3: Two-dimensional capacity curves combining Figures 5.1 and 5.2. Labels on curves indicate the value of (Ei,/No)b (E,1/No) Processing gain is 32 chips/bit.
(a) Single-carrier case; (b) 2-carrier case; (c) 4-carrier case.






69

and notching on CDMA performance. We have only considered two things, which nonetheless do impose some limitations on user capacity: the number of CDMA users for which the narrowband system's performance is severely degraded according to the criterion of equation (5.9) and the number of narrowband users for which the CDMA users would simply require too much notching. In the next section, we will look at the CDMA performance in more detail.

We next consider using multi-carrier CDMA with 2 carriers, and hence a processing gain per path of 16 chips/bit. In deciding how much notching is excessive here, we must note that only 8 unique notching locations are available in each carrier, and hence if there are more than 4 notches required in either carrier, the CDMA user will be dropped. With only one of the two carriers in use, this is equivalent to the singlecarrier case with only half of the processing gain, but the same amount of loading. The results for this case are also shown in Figure 5.2. For a given value of T, the probability that at least one of the two carriers will have more than 4 notches out of a possible 8 is greater than the probability that there will be 8 notches out of a possible 16 in the single-cell case, which agrees with intuition. In Figure 5.3, two-dimensional capacity curves for the 2-carrier case indicate performance inferior to the single-carrier case for a given value of ((Eb/No)b (E,/No)c). However, there is no significant conclusion to be drawn from this, and these results are only presented for future use. It will be seen later that when CDMA receiver performance is taken into account, the multi-carrier systems are able to operate at much lower values of (Eb/No)c than can the single-carrier case, as a result of the added frequency diversity. Thus it would be more fair to compare a curve in the single-carrier case with one of those from the multi-carrier case with a significantly larger value of ((Eb/No)b (Eb/No)c), which would lean more favorably toward the nmulti-carrier case.

Finally, we consider using 4 carriers, which means that the CDMA signals will have a processing gain per path of 8 chips/bit. Thus a carrier will be dropped if






70

more than 2 notches are necessary. In contrast to the 2-carrier case, if only one of the carriers must be dropped, 3 of the 4 carriers would still remain, and it might be possible that the CDMA receiver could still function reliably. This will be looked at in Section 5.3, but for now, the criterion that we will employ is that a CDMA user will be dropped if at least 2 of the 4 carriers have more than 2 notches. These results are shown in Figures 5.2 and 5.3 as well. In Figure 5.3, there is an improvement over the 2-carrier case, in which the CDMA user was dropped even if only one of the carriers needed significant notching.

It has been suggested previously that with the use of multi-carrier CDMA, it is possible to avoid the narrowband users in an overlay scenario by simply not transmitting on those carriers which might interfere with a narrowband user [27]. This possibility was also examined here for comparison. We will first utilize the previous notching criteria, and declare that if the CDMA signal on a given carrier is received at a high power level in terms of the notching threshold T, the carrier will not be used, analogous to simply placing a notch in the previous scenarios.

We will consider both 4 and 8 carriers in this type of system. It does not seem fruitful to raise the number of carriers beyond 8, with a composite processing gain of 32 chips/bit, for several reasons. First, even assuming that the CDMA signal on each carrier would experience independent fading, the incremental diversity advantage realized by using more carriers diminishes with such a high number of carriers. Second, it has been assumed that the CDMA system, when used with multiple carriers, can be split such that transmission takes place on disjoint frequency bands, so that independent fading can be realized. While this seems plausible with 2 or even 4 carriers, the possibility becomes less likely with a large number of carriers. Thus some of the carriers will undergo correlated fading, which will not give nearly as much diversity as will independent fading. Finally, the process of tracking the fading processes, which is






71

not considered in this paper, would become tremendously complicated with so many carriers.

It was observed in later simulations that the CDMA system suffered a large performance loss, in terms of the number of supportable users, if half of its carriers must be dropped. This would be essentially equivalent to doubling the load on a system with all of its carriers operational. Thus we can obtain an upper bound on capacity limits in this section by finding how many narrowband users may be present so that at least half of the carriers are still operational. As it is shown in Figure 5.2, for 4 and 8 carriers, even these upper bounds fall far below the performance of the systems which use notching. This suggests that a hybrid of these ideas must be used. When one or more of the carriers simply requires too much notching, transmission on it can be avoided, but the remaining carriers may still have some notches. Again, this must be tested in terms of the effect on CDMA performance, which will be done in the next section.


5.3 Performance of the CDMA System

In this section, the capacity limits of multi-carrier CDMA will be examined further. Results from Sections 5.1 and 5.2 will be extended to include the effects on CDMA performance of MAI, NBI, notching, and the possibility of operating on fewer carriers than the maximum. We consider the use of the MMSE receiver, which is well-suited to the overlay environment. Several of its desirable properties were mentioned in Section 3.1, such as its ability to reject MAI, NBI, and ISI as well as its ability to adapt to the desired user's signal without even knowing that its code has been filtered. It was shown by Miller et al. [28] that the MMSE can successfully realize diversity in a frequency-selective fading channel, and that there is a substantial performance loss when all of the paths of all of the interfering users are not tracked explicitly in forming the Wiener solution. The performance of the MMSE was evaluated in the multi-carrier case by Miller and Rainbolt [29], and it was reaffirmed that






72

all of the paths of all of the CDMA users must be tracked in order to avoid a sizable performance loss.

The performance in the overlay environment is a relatively straightforward extension of the analyses given by Miller et al. [28] and by Miller and Rainbolt [29]. The desired CDMA user now may operate with a filtered code sequence and narrowband noise must be added when necessary. We consider a general multi-carrier system with Q carriers, and a processing gain per path of N/Q. It is also assumed that the desired user's code sequence in the qth carrier will be filtered (when necessary) using the DFT-based filtering method from Section 2.4.4, which results in a code sequence of length greater than the processing gain, N/Q in this case. It will be expressed as the cascade of L individual sequences of length N/Q, as C1,q = (Cq_,-L/2 ... CT,q,-1, CT,q,0, CT,q, C,q,L/ T, with Cl,q,O in the middle associated with the desired component and the other sequences corresponding to ISI. Note that on each carrier, the filtered code sequence will be different as the notching necessary on each carrier is generally not the same. Also, for simplicity, it was verified in Section 4.4 that there is no significant difference in the reception of the desired user if the interfering CDMA users are left unfiltered.

For the qth carrier, the samples of a chip-matched-filter bank will be collected during the ith bit interval, resulting in a column-vector of N/Q samples given by L/2
rq(i) = 7Y,q(i)di (i)c1,q,o + E 71(cl(i 1m)ci,q,m + nq(i) + jq(i) + m=-L/2
m O (5.11) K P-k,qk (i) +d(i-l)gk]
E V Y-1"(Z) [dk(i)fk + dlk(i-- 1
k=2

where yk,q(i) is the fading process on the qth carrier of the kth user during the ith bit interval, and the fading processes for the same user on each carrier are independent. Also, fk and gk are the even and odd cyclic shifts of the kth user's code sequence, which were defined in equation (3.4) and nq(i) is a vector of length N/Q of independent






73

complex Gaussian noise samples, with the real and imaginary parts each having variance of a2 = N/(2Eb/No). The vector jq(i) consists of the sum of samples of all of the narrowband noise processes present in the qth carrier, if any. Each process is complex, with the real and imaginary parts independent, and each with a correlation matrix given by (for the mth narrowband user)

R,(i, Pb) = Sa(2(i- cos(QTAw(i j)) (5.12) for the (i,j)th element, where (PI/PI) is the narrowband-to-CDMA near-far ratio, and Aw is the frequency difference between the location of the narrowband user and the CDMA carrier frequency.

It was shown by Miller and Rainbolt [29] that the receiver will work best if the Q different received vectors of equation (5.11) are cascaded into a single composite vector of length N, given by


r(i) = (r'(i), r'(i),... ,rQ(i)) (5.13) and a single Wiener filter is formed, given by w(i) = R-'(i)p(i), with R(i) and p(i) the correlation matrix and steering vector. The composite correlation matrix R(i) is given by

Rl,1(i) R1,2() ... R1,Q(i)

R(i) = R2,1(i) R2,2(i) ... R2,Q(i) (5.14)


RQg,(i) RQ,2(i) ... RQ,Q(i)

and the sub-matrices are given by R,,,q(i) = E [rl,(i)r"(i)] (5.15)






74

The composite steering vector is given by p (i) E [d,(i)r, (i)]
p(i) p(i) E [dI (i)r2(i)]
p(i) (5.16) pQ(i) E [dl(i)rQ(i)]

The bit decision is then made as di (i) = sign(Re[w" (i)r(i)]) for coherent combining of the paths. It makes sense to use coherent combining in this case, as it was previously stated that all of the fading paths of all of the users would be tracked anyway in order to avoid a large performance loss.

The task of tracking the fading processes in a dynamic environment is currently an area of active research. In this work, it will be assumed that all of the fading processes on all of the paths are known, in which case we have L/2
Rp,q(i) = y1,p(i)Y,q(i)C1,p,oc1,,0 + 1),P (i)c( ,pmc l,,m + m=-L/2


k=2 m=2
(5.17)

where there are M narrowband users present on the carrier for which p = q. Also, IN/QxN/Q is an identity matrix of dimension N/Q. The qth steering vector is P,(i) = 71,,(i)c1,q,o (5.18) If the expression for the qth received vector in equation (5.11) is written as rq(i) = yi,,,(i)di (i)cl,q,o + rq(i) (5.19)


where iq(i) represents a composite interference process consisting of MAI, AWGN, NBI, and ISI, it can be shown with the matrix-inversion lemma that the probability






75

of error, conditioned on the fading processes 7yk,q(i), when coherent combining of the paths is used is given by [28]


Pr(error/F(i)) = Q (2pH (i)R-l(i)pH(i)) (5.20) where P(i) is a vector representing all of the fading processes of all of the users during the ith bit interval and R(i) = E[i(i)iH(i)] the composite interference correlation matrix.

The performance of the CDMA system using an MMSE detector was then simulated. As was done earlier in the paper, a cellular environment with two outer layers of cells beyond the center cell of interest was considered. The mobiles, both CDMA and narrowband, experienced lognormal shadowing with a standard deviation o = 8 dB, propagation loss with an exponent of n = 3, and Rayleigh fading. For a given density of narrowband users/cell, the corresponding density of CDMA users/cell that could be supported by the system was found. This density was based both on the capacity constraints examined in Sections 5.1 and 5.2, and also on the criterion


Pr(Pe,cDAIA > 0.05) < 0.02 (5.21) For a given realization of codes, delays, notching, and powers of the CDMA users and of powers and frequency locations of the narrowband users, 300 different realizations of the fading processes were generated, that is 300 realizations of F(i), and the conditional probability of error of the CDMA system was found using equation (5.20). The average probability of error was then found by averaging these 300 values. This process was repeated many times, that is for different realizations of the codes, delays, and so on, in order to give enough values for the average probability of error so that the criterion of equation (5.21) could be tested. Thus if a CDMA user's average probability of error was greater than 5%, it was dropped, and if these drops







76

20

4 carriers

2 carriers
10




:Single callier:

0 0.5 1 1.5 2 Narrowband users/cell

Figure 5.4: Two-dimensional capacity curves, taking into account both CDMA receiver performance and results from Figure 5.3. Processing gain is 32 chips/bit.



occurred more than 2% of the time, then the CDMA system was above its capacity limits.

In order to combine these results with those of Sections 5.1 and 5.2, the notching threshold T and the value of (Eb/No)c must be chosen so as to satisfy the capacity curves shown in Figure 5.3. For example, in the single-carrier case, if there are 2 narrowband users present, the system can support 7 CDMA users if the value of (Eb/NO)b (Eb/N)c = 7 dB, or equivalently (Eb/NO)c = 7 dB. But if the CDMA system is loaded up to this level, it will require much more than (Eb/No)c = 7 dB to satisfy the criterion of equation (5.21). Thus a higher value of (Eb/No), must be used, and hence a lower value of (Eb/No)b (Eb/No)c, which means that we must operate on one of the curves showing a lower joint capacity.

In Figure 5.4, the results of combining the criterion of equation (5.21) with the results of Sections 5.1 and 5.2 are shown. Similarly to the example just mentioned, the value of (Eb/No)c was optimized at each loading level. There is a noticeable improvement in capacity over the single-carrier case when 2 carriers are used, and a






77

slight additional increase when 4 carriers are used. Recall that in the multi-carrier scenarios, a smaller value of (Eb/No)c could be used in order to achieve the same performance in terms of CDMA reception. This in turn allows the limits of Sections

5.1 and 5.2 to be relaxed in comparison to the single-carrier case.


5.4 Summary

In this chapter, the performance of a cellular overlay system with a fading channel model was evaluated. The effects of the CDMA system on the narrowband system were quantified, and the effects of notch-filtering were found to be beneficial. It was found that the use of multiple carriers allows the CDMA users to transmit less power than in the single-carrier case, and thus more users can be supported without causing interference to the narrowband system. The possibilities for CDMA overlay are strongly reinforced by the results of this section.














CHAPTER 6
CONCLUSIONS AND FUTURE WORK

In this final chapter, the key contributions of this dissertation to the existing body of research will be summarized. Some areas of future research will also be suggested.


6.1 Conclusions

In this dissertation, the possibility of implementing CDMA overlay has been examined in detail. If overlay is to be done in a frequency band in which a narrowband system already exists, then it should be of vital importance to quantify the effects of the overlay on the narrowband system. Surprisingly, this problem had received little attention before this dissertation. On the other hand, the converse problem of the effects of the narrowband signals on the CDMA system had been examined very thoroughly.

It was shown first for a Gaussian channel model that the overlay poses quite a problem for the narrowband system. If the CDMA system is to be loaded to a level for which it is worthwhile to even implement it, the narrowband users experience too much degradation in performance.

In an effort to alleviate the effects of overlay on the narrowband system, the idea of employing notch filtering in the CDMA users' transmitters, which had been suggested previously by Davis [21], was examined in detail. Four filtering methods were examined in the current work. Two of the methods, the eigenvector filter and the null filter, which were presented by Davis [21], operated with the constraint that the filtered code sequence span only one bit interval, just as the unfiltered code sequence does. Two original methods were presented in this dissertation, which relaxed this




78






79

constraint, and allowed for a small amount of ISI. A digital Butterworth notch filter was used, and a filtering method based on the DFT was also considered.

The filtering methods for which the ISI resulted performed significantly better than did the other two methods, in terms of the amount of distortion caused to the CDMA signals' PSDs. They also provided more relief to the narrowband system. The resulting ISI, while an important issue that must be looked at in CDMA receiver design, was certainly manageable.

An important point that has been emphasized throughout this research, and has not received enough attention in the literature, is that the use of notch filtering is not simply a way to provide a modest improvement to the performance of an overlay system. Rather, it is absolutely essential if the CDMA system is to be loaded to levels for which the research community is actively striving.

Next, the problem of receiving the CDMA signals was considered, and it was shown that the MMSE is a good choice for this purpose. In addition to its ability to reject MAI and NBI, which has been demonstrated before, it was shown here that the MMSE can reject ISI and also that it can adapt to a code sequence which has been filtered, provided that a training sequence is used. The MMSE receiver's functionality in the overlay scenario was demonstrated throughout the dissertation, in both single-cell and cellular scenarios, and with both a Gaussian channel model and a fading channel model.

The application for which overlay has perhaps the most potential is the cellular scenario. The implementation of overlay could provide an efficient way for a frequency band which services narrowband users to transition its service to CDMA. For contractual reasons, providers cannot simply discontinue service to narrowband subscribers once it has been decided that the band will be converted to support CDMA. Overlay would allow the new CDMA technology to be introduced while the existing narrowband products are phased out gradually.






80

Issues arising in cellular overlay were considered, such as the necessity once again for CDMA transmitter notching and how much notching must be done. In a cellular environment, the CDMA users might have to notch for narrowband users in other cells. But they cannot notch for every narrowband user that is operational within the system, because that would probably constitute the entire system bandwidth. Thus a criterion must be established, and then evaluated to see how much notching the CDMA users must do. A criterion comparing the received powers of the CDMA and narrowband signals at the receiver of interest was adopted, wherein a notch was placed if the CDMA signal was received at too high a level above that at which the narrowband user was received. The amount of notching required was shown to be reasonable.

Another design issue that was addressed was the frequency assignment for the forward and reverse links of the CDMA and narrowband systems. It was shown that the forward links of the two systems should be supported by the same band, as should the reverse links, in contrast to supporting the forward link of one and the reverse link of the other in the same band. In the latter case, the fact that a signal will be transmitted from the base station antenna and would appear at the other system's receiver antenna a short distance away on the same tower would result in an unmanageable near-far interference problem.

Another conclusion reached was that the notching is much less of a problem for the CDMA system than is the reception of strong narrowband interference. The signals could be notched so that about 50% of their spectrum was missing, and suffer only a modest amount of degradation. Narrowband interference, however, was shown to cause significant problems if too strong.

Finally, cellular overlay was examined in the fading channel. Once again, it was concluded that the CDMA users must employ notching in order to avoid the narrowband system. But it was also found that the CDMA signals required a large amount






81

of notching. This imposed disappointing constraints on the joint capacity of the system, that is the number of CDMA and narrowband users that can simultaneously occupy the spectrum.

A solution for this problem is to use multi-carrier CDMA, in which the CDMA signal is transmitted on several carriers, such that the signals on each carrier undergo independent fading. This provides a significant amount of frequency diversity, which allows the CDMA users to transmit at lower power levels. Thus less notching is also necessary, and the joint capacity of the system is improved dramatically.

The results presented in this dissertation indicate that CDMA overlay has great potential for providing an increase in user capacity. It is especially valuable in cellular scenarios, in which a transition from narrowband service to CDMA service is in progress. There remains, however, some open issues which will be discussed in the next section.


6.2 Future Work

Some topics of future research will be suggested in this section. The results presented in this dissertation have clearly indicated that overlay has significant potential. The next step is to look at some of the implementation issues that were not addressed.

Throughout the research, two important tasks were assumed to have been done perfectly, the timing acquisition, that is the knowledge about when the desired CDMA user's code sequence begins, and the estimation of the fading processes of the CDMA users. They are certainly important problems that need to be addressed in future work. The results presented in this dissertation had only the goal of demonstrating that there is indeed a reason to pursue overlay. If the results had demonstrated otherwise, then the effects of imperfect estimation of the timing and the fading parameters would not be interesting or meaningful.

The timing acquisition problem has been investigated by many researchers, and there exists an extensive body of literature on the subject [30-35]. Obviously, these






82

works have not considered the effects of the notch-filtering presented in this dissertation. It must be determined what effects the notching will have on algorithms such as these, if used unmodified. It is likely that some modifications to fit the timing estimation problem to the case with filtered codes would be necessary and certainly would be beneficial. Also the possibility of the timing estimator working without knowing the code sequence, as the MMSE receiver can do for detection, might be useful. But it seems that this information would be known by the base stations, and the estimator would probably suffer a good deal of performance loss if the code sequence is not used in the algorithm. Additionally, in a frequency-selective fading channel, the estimator must be able to lock onto several paths with different delays.

Another significant area of future research is the estimation of the fading processes of the CDMA users. It was determined by Miller et al. [28] and by Miller and Rainbolt [29] that the MMSE receiver will take a large loss in performance if it is not able to track all of the fading processes of all of the users. This is a fairly undeveloped area, with a few solutions having been proposed. Barbosa and Miller used linear prediction in conjunction with an MMSE receiver to estimate the fading process of the desired user in a flat-fading channel [36]. A subspace-approach was investigated by Wang and Poor [37]. Methods based on a decorrelator idea, that is a transformation on the received signal which removes the data, are presented by Miller and Rainbolt [29] and by Juntti [38] in an effort to track the fading in a frequency-selective fading channel.

The estimation of the fading processes is very important, not only for the overlay scenario in this dissertation, but for the use of the MMSE in fading channels in general. This will continue to be a popular topic of research, as there has not been a tremendous amount of success realized.














REFERENCES

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[11] S. L. Miller, "An adaptive direct-sequence code-division multiple-access receiver
for multiuser interference rejection," IEEE Trans. Commun., vol. 43, pp. 17461755, Feb./ Mar./ Apr. 1995.





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44, pp. 488-495, Apr. 1996.

[15] M. Honig, U. Madhow, and S. Verdii, "Blind adaptive multiuser detection,"
IEEE Trans. Inform. Theory, vol. 41, pp. 944-960, July 1995.

[16] L. B. Milstein, D. L. Schilling, R. L. Pickholtz, V. Erceg, M. Kullback, E. G.
Kanterakis, D. S. Fishman, W. H. Biederman, and D. C. Salerno, "On the feasibility of a CDMA overlay for personal communication networks," IEEE J.
Select. Areas Commun., vol. 10, pp. 655-668, May 1992.

[17] J. W. Ketchum and J. G. Proakis, "Adaptive algorithms for estimating and
suppressing narrowband interference in PN spread-spectrum systems," IEEE
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[18] L. Li and L. B. Milstein, "Rejection of narrowband interference in PN spreadspectrum systems using transversal filters," IEEE Trans. Commun., vol. COM30, pp. 925-928, May 1982.

[19] R. A. Iltis and L. B. Milstein, "Performance analysis of narrowband interference
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[20] L. B. Milstein, "Interference rejection techniques in spread spectrum communications," Proc. IEEE, vol. 76, pp. 657-671, June 1988.

[21] M. E. Davis, Signal processing for interference avoidance and multiple-access
noise rejection in DS-CDMA, Ph.D. dissertation, University of California, San
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[23] H. V. Poor and X. Wang, "Code-aided interference suppression for DS/CDMA
communications part I: interference suppression capability," IEEE Trans. Commun., vol. 45, pp. 1101-1111, Sept. 1997.

[24] V. K. Garg, K. F. Smolik, and J. E. Wilkes, Applications of CDMA in Wireless/Personal Communications, Prentice-Hall, Upper Saddle River, NJ, 1997.






85

[25] T. S. Rappaport, Wireless Communications, Prentice-Hall, Upper Saddle River,
NJ, 1996.

[26] R. Johanneson and E. Paaske, "Further results on binary convolutional codes
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2, pp. 264-268, Mar. 1978.

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[28] S. L. Miller, M. L. Honig, and L. B. Milstein, "Performance analysis of MMSE
receivers for DS-CDMA in frequency selective fading channels," submitted to
IEEE Trans. Commun.

[29] S. L. Miller and B. J. Rainbolt, "MMSE detection of multi-carrier CDMA,"
submitted to 1999 IEEE International Conference on Communications.

[30] E. G. Strim, S. Parkvall, S. L. Miller, and B. E. Ottersten, "Propagation delay
estimation in asynchronous direct-sequence code-division multiple access systems," IEEE Trans. Commun., vol. 44, no. 1, pp. 84-93, Jan. 1996.

[31] S. E. Bensley and B. Aazhang, "Subspace-based channel estimation for code
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44, pp. 1009-1020, Aug. 1996.

[32] U. Madhow, "Blind adaptive interference suppression for the near-far resistant
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Signal Processing, vol. 45, no. 1, pp. 124-136, Jan. 1997.

[33] D. Zheng, J. Li, S. L. Miller, and E. G. Str6m, "An efficient code-timing estimator
for DS-CDMA signals," IEEE Trans. Signal Processing, vol. 45, no. 1, pp. 82-89,
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[34] Z. S. Liu, J. Li, and S. L. Miller, "An efficient code-timing estimator for receiver
diversity DS-CDMA systems," IEEE Trans. Commun., vol. 46, no. 6, pp. 826835, June 1998.

[35] R. F. Smith and S. L. Miller, "Acquisition performance of an adaptive receiver
for DS-CDMA systems," submitted to IEEE Trans. Commun.

[36] A. N. Barbosa and S. L. Miller, "Adaptive detection of DS/CDMA signals in
fading channels," IEEE Trans. Commun., vol. 46, no. 1, pp. 115-124, Jan. 1998.

[37] X. Wang and H. V. Poor, "Blind multiuser detection: a subspace approach,"
IEEE Trans. Inform. Theory, vol. 44, no. 2, pp. 677-690, Mar. 1998.

[38] M. Juntti, Multiuser demodulation for DS-CDMA systems in fading channels,
Ph.D. dissertation, University of Oulu, 1997.














BIOGRAPHICAL SKETCH

Brad J. Rainbolt was born in Normal, IL, in 1972. He received the B.S. and M.E. degrees, both in electrical engineering, in August 1993 and December 1994 from the University of Florida, Gainesville, FL. He was employed by Motorola Land Mobile Products Sector, Plantation, FL, from May 1994 through August 1995 as an engineer in the Applied Research Group, where he worked on the design of digital communication systems. In August 1995, he returned to the University of Florida, and received the Ph.D. degree in electrical engineering in December 1998.

































86









I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy.


Scott L. Miller, Chairman Associate Professor of Electrical and Computer Engineering

I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy.


Leon W. Couch II
Professor of Electrical and Computer Engineering

I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy.


Haniph A. Latchman
Associate Professor of Electrical and Computer Engineering

I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy.


Jian Li
Associate Professor of Electrical and Computer Engineering

I certify that I have read this study and that in my opinion it conforms to acceptable standards of scholarly presentation and is fully adequate, in scope and quality, as a dissertation for the degree of Doctor of Philosophy.


Ulrich H. Kurzweg
Professor of Aerospace Engineering, Mechanics, and Engineering Science









This dissertation was submitted to the Graduate Faculty of the College of Engineering and to the Graduate School and was accepted as partial fulfillment of the requirements for the degree of Doctor of Philosophy.

December 1998 Winfred M. Phillips Dean, College of Engineering


M. J. Ohanian Dean, Graduate School




Full Text
CHAPTER 6
CONCLUSIONS AND FUTURE WORK
In this final chapter, the key contributions of this dissertation to the existing body
of research will be summarized. Some areas of future research will also be suggested.
6.1 Conclusions
In this dissertation, the possibility of implementing CDMA overlay has been ex
amined in detail. If overlay is to be done in a frequency band in which a narrowband
system already exists, then it should be of vital importance to quantify the effects
of the overlay on the narrowband system. Surprisingly, this problem had received
little attention before this dissertation. On the other hand, the converse problem of
the effects of the narrowband signals on the CDMA system had been examined very
thoroughly.
It was shown first for a Gaussian channel model that the overlay poses quite a
problem for the narrowband system. If the CDMA system is to be loaded to a level
for which it is worthwhile to even implement it, the narrowband users experience too
much degradation in performance.
In an effort to alleviate the effects of overlay on the narrowband system, the
idea of employing notch filtering in the CDMA users transmitters, which had been
suggested previously by Davis [21], was examined in detail. Four filtering methods
were examined in the current work. Two of the methods, the eigenvector filter and the
null filter, which were presented by Davis [21], operated with the constraint that the
filtered code sequence span only one bit interval, just as the unfiltered code sequence
does. Two original methods were presented in this dissertation, which relaxed this
78


65
Without the CDMA notching that has been mentioned, the amount of CDMA
loading that the narrowband system can tolerate is practically zero. To implement
the notching, when a. CDMA signal is received such that the BPSK users received
power is less than T dB above that CDMA signal, a. notch is placed in the CDMA
signal, and the near-far ratio, with the PDF given by equation (5.1), is then reduced
by about 40 dB. This reduction assumes that the code sequences will be filtered when
necessary by using the DFT-based filtering from Section 2.4.4, with the filtered code
sequences zero-padded to 8 bits.
In Figure 5.1, for a range of values for the notching threshold T and for several
values of the difference (Ei,/No)b {Eb/N0)c, the amount of CDMA loading tolerable
to the BPSK user was found such that the criterion of equation (5.9) was satisfied.
As expected, for larger values of (EiJNq)t (Ei,/No)c, the PDF of (Pk/Pb) tends to
shift toward lower values and thus more CDMA users can be tolerated by the BPSK
user. And as the notching threshold T increases, and the CDMA users are therefore
more likely to place notches, the BPSK user also can tolerate more CDMA users.
In order to make use of these results we must next investigate how much notching
the CDMA system can handle before its signals become too distorted to be received
reliably.
5.2 Limits on Narrowband Capacity
In this section, we will look at the effects of notching from the perspective of the
CDMA system. As more notches are necessary, there will be a point at which an
excessive amount of some of the CDMA signals spectra must be notched out, and
hence many of the CDMA users would have to be dropped. This would occur not
only in cases for which the notching threshold T is large, but would also occur when
the quantity (Eb/No)b {Ei,/Nq)c is decreased, or equivalently the value of (Eb/No)c
is increased.


80
Issues arising in cellular overlay were considered, such as the necessity once again
for CDMA transmitter notching and how much notching must be done. In a cellular
environment, the CDMA users might have to notch for narrowband users in other
cells. But they cannot notch for every narrowband user that is operational within
the system, because that would probably constitute the entire system bandwidth.
Thus a criterion must be established, and then evaluated to see how much notching
the CDMA users must do. A criterion comparing the received powers of the CDMA
and narrowband signals at the receiver of interest was adopted, wherein a notch was
placed if the CDMA signal was received at too high a level above that at which the
narrowband user was received. The amount of notching required was shown to be
reasonable.
Another design issue that was addressed was the frequency assignment for the
forward and reverse links of the CDMA and narrowband systems. It was shown
that the forward links of the two systems should be supported by the same band, as
should the reverse links, in contrast to supporting the forward link of one and the
reverse link of the other in the same band. In the latter case, the fact that a signal
will be transmitted from the base station antenna and would appear at the other
systems receiver antenna a short distance away on the same tower would result in
an unmanageable near-far interference problem.
Another conclusion reached was that the notching is much less of a problem for the
CDMA system than is the reception of strong narrowband interference. The signals
could be notched so that about 50% of their spectrum was missing, and suffer only
a modest amount of degradation. Narrowband interference, however, was shown to
cause significant problems if too strong.
Finally, cellular overlay was examined in the fading channel. Once again, it was
concluded that the CDMA users must employ notching in order to avoid the narrow-
band system. But it was also found that the CDMA signals required a large amount


63
verified by simulation that with respect to the codes and delays, the variance can be
well-approximated as an exponential random variable.
Assuming coherent detection for the BPSK user, the decision on the th BPSK
data bit is db(i) = sign(Re[Z¡ exp{jZ.7/,(?'))]) Invoking a Gaussian approximation
on the CDMA interference contribution, the probability of bit error, conditioned on
the BPSK users fading process 7/,(/), is
Pr(error/76()) = Q
|76|2
v\ (2 (^)J + N I7*(0I* cos2(Z7fc(0) (it) Vk
(5.6)
where (Eb/No)b has been clarified to apply to the BPSK user, not to be confused
with the CDMA system, for which (Eb/No)c will be used. Also, Vk is a unit-mean
exponential random variable. Note that the probability of bit error for the BPSK user
does not depend on the number of carriers used in the multi-carrier CDMA signaling,
which checks with intuition. When the number of carriers is doubled, for example,
the CDMA users on each carrier are only spread by half of the original processing
gain, but in turn, they transmit only half of the power on each carrier.
In order to determine how many CDMA users may be tolerated by the BPSK
system before the overlay is excessive, consider the probability of error in the presence
of no overlay, conditioned again on the BPSK users fading process, which is
Pr(error/7t(?)) Q
'2
Nr
0/6
MOP
(5.7)
We denote SNR as the square of the argument of the Q-function of equation (5.7)
and SNReff as the same for equation (5.6). Thus with the addition of the overlay,
the BPSK user must increase its power by a factor of
SNR ( 2 \
SNReff ~ +\n)
Eh
ay,
k
l7A-(v')|2cos2(Z7fc(0)
6=1
vk
(5.8)


67
Later in this chapter, the performance of the CDMA system employing the MMSE
receiver will be investigated. The sampling rate used in the MMSE is 1 /QTC, or
1 /Tc in the single-carrier case. The CDMA signals, with spectrally efficient pulse
shapes, will typically be contained within the frequency range (1/TC < / < 1 /Tc).
However, the notching can really only be done uniquely within the range (0.5/Tc <
f < 0.5/Tc) as a result of the sampling rate. Each notch within this range, therefore,
gives rise to a second notch outside of this range, but still within the range (1 /Tc <
f < l/Tc). Thus, recalling that the DPSK and CDMA systems have the same data
rate, there are only 16 unique notching locations when the processing gain is 32
chips/bit.
In the single-carrier case, a CDMA user will be dropped if more than half of its
signal must be notched, or 8 unique notching locations. The density of narrowband
users/cell for which this criterion can be satisfied was found for a range of values of T
((Eb/No)b~ {Eb/No)c), in dB, and the results appear in Figure 5.2. Notice as expected
that as T gets larger, and hence more notching is necessary, fewer narrowband users
can be present. Also, as ((Eb/N0)b (Eb/N0)c) gets larger, the CDMA users are less
likely to need notches and more narrowband users can be present.
In Figure 5.3, a combination of the results of Figures 5.1 and 5.2 is shown for the
single-carrier case. Several two-dimensional capacity curves, each with a constant
value of ((Eb/No)b (Eb/N0)c). were formed by finding the tolerable densities of
CDMA users/cell from Figure 5.1 and narrowband users/cell from Figure 5.2 for a
given value of the notching threshold T. This was repeated for a range of values of
T. As ((Eb/N0)b (Eb/No)c) gets larger, the CDMA users are less likely to interfere
with the BPSK user and are less likely to require notches, and thus more users of
each type should be supportable.
It is important to keep in mind that we have not yet considered how much self
interference the CDMA system can handle, nor the effects of narrowband interference


34
It would also be interesting to observe the transient behavior of the MMSE receiver
in the overlay environment, in addition to its steady-state operation reported above.
The performance of the RLS algorithm will be looked at for this purpose, as its
speed of convergence does not depend on the input power as in the case of the LMS
algorithm. For 200 trials, the RLS algorithm was run first with 20 CDMA users
and without narrowband users and notches, and then with 2 narrowband users and
notches added. The squared error was averaged over the 200 trials in Figure 3.4.
Both of the previously described MMSE criteria were used for comparison.
In the first case with no narrowband users or notches, the mean-squared error
is seen to converge to a steady-state value in about 150 bits. Notice that there
is a significant improvement in the mean squared-error when the receiver mini
mizes J = E[{Re(Z,- c/i())}2] as opposed to J E[|Z di(i)\2], but the re
quired convergence time is about the same. Also notice that in the case when
J = E[{Re(Z di(?'))}-] is minimized, the corresponding absolute value of the
mean squared-error is very high. As stated before, the separe of the real part of the
error, which is used in making the bit decision, is minimized at the cost of allowing
a large increase in the imaginary part of the error, which will not be used anyway.
The same environment was simulated with 2 narrowband users received at a near-far
ratio of 20 dB and with the corresponding notches added. The same amount of time,
about 150 bits, was required for convergence to a steady-state value, which is seen to
be somewhat higher than when no narrowband users are present. It is worth noting
that the computational complexity of the two algorithms is the same, as every com
plex computation that is required for minimizing J E[|Z d\ ()|2] requires two
real computations in the other case. Thus minimizing J = E[{Re(Z fers a substantial improvement in performance with no added complexity or required
training time.


8
in Section 3.1. Performance equations for the MMSE receiver are presented in Section
3.2. Simulation results are then presented in Section 3.3, both for a receiver which is
able to track the ideal Wiener solution and for one which uses an adaptive algorithm.
The MMSE receiver was compared to a conventional matched filter receiver, and was
clearly superior, showing a capacity gain of 8-11 times when using the Wiener solution
and 6-8 times when using an adaptive algorithm. It is also important to note that
the MMSE receiver using an adaptive algorithm was able to perform well although
it did not even know that the code sequence was filtered, a very attractive feature
in this scenario. The results of these simulations, combined with the results on the
performance of the narrowband system presented in Chapter 2, present a strong case
for the feasibility of CDMA overlay.
The previous results simply demonstrated that overlay can be done if the CDMA
users employ transmitter notching. In Chapter 4, a compelling motivation for overlay
is presented, as these results are extended to the cellular scenario, where overlay
seems to have the most potential from a commercial point of view. If a frequency
bandwidth which supports a narrowband cellular system is designated for conversion
to a CDMA cellular system, overlay is an ideal way to make this transition gradually.
Over the long term, the number of subscribers still using the narrowband products
would shrink while the number of subscribers using the new CDMA products would
increase. Conclusions similar to those reached in Chapters 2 and 3 will be realized in
the cellular case. In Section 4.1. the cellular environment will be characterized. The
effects of overlay on the narrowband system will be examined in Section 4.2, and it
will be seen again that the narrowband users undergo a large amount of performance
degradation as a result of the overlay. In Section 4.3, the idea of notch-filtering the
CDMA signals will be applied, and will again provide tremendous benefits to the
narrowband system. Simulations and results will be presented in Section 4.4.


68
O
C/5
u
0)
C/5
3
Xl
£
o

&
Figure 5.2: Narrowband users/cell tolerable to CDMA system before too much notch
ing is required. Shown are single-carrier and multi-carrier cases. The no notching
curves represent cases in which a carrier is dropped if even one notch is necessary.
NB users/cell
(a)
NB users/cell
(b)
NB users/cell
(c)
Figure 5.3: Two-dimensional capacity curves combining Figures 5.1 and 5.2. Labels
on curves indicate the value of (Ei)/Aro)ii (Ei,/Nq)c. Processing gain is 32 chips/bit.
(a) Single-carrier case; (b) 2-carrier case; (c) 4-carrier case.


48
to an adjacent cell or even to a cell that is two layers away. But it obviously cannot
notch for all of the narrowband users in the system, as that would likely constitute
the entire system bandwidth, nor does it need to. As a result of the shadowing
described in Section 4.1, there will be in some cases narrowband users near to the
CDMA mobile that are not significantly degraded by the CDMA signal, and hence
a notch is not necessary for them. This also holds for a significant percentage of the
users that are not near to the CDMA mobile.
The total CDMA interference seen by a narrowband user depends on the CDMA
signals received powers, phases, and on the 14 variables according to equation (4.9).
When deciding whether or not a notch is necessary, the power can be estimated and
the information exchanged between base stations, but the phases and the 14- obviously
will be unknown. Hence a specific criterion that will be used is that a CDMA signal
must be notched if the power level at which it arrives at the corresponding narrowband
receiver relative to the narrowband signal is higher than a given threshold.
From Table 2.3, when the DFT-based filtering method is used with 8 bits of zero
padding, the interference contribution is reduced by about 40 dB. The experiment
of Section 4.2 was repeated, that is the number of CDMA users for which the ex
cessive overlay criterion of equation (4.11) could be met was found, with transmitter
filtering employed in those users for which the narrowband-to-CDMA power ratio at
the narrowband receiver was less than a threshold T, given in dB. The results are
shown in Figure 4.4 for T = 7,9,11 dB. In contrast to the 0.75 CDMA users/cell
that was found in the unfiltered case, it is possible that with T = 9 dB, 19 users/cell
can be tolerated by the narrowband system when filtering is employed, a tremendous
increase in capacity. As the threshold is raised to T = 11 dB, and hence a CDMA user
is more likely to need a notch, the amount of CDMA loading that can be tolerated by
the narrowband system increases substantially to 29 users/cell, a level at which the
CDMA system itself probably cannot function. And if it is reduced to T = 7 dB, the


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sequence spread-spectrum CDMA, IEEE Trans. Commun., vol. 42, pp. 3178-
3188, Dec. 1994.
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for multiuser interference rejection, IEEE Trans. Commun., vol. 43, pp. 1746-
1755, Feb./ Mar./ Apr. 1995.
83


64
As mentioned before, it should be stipulated that the overlay cause only a minor
amount of degradation to the existing narrowband system. For a fixed number of
CDMA users, the quantity in equation (5.8) is a random variable depending on the
CDMA users fading processes and near-far ratios (with respect to the BPSK user)
and also on the exponentially-distributed 14 variables. As the criterion here, we will
say that the number of CDMA users is excessive if the random variable of equation
(5.8) is greater than 3 dB more than 2% of the time. That is, we find the maximum
value of K such that
Pr (((I) l7(i)|W(ZT(i)) (t)Vk) >1)< '02 (5'9)
The capacity limits dictated by equation (5.9) will be found for a system with a
composite processing gain of AT = 32 chips/bit and with (Eb/No)b = 14 dB for the
BPSK system. This choice results from averaging the conditional probability of error
of equation (5.7) over the Rayleigh fading process 7b(i), which gives the well-known
result
P,
0.25
(5.10)
(Eb/N0)b
and choosing (Eb/No)b = 14 dB to get a bit error rate of 0.01 in the absence of overlay.
The maximum number of users K will be found for a range of values of (Eb/N0)c.
Recall that the results will not depend on the number of carriers used. However, the
added frequency diversity resulting from multiple carriers allows for a smaller value
of (Eb/No)c in order to achieve the same probability of error with the same number
of CDMA users. For a CDMA user which is assigned to one of the cells within three
layers of the center cell of interest at random, its near-far ratio in dB, (Pk/Pb), will
come from the approximate PDF of equation (5.1), with an adjustment to account
for the difference in the values of Eb/N0 for a CDMA and a BPSK user assigned to
the same cell.


84
[12] M. Abdulrahman, A. Sheikh, and D. Falconer, Decision feedback equalization
for CDMA in indoor wireless communications, IEEE J. Select. Areas Commun.,
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[13] C. N. Pateros and G. J. Saulnier, An adaptive correlator receiver for direct-
sequence spread-spectrum communication, IEEE Trans. Commun., vol. 44, pp.
1543-1552, Nov. 1996.
[14] S. L. Miller, Training analysis of adaptive interference suppression for direct-
sequence code-division multiple-access systems, IEEE Trans. Commun., vol.
44, pp. 488-495, Apr. 1996.
[15] M. Honig, U. Madhow, and S. Verd, Blind adaptive multiuser detection,
IEEE Trans. Inform. Theory, vol. 41, pp. 944-960, July 1995.
[16] L. B. Milstein, D. L. Schilling, R. L. Pickholtz, V. Erceg, M. Kullback, E. G.
Kanterakis, D. S. Fishman, W. H. Biederman, and D. C. Salerno, On the
feasibility of a CDMA overlay for personal communication networks, IEEE J.
Select. Areas Commun., vol. 10, pp. 655-668, May 1992.
[17] J. W. Ketchum and J. G. Proakis, Adaptive algorithms for estimating and
suppressing narrowband interference in PN spread-spectrum systems, IEEE
Trans. Commun., vol. COM-30, pp. 913-924, May 1982.
[18] L. Li and L. B. Milstein, Rejection of narrowband interference in PN spread-
spectrum systems using transversal filters, IEEE Trans. Commun., vol. COM-
30, pp. 925-928, May 1982.
[19] R. A. litis and L. B. Milstein, Performance analysis of narrowband interference
rejection techniques in DS spread spectrum systems, IEEE Trans. Commun.,
vol. COM-32, pp. 1169-1177, Nov. 1984.
[20] L. B. Milstein, Interference rejection techniques in spread spectrum communi
cations, Proc. IEEE, vol. 76, pp. 657-671, June 1988.
[21] M. E. Davis, Signal processing for interference avoidance and multiple-access
noise rejection in DS-CDMA, Ph.D. dissertation, University of California, San
Diego, 1993.
[22] R. L. Pickholtz, L. B. Milstein, and D. L. Schilling, Spread spectrum for mobile
communications, IEEE Trans. Veh. Technol, vol. 40, pp. 313-321, May 1991.
[23] H. V. Poor and X. Wang, Code-aided interference suppression for DS/CDMA
communications part I: interference suppression capability, IEEE Trans. Com
mun., vol. 45, pp. 1101-1111, Sept. 1997.
[24] V. K. Garg, K. F. Smolik, and J. E. Wilkes, Applications of CDMA in Wire
less/Personal Communications, Prentice-Hall, Upper Saddle River, NJ, 1997.


4
sends information back to the mobile users, telling them to either raise or lower their
transmit powers. With perfect power control, all of the signals are received at the
same power level at the base station.
In response to the near-far problem, researchers have developed a large number
of receiver structures with varying degrees of complexity and performance. A key
feature of these near-far resistant receivers is that they utilize information about
the other users signals, either explicitly or implicitly in their processing. They take
advantage of the known form of the MAI and hence they also are referred to as
multi-user detectors. The matched-filter receiver, on the other hand, treats the MAI
as white noise which simply increases the thermal noise floor.
The optimum multiple-user detector [4,5] consists of a bank of matched filters and
uses a Viterbi algorithm to demodulate the data streams of all of the CDMA users.
While it does minimize the probability of bit error, its complexity increases expo
nentially with the number of users, rendering it infeasible in practice. The optimum
detector is very important, however, because at the time of its inception, common
sentiment was that the near-far problem was an inherent shortcoming of CDMA that
could not be overcome. The existence of this near-far resistant detector served as mo
tivation for the development of implementable receivers that could outperform the
conventional matched-filter receiver.
Because the optimum detector has such a high complexity, and requires a large
amount of side information about all of the CDMA users, several sub-optimum near-
far resistant receivers have been developed which have more manageable complexities.
A few notewortlty receivers include the decorrelator [6,7] and the multistage detector
[8]. The minimum mean-squared error (MMSE) receiver [9-15] has received a great
deal of attention during the past few years as it also offers near-far resistance and is
very simple to implement. The MMSE also has an inherent resistance to narrowband
interference (NBI), a feature that is very beneficial in an overlay scenario, which will


36
The resulting histograms of the probability of bit error are shown in Figure 3.5
for the three different near-far ratios and each is compared to the case in which no
narrowband signal is present. It is seen that when the narrowband signal is received
at 0 dB, there is little difference, but the performance does degrade somewhat for
the 20 dB case, and degrades significantly for the 40 dB case. Hence it appears that
the MMSE receiver is relatively robust to the presence of the narrowband signal,
but for large near-far ratios its performance will be degraded. This is consistent
with the conclusions reached by Poor and Wang [23], that while the MMSE receiver
does outperform conventional narrowband interference rejection schemes, the output
signal-to-interference ratio of the MMSE receiver will degrade for high-powered nar
rowband interference. Fortunately, the probability that a narrowband user will have
such a large near-far ratio is low, as this would occur only in a small geographic region
around the CDMA receiver.
3.4 Summary
In this chapter, we have shown that with the notch-filtering which was determined
necessary in Chapter 2, the MMSE receiver can function quite well in an overlay en
vironment. In the simulations performed here, the CDMA system could be loaded up
to about 20 users for a processing gain of 32 chips/bit when 5 narrowband users were
present, or about 15% of the band was jammed. It offers a substantial performance
improvement over a conventional matched-filter receiver. These results, along with
those of Chapter 2, are quite encouraging for the prospects of CDMA overlay.


41
dB
Figure 4.2: Exact PDFs (solid) and Gaussian approximations (dashed) for Y\ and
W, defined in equation (4.3), for a user at d\ = 0.75 and 9\ = 0.
where rnyy and ayi are the mean and variance of Yt, which again depend on the users
position, and must be found numerically.
The variables in equations (4.2) and (4.3) can also be used to describe the effect
that power control will have on the power levels at which users will be received at
a base station. In practice, the transmitted powers of the mobiles assigned to a cell
are adjusted so that the received powers of all of those users are the same at the
base station. For both narrowband and CDMA systems, the users employ power
control as a means of conserving battery life. It is wasteful for a mobile that has
a strong path to the base station to transmit as much power as does a user with a
severely attenuated path. In CDMA systems only, there is the additional motivation
of alleviating the near-far problem amongst a systems own users, so that one strong
user does not disrupt communication for all the rest.
Consider again a user located in cell 1 at a position of d\ and 9\ from Figure 4.1.
As mentioned before, the user will be assigned to the *th cell, i = 1,2,... ,19, for
which G{ in equation (4.2) is maximum. If the minimum acceptable received power


13
where the notation N(m, a2) is used to denote a Gaussian random variable with mean
m and variance a2. The probability of error can then be approximated as
Pe Q
2 Eu
V 2PkT} cos2(e,,.)Var(4i 4- N
(2.5)
where the Q-function is defined as
Equation (2.5) then sim
Pe^Q
Q(X) =
:S tO
\/2n
exp(-)du
(2.6)
2Eb + N ^ V A
cos2 (6k) Var (4)
-i/2\
(2.7)
where Pb = Eb/Tb is the BPSK users average power. The variance of Ik, with the
averaging done only with respect to the data bits, is then found as
LN
Var (Ik) = Tc-Tk)f
m i=LN
LN
+ ^ h(ni\Tc Tk)h(m2Tc rfc)
m i = L N m > ^ rn j
W-H
(2.8)
X C-Ar.motl(r?xi,A')(ni i.N)
Because the variance is dependent on the particular code sequence, it may take on a
range of values. If the expectation is further taken over all code sequences, the second
term of equation (2.8) drops out, and the variance is equal to the sum of samples of
h2(t) spaced at intervals of Tr. Because h(t) was normalized such that the integral
of h2(t) on (00,00) is unity, then this variance can be approximated by invoking


33
(a) (b)
Figure 3.4: Transient behavior of mean-squared error using the RLS algorithm and a
training sequence. (1) is for minimizing J = E[{Re(Zdi(*))}2], (2) is for minimizing
J = E[|Zi di(i)|2], (3) is resulting absolute squared-error under criterion of (1).
(a) 20 CDMA users, 0 narrowband users and 0 notches; (b) 20 CDMA users, 2
narrowband users with near-far ratio of 20 dB, and 2 notches.
algorithm may have stability problems, the training was avoided for now by initial
izing the tap weights to the Wiener solution and allowing an LMS algorithm to run
with a known preamble for many bits. This allows the filter to reach a steady state
solution which takes into account the excess mean-squared error which would result
from an adaptive algorithm. For a step size of 0.1 /tip, where tip is the total input
power, almost no difference was seen in comparison to the Wiener solution. For a
step size of 0.2/tip, some difference was seen as shown in Figure 3.3. Thus if the
filter is trained well, results close to the ideal ones with the Wiener solution can be
achieved for a small enough step size.



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TABLE OF CONTENTS
ACKNOWLEDGMENTS iii
LIST OF ABBREVIATIONS vi
ABSTRACT viii
CHAPTERS
1 INTRODUCTION 1
1.1 Code-Division Multiple-Access 1
1.2 CDMA Overlay 5
1.3 Overview of the Dissertation 6
2 NARROWBAND SYSTEM PERFORMANCE IN THE AWGN
CHANNEL 10
2.1 Effects of Overlay on a Narrowband User 10
2.2 CDMA Transmitter Filtering 15
2.3 Filtering Performance Criteria 16
2.3.1 Gain of the BPSK System 16
2.3.2 Effect on the PSD of the CDMA Signal 17
2.3.3 Effect on the CDMA Code Sequence 17
2.4 Filtering Methods and Results 18
2.4.1 Eigenvector Filtering 18
2.4.2 Null Filtering 20
2.4.3 Butterworth Filtering 20
2.4.4 DFT-Based Filtering 22
2.5 Summary 24
3 MMSE DETECTION OF FILTERED CDMA SIGNALS 25
3.1 The MMSE Receiver 25
3.2 MMSE Detection of Filtered CDMA Signals 26
3.3 Simulation Results 29
3.4 Summary 36
4 CDMA OVERLAY IN A CELLULAR SYSTEM 37
4.1 Characterization of the Cellular Environment 38
IV


12
(b)
Figure 2.1: Histograms for CDMA interference caused to a BPSK user, (a) Single
CDMA user, BPSK user employing root-raised cosine pulses; (b) Single CDMA user,
BPSK user employing square pulses; (c) 3 CDMA users, BPSK user employing root-
raised cosine pulses; (d) 3 CDMA users, BPSK user employing square pulses.
approximation does not hold for each individual //,, the total CDMA interference is
the sum of K of these terms, and for relatively small values of K, the distribution
of the sum of the /*. terms does approach Gaussian. An example is shown in Figure
2.1. The histograms for a single CDMA users interference contribution are shown
for the case when the BPSK signal uses root-raised cosine pulses, and also for the
case when square pulses are used. In both cases, the interference is clearly non-
Gaussian. However, when the root-raised cosine filter is used, the interference does
take on somewhat of a continuum of values concentrated in three areas, in contrast
to the discrete 4-valued variable resulting in the square pulse case. As a result of this
continuum, the sum of only 3 such variables is seen to be well-approximated by a
Gaussian distribution, while in the square pulse case, the sum of 3 interference terms
is still not close to Gaussian. Using the Gaussian approximation, and the fact that
Ik{j) is of zero mean, the decision statistic from equation (2.2) can be rewritten as
Zj = y/2EbdbJ + N ^0, 2P/,Xy cos2(0,)Var(4) + N0 ] (2.4)


Overlay has great potential in a situation in which a frequency band which cur
rently provides narrowband cellular service is designated to provide CDMA cellular
service in the future. This transition can be made gradually with the implementa
tion of overlay. Such a scenario is investigated in this research and promising results
are presented. The use of multi-carrier CDMA (MC-CDMA) is investigated for this
purpose, and is seen to perform quite well. In a fading channel, diversity such as that
offered by the use of multiple carriers improves the performance of a system operating
at a given power level. In the overlay scenario in particular, there is the additional
benefit to overall system performance, in terms of both CDMA and narrowband, that
the CDMA users can lower their power in a multi-carrier scenario and thus can reduce
the amount of interference on the narrowband system.
The feasibility of CDMA overlay is bolstered by the results presented in this disser
tation, and a strong motivation for its use as a method of transition from narrowband
service to CDMA service is argued as well.
IX


55
was satisfied:
Pv((Pe,cDMA > 0.05) U (#notches > 10)) < 0.02 (4.15)
In this criterion, a CDMA user will be blocked if its bit error rate is too high, or if
it needs more than 10 notches. As the sampling rate of the system is 1/TC, the range
in which notching can be done is actually (0.5/Tc < f < 0.5/Tc). Any frequency
locations outside of this range must be notched in the appropriate location mirrored
around 0.5/Tc. Thus with a processing gain of 32, there are effectively only 16
notching locations. With more than 60% of the CDMA signal notched out, the user
must be dropped.
A two-dimensional capacity plot is shown in Figure 4.7 for the same-link case,
with notching thresholds of T = 7,9,11 dB. The notching threshold may affect the
capacity criterion of equation (4.15) in two ways. First, as more notching becomes
necessary, it is more likely that the desired user will have more than 10 notches
and will be dropped. Also, it should be more difficult to demodulate the desired
users signal as more notches are added, and hence the probability of error should be
higher on average. Notice that when the narrowband system is lightly-loaded, there
is little difference in the amount of CDMA loading possible for each threshold. It
was observed that when the loading was at most 1.5 narrowband users/cell, no drops
occurred as a result of excessive notching. The fact that the threshold had little effect
at these loading levels suggests that the notching has a minimal effect on the bit error
rate, an idea which later will be investigated further.
As the narrowband loading increases beyond 1.5 users/cell, the system in which
a notch is placed if the narrowband-to-CDMA power ratio is less than T = 11 dB
immediately shows the effects of having users dropped as there now are some instances
in which the desired user requires more than 10 notches. For the other values T 7, 9
dB, the effects of dropping users show up for higher values of narrowband loading.


I certify that I have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Scott L. Miller, Chairman
Associate Professor of Electrical and
Computer Engineering
I certify that I have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Leon W. Couch II
Professor of Electrical and Computer
Engineering
I certify that I have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Haniph A. Latchman
Associate Professor of Electrical and
Computer Engineering
I certify that I have read this study and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Jian Li
Associate Professor of Electrical and
Computer Engineering
I certify that I have read this stud}'' and that in my opinion it conforms to accept
able standards of scholarly presentation and is fully adequate, in scope and quality,
as a dissertation for the degree of Doctor of Philosophy.
Ulrich H. Kurzweg
Professor of Aerospace Engineering,
Mechanics, and Engineering Science


3
noise and hence would not even know that a communication is taking place. This is
referred to as low probability of detection (LPD) capability.
In the past two decades, the research in this area has shifted from military to
commercial applications, particularly in the study of CDMA systems, in which many
direct-sequence spread-spectrum signals are transmitted in the same bandwidth and
the code sequences are used as a means of providing separation between them. When
the code sequences have some degree of orthogonality to each other, the job of the
receiver is made easier, although exact orthogonality is not necessary, nor is it achiev
able in asynchronous communication systems. The problem of choosing good code
sequences has been studied, and a good summary of many of the major results is
found in Sarwate and Pursley [1],
CDMA is a very promising technology for several reasons. Most importantly, in a
cellular scenario, there is the potential for a many-fold increase in user capacity over
traditional frequency-division multiple-access (FDMA) systems. The cellular scenario
will be looked at in detail in Chapters 4 and 5. Another advantage of using CDMA
over FDMA is the inherent ability of a wideband signal, such as a CDMA signal, to
realize diversity due to the frequency selectivity of the fading channel. An additional
attribute of CDMA is the potential for privacy through the unique spreading codes
of the different users.
A survey of the receiver structures that have been proposed in the literature begins
with the conventional matched filter receiver, which was analyzed by Pursley [2]
and by Yao [3] for an additive white Gaussian noise (AWGN) channel. One of the
principal shortcomings of this receiver is its susceptibility to the near-far problem, a
situation in which one or more users are physically located much closer to the CDMA
receiver than is the desired user, and the desired users signal is thus overwhelmed
by this multi-access interference (MAI). In such an environment, the system must
use power control, a process in which the base station, a centralized control center,


5
be discussed in the next section. It will also be seen that the MMSE can reject
inter-symbol interference (ISI). A significant portion of the research presented in this
dissertation focuses on the MMSE.
1.2 CDMA Overlay
In communication systems, a major design factor involves the limited amount
of frequency spectrum that is available. With this as motivation, the overlay of a
CDMA system on a frequency band that is also populated by narrowband users from
another system has been examined bv Milstein et al. [16]. An actual CDMA overlay
system was simulated in this field study, and gave preliminary indications that it is
an attainable goal, as both the CDMA users and the narrowband users were able to
communicate reliably. It would be very beneficial if some of the frequency bands which
are currently occupied by sparsely-populated narrowband systems could increase their
overall capacity by adding CDMA technology. Of particular interest is the possibility
of implementing overlay in a cellular scenario as a means of gradually phasing-out
an existing narrowband cellular system in a frequency band which ultimately will
support exclusively a CDMA cellular system. This will be looked at in detail in
Chapters 4 and 5.
In theory, the two systems, CDMA and narrowband, can coexist in the same
frequency band a,s a result of their intrinsic properties. Consider first the effect of
interference from a CDMA system on a narrowband system. Using the same idea
as that used in low probability of detection systems, CDMA users that are spread
will have only a fraction of their power affecting the narrowband system which has
a relatively small bandwidth. The effect of the CDMA system on the narrowband
system may be tolerable if the processing gain is large enough and if the ratio of
CDMA users to processing gain is small enough.
Conversely, when narrowband interference appears at a CDMA receiver, its effect
can be lessened to some extent by using various interference rejection techniques


52
Figure 4.6: Notching probability as a function of dx for same-link case. Notching
thresholds are T = 1, 3,... 15 dB.
the number of cells, the number of notches required for the CDMA signal is then a
binomial random variable with success probability pn.
4.3.2 Staggered-Link Assignment
In contrast to the previous case, the CDMA mobiles and the narrowband base
station are now transmitting in the same band. It is not necessary to perform a
detailed analysis in this case. The signal on the narrowband forward link will have a
composite gain from the base stations transmitter antenna and the mobiles receiver
antenna, while the interference from a CDMA mobile to the narrowband mobile will
only be amplified by its own transmit antenna and the narrowband mobiles receiver
antenna. Obviously, the base station antennas will be much larger in effective area
than will a size-limited mobile antenna. So the narrowband forward-link signal is
likely to arrive at the mobile at a much higher level than would the interference from
the CDMA mobile. Hence it is possible that notching is not required of the CDMA
mobiles in the staggered-link case.


SNR: signal-to-noise ratio
SS: spread-spectrum


BIOGRAPHICAL SKETCH
Brad J. Rainbolt was born in Normal, IL, in 1972. He received the B.S. and
M.E. degrees, both in electrical engineering, in August 1993 and December 1994
from the University of Florida, Gainesville, FL. He was employed by Motorola Land
Mobile Products Sector, Plantation, FL, from May 1994 through August 1995 as an
engineer in the Applied Research Group, where he worked on the design of digital
communication systems. In August 1995, he returned to the University of Florida,
and received the Ph.D. degree in electrical engineering in December 1998.
86


CHAPTER 4
CDMA OVERLAY IN A CELLULAR SYSTEM
We will now extend the ideas of the previous two chapters to the cellular envi
ronment, an application for which CDMA overlay has perhaps the most potential
for increasing user capacity. Because overlay is feasible only when the existing nar
rowband system is sparsely-populated, the cellular concept seems quite conducive to
overlay, as each cell in a narrowband system only utilizes a fraction of the system
bandwidth, even when full}' loaded. A cellular overlay system would be quite ben
eficial in a situation in which a narrowband cellular system is to be phased out in
favor of a CDMA system [24], With overlay, the transition could be gradual, as a
new CDMA product could be introduced while the system still provides support to
the existing narrowband products. In this chapter, it will be shown that overlay can
be realized in the cellular scenario.
The total system bandwidth of the narrowband system is divided into several
frequency groups, each consisting of a number of narrowband channels separated in
frequency so as to minimize adjacent-channel interference. The groups are assigned to
the cells in an intelligent manner which minimizes the co-channel interference, that is
interference caused by users in different cells using the same channel. Thus even when
fully-loaded, each cell only utilizes a small fraction of the total system bandwidth,
as would be necessary for overlay. A CDMA system could be implemented using the
same cellular layout, with the CDMA users in each cell spread in frequency over the
whole system bandwidth.
37


23
Table 2.3: Gains in clB for BPSK system for DFT-based filter.
Length (bits)
1
2
4
8
16
Gain (clB)
11.2
22.8
31.4
39.2
46.3
be performed by forcing to zero those values of the DFT that correspond to frequen
cies within the desired notching range and taking an inverse DFT. The frequencies
represented are spaced by 1 /N in the digital frequency domain, corresponding to a
frequency spacing of 1/T in the analog domain. Thus if a notch of width 2/TJ, is
desired, there are three DFT coefficients, two surrounding the range and one in the
middle of it, which should Ire set to zero. A plot of |C(/)|2 is shown in Figure 2.3,
in the graph for no zero-padding.
Notice that there are deep nulls, but there are also high peaks between the nulls.
When an IV-point DFT of the unfiltered code sequence is used, no more resolution
is available for notching. However, if the code sequence is padded with zeros so that
an IV-point DFT with N > N is performed, there will be more resolution. As shown
again in Figure 2.3 for the case when the sequence is padded to cover 8 bits, the
resulting notch is much deeper.
The DFT-based method was tested for an unpadded sequence and for sequences
padded with zeros to cover 2, 4, 8. and 16 bits. The gains are shown in Table
2.3. To achieve a gain comparable to that of the Butterworth filtering method, a
sequence padded with zeros up to 16 bits must be used. In Figure 2.4, the code
sequence resulting from zero-padding up to 8 bits dies off pretty quickly, with much
less spillover than was seen in the Butterworth case. The DFT-based filtering method
also seems like a viable filtering method, perhaps in situations where the large gains
given to the narrowband system by the Butterworth filtering are not needed. It will
be seen later that the DFT-based filtering method is the better choice in terms of
performance of the CDMA system.


57
This is a significant capacity improvement which would be very useful as mentioned
in the transition from a narrowband cellular system to a CDMA cellular system.
It would also be of interest to investigate separately the effects of notching and
the effects of narrowband noise on the CDMA system. This was done by comparing
results for the staggered-link case, which naturally has a very high level of narrowband
interference, and the same-link case explicitly in terms of the number of notches in
the desired user and in the number of narrowband users which interfere with the
CDMA signal. Recall that these will likely be different as the CDMA mobiles often
must notch for narrowband users that are assigned to other cells. Also, although it
was stated earlier that notching will not likely be required in the staggered-link case,
it will be done here only in an effort to look specifically at the difference in the effects
of notching and narrowband noise.
In the capacity plot shown in Figure 4.8, results for the staggered-link case are
shown as solid lines while the one dashed line applies to the same-link case. For the
staggered-link results, the number of narrowband users assigned to the desired users
cell was held constant at 0, 1, 2, 3. or 4, while the number of notches in the desired
user was varied, and the CDMA density was found according to only the bit error
rate part of the criterion of equation (4.15). Recall that in this configuration, the
signals on the narrowband systems forward link will appear on the CDMA reverse
link as interference at a very high near-far ratio. Assuming that the problem can be
alleviated to some extent by shielding the two antennas, the near-far ratio was fixed
at 20 dB. In going downward from curve to curve, it is seen that the effect of an
additional narrowband user is to decrease the CDMA density by about 4 users/cell,
which is significant.
For the same-link case, when there are no narrowband users assigned to the desired
CDMA users cell, the capacity curve is the same as in the staggered-link case. The
narrowband users that are assigned to the cell will arrive at 0 dB with respect to the


21
O 0.25 0.5
Digital frequency
Figure 2.3: PSDs for notch-filtered signals. Processing gain is 32 chips/bit. (a)
Eigenvector filter, M 7 taps on each sick1: (1)) Null filter, M 8 taps on each
side; (c) Butterworth filter, 8th order, 3-dB B\Y 1/32; (d) DFT-based filtering, no
zero-padding; (e) DFT-based filtering, zero-padded to 8 bits. Solid curves are for
unfiltered, dashed curves are for filtered.


70
more than 2 notches are necessary. In contrast to the 2-carrier case, if only one of
the carriers must be dropped, 3 of the 4 carriers would still remain, and it might be
possible that the CDMA receiver could still function reliably. This will be looked at
in Section 5.3, but for now, the criterion that we will employ is that a CDMA user
will be dropped if at least 2 of the 4 carriers have more than 2 notches. These results
are shown in Figures 5.2 and 5.3 as well. In Figure 5.3, there is an improvement
over the 2-carrier case, in which the CDMA user was dropped even if only one of the
carriers needed significant notching.
It has been suggested previously that with the use of multi-carrier CDMA, it is
possible to avoid the narrowband users in an overlay scenario by simply not trans
mitting on those carriers which might interfere with a narrowband user [27]. This
possibility was also examined here for comparison. We will first utilize the previous
notching criteria, and declare that if the CDMA signal on a given carrier is received
at a high power level in terms of the notching threshold T, the carrier will not be
used, analogous to simply placing a notch in the previous scenarios.
We will consider both 4 and 8 carriers in this type of system. It does not seem
fruitful to raise the number of carriers beyond 8, with a composite processing gain of
32 chips/bit, for several reasons. First, even assuming that the CDMA signal on each
carrier would experience independent fading, the incremental diversity advantage re
alized by using more carriers diminishes with such a high number of carriers. Second,
it has been assumed that the CDMA system, when used with multiple carriers, can
be split such that transmission takes place on disjoint frequency bands, so that inde
pendent fading can be realized. While this seems plausible with 2 or even 4 carriers,
the possibility becomes less likely'- with a large number of carriers. Thus some of the
carriers will undergo correlated fading, which will not give nearly as much diversity as
will independent fading. Finally, the process of tracking the fading processes, which is


15
-2
10
-10 dB
-14 dB
-2 dB
-6 dB
2 dB
7
8
9
10
11
12
Eb/N0 (dB)
Figure 2.2: Probability of error, Pe of BPSK user vs. E\¡/Nq with CDMA overlay of
3 users with 31 chips/bit. Solid curve is for numerical integration, dashed curve is
for approximation of equation (2.11).
and the narrowband system. These results cast considerable doubt on the feasibility of
CDMA overlay. It may not even be worthwhile to implement a CDMA system with a
loading of K/N = 3/31, and these results indicate that this very lightly-loaded system
still causes severe degradation to the narrowband system. Obviously, something must
be done to lessen the effect of the C'DMA interference on the narrowband system,
and one such method will be investigated in the next section.
2.2 CDMA Transmitter Filtering
In an effort to improve the previous results, which seem to preclude the chance
of CDMA overlay, an idea which was suggested both by Milstein et al. [16] and by
Davis [21] will be investigated. The energy from a CDMA signal that does appear
in the same bandwidth of a narrowband user apparently requires more attenuation
than that which results solely from the processing gain. The attractive properties of
a CDMA signal, such as its inherent separation from other CDMA signals as a result
of the spreading codes, its inherent separation from narrowband signals as a result of
the processing gain, and its robustness to multipath, may not be sacrificed too much
if only a small notch is placed in its spectrum. And if the frequency ranges occupied


30
Figure 3.2: Two-dimensional capacity plot for DFT-based filtering, zero-padded to 8
bits. Processing gain is 32 chips/bit. (a) MMSE receiver, minimizing J = E[|Z,
dx(*)|2]) (b) MMSE receiver, minimizing J = E[{Re(Z di(z))}2]; (c) matched filter.
In Figure 3.2, a two-dimensional capacity plot is shown for a system which employs
DFT-based filtering, with zero-padding up to 8 bits. The curve labeled (a) represents
possible operating points for the system, in terms of the number of CDMA users and
the number of narrowband users that can simultaneously use the frequency band and
still satisfy the CDMA systems performance criterion given in equation (3.7).
It should be noted that in this receiver, the bit decision is made by looking only at
the real part of the filter output Z, w;/u(?'). Hence better results would probably be
obtained by choosing an algorithm to minimize J = E[{Re(Z di(z))}2] as opposed
to minimizing J = E[|Z c/i(?')|2]. In this case, the imaginary part of the error can
be ignored since it will not be used. With the same equalizer contents as in equation
(3.3), the filter output can be written as
Z[ = (w0i, + iw0s)"(u,(t) + ju(i))
(3.8)


53
The major drawback to this configuration, however, is the severe near-far problem
that results at the CDMA base station as it must receive signals from its mobiles in
the presence of the signals sent from the narrowband base station, located a short
distance away on the same tower, to its own mobiles. It will be seen later that
this disadvantage outweighs by far the advantage of needing few, if any, notches
in the CDMA mobiles, and that the same-link assignment is the better of the two
configurations.
4.4 Simulations and Results
In order to investigate the performance of the CDMA system, an environment
similar to that used in the single-cell results of Chapter 3 was constructed, incorpo
rating the cellular layout of Figure 4.1, and log-normal shadowing and power control
as described earlier. The CDMA system had a processing gain of Ar = 32 chips/bit,
an Eb/No value of 10 dB, and used the DFT-based filtering method with 8 bits of
zero-padding when filtering was necessary. For a 1/7 frequency reuse system, each
cell would have at most 4-5 narrowband users.
In a brute-force simulation of the cellular overlay system, the coverage area that
must be considered would consist of 6 layers of cells surrounding the center cell of
interest. It was observed that a CDMA user might have to notch for a narrowband
user that is 2 layers away from its geographic location. And any user could be assigned
to a cell at most usually 2 layers away from its geographic location. So a CDMA user
in the second layer out might have to notch for a narrowband user in the fourth layer
out whose base station could be in the sixth layer out.
The total number of cells in the geographic coverage area multiplied by the density
of users/cell gives the total number of users, either CDMA or narrowband, which
would then be distributed uniformly about the coverage area. Each user would then
be assigned to the cell at which its received power is maximum, and power control
would be implemented. After it is determined how much of an increase or decrease


51
First we define / = (Received narrowband power) (Received CDMA power),
where the received power refers to the power in dB at the base station to which the
narrowband user is assigned. A notch will then be required if / < T, with T given
in dB. Recall that at this liase station, the narrowband users received power will be
a specified value, denoted 7. It was stated earlier that the CDMA and narrowband
users would be power-controlled to the same level if assigned to the same base station.
In that case, I 0 and there is certainly a notch required.
For a CDMA user that is not assigned to the same cell as the narrowband user,
denoted cell k, the conditional PDF of the CDMA received power at the narrowband
users base station is
exp f -
fHt(h/(Gk < Yk)) = ~1 u(-h) (4.12)
/27r(^ + 4,)(Pr(G, where again m9ik, nhy.k, and a2 k depend on cl\, and Pr(G'/, < Yk) is the probability
that the CDMA user is not assigned to the A th cell. The notching probability, pn, is
then found as
19 r
Pn = I]
k= 1 L
Pr(/ < T, NB to cell k, CDMA to cell k)
+ Pr(I < T, NB to cell k, CDMA not to cell k)
which simplifies to
19
1 1 y '
Pn ~ 19 + 19 ^
fc=1
Q
-T (mgik myik)
a\ + ab
QI
img,k mVtk)
+ aU
(4.13)
(4.14)
The notching probability is plotted in Figure 4.6, as a function of d\, for T
1,3,... ,15 dB. As expected, it is highest at the edge of the cell, as those users
are more likely to be transmitting at a higher power than are those nearer to the
base station, as a result of the power control. For a number of narrowband users
located throughout the region, that is the density of users/cell multiplied by 19 for


19
Table 2.1: Gains in clB for BPSK system for eigenvector and null filters.
Taps
6
7
8
9
10
Eigenvector
32.8
36.8
35.5
24.0
20.0
Null
9.7
14.9
20.9
15.5
10.6
row vector of tap weights, B is a matrix whose (i,j)th element is given by
or \ N ~ I* JI cs((* ])AuTc)
B(bj) = ^
where N is the processing gain and Au> is the difference of the two systems carrier
frequencies. If the quantity aBaT is minimized, then the effect of the CDMA inter
ference on the BPSK system will also lie minimized. This minimization is performed
by letting a be the eigenvector of B corresponding to its smallest eigenvalue. Then
the quantity aBaT is equal to this eigenvalue.
It will be the convention throughout this dissertation to denote vector and matrix
quantities in boldface type.
In Table 2.1, the gains achieved by the eigenvector filter are shown when the
number of taps, M, on each side of the center tap varies from 6 to 10, and the
processing gain is 32 chips/bit. Although it seems that the gain should increase and
eventually level off as the number of taps is increased, the maximum gain is 37 dB,
occurring for M = 7. An explanation for this behavior might be that the eigenvector
filter was derived for the case when the BPSK system uses square pulses, not root
raised cosine pulses.
In Figure 2.3, a plot of |C(/)|2 for an eigenvector filter with M = 7 and Acn =
27r(0.125) shows that the filter severely distorts the CDMA signal. The desired re
sponse should have a deep null of finite width around the desired frequency, and as
little distortion as possible in the passband. This filter does not even have a parame
ter to control the width of the notch. Although it does provide a pretty sizable gain


69
and notching on CDMA performance. We have only considered two things, which
nonetheless do impose some limitations on user capacity: the number of CDMA users
for which the narrowband systems performance is severely degraded according to the
criterion of equation (5.9) and the number of narrowband users for which the CDMA
users would simply require too much notching. In the next section, we will look at
the CDMA performance in more detail.
We next consider using multi-carrier CDMA with 2 carriers, and hence a process
ing gain per path of 16 chips/bit. In deciding how much notching is excessive here,
we must note that only 8 unique notching locations are available in each carrier, and
hence if there are more than 4 notches required in either carrier, the CDMA user will
be dropped. With only one of the two carriers in use, this is equivalent to the single
carrier case with only half of the processing gain, but the same amount of loading.
The results for this case are also shown in Figure 5.2. For a given value of T, the
probability that at least one of the two carriers will have more than 4 notches out of a
possible 8 is greater than the probability that there will be 8 notches out of a possible
16 in the single-cell case, which agrees with intuition. In Figure 5.3, two-dimensional
capacity curves for the 2-carrier case indicate performance inferior to the single-carrier
case for a given value of {{Eb/No)b (Eb/No)c). However, there is no significant con
clusion to be drawn from this, and these results are only presented for future use. It
will be seen later that when CDMA receiver performance is taken into account, the
multi-carrier systems are able to operate at much lower values of (Eb/No)c than can
the single-carrier case, as a result of the added frequency diversity. Thus it would
be more fair to compare a curve in the single-carrier case with one of those from the
multi-carrier case with a significantly larger value of ((Eb/No)b (Eb/N0)c), which
would lean more favorably toward the multi-carrier case.
Finally, we consider using 4 carriers, which means that the CDMA signals will
have a processing gain per path of 8 cliips/bit. Thus a carrier will be dropped if


82
works have not considered the effects of the notch-filtering presented in this disserta
tion. It must be determined what effects the notching will have on algorithms such
as these, if used unmodified. It is likely that some modifications to fit the timing
estimation problem to the case with filtered codes would be necessary and certainly
would be beneficial. Also the possibility of the timing estimator working without
knowing the code sequence, as the MMSE receiver can do for detection, might be
useful. But it seems that this information would be known by the base stations,
and the estimator would probably suffer a good deal of performance loss if the code
sequence is not used in the algorithm. Additionally, in a frequency-selective fading
channel, the estimator must be able to lock onto several paths with different delays.
Another significant area of future research is the estimation of the fading processes
of the CDMA users. It was determined by Miller et al. [28] and by Miller and
Rainbolt [29] that the MMSE receiver will take a large loss in performance if it is
not able to track all of the fading processes of all of the users. This is a fairly
undeveloped area, with a few solutions having been proposed. Barbosa and Miller
used linear prediction in conjunction with an MMSE receiver to estimate the fading
process of the desired user in a flat-fading channel [36], A subspace-approach was
investigated by Wang and Poor [37], Methods based on a decorrelator idea, that
is a transformation on the received signal which removes the data, are presented
by Miller and Rainbolt [29] and by Juntti [38] in an effort to track the fading in a
frequency-selective fading channel.
The estimation of the fading processes is very important, not only for the overlay
scenario in this dissertation, but for the use of the MMSE in fading channels in
general. This will continue to be a popular topic of research, as there has not been a
tremendous amount of success realized.


50
Figure 4.5: Effects of missing notches on CDMA loading that narrowband system
can tolerate. Processing gain is 32 chips/bit. CDMA user notched if NB-to-CDMA
power ratio is less than the notching threshold, T = 7,9,11 dB.
two systems should use the same frequency band for the forward link, and corre
spondingly for the reverse link, or if they should be staggered such that one band
covers the forward link of one system and the reverse link of the other. These two
scenarios will be referred to as the same-link and staggered-link cases, and will be
compared now based on the reverse link of the CDMA system.
4.3.1 Same-Link Assignment
In this case, the CDMA mobiles and the narrowband mobiles are transmitting in
the same band, and thus the narrowband base station is taken to be the receiver. To
determine the required notching, consider again a CDMA user located at a distance
d\ from the first base station as shown in Figure 4.1. We will find the probability
that a CDMA user located at this position must notch for a single narrowband user
that is located uniformly within the hexagonal enclosure of the three layers of cells.
This will require for = 1,2,... ,19, the values of my and crjA, which are numerically
calculated, as well as the which are easily found using the law of cosines.


42
in dB at the base station is 7, the users transmitted power will be adjusted to 7 W,
where W is defined in equation (4.3), so that it will arrive at a power 7 at its own base
station. At a base station to which the user is not assigned, in cell k, the received
power is 7+ (Gk~Yk). Note that it is necessary to know Y¡. under this condition, that
is (Y*, > Gk)i as it determines the users transmitted power. But it is not necessary to
know which of the base stations other than the fcth that the user is assigned to. We
must then find the PDF of Hk, which is the interference power level at the fcth base
station relative to those users assigned to the Atth base station. Under the condition
that the user is not assigned to the kth. base station, H¡¡ will always be less than 0
dB.
The PDF of H/, will have a discrete part, which is an impulse at 0 dB, with a
weight equal to Pr(G. > Y), the probability that the user is assigned to the kth cell.
It will also have a continuous part, resulting from the event that it is not assigned to
the Ath cell, and appears as outer-cell interference. To find this part of the PDF, we
first find the joint cumulative distribution function (CDF)
(4.6)
The derivative of equation (4.6) with respect to h gives the continuous part of the
PDF of Hk, and the complete PDF is
(47)
where u(h) is the unit-step function. The continuous part of this PDF is just a
Gaussian PDF that is truncated at h = 0.
The expression in equation (4.7) is dependent on the exact position of the user.
This will be useful in some cases, but it would also be helpful to have a PDF for


54
in transmitted power from the mobiles is required, the necessary notching for each
CDMA mobile would be found by comparing its received power with that of each of
the narrowband mobiles assigned to one of the cells within a three-layer cluster of the
CDMA mobiles base station. This procedure would obviously require a great deal of
simulation time, which can be decreased significantly with some simplifications.
The first simplification results from the observation, which was verified by sim
ulation, that if an interfering CDMA user is left unfiltered, there is no noticeable
difference in its effect on the desired CDMA user. The notching probability for a
CDMA user depends jointly on its position and its transmitted power. But since it
does not need to be known in the simulations, it is sufficient only to know the in-
terferers received power relative to the desired user, and its position is unimportant.
So we can further simplify the simulations by using equation (4.8), which gives the
approximate PDF of the received power for a user that is located uniformly through
out a three-layer cluster around the cell of interest, taking into account both cell
assignment and power control. This was used to generate the near-far ratios of both
the interfering CDMA users and the narrowband users.
For the desired user, it was assigned to the center cell, and based on its position,
its notching probability was found from a numerically-evaluated table. The number
of notches required was then a binomial random variable dependent on the density
of narrowband users. Each CDMA user was given a random code sequence, delay,
and phase, and each narrowband user was assigned to a random frequency location.
The desired user was demodulated using an MMSE receiver, with the true Wiener
solution. As explained in Section 3.3, the best performance is obtained by choosing
the tap weights to minimize in expected value the square of the real part of the error as
opposed to the square of its absolute value. The system capacity in CDMA users/cell
was determined to be the maximum density for which the following blocking criterion


2
(a)
Time
Figure 1.1: Illustration of DS-SS waveforms and PSDs, 7 chips/bit. (a) Unspread
signal waveform; (b) PSD of unspread signal; (c) Spread signal waveform; (d) PSD
of spread signal.
of the unspread signal, but has a null bandwidth of l/Tc = N/T¡,, which is N times
larger than the null bandwidth of the unspread signal. Also note that since the total
power is the same in the two signals, the height of the PSD is reduced.
For many years, spread spectrum has been used in military applications, due
mainly to three of its features. First, it has a resistance to jamming, a process in
which an adversary transmits an interference signal, which is usually narrowband,
in an attempt to destroy communication, but not to intercept and make sense of it.
Spread spectrum also has low probability of intercept (LPI) capability, meaning that
it is difficult for an adversary to receive and demodulate the signal without knowing
the spreading code. Finally, because the power is spread over such a large bandwidth,
the spectral height of the spread-spectrum signal is reduced significantly, possibly to
the point where an adversary would not be able to distinguish it from the channel


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58
Figure 4.8: CDMA users/cell vs. number of notches in the desired user. Solid line is
staggered-link case, with narrowband-to-CDMA near far ratio at CDMA base station
of 20 dB, and 0, 1, 2, 3, or 4 narrowband users assigned to cell of interest. Dashed
line is same-link case, with 4 narrowband users with near-far ratio of 0 dB assigned
to cell of interest. E't/A'o of CDMA system is 10 dB.
CDMA users power level, as mentioned before. The plot when there are 4 narrowband
users assigned to the cell of interest is shown, and the plots for 1,2, and 3 users will
naturally fall between it and the plot for no narrowband users present. It is seen that
4 narrowband users received at a near-far ratio of 0 dB have the effect of decreasing
the CDMA capacity by only about 4 users/cell, as compared to a degradation of
about 4 CDMA users/cell for each narrowband user in the staggered-link case.
These results are not surprising, but they do give useful insight as to how much
effect the narrowband interference has. It is interesting that in all of the curves
shown, the CDMA capacity degrades slowly as the number of notches is increased to
around 7 or 8, and then degrades more rapidly. Clearly, the presence of narrowband
interference has more effect on CDMA capacity than does the notching.


81
of notching. This imposed disappointing constraints on the joint capacity of the sys
tem, that is the number of CDMA and narrowband users that can simultaneously
occupy the spectrum.
A solution for this problem is to use multi-carrier CDMA, in which the CDMA
signal is transmitted on several carriers, such that the signals on each carrier undergo
independent fading. This provides a significant amount of frequency diversity, which
allows the CDMA users to transmit at lower power levels. Thus less notching is also
necessary, and the joint capacity of the system is improved dramatically.
The results presented in this dissertation indicate that CDMA overlay has great
potential for providing an increase in user capacity. It is especially valuable in cellular
scenarios, in which a transition from narrowband service to CDMA service is in
progress. There remains, however, some open issues which will be discussed in the
next section.
6.2 Future Work
Some topics of future research will Ire suggested in this section. The results pre
sented in this dissertation have clearly indicated that overlay has significant potential.
The next step is to look at some of the implementation issues that were not addressed.
Throughout the research, two important tasks were assumed to have been done
perfectly, the timing acquisition, that is the knowledge about when the desired CDMA
users code sequence begins, and the estimation of the fading processes of the CDMA
users. They are certainly important problems that need to be addressed in future
work. The results presented in this dissertation had only the goal of demonstrating
that there is indeed a reason to pursue overlay. If the results had demonstrated other
wise, then the effects of imperfect estimation of the timing and the fading parameters
would not be interesting or meaningful.
The timing acquisition problem has been investigated by many researchers, and
there exists an extensive body of literature on the subject [30-35]. Obviously, these


17
performance will be the same as in the unfilterecl case. Thus the ratio of the variance
without filtering to the variance with filtering should be found, and it will indicate
how much additional near-far effect the BPSK system can tolerate. The amount of
gain required depends strongly upon environmental factors such as the cell geometry
and path-loss exponent [16]. It is conceivable that gains on the order of 50 dB may
be required. This could be the case when many CDMA users are present and/or a
severe near-far problem results from one or more of these users transmitting from a
location much closer to the narrowband receiver than that of the narrowband trans
mitter. If the CDMA users and the BPSK user are not power-controlled by the same
mechanism, then large near-far ratios are very possible.
2.3.2 Effect on the PSD of the C'DMA Signal
To see how certain filters perform in notching the CDMA signal, consider the PSD
of a CDMA users signal which is given as
SssU)
\Q(f)\2
Tb
A'-l
11=0
I qmi
%
|C(/)|2
(2.12)
where Q(f) is the Fourier transform of the chip pulse shape, c is the nth chip, and
the number of chips in the spreading sequence is N, which may be greater than the
processing gain N. From this expression, it is clear that the effects of filtering will
appear only in the rightmost magnitude-squared term, |C(/)|2 which can be plotted
as a function of frequency to show these effects.
2.3.3 Effect on the CDMA Code Sequence
In two of the four filtering methods examined in this dissertation, the output
code sequences are of length greater than N, which means that they span more than
a single bit. While this spillover greatly alleviates the effect of CDMA interference on


20
of 37 dB for the BPSK system, the eigenvector filter does not seem to be a plausible
option based on its detrimental effect on the CDMA signal.
2.4.2 Null Filtering
In the second method proposed by Davis [21], the filter puts a spectral null at the
BPSK systems carrier frequency. The tap weights a are given as
Po = 1
Pm =
2 cos( n) AuTc ]
2 M 1 +
sin((2Ai + l)AwTc)
sin(Au.'7c)
in = 1, 2,... AM
(2.14)
a = 0/\0\
and the filtered code sequence is formed again from the delayed output of the FIR
filter with tap weights given by a. The gains achieved by the null filter are shown in
Table 2.1 for the same values of M as for the eigenvalue filter and also for a processing
gain of 32 chips/bit. A maximum gain of 21 dB. significantly lower than that of the
eigenvalue filter, occurs for M = 8, and again an explanation for this behavior could
be that this filter was derived for the case of square pulses in the BPSK system.
A plot of \C(f)\2 for the null filter with M = 8 and Au> = 27t(0.125) is also
shown in Figure 2.3. Again, the CDMA signal is somewhat distorted, and there is
only a minor notch at the desired notched frequency, and no parameter to control
this width explicitly. Based on this, the null filtering method does not seem like a
plausible option, either.
2.4.3 Butterworth Filtering
We next consider the use of a digital Butterworth notch filter, which is an infinite
impulse response (HR) filter. The response when one period of the code sequence
appears at the input lasts forever in theory, although it is negligible beyond a few bits.
Nonetheless, the filtered code sequence will spill over into other bit intervals, resulting
in ISI. To form the output code sequence, the unfiltered code sequence, which is one
bit long and has N chips, is padded with several bits of zeros and clocked into the HR


39
(a)
(b)
Figure 4.1: Illustration of a narrowband cellular system, (a) Cellular layout for three-
layer cluster. Cells numbered 1-19. Letter is the cells channel-group assignment,
chosen from A-G; (b) Magnified view of Cell 1.
When comparing the paths to different base stations, it is only necessary to com
pare the rightmost term in the second line of equation (4.1), that is
Gj = [Ar(0, cr) 10ralog10(d,-)] (4.2)
where dl is the distance from the mobile to the z'tli base station, normalized such
that the cells are of unit radius. Also note that the quantity G, in equation (4.2)
will be referred to as a channel gain, as it is the sum of the path loss and shadowing,
but this is not intended to imply that there is an amplification of the signal through
the channel. This quantity will be used in comparing different paths on a relative
basis only. Without loss of generality, it will be assumed that the user of interest is
physically located in cell 1, and at a distance d\ and angle as shown in Figure 4.1.
The rest of the G¡ quantities may bo found in terms of d\ and B\ by using the law of
cosines. We define the following quantities, also in dB units:
W = max(Gj, G>,... Gfig)
I,- max(G'i, Go, .. G19)
Â¥=>
(4.3)


79
constraint, and allowed for a small amount of ISI. A digital Butterworth notch filter
was used, and a filtering method based on the DFT was also considered.
The filtering methods for which the ISI resulted performed significantly better
than did the other two methods, in terms of the amount of distortion caused to the
CDMA signals PSDs. They also provided more relief to the narrowband system.
The resulting ISI, while an important issue that must be looked at in CDMA receiver
design, was certainly manageable.
An important point that has been emphasized throughout this research, and has
not received enough attention in the literature, is that the use of notch filtering is
not simply a way to provide a modest improvement to the performance of an overlay
system. Rather, it is absolutely essential if the CDMA system is to be loaded to levels
for which the research community is actively striving.
Next, the problem of receiving the CDMA signals was considered, and it was
shown that the MMSE is a good choice for this purpose. In addition to its ability
to reject MAI and NBI, which has been demonstrated before, it was shown here
that the MMSE can reject ISI and also that it can adapt to a code sequence which
has been filtered, provided that a training sequence is used. The MMSE receivers
functionality in the overlay scenario was demonstrated throughout the dissertation,
in both single-cell and cellular scenarios, and with both a Gaussian channel model
and a fading channel model.
The application for which over la}' has perhaps the most potential is the cellular
scenario. The implementation of overlay could provide an efficient way for a fre
quency band which services narrowband users to transition its service to CDMA. For
contractual reasons, providers cannot simply discontinue service to narrowband sub
scribers once it has been decided that the band will be converted to support CDMA.
Overlay would allow the new CDMA technology to be introduced while the existing
narrowband products are phased out gradually.


74
The composite steering vector is given by
P(0 =
Pi (0
E[di (*>!(*')]
P20
=
E [d\ (?)r-2(*)]
_Pg(0.
_E [^(*>0 (*)].
(5.16)
The bit decision is then made as d\(i) = sign(Re[w/()r(z)]) for coherent combining of
the paths. It makes sense to use coherent combining in this case, as it was previously
stated that all of the fading paths of all of the users would be tracked anyway in order
to avoid a large performance loss.
The task of tracking the fading processes in a dynamic environment is currently
an area of active research. In this work, it will be assumed that all of the fading
processes on all of the paths are known, in which case we have
L/2
= 7l,pW7l,9(*)Cl,p,oCli(r/)0 + 'y ] 7l,p(*)7l1,(*)Cl,p,mCli,im T
m.= L/2
?7l/0
(jr) 7fc,p(*)7,9() [tfj + gfcg*] + 2ct2Inx 2RJim] Sp k=2 1 2 \m=1 /
(5.17)
where there are M narrowband users present on the carrier for which p = q. Also,
In/QxN/q is an identity matrix of dimension N/Q. The qth steering vector is
P9(0 = 7i,r/(*)ci,9,o (5.18)
If the expression for the qth received vector in equation (5.11) is written as
r,(0 = 7i,i(0di(0ci,i,o + r,(t) (5.19)
M
where ?q(i) represents a composite interference process consisting of MAI, AWGN,
NBI, and ISI, it can be shown with the matrix-inversion lemma that the probability


I dedicate this work to my parents, Patricia A. and Ronald J. Rainbolt.


6
that have been thoroughly studied [17-20]. These techniques in general exploit the
predictability of the narrowband interference and the unpredictability of the wideband
CDMA signals to form an estimate of the narrowband interference. This estimate
is then subtracted off of the received signal. The resulting signal will have a weaker
contribution from the narrowband interference, but will also have some distortion
on the wideband signals. The net effect of the interference rejection on the CDMA
system should be favorable, however.
The design of an overlay system has many important trade-offs. In terms of
the CDMA system, the ratio of users to processing gain should be maximized. But
increasing this ratio too high might make the narrowband system inoperable. On
the other hand, if the bandwidth of the narrowband users is increased too much, the
interference rejection techniques employed in the CDMA system become less effective.
And if either system operates at an excessive power level, it will render the other
system inoperable. These considerations will be examined in detail in subsequent
chapters.
1.3 Overview of the Dissertation
The focus of this dissertation will be those issues arising when a CDMA system
is overlaid on an existing narrowband system. The material can be divided broadly
into three parts. First, overlay in an AWGN channel will be investigated in Chapters
2 and 3. This material will be extended to a cellular system in Chapter 4. Finally, in
Chapter 5, the results for the cellular system will be extended to the fading channel,
which is a much more realistic model for a wireless environment. Conclusions and
related topics of future research will be looked at in Chapter 6.
Previous research in this area has focused almost exclusively on the performance
improvement of a CDMA system when techniques are applied to reject narrowband
interference in the same frequency band. While this problem is certainly applicable
and important, an equally and perhaps more important task is to quantify the effect


CHAPTER 5
CELLULAR OVERLAY IN A FADING CHANNEL
In this chapter, the use of CDMA overlay in a cellular scenario will be extended
to the fading channel. As has been the case throughout this research, the overlay will
again cause severe problems for the existing narrowband system. The narrowband
users also will benefit once again from notch-filtering in the CDMA transmitters. But
in a flat fading channel, there is a large amount of notching necessary in order that
enough relief is provided to the narrowband system. This places a strict constraint
on user capacity in terms of the number of CDMA and narrowband users which
can simultaneously share the spectrum. The use of multi-carrier CDMA, however,
allows the CDMA users to realize frequency diversity, and thus they may transmit
at lower power levels. This reduces the amount of notching necessary, and provides
a substantial improvement in joint user capacity.
5.1 Limits on CDMA Capacity
The idea of multi-carrier CDMA has recently received significant attention as an
alternative to traditional single-carrier CDMA [27]. The transmission of a CDMA
signal on two or more disjoint carrier frequencies, with enough frequency spacing so
that the fading on each signal is independent, allows for the possibility of frequency
diversity, and therefore an increase in user capacity.
In this section, a development of user capacity limits for overlay in the fading
channel begins with a quantification of how many CDMA users can be tolerated by
the narrowband system before its performance is degraded too severely. We will then
look at the resulting improvement due to the CDMA users employing notch-filtering
in their transmitters.
60


24
2.5 Summary
It has been shown in this chapter that CDMA overlay has quite a damaging effect
on a typical narrowband user. A very good solution is to employ notch-filtering in the
CDMA signals to avoid active narrowband users. For Butterworth notch-filtering and
DFT-based notch-filtering, substantial benefits were seen by the narrowband users,
while the CDMA signals experienced little distortion in their PSDs and a manageable
amount of ISI.


27
occupies. If this notch is not to be placed symmetrically about the carrier frequency,
as will generally be the case, then the baseband CDMA signal will have a PSD that
is not symmetric about zero frequency. Thus the notched code sequence will be
complex. For the Butterworth filter, instead of doing a bandstop filtering operation
in the appropriate frequency range, the impulse response of a highpass filter with the
same bandwidth can be found, and then multiplied by a complex exponential sequence
to shift the notch to the appropriate frequency range. For DFT-based filtering, the
DFT points represent both positive and negative frequency ranges, and thus only the
appropriate one-sided range of coefficients should be set to zero.
The received signal at baseband, denoted as r(t) in Figure 3.1, is given by
K co
Ht) = J2 v/m (l^c^f iTb ~ rk) exp(jOk)
k-1 ioc \y-)
+2n[t.) exp{-juct.) + 2j{t) exp(~ju>ct)
where Pk and 6k are the fcth users average power and phase, and dk(i) is the ith data
bit of the kth user. Also in this equation, n(t) is a white Gaussian noise process with
spectral height Nq/2. The noise process resulting from a narrowband user is given
by j(t). Its PSD is modeled as a square pulse centered at an offset of Acj from the
CDMA carrier frequency, and having width 2p, where p is a number between 0 and
1, most likely close to 0, that represents the fraction of the bandwidth (null-to-null)
that the narrowband user occupies.
The receiver forms a bank of samples by integrating r(t) over chip-length intervals,
as shown in Figure 3.1. The vector of matched-filter samples is given by
L 1
u(t) =^exp(jh)r/i(v' l)c\j + n(*) +j(i)
/=o
i<
L-1
exp(jY4) ^2 [4(/ + dk{i l l)gfc,/]
/=o
(3.3)


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
DIRECT-SEQUENCE CODE-DIVISION MULTIPLE-ACCESS OVERLAY
SYSTEMS
By
Brad .J. Rainbolt
December 1998
Chairman: Dr. Scott L. Miller
Major Department: Electrical and Computer Engineering
In this dissertation, the possibility of code-division multiple-access (CDMA) over
lay, that is the simultaneous sharing of a frequency band by a narrowband system and
a CDMA system, is investigated. In contrast, to the majority of existing studies on
overlay, which investigate almost exclusively the degradation experienced by CDMA
users as a result of the narrowband users, the results presented here focus specifically
on the effects of the overlay on the narrowband system. It is shown that even for
CDMA systems operating with a small number of users in comparison to the system
capacity in the absence of overlay, the narrowband system will experience a substan
tial loss in performance. The use of notch-filtering in the CDMA users transmitters
in order to avoid active narrowband users can alleviate the degradation experienced
by the narrowband system. In turn, the effects of the notching on the CDMA system
itself are seen to be quite modest.
viii


35
(a)
O 0.05 0.1
Pe
(b) (c)
Figure 3.5: Histograms of CDMA probability of bit error, Pe, for overlay system with
42 CDMA users and 1 narrowband user. Processing gain is 32 chips/bit. MMSE
receiver minimizes J = E[{Re(Z,- di(v'))}2]. DFT-based filtering, zero-padded to 8
bits. Solid curve is for no narrowband signal present, dashed curve is for narrowband
signal present with a given narrowband-to-CDMA near-far ratio, (a) Ratio is 0 dB;
(b) Ratio is 20 dB; (c) Ratio is 40 dB.
It is also interesting to look more closely at the ability of the MMSE receiver to
inherently reject strong narrowband interference. It was determined previously that
when J = E[{Re(Z¡ di(*))}2] IS minimized, 42 CDMA users could share the channel
with a single narrowband user. In order to examine the effect of the narrowband noise,
a system was simulated with 42 CDMA users with a single notch and a narrowband
user with varying levels of power. In each trial, a new set of code sequences, delays,
and powers were chosen for the CDMA users and a new frequency location was chosen
for the narrowband user, all using the same parameters as in the previous simulations.
Then the probability of bit error was found for the CDMA system for narrowband-to-
CDMA near-far ratios of 0, 20, and 40 dB. and also for the case when the narrowband
signal was not present but the notching was still performed.


LIST OF ABBREVIATIONS
AWGN: additive white Gaussian noise'
BPSK: binary phase-shift keying
CDF: cumulative distribution function
CDMA: code-division multiple-access
DFT: discrete Fourier transform
DS: direct-sequence
FDMA: frequency-division multiple-access
FH: frequency-hopped
FIR: finite impulse response
IEEE: The Institute of Electrical and Electronics Engineers, Inc.
HR: infinite impulse response
ISI: inter-symbol interference
LMS: least mean-squared
LPD: low probability of detection
LPI: low probability of intercept
MAI: multi-access interference
MC-CDMA: multi-carrier code-division multiple-access
MMSE: minimum mean-squared error
MSE: mean-squared error
NBI: narrowband interference
PDF: probability density function
PSD: power spectral density
RLS: recursive least-squares
vi


72
all of the paths of all of the CDMA users must be tracked in order to avoid a sizable
performance loss.
The performance in the overlay environment is a relatively straightforward ex
tension of the analyses given by Miller et al. [28] and by Miller and Rainbolt [29].
The desired CDMA user now may operate with a filtered code sequence and nar
rowband noise must be added when necessary. We consider a general multi-carrier
system with Q carriers, and a processing gain per path of N/Q. It is also as
sumed that the desired users code sequence in the qth carrier will be filtered (when
necessary) using the DFT-based filtering method from Section 2.4.4, which results
in a code sequence of length greater than the processing gain, N/Q in this case.
It will be expressed as the cascade of L individual sequences of length N/Q, as
ci,9 = (CJ9,-L/2> > cL-i>cLo, CU/,1> clq,L/2)T. with ci,9,o in the middle associ
ated with the desired component and the other sequences corresponding to ISI. Note
that on each carrier, the filtered code sequence will be different as the notching nec
essary on each carrier is generally not the same. Also, for simplicity, it was verified in
Section 4.4 that there is no significant difference in the reception of the desired user
if the interfering CDMA users are left unfiltered.
For the gth carrier, the samples of a chip-matched-filter bank will be collected
during the zth bit interval, resulting in a column-vector of N/Q samples given by
L/2
r,(*) = 'h,q{i)di{i)chq<0 + 7i,9(*)di(* )ci,9,m + nq{i) + j9(i) +
m=L/2
0
Jrr'fkAi) dk(i)fk + dk(i i)gfc]
k=2 1
(5.11)
where 7fc,9(f) is the fading process on the qth carrier of the kth user during the ith bit
interval, and the fading processes for the same user on each carrier are independent.
Also, 4 and gk are the even and odd cyclic shifts of the kth users code sequence, which
were defined in equation (3.4) and nq(i) is a vector of length N/Q of independent


29
3.3 Simulation Results
In order to get an idea of how filtering affects the performance of the MMSE
receiver, an overlay system was simulated. The CDMA users operated with filtered
random sequences and a processing gain of N 32 chips/bit. The value of Eb/No
was fixed at 10 dB. The powers of the interfering CDMA users were chosen from
a log-normal distribution with a standard deviation of 1.5 dB, to simulate power-
control error. The notch-filtering was done using a DFT-based filter with 8 bits of
zero-padding. The narrowband users were generated by putting white Gaussian noise
through a Butterworth bandpass filter with a digital 3-dB bandwidth of 0.5/32. Their
center frequencies were chosen to fall within the analog frequency range (0.5/Tc <
nb < 0.5/Tc), which corresponds to the digital frequency range of (0.5 < fuB,d <
0.5) as the sampling rate is 1/TC. Their powers (near-far ratios) were chosen from
a distribution that results from a situation in which they are uniformly distributed
spatially around the CDMA receiver, a path-loss exponent of n = 3 is used, and the
maximum near-far ratio is set to 40 dB.
For different numbers of narrowband users, the number of CDMA users was varied
to find the maximum number that could lie tolerated by the CDMA system. For each
simulation, the code sequences, delays, and powers of the CDMA users as well as the
frequency locations and powers of the narrowband users were varied. The criterion
chosen was that the blocking probability had to be less than 0.02, where a block was
defined as a scenario in which the probability of bit error of the desired CDMA user,
Pe,CDMA, was greater than 0.05. So the capacity of the CDMA system for a given
number of narrowband users was the maximum number of CDMA users that could
be present and still satisfy the performance criterion
Pi'{Pe.CDMA > 0.05) < 0.02
(3.7)


This dissertation was submitted to the Graduate Faculty of the College of En
gineering and to the Graduate School and was accepted as partial fulfillment of the
requirements for the degree of Doctor of Philosophy.
December 1998
Winfred M. Phillips
Dean, College of Engineering
M. J. Ohanian
Dean, Graduate School


CHAPTER 2
NARROWBAND SYSTEM PERFORMANCE IN THE AWGN CHANNEL
In an overlay scenario, it is especially important to make sure that the CDMA
system does not degrade the narrowband systems performance to the point of in
operability. One possible situation occurs when a CDMA system is overlaid on a
sparsely-populated narrowband system that is already in operation. The designers of
the CDMA system must work around the narrowband system and should not expect
the designers of the narrowband system to make significant modifications to their de
sign in order to accommodate the CDMA system. Another situation is one in which
the two systems are to be designed jointly. It is the goal of this chapter to quantify
the effect of the CDMA system on the performance of a narrowband user.
2.1 Effects of Overlay on a Narrowband User
As mentioned before, little attention has been given to quantifying the effects of
CDMA interference on a narrowband user in an overlay scenario. The subject was
treated by Davis [21] and it was reported that the CDMA overlay can cause problems
for the narrowband users. Results were given by Pickholtz et al. [22] for the case of
a single spread-spectrum user and actual measurements were reported in the CDMA
overlay field study performed by Milstein et al. [16]. We will demonstrate in this
paper exactly how much degradation is caused to a typical narrowband system in
such an environment.
Toward this end, consider the performance of a BPSK user operating in an overlay
scenario in an AWGN channel. In order to band-limit the BPSK users signal, a root-
raised cosine pulse shape will be used in the transmitter and in the matched-filter
receiver. Assuming equal carrier frequencies for the narrowband and CDMA systems,
10


61
Throughout this chapter, a cellular system identical to the one in Chapter 4, with
the addition of fading, will be considered. From Figure 4.1, interference from cells
within two outer layers of the center cell of interest will be taken into account. The
PDF of the near-far ratio of an interfering user, either CDMA or narrowband, located
uniformly throughout the three-layer area, was approximated in equation (4.8) as
(5.1)
We will now look at the performance of a BPSK user received in the presence
of overlay in a fading channel. A general multi-carrier CDMA format will be used,
where there are Q carriers, and the total power of each CDMA user is divided equally
amongst the Q carriers. The identical CDMA signal will be transmitted simultane
ously on each carrier. The fading process on each carrier will be taken as frequency-
nonselective, and independent of the fading processes on other paths. The CDMA
bandwidth in the single-carrier case must be smaller than, or on the order of, the co
herence bandwidth of the channel in order that the fading be frequency-nonselective.
Thus in the realization of multi-carrier CDMA, the carriers must have sufficient fre
quency spacing between themselves in order for the fading on each carrier to be
independent.
It will be assumed that only the particular CDMA signal which overlaps the BPSK
signal at bandpass will pass through the BPSK receiver, and thus we will concentrate
only on that signal in the equations which follow. The BPSK user employs square
pulses of width Tb, the bit time, and a matched-filter receiver. The complex baseband
received signal can be written as
OO
r(t) = X \Z2Pb-yb(i)db{i)n{{t iTb)/Tb) + 2n(t) exp(ju>ct)
oo K
+ EE VmjQlk{i)dk(i)ck(t iTb Tk)
(5.2)


38
4.1 Characterization of the Cellular Environment
In this section, some aspects of the cellular environment, such as the assignment
of users to cells, the power control that is employed, and the interference that users
cause to base stations other than their own will be described. We will look at a
system with a frequency reuse of 1/7, which means that the total system bandwidth
will be divided into seven groups which are then assigned to the cells in a manner
which minimizes the co-channel interference. Each group will consist of a number
of narrowband channels separated in frequency so as to minimize adjacent-channel
interference.
As shown in Figure 4.1, with cell 1 as the cell of interest, effects from users in
those cells beyond the two outer layers of cells shown will be considered negligible.
The individual cells, numbered 1-19, are also given a letter from A-G which indicates
which of the seven channel groups it will use. The coverage areas are shown as circles
for simplicity, but in practice and in this research, a user will be assigned to the
cell for which the path between the mobile and the base station is least attenuated.
This will depend not only on the distance of propagation, but also on log-normal
shadowing, which may be severe. So a user often will be assigned to a base station
that is not the closest one geographically.
We begin by looking at the received power at a distance dr from a transmitter
which may be either CDMA or narrowband. The power is typically modeled by
first finding the received power at a close-in reference distance do, denoted Pq. Then
with n as the path-loss exponent and a(J as the standard deviation of the log-normal
shadowing, the received power at dr is given in dB units as [25]
Pr = P(i 10?ilogj0 + Ar(0, a'g)
= [P0 + 10nlog10(do)] + [N{0,v2g) 10nlog10(dP)]
(4.1)


62
where n(f/T¡,) is a unit-amplitude square pulse of width T, Pb is the BPSK users
average power, Pb is the fcth CDMA users composite average power from all of its
carriers, 7() and 7¡¡(i) are the BPSK users and kth CDMA users fading process
during the th bit interval, with each a zero-mean complex Gaussian random variable.
The Hh users spreading waveform, has a period of Tb and consists of unit-
amplitude square pulses of width QTC where the single-carrier chip-time is Tc = Tb/N
and N is the composite processing gain. The output of the BPSK users matched-filter
in the th bit interval is
(i+l)Tb k I
z(i) = 7m / T{f)dt =Tw iTb t-1 V
(5.3)
where Nx(i) and Ny(i) are zero-mean Gaussian random variables each with variance
cr2 = (2Eb/No)~1, Eb is the average energy-per-bit of the BPSK system, and the term
due to interference from the kth CDMA user during the th bit interval, /*,(*), is
Ti
Tfc
h(i)=dk(i- 1) Ck(t)dt +dk{i) / Ck(t)dt
(5.4)
Tk 0
Denoting the nth chip of the kth users spreading code as cin, and assuming that the
per-carrier processing gain N/Q is an integer, we have
h(i)
Tb
/ N/Q-1 \
4( 1) SkCk,N/Q-pk-i + ^ Ckj I +
V j=N/Q-Pk /
dk{i)
N/Qpit2
Ck' + 1 ~ tik)Ck,N/Q-pk-l
i=0
(5.5)
where the delay has been written as 77 = (pb + Sb)QTc with pb an integer in the
range (0,1,... {N/Q) 1) and Sb a non-integer in the range (0,1). The variance
of this term, for fixed codes and delays, and hence with the expectation taken only
with respect to the data bits, is itself a random variable. From Section 4.2, it can be


16
by narrowband signals are notched out, the CDMA signal will effectively avoid the
narrowband system.
To perform the notch filtering, the code sequence is altered to a new code se
quence, which consists of pulses, most likely square, whose amplitudes are no longer
constrained to the values 1. The filtered code sequence is then modulated with the
data waveform and converted up to bandpass and transmitted, just as the unfiltered
code sequence would be.
Four methods of filtering the code sequence will be examined and will be compared
based on three criteria which will be elaborated on in the next section: the gain
realized in the BPSK system, the effect on the PSD of the CDMA signal, and the
effect on the CDMA code sequence.
2.3 Filtering Performance Criteria
In this section, three criteria will be presented which will measure the effectiveness
of a given method of notching at the CDMA transmitter. The gain of the BPSK
system, the effect on the PSD of the CDMA signal, and the effect on the CDMA
code sequence will now be explained in detail.
2.3.1 Gain of the BPSK System
The probability of error of the BPSK system given in equation (2.7) depends on
the variance of Ik, given in equation (2.8), which in turn depends on the users code
sequences. As will be seen later, two of the four filtering methods used in this work
result in ISI, and hence the expression for Ik must be modified in those cases to
include the appropriate contributions which result from the spillover.
The evaluation of the variance of ty requires simulation. It is then used in equa
tion (2.7) to get the probability of error. Because the variance is multiplied by the
CDMA-to-BPSK power ratio (Pk/Pb), if the filtering reduces the variance by a certain
multiplicative factor, the power ratio can be increased by the same factor and the


71
not considered in this paper, would become tremendously complicated with so many
carriers.
It was observed in later simulations that the CDMA system suffered a large per
formance loss, in terms of the number of supportable users, if half of its carriers must
be dropped. This would be essentially equivalent to doubling the load on a system
with all of its carriers operational. Thus we can obtain an upper bound on capacity
limits in this section by finding how many narrowband users may be present so that
at least half of the carriers are still operational. As it is shown in Figure 5.2, for 4
and 8 carriers, even these upper bounds fall far below the performance of the systems
which use notching. This suggests that a hybrid of these ideas must be used. When
one or more of the carriers simply requires too much notching, transmission on it can
be avoided, but the remaining carriers may still have some notches. Again, this must
be tested in terms of the effect on CDMA performance, which will be done in the
next section.
5.3 Performance of the CDMA System
In this section, the capacity limits of multi-carrier CDMA will be examined fur
ther. Results from Sections 5.1 and 5.2 will be extended to include the effects on
CDMA performance of MAI, NBI, notching, and the possibility of operating on fewer
carriers than the maximum. We consider the use of the MMSE receiver, which is
well-suited to the overlay environment. Several of its desirable properties were men
tioned in Section 3.1, such as its ability to reject MAI, NBI, and ISI as well as its
ability to adapt to the desired users signal without even knowing that its code has
been filtered. It was shown by Miller et al. [28] that the MMSE can successfully re
alize diversity in a frequency-selective fading channel, and that there is a substantial
performance loss when all of the paths of all of the interfering users are not tracked
explicitly in forming the Wiener solution. The performance of the MMSE was evalu
ated in the multi-carrier case by Miller and Rainbolt [29], and it was reaffirmed that


CHAPTER 1
INTRODUCTION
In this chapter, the concept of code-division multiple-access (CDMA) will be
presented. The benefits that CDMA offers as well as some of the main works of
research in this field will be summarized. This chapter will also introduce CDMA
overlay, the focus of this dissertation, which is the sharing of frequency spectrum by
a CDMA system and a sparsely-populated narrowband system. An overview of the
dissertation will conclude this introductory chapter.
1.1 Code-Division Multiple-Access
CDMA is an emerging technology which employs spread-spectrum (SS) signaling,
that is the intentional spreading of a digital signal over a bandwidth that is much
greater than its information bandwidth, typically on the order of a 100-fold increase
or more. Although spread-spectrum systems are generally divided into two categories,
direct-sequence (DS) and frequency-hoppecl (FH), depending on the method used to
spread the users bandwidth, this research will only be concerned with direct-sequence
spread-spectrum, which is illustrated in Figure 1.1.
In the direct sequence method, a digital signal is multiplied in the transmitter
by a periodic waveform of narrow pulses called the spreading code. In the example
shown, an unspread binary phase-shift keying (BPSK) signal is shown at baseband
as a series of unit-amplitude square pulses of width T/;, the bit time, and its power
spectral density (PSD) has a null bandwidth of 1/T. The resulting waveform after
spreading also consists of a series of pulses, but the width is reduced to Tc = T^/N,
where Tc and N are referred to as the chip time and the processing gain, respectively,
and IV = 7 in this case. The PSD of the spread signal has the same form as that
1


31
where w0iX, wo)3/, ux(), and ny[i) are all real vectors of length N. For the new
definition of the error, we have
J = E[{di(i) (wjau*(*) + w^uy())}2] (3.9)
Now in choosing the taps to minimize J, it is clear that this is equivalent to a real
Wiener filtering problem with 2N taps. The first N taps are filled with ux(z) while the
last N taps are filled with u,,(). The Wiener-Hopf equation given in (3.6) can then be
applied, with the understanding that u(/) = [ux(z),Uy(i)]T and w0 = [w^,w^]T
and p = E[di()u(z)] are now real vectors of length 2N and R = E[u()uT()] becomes
a 2N x 2N matrix.
The results for this variation of the MMSE receiver are shown in Figure 3.2 as
well, in the curve labeled (b). There is clearly an advantage realized over the case
of minimizing the square of the absolute error. It is seen that between 1 and 2
additional narrowband users can be tolerated for a fixed number of CDMA users, for
operating points at which there are 6 or less narrowband users. If the narrowband
users employ spectrally efficient digital modulation at the same signaling rate as the
CDMA system, then this range can fit N = 32 users without guard bands. So with 5
narrowband users, the band is about 15% populated, and the system can still support
about 20 CDMA users.
The results for the matched filter in which the receiver is matched to the filtered
code sequence are also shown in Figure 3.2 for comparison, in the curve labeled (c).
Note that there is a substantial performance improvement realized by the MMSE
receiver over the matched filter. When there are 8 narrowband users present, the
MMSE receiver performs as well as the matched-filter performs in the case of no
overlay.
The performance of the DFT-based filtering method was also compared to the
Butterworth filtering method in Figure 3.3. The DFT-based filtering method is clearly


49
Figure 4.4: Maximum CDMA loading tolerable to narrowband system. Processing
gain is 32 chips/bit. CDMA user notched if NB-to-CDMA power ratio is less than
the notching threshold.
possible loading drops to 13 users/cell. In the next section, the capacity limit will be
looked at based on how much notching the CDMA system can handle.
It should be pointed out that there is a good deal of information that must be
exchanged between base stations, such as the received powers of both the CDMA
and narrowband users. This combined with possible inaccuracies in estimating the
received powers could lead to cases in which the CDMA users need to notch for certain
narrowband users, but they do not. To measure this effect, we will declare that the
CDMA users miss a necessary notch with probability pm. In Figure 4.5, the number
of CDMA users/cell that can be tolerated is shown to degrade quite rapidly as pm
increases, which indicates that careful attention must be given to the estimation of
the received powers.
Next, the amount of notching that must be done by the CDMA signals will be
determined. This brings up an important design issue involving whether or not the


76
Narrowband users/cell
Figure 5.4: Two-dimensional capacity curves, taking into account both CDMA re
ceiver performance and results from Figure 5.3. Processing gain is 32 chips/bit.
occurred more than 2% of the time, then the CDMA system was above its capacity
limits.
In order to combine these results with those of Sections 5.1 and 5.2, the notching
threshold T and the value of (Ei,/Nq)c must be chosen so as to satisfy the capacity
curves shown in Figure 5.3. For example, in the single-carrier case, if there are 2
narrowband users present, the system can support 7 CDMA users if the value of
(Eb/No)b (Eb/No)c = 7 dB, or equivalently (Ei)/No)c = 7 dB. But if the CDMA
system is loaded up to this level, it will require much more than (Eb/No)c = 7 dB
to satisfy the criterion of equation (5.21). Thus a higher value of (£,/Aro)c must be
used, and hence a lower value of (Eb/No)i, (Eb/N0)c, which means that we must
operate on one of the curves showing a lower joint capacity.
In Figure 5.4, the results of combining the criterion of equation (5.21) with the
results of Sections 5.1 and 5.2 are shown. Similarly to the example just mentioned,
the value of (Eb/No)c was optimized at each loading level. There is a noticeable
improvement in capacity over the single-carrier case when 2 carriers are used, and a


CHAPTER 3
MMSE DETECTION OF FILTERED CDMA SIGNALS
In this chapter, we will focus on how the filtering described in Chapter 2 affects
the performance of the CDMA system in an overlay scenario. It will be shown that
the MMSE receiver performs very well in this environment.
3.1 The MMSE Receiver
The MMSE receiver has received significant attention due to many of its features
such as near-far resistance to multi-access interference [9-11]. For the case of a single
spread-spectrum user in the presence of narrowband noise, it was observed by Pateros
and Saulnier [13] that the frequency response of the MMSE filter will adapt such
that there is a notch at the location of the narrowband noise, thus providing inherent
resistance to this type of interference as well. It was shown by Poor and Wang [23] that
the MMSE outperforms conventional narrowband interference rejection techniques,
and that it can simultaneously suppress MAI along with the narrowband interference.
It will be seen that the MMSE receiver also has the ability to reject inter-symbol
interference. Another feature of the MMSE that is useful in the overlay scenario is
its ability to work without previous knowledge of the desired users spreading code.
In fact, it does not even need to know that the code has been filtered.
A block diagram of the MMSE receiver is shown in Figure 3.1. The received
signal is passed through a chip-matched filter, and the samples are stored until one
bit time has passed. The contents of the equalizer are then correlated with the tap
weights and compared to the desired output, which is the data bit of the desired user.
For an initial training period, a known preamble is sent and thus the desired output
is already known at the receiver. After training, the taps should have had time to


56
Figure 4.7: Capacity plot for same-link case. Processing gain is 32 chips/bit. Eb/N0
of CDMA system is 10 dB. Notching thresholds are T = 7,9,11 dB. For 2.3, 2.8,
and 3.5 NB users, respectively, the CDMA system reaches capacity in terms of those
drops which result from needing too many notches.
Notice that the CDMA system is constrained by the fact that for a high enough
narrowband loading, the probability that a CDMA user is dropped is greater than
2%, and the criterion of equation (4.15) cannot be satisfied for any amount of CDMA
loading. From Figure 4.7, this occurs at 3.5, 2.8, and 2.3 narrowband users/cell
respectively for T 7,9,11 dB.
The results of Figure 4.7 characterize the joint capacity limits of the system as
dictated by the CDMA system. In conjunction with the limits resulting from consid
erations of the narrowband system as shown in Figures 4.4 and 4.5, it is clear that
the notching threshold T 9 dB is the best choice, as its limits according to each
of the two systems are relatively close. From Figure 4.5, if the probability of missing
a notch is 1%, then about 15 CDMA users/cell can be tolerated by the narrowband
system. And if the narrowband system is about half-loaded with 2 users/cell, then
the CDMA system itself can support about 15 users/cell according to Figure 4.7.


14
the definition of a Rieman sum, which states that
6
J /(:t) clx = Ji
b-a
M
(2.9)
a
Thus for sufficiently large N, the variance is approximately l/Tc. Combining this
with equation (2.7) gives
(2.10)
The same expression for the probability of error was obtained by Davis [21], and was
also derived by Pickholtz et, al. [22] for the single-user case, when square pulses are
used in the transmitter, and the corresponding matched filter is an integrate-and-
dump. An approximation for the case of square pulses was also given as [21]
(2.11)
This expression is much easier to evaluate than is equation (2.10), which requires a
K-dimensional numerical integration over the K CDMA users random phases, a very
time-consuming process even for a small number of users. The numerical integration
was performed, and a plot of the probability of error vs. E^/Nq for the BPSK system
is shown in Figure 2.2 for the case of 3 CDMA users of equal power ratio, (Pc/p,),
and a processing gain of 31 chips/bit. The different curves represent different values
of (Pc/P(,), and the case of no overlay is shown for reference. The approximation of
equation (2.11) is also shown and matches the numerical results pretty well. Although
each CDMA signal may have only a small fraction of its energy in the same bandwidth
as the BPSK user as a result of the processing gain, that energy obviously has a
non-negligible effect. The collective effect of the 3 CDMA users clearly degrades
the performance significantly even when they are received at 0 dB, a situation which
would require strict power control working cooperatively with both the CDMA system


66
5
-3
dB
dB
Figure 5.1: CDMA users/cell tolerable to the BPSK system. CDMA user is notched
if BPSK power is less than T dB above CDMA power. Curves are for (Eb/No)b
(.Eb/No)c values of 7,5,... 3 dB. (EijNo)^ and (Eb/No)c represent values after
power control at the base station to which the BPSK or CDMA mobile is assigned.
This problem was examined in Section 4.3.1, where a narrowband user was located
at random such that it was equally likely to be assigned to any of the cells within two
outer layers of a center cell of interest. Then a CDMA user located at a normalized
distance 0 < d < 1 from the center cell of interest, must notch for that narrowband
user with probability pn, which is plotted in Figure 4.6. It must be noted however,
that in Chapter 4, the narrowband and CDMA users, when assigned to the same base
station, were power-controlled so as to arrive at that base station at the same level.
In this chapter, that level will be allowed to vary, and hence the quantity T in Figure
4.6 will actually be replaced by T ((E/JNq) (EiJNq)c).
We will now look at several different multi-carrier CDMA schemes, and for each
the number of narrowband users which can be present so that the CDMA users do
not require an excessive amount of notching will be found. A different quantification
of how much notching is excessive will be given for each case.


77
slight additional increase when 4 carriers are used. Recall that in the multi-carrier
scenarios, a smaller value of (Eb/No)c could be used in order to achieve the same
performance in terms of CDMA reception. This in turn allows the limits of Sections
5.1 and 5.2 to be relaxed in comparison to the single-carrier case.
5.4 Summary
In this chapter, the performance of a cellular overlay system with a fading channel
model was evaluated. The effects of the CDMA system on the narrowband system
were quantified, and the effects of notch-filtering were found to be beneficial. It
was found that the use of multiple carriers allows the CDMA users to transmit less
power than in the single-carrier case, and thus more users can be supported without
causing interference to the narrowband system. The possibilities for CDMA overlay
are strongly reinforced by the results of this section.


59
4.5 Summary
In this chapter, we have looked at applying CDMA overlay to the cellular case, as
narrowband cellular systems by design only use a fraction of the system bandwidth
in each cell. The CDMA overlay, if not very lightly-loaded, was shown to have
an adverse effect on the existing narrowband system. The use of notch-filtering at
the CDMA transmitters to avoid active narrowband users can greatly increase the
amount of loading that the narrowband system can tolerate. Simulations showed that
while the CDMA signals may at times require a large amount of notching to avoid
narrowband users located throughout the cellular coverage region, the performance
degradation is not severe. It was observed that the CDMA system is much more
sensitive to the presence of strong narrowband interference than it is to notching.
It was also found that the CDMA and narrowband users should have their forward
links supported by the same frequency band. The results indicate that CDMA overlay
is very promising for cellular systems, particularly as a means of transition from a
system which exclusively supports narrowband service to one which supports CDMA
service but can still meet previous commitments to narrowband subscribers.


ACKNOWLEDGMENTS
I would like to thank Professor Leon W. Couch II, Professor Ulrich H. Kurzweg,
Professor Haniph A. Latchman, and Professor Jian Li for serving as members of my
committee. I extend special thanks to my adviser, Professor Scott L. Miller, not only
for his time, but also for his expert guidance throughout my studies, as related both
to research issues and to professional issues.
I thank my family, my parents Patricia A. and Ronald J. Rainbolt in particular, for
their support and encouragement throughout my studies. I also wish to acknowledge
all of my friends at the University of Florida and elsewhere, especially my colleagues
Ron Smith and Ali Almutairi.
Finally, I acknowledge with gratitude financial support from the Robert C. Pittman
Fellowship and from the National Science Foundation.


DIRECT-SEQUENCE CODE-DIVISION MULTIPLE-ACCESS OVERLAY
SYSTEMS
By
BRAD J. RAINBOLT
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
1998


9
In Chapter 5, the results of the cellular overlay system presented in Chapter 4,
for which an AWGN channel model was used, will be extended to the fading channel,
which is a more realistic model for wireless communication. In a flat-fading channel,
the number of CDMA and narrowband users which can be supported simultaneously
is very low, as will be shown in Sections 5.1 and 5.2. The effect of the CDMA overlay
on the narrowband system is substantial, and can be solved by CDMA transmitter
notching once again. However, in order to support a reasonable amount of narrow-
band users, the CDMA users must do a large amount of notching. A solution to
this is to use multi-carrier CDMA (MC-CDMA), which has recently become quite
popular. The transmission of the CDMA signal on several carriers, which are spaced
in frequency so that the fading on each will be independent, allows for frequency
diversity. Thus the CDMA users may transmit at lower powers, and will therefore
not require as much notching as in the single-carrier case with a flat-fading channel.
It will be seen that overlay is realizable in cellular scenarios, and can provide a very
efficient means of transition from narrowband cellular to CDMA cellular.
In Chapter 6, the overall conclusions of this research will be summarized by two
major points. First, it is not practical in terms of maximizing user capacity to
implement overlay without the use of transmitter notching in the CDMA signals.
Their effect otherwise is too harmful to the narrowband system. Second, there exists
great potential for CDMA overlay as a means for the cellular service provided in a
given frequency bandwidth to be transitioned gradually from narrowband to CDMA.


46
10G to greater than 10-5 as a result only of the overlay, that is while its signal-to-
noise-ratio (SNR) remains constant, then the overlay is excessive. This criterion was
employed in conjunction with a convolutional code of rate r 2/3 and a constraint
length m = 9. The optimum code has a free distance clfree = 8, as was found through
an exhaustive computer search [26]. A tight lower bound for the probability of bit
error of the coded system is
Pe>~
m
(4.10)
The values of 2Eb/No required for this bound to achieve bit error rates of 10~6 and
10-5, denoted SNRG and SNR5 respectively, are 5.43 dB and 4.27 dB.
In order to apply this to the overlay system, note that the square of the argument
of the Q-function in equation (4.9) must Ire greater than SNR$, and also note that
SNRq 2Eb/No, to give the necessary condition
*£(*) <{sm-sm)=om (4-n)
for which the overlay is not excessive. The number of CDMA users that can satisfy
this condition for all but a specified percentage statistically, say 2%, will be the limit
on the CDMA capacity from the narrowband systems perspective. This should not
be confused with a different limit, which may or may not be greater than this one,
which is the number of users for which the MAI eventually becomes too severe for
the CDMA system itself. That limit will be looked at in Section 4.4.
Before the capacity limit defined by equation (4.11) can be found, it is necessary
to specify that, in this chapter, it will be assumed that the received powers of the
CDMA and narrowband users at their respective assigned base stations are power-
controlled to the same level. The approximate PDF of the received power given in
equation (4.8) was used to generate realizations of the CDMA-to-BPSK near far ratio
Pk/Pb Then 10000 different realizations of the sum on the left-hand side of equation


40
The meaning of the random variable W should be clear. And the random variable
Y3, for instance, is I3 = max(Gi, Go, G4 G19) with G3 excluded from the argu
ment of the max function. The use of the Y, allows the assignment of a user to the
jth cell to be characterized simply by two exhaustive events, namely that the user
is in fact assigned to the jth cell, (Gj > V)), or is not, (Gj < Yj). Certain pieces of
information, such as the exact cell to which the user is assigned and the exact number
of cells for which the corresponding G¡ are greater than Gj, are not contained in the
quantity Yj. In the results obtained in this work, this information is not necessary,
and the corresponding simplification makes the analysis much more tractable.
These random variables in equation (4.3), which depend implicitly on d\ and 91,
can be described by using the fact that for fixed values of cl\ and 6\, the rest of the dt
will also be fixed and the G¡ are then independent Gaussian random variables with
means of mg = 10?r log10(c/) and each with variance ag. It is important to keep
in mind that the independence holds only when the d¡ are treated as fixed quantities
and not as random variables themselves. The probability density function (PDF) of
W can be shown to be
fw(w)
(4.4)
The expressions for the PDFs of the 1) are almost identical, with the only change
being that the indices of the product and summation are adjusted so as not to include
the zth term. As shown in Figure 4.2, for a user located at a distance of d\ = 0.75
and at an angle 0\ = 0, and with a(J = 8 dB and n 3, the PDFs of W and Yt can be
well-approximated as Gaussian. We can then find, for example, the probability that
a user is assigned to the ?'th cell as
lllyj 777,g A
^J0li + 0V
Pr(G, > Yi) Q
(4.5)


45
unity, but close to it. The function in equation (4.8), for example, integrates to 1.032.
It is simple to generate random variables with PDFs very close to these ones, however,
and there is a substantial savings in time in comparison to the task of generating a
users position and shadowing processes to each base station. The approximate PDF
of equation (4.8) will also be useful in the next section in investigating the effects of
overlay on the existing narrowband system.
4.2 Performance of the Narrowband System
Given the characterization of the mobiles received powers, the effect that the
CDMA overlay has on the narrowband system can now be examined. It would be
best if the overlay necessitated as little change as possible for the narrowband system,
which is assumed to already be in existence. However, it will cause degradation to
some extent, and it is thus necessary to define an acceptable level of degradation, and
then to quantify the number of CDMA users for which this level is not exceeded.
We begin by considering the effects of overlay, either in the single- or multi-cell
case, on the performance of a single BPSK user operating in the presence of additive
white Gaussian noise of spectral height No/2. The probability of error of the BPSK
matched-filter receiver was found in equation (2.7) which will be repeated here with
a slight modification.
/D
Q
No
+ T7E
'2 Ei, N
k-=i
Vft
cos2(6k) Vk
1-1/2''
(4.9)
with 14 = TcVar(Ik), which is a random variable with respect to the CDMA users
codes and delays. As verified bv simulation, the 14 variables can be well-approximated
as unit-mean exponential random variables.
Now a criterion must be established to determine if the overlay causes too much
degradation to the narrowband user. Such a criterion is described by Milstein et
al. [16], which states that if the BPSK users probability of error is increased from


4.2 Performance of the Narrowband System 45
4.3 Effects of CDMA Transmitter Notching 47
4.3.1 Same-Link Assignment 50
4.3.2 Staggered-Link Assignment 52
4.4 Simulations and Results 53
4.5 Summary 59
5 CELLULAR OVERLAY IN A FADING CHANNEL 60
5.1 Limits on CDMA Capacity 60
5.2 Limits on Narrowband Capacity 65
5.3 Performance of the CDMA System 71
5.4 Summary 77
6 CONCLUSIONS AND FUTURE WORK 78
6.1 Conclusions 78
6.2 Future Work 81
REFERENCES 83
BIOGRAPHICAL SKETCH 86
v


75
of error, conditioned on the fading processes 7when coherent combining of the
paths is used is given by [28]
Pr(error/r(*)) = Q 2pH (i)pH (i)\ (5.20)
where T(i) is a vector representing all of the fading processes of all of the users during
the ith bit interval and R(i) = E[r()f//(?')] the composite interference correlation
matrix.
The performance of the CDMA system using an MMSE detector was then simu
lated. As was done earlier in the paper, a cellular environment with two outer layers
of cells beyond the center cell of interest was considered. The mobiles, both CDMA
and narrowband, experienced lognormal shadowing with a standard deviation <7 = 8
dB, propagation loss with an exponent of n = 3, and Rayleigh fading. For a given
density of narrowband users/cell, the corresponding density of CDMA users/cell that
could be supported by the system was found. This density was based both on the
capacity constraints examined in Sections 5.1 and 5.2, and also on the criterion
Pv(Pe,CDMA > 0.05) < 0.02 (5.21)
For a given realization of codes, delays, notching, and powers of the CDMA users
and of powers and frequency locations of the narrowband users, 300 different real
izations of the fading processes were generated, that is 300 realizations of r(f), and
the conditional probability of error of the CDMA system was found using equation
(5.20). The average probability of error was then found by averaging these 300 val
ues. This process was repeated many times, that is for different realizations of the
codes, delays, and so on, in order to give enough values for the average probability of
error so that the criterion of equation (5.21) could be tested. Thus if a CDMA users
average probability of error was greater than 5%, it was dropped, and if these drops


28
The cyclic shifts of the /th partition of the A th CDMA users code sequence are given
by
fk,l =(1 4)(0, 0, . ,0, C^/./y, CicjN+i, . Ck,lN-pk-l)T
+ 4(0, 0, . ,0, Ck'lN, Ck'lN+1, Ck,lN-pk-2)T
(3-4)
gfc,/ =(1 &k)(CkJN-pk, CkJN-iik + l, Ck,lN l, 0, 0, . ,0)
+ 4(Cfc,/V-Pl.-i, Ck,lN-Pk, Ck,liv-1,0, 0, . ,0)T
where the Ath users delay has been written as r*. = p*.Tc + 4 with pk an integer in
the range (0,1,... N 1) and 77. a non-integer in the range (0,1). Also in equation
(3.3), n(z) is an N-length vector of independent complex Gaussian random variables
with the real and the imaginary parts independent of each other and each having
zero mean and variance a2 = N/(2E¡j/No). The vector j(i) consists of complex
narrowband interference samples with the real and imaginary parts independent of
each other. The (, j)th element of the matrix representing the correlation between
the real parts of two samples is given by
R= §Sa(2p7r(-j))cos((Au;)Tc( j)) (3.5)
i \
where Pj is the narrowband users average power and the same result holds for the
imaginary parts of the /th and j'tli samples. Also in equation 3.5, Sa(ar) sin(a;)/a;.
Denoting the tap weights as w = (iuq, iu¡,... xu^-i)r, the output of the tapped
delay line is given as Zt w//u(/'), which is generally a. complex number. The
receiver then compares Z, with the desired output di(i). The tap weights w0 which
will minimize the mean-squared error between the two, J = E[|Z di()|2], are the
solution to the Wiener-Hopf equation
Rw0 = p (3.6)
where R = E[u(z)u/7(/)] and p = E[di(?)u(/)] = cpo are the correlation matrix and
steering vector, respectively. The bit decision is made as d\(i) =sign(Re(Z,)).


73
complex Gaussian noise samples, with the real and imaginary parts each having
variance of a'2 = N/(2Eb/No). The vector j(/() consists of the sum of samples of all
of the narrowband noise processes present in the complex, with the real and imaginary parts independent, and each with a correlation
matrix given by (for the mtli narrowband user)
Sa cos(QTcAu>(i j)) (5.12)
for the (,j)th element, where (P¡,/P\) is the narrowband-to-CDMA near-far ratio,
and Au is the frequency difference between the location of the narrowband user and
the CDMA carrier frequency.
It was shown by Miller and Rainbolt [29] that the receiver will work best if the
Q different received vectors of equation (5.11) are cascaded into a single composite
vector of length N, given by
i'(') = (r| (i), r! (i),... Tn(i)y
(5.13)
and a single Wiener filter is formed, given by w() = R_1(z)p(), with R() and p(f)
the correlation matrix and steering vector. The composite correlation matrix R(z) is
given by
R(0
R-u(f)
Rl,2(0
R-UQ1
R2,l(0
R2i2(*)
... R2iQi
Rq,i(0
Rq,2(*)
Rq,Q
and the sub-matrices are given by
(5.14)
RM(0 = E [rp(i)r"(i)]
(5.15)


22
Table 2.2: Gains in (IB for BPSK system for Butterworth filter.
BW
1/N
1.25/N
1.5/N
Gain (dB)
50.5
67.9
80.5
1
-1
0 Th 2Tb 3Tb
(a)
Figure 2.4: Real part of filtered code sequences. Processing gain is 32 chips/bit. (a)
Butterworth filter, 8th order, 3-dB BW 1/32; (b) DFT-based filtering, zero-padded
to 8 bits.
filter. The gains realized by the Butterworth filter are shown in Table 2.2 for an 8th
order filter with 3-dB bandwidths of 1/AC 1.25/N, and 1.5/AC The plot of |C(/)|2
in Figure 2.3 for a bandwidth of 1/N shows that the notch is very pronounced and
that the signal in the passband is not distorted. As shown in Figure 2.4, also for a
filter of bandwidth 1 /JV, the code sequence continues well beyond one bit time, but
is negligible beyond about 2 bits.
When a receiver is used that can handle sequences with spillover, the Butter
worth filter seems like a very good option. It gives the BPSK system a large gain
without distorting the CDMA signals frequency response and without causing ex
cessive spillover.
2.4.4 DFT-Based Filtering
Another way to filter the code sequence is to use a Discrete Fourier Transform
(DFT), which provides a representation of the code sequence in the frequency domain.
Because the inverse DFT is the sum of discrete frequency components weighted by
the corresponding value of the DFT coefficient, notch filtering of the code signal can
^ /I
M
e-
w
-> One bit
3-5 Tb 4.57*
(b)
Hi
fp
-> One bit


18
the BPSK system bv making deep notches in the PSD, it may cause obvious problems
in the CDMA receiver. Even if the receiver can handle this ISI, it is obviously desirable
to minimize it.
2.4 Filtering Methods and Results
In this section, four filtering methods will be presented and compared based on
the three previously described criteria. Simulations were performed in which a BPSK
user employed root-raised cosine pulse shapes with a rolloff of a 0.35. The BPSK
user and an interfering CDMA user were assumed to have the same data rate, 1/T,
with the CDMA user employing a random code sequence of length N = 32 chips/bit,
or a filtered version of this sequence, and a delay chosen from a uniform distribution
on (0,TC). Then 10000 trials were run, each of which generated a sample of /*. when
filtering was employed and a sample when no filtering was employed. The ratio of
sample variances of //. for the filtered and unfiltered cases was then computed. This
gain and a plot of |C(/)|2 in equation (2.12) will be presented for each filtering
method. A plot of the filtered code sequence will be presented for the two methods
in which ISI results.
2,4.1 Eigenvector Filtering
This method was proposed by Davis [21] and will be summarized briefly. The
code sequence is clocked through a finite impulse response (FIR) filter with 2M + 1
taps, and the filtered code sequence will be taken from the delayed output. The
weights are chosen so as to minimize the effects of the CDMA interference on the
BPSK system. For the case when the BPSK system uses square pulses, not root
raised cosine pulses, the variance of the CDMA systems contribution to the BPSK
systems matched filter was derived with and without transmitter filtering [21]. The
two quantities were found to differ by a multiplicative factor of aBaT, where a is a


47
(4.11) were formed and compared with the value 0.09 for a fixed value of the number
of users K, and for a processing gain N = 32. Then K was varied until the sum
was greater than 0.09 for more than 2% of the 10000 realizations. It was found that
K = 14 users was the maximum number which could meet the criterion. Note that
there are 14 users spread over the three layers, or 19 cells, which is 0.75 users/cell,
which is extremely low for a processing gain of 32.
A similar conclusion, that the overlay is excessive even for a lightly-loaded CDMA
system, was observed in Chapter 2 for the single-cell case. One way to improve
this loading relative to a fixed processing gain is to increase substantially the power
level at which the narrowband users arrive at their own base stations. Doing so
would not lead to increased co-channel interference amongst the narrowband users,
because all the narrowband users in the system would increase their powers equally.
It would, however, decrease their battery life, which is inconsistent with the idea that
the overlay should require that the narrowband system change as little as possible.
Another solution is to employ notch-filtering in the CDMA transmitters to avoid
certain narrowband users, as was done in Chapter 2 for the single-cell case. This will
be explored in the next section.
4.3 Effects of CDMA Transmitter Notching
In an effort to alleviate the severe degradation caused to the narrowband system
as a result of the CDMA overlay, the idea of notching the CDMA signals at their
transmitters in order to avoid narrowband users was investigated in Chapter 2 for
the single-cell case. The DFT-based filtering method, described in Section 2.4.4, will
be employed here in the cellular case.
The use of notching is more involved than in the single-cell case, where the CDMA
signals were notched to avoid all of the narrowband users present. In the cellular
case, it is very possible that in addition to those narrowband users located near to
it physically, a CDMA mobile may have to avoid a narrowband user that is assigned


44
Figure 4.3: Histograms and Gaussian approximations for interference caused to base
station 1. (a) Interference from a user in cell 1, in a 2nd layer cell, and in a 3rd layer
cell. For each, there is also an impulse at h = 0 with a weight of p0; (b) Interference
from a user located uniformly throughout the 3 layers. There is an impulse at h = 0,
with weight po = 1/19.


26
KO
Figure 3.1: Block diagram of the MMSE receiver.
approach the ideal Wiener solution, but will fluctuate around it. Then the receiver
uses decision feedback, in which the bit decision is used as the desired output.
3.2 MMSE Detection of Filtered CDMA Signals
The performance of the MMSE receiver in an overlay scenario will now be exam
ined. We will consider a A'-user CDMA system, which uses code sequences of length
N chips/bit that are filtered to give sequences of length N, which will be greater than
N. The kth. users filtered sequence will be denoted as c* = (c^o, Cfc,i,... ,ck ft_i)T,
where Cfc,n is the nth filtered chip. Then c*. is partitioned into L = \N/N] sequences
each of length N, giving
(3.1)
Ck = (ci;0,ci... ,cIl-i)T
Ck.l = {CkJN i ckJN+\, Ck,lN+N-l)T
with / = 0,1,... L 1. The last sequence, Ck,L-i, may be padded with zeros to
make it of length N.
It should be noted that in this application, it is desired to place a notch in the
bandpass CDMA signal in order to avoid a frequency range that a narrowband user


43
Table 4.1: Composite mg, my, and E[Y'2] averaged with position.
dB quantities
my
a2 + m2v
Cell 1
6.51
3.07
34.93
Layer 2
-9.03
9.28
151.56
Layer 3
-18.06
9.52
153.86
Over all 3 layers
-13.92
9.11
146.88
which the position is somehow averaged out. For instance, it may be necessary to
know the PDF of the interference level caused to the cell of interest for a user that
is located uniformly in a second-layer cell, without having to know its position and
then look up the corresponding values of my.¡ and a'y i in a table. A true averaging of
the PDF in equation (4.7) can loe done numerically, with the help of a table of my
and ay i values. However, it was observed that a very good approximation may be
obtained by first averaging mg,¡, myj, and the second moment ay + my i with respect
to position over the cell of interest, over a second-layer cell, and over a third-layer cell,
and then forming for each an expression similar to equation (4.7), with the averaged
parameters substituted appropriately. This approximation to the true averaging was
done, and is shown to match pretty well with simulated results, which are shown in
Figure 4.3. The average values are shown in Table 4.1.
Then because there are 1, 6, and 12 cells in the 1st, 2nd, and 3rd layers, respec
tively, the averaging can be further extended to give averages which can be used to
characterize the interference caused to cell 1 by a user located uniformly throughout
the 3 layers of cells. This also matches the simulation results very well, as shown in
Figure 4.3, and the averages with respect to position are also shown in Table 4.1.
The approximate PDF is written below for use later:
fnk(h)
6(h) H
19 n/2tt(12S)
exp
(.h + 23)2
2(128)
(4.8)
It should be noted that while this function and the others in Figure 4.3 are good
approximations, they are not truly valid PDFs as they do not integrate exactly to


7
that CDMA overlay has on a typical narrowband system. Because the CDMA is
being added to a frequency band that is already established, it seems logical that the
operation of the existing narrowband system should be given top priority. A careful
evaluation of the degradation due to overlay which is experienced by a BPSIv user
in an AWGN channel is given in Section 2.1. It is shown that the BPSK user can
only tolerate the overlay if the loading of the CDMA system is extremely light. In
this case, it is questionable as to whether or not it is cost-effective to even design and
implement a new CDMA system when the added benefits seem to be very limited.
A technique to alleviate the severe degradation seen by the narrowband system is
presented in Section 2.2. By employing a notch filter in the CDMA transmitter, the
frequency bands occupied by narrowband users can be avoided, and the effects of the
CDMA overlay on the narrowband users will be reduced dramatically. The rationale
behind this is that the wideband CDMA signals should still maintain their desirable
properties to a large degree if the notch is not too wide. Some criteria to measure the
effectiveness of different filtering methods are given in Section 2.3, and are applied to
four filtering methods presented in Section 2.4. The narrowband system is found to
benefit tremendously from this filtering, even if the CDMA users are received at large
near-far ratios. It is found that the narrowband system can tolerate the overlay of a
CDMA system that is loaded up to levels far beyond that which the CDMA system
itself can realistically handle. A significant conclusion of this dissertation is that the
proposed filtering operations are vital for the realization of CDMA overlay.
Given that CDMA transmitter filtering is necessary in order for the narrowband
system to work, the next step is to quantify the effects that the filtering will have
on the performance of the CDMA system. This is done in Chapter 3 for the AWGN
channel. With filtering added, tin' problem amounts to more than just receiving
a CDMA signal corrupted by MAI and narrowband noise, which has been studied
extensively. The MMSE receiver, first mentioned in Section 1.1, is described in detail


32
Figure 3.3: Two-dimensional capacity plot for MMSE receiver minimizing J =
E[{Re(Z,- di(z))}2]. Shown for DFT-based filtering, zero-padded to 8 bits, and
Butterworth filter, 8th order, 3-dB BW 1/32. Processing gain is 32 chips/bit. Solid
curves are for Wiener solutions, dashed curves are for adaptive solutions for LMS
algorithm with step size 0.2/(total input power).
superior, and this can be explained by examining the filtered code sequences in Figure
2.4. The code sequence resulting from the Butterworth filtering had more energy that
spilled over into other bit intervals than did the code sequence that used the DFT-
based filtering method, which obviously degrades the CDMA systems performance.
Another important issue is the implementation of these algorithms. The previous
results assume that the receiver will be operating at the Wiener solution, and thus are
best-case results. In practice, an adaptive algorithm, such as a least mean-squared
(LMS) or recursive least-squares (RLS), would be used. Some simulations were per
formed to take this into account. In Figure 3.3, results are shown for both Butter
worth filtering and DFT-based filtering, for the case when J = E[{Re(Z <^i(*))}2]
is minimized. As the LMS algorithm converges slowly, and the fast-converging RLS


85
[25] T. S. Rappaport, Wireless Communications, Prentice-Hall, Upper Saddle River,
NJ, 1996.
[26] R. Johanneson and E. Paaske, Further results on binary convolutional codes
with an optimum distance profile, IEEE Trans. Inform. Theory, vol. IT-24, no.
2, pp. 264-268, Mar. 1978.
[27] S. Kondo and L. B. Milstein, Performance of multicarrier DS-CDMA systems,
IEEE Trans. Commun., vol. 44, no. 2, pp. 238-246, Feb. 1996.
[28] S. L. Miller, M. L. Honig, and L. B. Milstein, Performance analysis of MMSE
receivers for DS-CDMA in frequency selective fading channels, submitted to
IEEE Trans. Commun.
[29] S. L. Miller and B. J. Rainbolt, MMSE detection of multi-carrier CDMA,
submitted to 1999 IEEE International Conference on Communications.
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estimation in asynchronous direct-sequence code-division multiple access sys
tems, IEEE Trans. Commun., vol. 44, no. 1, pp. 84-93, Jan. 1996.
[31] S. E. Bensley and B. Aazhang, Subspace-based channel estimation for code
division multiple access communication systems, IEEE Trans. Commun., vol.
44, pp. 1009-1020, Aug. 1996.
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acquisition and demodulation of direct-sequence CDMA signals, IEEE Trans.
Signal Processing, vol. 45, no. 1, pp. 124-136, Jan. 1997.
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11
the received signal at the input to the BPSK matched filter after down-conversion is
OO l\ OG
r(t) = y/2Eb db,Mt iTb) + Y2 Vm- Y2 dkjCkit ~ iTb ~ n) cos(0k) + n(t)
ioo A-=l ¡= 00
(2.1)
where Eb is the average energy-per-bit of the BPSK system, Tb is the bit time for
both systems, and db and dk are the ?'tli data bits of the BPSK users and the
A;th CDMA users data stream, and h(t) is the BPSK users root-raised cosine pulse
shape, which is normalized so that the integral of h2(t) on (00,00), its energy, is
unity. Also, K is the number of CDMA users, Pk is the average power of the kth
CDMA user, ck(t) is the kth users spreading waveform consisting of unit-amplitude
positive and negative pulses of duration Tc, the chip time, and N is the processing
gain, or the number of chips/bit. The kth. CDMA users delay and phase, rk and
9k are taken as constant throughout transmission, as the channel is assumed to be
non-fading and stationary. Also. n(t) is a white Gaussian noise process with spectral
height Nq/2 The jth sample of the output of the matched filter is
A'
Zj = y/2Ebdb + V2PkTc cos(6k)Ik(j) + Nj (2.2)
fc=i
where Nj is a zero-mean Gaussian random variable with variance Aro and the random
process Ik(j) associated with the contribution from the kth CDMA user in the jth
bit interval is given by
LN
Ik{j) 'y ] dk^j+^w^^Ck'lnod(Tn,N)h{?TlTc Tk) (2-3)
m=LN
and [zj is the floor function. It is assumed in this expression that h(t) is negligible
for |i| > LTb Thus the interference contribution from each CDMA user is the sum of
samples of the root-raised cosine pulse weighted by both a data bit and a spreading
chip. It appears that the central limit theorem may be invoked to approximate Ik
as a Gaussian process since it is the sum of many random variables. Although this