SIGNAL-TO-NOISE-PLUS-INTERFERENCE RATIO ESTIMATION AND STATISTICS FOR DIRECT SEQUENCE SPREAD SPECTRUM CODE DIVISION MULTIPLE ACCESS COMMUNICATIONS

Transcription

1 SIGNAL-TO-NOISE-PLUS-INTERFERENCE RATIO ESTIMATION AND STATISTICS FOR DIRECT SEQUENCE SPREAD SPECTRUM CODE DIVISION MULTIPLE ACCESS COMMUNICATIONS A Thesis Presented to The Faculty of the Fritz J. and Dolores H. Russ College of Engineering and Technology Ohio University In Partial Fulfillment of the Requirement for the Degree Master of Science by Amit Gupta June, 2004

2 ACKNOWLEDGEMENTS I would like to thank my advisor Dr. D.W. Matolak for his invaluable support and guidance during the course of this thesis. I thank him for teaching me the importance of word "research". I would also like to thank my thesis committee members, Dr. J. Dill and Dr. J. Starzyk for reviewing my thesis and the knowledge they imparted to me through their classes. I would also like to thank my friends for their help. Finally, I thank my parents for their love and infinite support.

3 TABLE OF CONTENTS i v Acknowledgements ZLG Table of Contents... iv List of Figures... vi Chapter 1 Introduction Digital Communication Spread Spectrum (Direct Sequence) Communication Motivation For Signal Quality Estimation... 6 Chapter 2 System Model and Overview System Description Statistical Model For SNIR SNIR Estimators SNIR Probability Density Functions Chapter 3 Estimation of Signal Quality Amplitude Estimator MU1 Energy Estimator Chapter 4 Numerical Results Amplitude Estimator Average Amplitude vs. E, 1 No and NMSE Amplitude NMSE vs. K Amplitude Estimate vs. User index MU1 Energy Estimator... 52

4 4.2.1 NMSE of average MU1 energy vs. Eb 1 No NMSE of average MU1 energy vs. K NMSE of MU1 energy vs. User index SNIR Estimator Average SNIR vs. Eb I No Average SNIR vs. K BER fiom SNIR Average BERvs. E, /No Average BER vs. K PDF and Histogram for SNIR Chapter 5 Summary and Recommendations for Future Work References Appendix: Matlab Program... 79

5 LIST OF FIGURES vi Figure 1.1: Figure 1.2: Figure 1.3: Figure 1.4: Figure 1.5: Figure 2.1 : Figure 2.2: Figure 2.3: Basic elements of a digital communication system Spectnun of the signal before and after spreading Example of the user signal, code signal and coded signal Reverse link of a wireless system Near-far effect depicted by user A and user B Block Diagram of K-user asynchronous DS-SS-CDMA system Diagram showing the partial overlapping of bits between two asynchronous users (i & k) that gives rise to partial correlation i7 Example plot for pdf of true SNIR (using SGA and chi-squared distribution), Rayleigh and Gaussian with Nb=lOO bits & = 2 (- ~ l )~, /(3 N) + No where K=10 users, N=15 og chipslsample Figure 4.1 (a): Average amplitude (estimated, Nb -bit estimate, and true amplitude) vs. Eb 1 No for a system with K=10 users, N=15, N, =lo%, N, =I2000 bits and Np =200 bits1 packet Figure 4.l(b): Amplitude normalized mean s quare error (NMSE for Nt -bit e stimate) vs. E, 1 No for a system with K=10 users, N=15, Nt =lo%, Nb =I2000 bits and Np =200 bits1 packet Figure 4.2(a): Amplitude (estimated, N, -bit estimate, and true amplitude) vs. E, 1 No for a system with K=10 users, N=15, Nt=25%, Nb=12000 bits and N, =200 bits1 packet Figure 4.2(b): Amplitude normalized mean square error (NMSE for N, -bit estimate) vs. Eb 1 No for a system with K=10 users, N=15, Nt =25%, Nb =I2000 bits and N =200 bits/ packet P

6 vii Figure 4.3(a): Amplitude (estimated, N, -bit estimate, and true amplitude) vs. E, IN, for a system with K=l0 users, N=31, N,=10%, Nb=12000 bits and N, =200 bits1 packet Figure 4.3(b): Amplitude n ormalized mean square error (NMSE for N, -bit e stimate) vs. E, I No for a system with K=10 users, N=3 1, N, =lo%, Nb =I2000 bits and N, =200 bits/ packet Figure 4.4(a): Amplitude (estimated, Nb -bit estimate, and true amplitude) vs. E, IN, for a system with K=10 users, N=31, N, =25%, Nb =I2000 bits and Np =200 bits/ packet Figure 4.4(b): Amplitude n ormalized mean s quare error (NMSE for N, -bit e stimate) vs. E, IN, for a system with K=10 users, N=3 1, N, =25%, Nb =I2000 bits and N, =200 bits/ packet Figure 4.5(a): Amplitude normalized mean square error (NMSE for estimated, Nb -bit estimate, and true amplitude) vs. K (number of active users) for a system with Eb / N, =7 db, N=15, N, =lo%, Nb =I2000 bits and Np =200 bits/ packet Figure 4.5(b): Amplitude normalized mean square error (NMSE for estimated, Nb -bit estimate, and true amplitude) vs. K (number of active users) for a system with Eb 1 No =7 db, N=15, N, =25%, Nb =I2000 bits and Np =200 bits/ packet Figure 4.6(a): Amplitude normalized mean square error (NMSE for estimated, N, -bit estimate, and true amplitude) vs. K (number of active users) for a system with E, / No =7 db, N-3 1, N, =I 0%, Nb =I2000 bits and Np =200 bits/ packet Figure 4.6(b): Amplitude normalized mean square error (NMSE for estimated, N, -bit estimate, and true amplitude) vs. K (number of active users) for a system with E, / N, =7 db, N=3 1, N, =25%, Nb =I2000 bits and Np =200 bits/ packet

7 ... Vlll Figure 4.7(a): Amplitude normalized mean square error (NMSE for estimated, N, - bit estimate, and true amplitude) vs. i (user index) for a system with E, l No =7 db, N=15, N, =lo%, N, =I2000 bits and N, =200 bits1 packet Figure 4.7(b): Amplitude normalized mean square error (NMSE for estimated, N, -bit estimate, and true amplitude) vs. i (user index) for a system with E, 1 No =7 db, N=15, N, =25%, N, =I2000 bits and Np =200 bitsl packet Figure 4.8(a): Amplitude normalized mean square error (NMSE for estimated, N, -bit estimate of and true Amplitude) vs. i (user index) for a system with E, 1 No =7 db, N=3 1, N, =lo%, N, =I2000 bits and Np =200 bits/ packet Figure 4.8(b): Amplitude normalized mean square error (NMSE for estimated, N, -bit estimate, and true amplitude) vs. i (user index) for a system with Eb 1 No =7 db, N=3 1, N, =25%, N, =I2000 bits and Np =200 bitsl packet Figure 4.9(a): MU1 energy normalized mean square error (NMSE of estimator I (N,- bit estimate, Nb -bit estimate), estimator 111) vs. E, IN, plot for a system with K=10 users, N=15, N, =lo%, Nb =I2000 bits and Np =200 bits1 packet Figure 4.9(b): MU1 energy normalized mean square error (NMSE of estimator I ( N, - bit estimate, N, -bit estimate), estimator 111) vs. E, 1 No for a system with K=10 users, N=15, N,=25%, Nb=12000 bits and Np=200 bitsl packet Figure 4.10(a): MU1 energy normalized mean square error (NMSE of estimator I ( N, - bit estimate, N, -bit estimate), estimator 111) vs. E, 1 No for a system with K=10 users, N=31, N, =lo%, N, =I2000 bits and N, =200 bits/ packet....54

8 Figure 4.10(b): MU1 energy normalized mean square error (NMSE of estimator I ( N, - bit estimate, N, -bit estimate), estimator 111) vs. E, IN, plot for a system with K=10 users, N=3 1, N, =25%, N, =I2000 bits and N, =200 bits/ packet ix Figure 4.1 1(a): MU1 energy normalized mean square error (NMSE of estimator I (N, - bit estimate, Nb -bit estimate), estimator 111) vs. K (number of active users) for a system with E, I No =7 db, N=15, N, =I 0%, N, =I 2000 bits and N, =200 bits1 packet Figure 4.1 l(b): MU1 energy normalized mean square error (NMSE of estimator I ( N, - bit estimate, N, -bit estimate), estimator 111) vs. K (number of active users) for a system with E, IN, =7 db, N=15, N, =25%, N, =I2000 bits and Np =200 bits1 packet Figure 4.12(a): MU1 energy normalized mean square error (NMSE of estimator I (N,- bit estimate, Nb -bit estimate), estimator 111) vs. K (number of active users) for a system with Eb I No =7 db, N=3 1, N, =lo%, Nb =I2000 bits and N, =200 bits1 packet Figure 4.12(b): MU1 energy normalized mean square error (NMSE of estimator I (N,- bit estimate, N, -bit estimate), estimator 111) vs. K (number of active users) for a system with E, I No =7 db, N=31, N, =25%, N, =I2000 bits and N, =200 bits1 packet Figure 4.13(a): MU1 energy normalized mean square error (NMSE of estimator I ( N, - bit estimate, N, -bit estimate), estimator 111) vs. i (user index) for a system with E, 1 N, =7 db, N=15, N,=10%, Nb =I2000 bits and N, =200 bits1 packet Figure 4.13(b): MU1 energy normalized mean square error (NMSE of estimator I (N,- bit estimate, Nb -bit estimate), estimator 111) vs. i (user index) for a

9 x system with E, I N,=7 db, N=15, N,=25%, N,=12000 bits and N, =200 bits1 packet Figure 4.14(a): MU1 energy normalized mean square error (NMSE of estimator I (N, - bit estimate, N, -bit estimate), estimator 111) vs. i (user index) for a system with E, ln,,=7 db, N=31, N,=10%, N,=12000 bits and N, =200 bits1 packet Figure 4.14(b): MU1 energy normalized mean square error (NMSE of estimator I (N, - bit estimate, N, -bit estimate), estimator 111) vs. i (user index) for a system with E, ln,=7 db, N=31, N,=25%, N,=12000 bits and N, =200 bits/ packet Figure 4.15(a): Average SNIR (estimator I ( N, -bit estimate, N, -bit estimate), true, estimator 111) vs. E, I No plot for a system with K=10 users, N=15, N, =lo%, N, =I2000 bits and N, =200 bits/ packet Figure 4.15(b): Average SNIR (estimator I (N,-bit estimate, N, -bit estimate), true, estimator 111) vs. E, IN, plot for a system with K=10 users, N=15, N, =25%, N, =I2000 bits and N, =200 bits/ packet Figure 4.16(a): Average SNIR (estimator I (N, -bit estimate, N, -bit estimate), true, estimator 111) vs. E, I No for a system with K=10 users, N=3 1, N, =lo%, N, =I2000 bits and N, =200 bits/ packet Figure 4.16(b): Average SNIR (estimator I (N, -bit estimate, N, -bit estimate), true, estimator 111) vs. E, I N, for a system with K=10 users, N=3 1, N, =25%, N, =I2000 bits and N, =200 bits1 packet Figure 4.17(a): Average SNIR (estimator I ( N, -bit estimate, N, -bit estimate), true, estimator 111) vs. K (number of active users) for a system with E, I No =7 db, N=15, N, =100/0, N, =I2000 bits and N, =200 bits/ packet

10 xi Figure 4.1 7(b): Average SNIR (estimator I ( N, -bit estimate, N, -bit estimate), true, estimator 111) vs. K (number of active users) for a system with E,) 1 No =7 db, N=15, N, =25%,, N, =I2000 bits and Np =200 bits/ packet Figure 4.1 8(a): Average SNIR (estimator I ( N, -bit estimate, N, -bit estimate), true, estimator 111) vs. K (number of active users) for a system with E, 1 No =7 db, N=3 1 chips, N, =lo%, N, = bits and N, =200 bits/ packet Figure 4.18(b): Average SNIR (estimator 1 (N,-bit estimate, N, -bit estimate), true, estimator 111) vs. K (number of active users) for a system with E, 1 N,, =7 db, N=3 1, N, =25%, Nb =I2000 bits and N, =200 bits1 packet Figure 4.19(a): Average BER (estimator I ( Nl-bit estimate, N, -bit estimate), true, estimator 111) vs. E, IN, for a system with K=10 users, N=15, N, =lo%, Nb =I2000 bits and N, =200 bits1 packet Figure 4.19(b): Average BER (estimator I (N, -bit estimate, N, -bit estimate), true, estimator 111) vs. E, IN, for a system with K=10 users, N=15, N, =25%, N, =I2000 bits and N, =200 bits1 packet Figure 4.20(a): Average BER (estimator I ( N, -bit estimate, N, -bit estimate), true, estimator 111) vs. E, IN, for a system with K=10 users, N=31, N, =lo%, N, =I2000 bits and N, =200 bits1 packet Figure 4.20(b): Average BER (estimator I ( N, -bit estimate, N, -bit estimate), true, estimator 111) vs. E, IN, for a system with K=10 users, N=31, N, =25%, N, =I2000 bits and Np =200 bits1 packet Figure 4.2l(a): Average BER (estimator I ( N, -bit estimate, N, -bit estimate), true, estimator 111) vs. K (number of active users) for a system with E, IN, =7 db, N=15, N, =lo%, N, =I2000 bits and N, =200 bits1 packet

11 xii Figure 4.21(b): Average BER (estimator I ( N, -bit estimate, N, -bit estimate), true, estimator 111) vs. K (number of active users) for a system with E, 1 No=7 db, N=15, N,=25%, Nb=12000 bits and N,=200 bits/ packet Figure 4.22(a): Average BER (estimator I (N,-bit estimate, N, -bit estimate), true, estimator 111) vs. K (number of active users) for a system with E, l No =7 db, N=3 1, N, =lo%, N, =I2000 bits and N, =200 bits/ packet Figure 4.22(b): Average BER (estimator I ( N, -bit estimate, N, -bit estimate), true, estimator 111) vs. K (number of active users) for a system with E, 1 No =7 db, N=31, N, =25%, N, =I2000 bits and N, =200 bits1 packet Figure 4.23: PDF & histograms for estimated (using bits), and analytical SNIR for SGA approximation and analytical SNIR using chi2 distribution for a system with EJNo=5 db, K=10, N=l

12 Chapter 1 Introduction Digital communication systems are the most widely used communication systems for military as w ell a s commercial purposes. W ith the recent d evelopments i n d igital signal processing capabilities and the attainment of faster processor speeds, even the most complicated communication systems can be implemented digitally with relative ease and cost-effectiveness. The main advantage of digital systems over analog systems is that they are less subject to distortion and interference since they operate in one of the two predictable states - fully on (1) or fully off (0) [I]. 1.1 Digital Communication Digital communication has numerous advantages over traditional analog communication. D igital c ommunication i s relatively e asy to implement and o ffers far better performance than its analog counterpart. In analog communication, the receiver design and architecture can be too complicated because the analog receiver needs to be designed to regenerate the original signal waveform from the channel-attenuated and noise-distorted received signal. On the other hand, in digital communications it is enough to detect in which state the sent signal might have been originally. Then the original signal, voice, data, or video, etc., can be recomposed using the sequence of the detected states of the signal. A simplified diagram showing the main elements of digital communication system is shown in Figure 1.1 [ 11.

13 Information source From other sources Dlgital (bandpass waveform) Digital Digital Digital Digital (bits) (bits) (bits) (bits) n Channel Information sink Digital (bandpass waveform) Figure 1.1. Basic elements of a digital communication system [I] In Figure 1.1, the original source information can be analog, which is quantized to digital, or the source information can be digital itself. The signal gets attenuated when it is transmitted through the channel and also can get distorted due to a non-ideal channel response, noise andlor interference. These undesired changes in the signal make it difficult for the receiver to detect the transmitted signal. When the signal is transmitted through the channel it is in the form of an analog continuous wave, but all the processing and detection is done digitally. By digitally, we mean the received analog signal is preprocessed and converted to digital format using quantization and sampling methods followed by the detection of the states of the sent signal. In any communication system, the channel can be either wired or wireless (typically using a radio frequency (RF) link). On the one hand, a wired channel typically causes less distortion as compared to the wireless channel. On the other hand, wireless systems are easy to implement irrespective of geographical limitations and most

14 importantly they provide mobility to the user. The mobility as well as the relative independence from the geographic limitations to communication coverage has helped the dramatic increase in the growth of wireless systems throughout the world. The high growth in the usage of wireless systems and the proliferation of Internet based applications has increased the challenges of enhancement and maintenance of wireless system performance. Ideally, no degradation in performance should take place even with a substantial increase in capacity Spread Spectrum (Direct sequence) Communication Spread Spectrum (SS) technologies are widely used in both commercial and military communication systems. Direct Sequence Spread Spectrum (DS-SS) is the most widespread SS technology used to facilitate multiple access in commercial wireless systems. In DS-SS systems, the carrier is modulated by a digital code in which the code bit rate (E transmission bandwidth) is much larger than the information bit rate (E information bandwidth). DS-SS systems are also called pseudonoise (PN) systems due to the fact that after spreading the information signal by a pseudorandom code, the spectrum of the signal "hides behind" the noise-like code spectrum. DS-SS based multiple access systems are called Direct Sequence - Code Division Multiple Access (DS-CDMA) systems. DS-CDMA systems are wideband systems, i.e., each user uses the entire bandwidth. These are in contrast to narrow band systems, namely Frequency Division Multiple Access (FDMA) and Time Division Multiple Access (TDMA) systems. Historically, DS-SS systems were originally made for military purposes in the mid 1950's, to provide secure and highly interference resistant

15 4 communication systems. Along with the inherited features of DS-SS, viz. security and interference resistance capability, DS-CDMA systems also provide advantages over other multiple access techniques mainly in terms of cost, capacity, security and multipath protection [5]. All these attributes make DS-SS an ideal candidate for its use in military as well as commercial applications. DS-SS-CDMA signaling is also proposed and is being used in third generation (3G) wireless systems [2]. As noted, DS-CDMA is a wideband communication technique, in which each user signal occupies the entire bandwidth at all times, hence it offers high capacity for a given bandwidth as compared to narrowband techniques (FDMA and TDMA). In DS- CDMA, the users are multiplexed by distinct codes rather than by orthogonal frequency bands as in FDMA, or by orthogonal time slots as in TDMA. In this way, each user is able to use the entire allocated frequency spectrum for transmission. Mutual interference amongst the users using the same frequency spectrum is low in DS-CDMA systems when compared to other systems, because the power spectral density of the users' signal becomes very low due to the spectral spreading, as shown in the Figure 1.2.

16 After spreading Figure 1.2. Spectrum of the signal before and after spreading. In DS-CDMA, each user's bit is spread by multiplying it with a distinct, high-rate, unique spreading waveform often called a code signal, as shown in Figme 1.3. This high rate spreading waveform is independent of the data waveform. Also, the transmission bandwidth of the spread (data) waveform is many times that of the minimum bandwidth required for transmitting the original data waveform (the information bandwidth), hence the system is called spread spectrum. A very important parameter of CDMA systems is processing gain, which is the ratio of the transmission bandwidth (RF bandwidth) to the information rate. The higher the processing gain for a system, the higher is its interference suppression capability. At the receiver, despreading is accomplished by the cross-correlation of the received spread signal with a synchronized replica of the same signal used to spread the data at the transmitter.

17 181t Period 1 chrp period : 4 > Tc fh -----, Figure 1.3. Example of the user signal, code signal and coded signal. 1.3 Motivation for Signal Quality Estimation At the receiver front end, the detector receives the signal that is the sum of the desired user's signal, other users' signals and channel and system noise. A simple diagram of a reverse link of a (cellular-like) wireless system, which consists of a centralized base station receiver, and the different users' transmitters, at different locations, is shown in Figure 1.4. Figure 1.4. Reverse link of a wireless system.

18 7 In such a setting, the DS-CDMA detector suffers from the following main limitations: a) Near-far effect - If an interfering signal is very strong compared to the desired signal, then its contribution to the total received signal will make the reliable reception of the desired signal difficult. For instance, the signal of the user near the base station will overwhelm the signal of a distant user if their transmit powers are comparable as shown in Figure 1.5. b) Interference floor - As the number of users increases, the interference floor increases. This poses a difficulty to the detector in making reliable decisions. NEAR - user 1 / / FAR - user 2 Figure 1.5. Near-far effect depicted by user A and user B. Strict power control is used in the CDMA cellular reverse link (mobile-to-base link) to alleviate the near-far effect. Excellent power control is required in the reverse link due to noncoherent detection (in present systems) at the basestation. Power control

19 8 works in a centralized manner, in which the powers of the transmitters (mobile handsets) in the reverse link are adjusted so that the average power reaching the base station remains almost the same irrespective of the distance from the base station. In power control (closed loop scheme), the base station makes decisions to send the power control bit (0 or 1) to different users through the power control subchannel for each user. A 0 bit indicates to the mobile that it should increase its mean output power level, whereas a 1 bit indicates to the mobile that it should decrease its mean output power level [2]. The basestation decides to send a 0 or 1 bit mainly on the basis of the signal quality estimates of all the users. Hence, reliable signal quality estimates are required to ensure efficient operation of DS-CDMA system. Power control and the soft handoff features are closely related to each other in DS-CDMA systems, for instance in IS-95 systems [2]. Since the system with power control dynamically adjusts transmitter power while in operation, it allows implementation of the soft handoff capability in DS-CDMA systems. This implies that good signal quality estimates are also very important for proper implementation of soft handoff features in DS-CDMA systems. Reliable signal quality estimates are also of crucial importance in the implementation of highly advanced multiuser detectors (MUD). The multiuser detectors have been proposed and are being used in third generation (3G) CDMA systems [2]. In practice, suboptimal multiuser detectors are used since optimal detectors are hard to implement because they are highly complex and computation-intensive when the number of users is high. The MUD exploits the fact that the structure of the interference is known, so it can be detected and in effect, subtracted out. Some of the suboptimal

20 9 MUDS, namely serial interference cancellation (SIC) and group interference cancellation (GIC), involve reordering of the users' signals. The "marshalling" or "grouping" of users' signals is done on the basis of the received signal power estimates and the users' signals are mutually cancelled. In this way, the mutual interference is reduced and the system performance is enhanced. The employment of MUD is another important application of signal quality estimates. In summary, there are various algorithms in spread spectrum (some mentioned above) or non-spread spectrum systems (see references 1-3 of [9]) that require good estimates of the signal quality for their optimal performance. The signal quality can be defined using different parameters. The appropriateness of any signal quality parameter depends on the nature of application. One rather primitive method is to estimate the signal quality using just the signal amplitude, which does not give a good estimate of the overall signal and channel quality. Some of the more sophisticated and commonly used signal quality parameters in the context of the physical layer of present wireless communication are signal-to-noise ratio (SNR), signalto-interference ratio (SIR) and signal-to-noise-plus-interference ratio (SNIR). Of these, SNIR is most appropriate for critical applications like strict power control, soft handoff and in MUD, since it accounts for both disturbances (noise and interference) that affect the signal. In practice, signal quality estimates are often based on SNR or SIR estimates mainly due to the computation involved in finding the SNIR estimate. In this work, we show that a reliable SNIR estimate can be more rapidly estimated than actual performance based upon error rates, and with a modest computation increase over simpler SNR estimation.

21 10 There are two important classes of signal quality estimators. First, those that derive the estimates solely from the unknown, information-bearing portion of the signal (known as "in-service" estimators, I SE) and second, the ones that use the data known (transmitted data) to the receiver, for instance training sequences provided for synchronization and equalization [9]. In this work, we consider the second category of estimator known as "data aided" estimators (DAE). We chose to investigate DAE for DS-SS communication because of the following reasons: (1) The information that is put to use is usually available in the form of "training bits" in all modern SS receivers. (2) Available literature (e.g., [9]) suggests that there is a significant difference in the performance of the DAE and the ISE, with DAE on the better side, since ISE uses the error-corrupted recovered data. (3) There is no additional penalty imposed on throughput if a receiver employs DAE if the receiver already uses a training sequence for equalizer or synchronizer training. In fact, in one sense DAE involves less complexity than ISE in terms of the length of processing (correlation) required. In this work, we consider single carrier direct-sequence spread-spectrum (DS-SS) signaling in a code-division multiple access (CDMA) system. An additive white Gaussian noise (AWGN) channel and binary phase-shift-keying (BPSK) signals are used in the analysis. The channel description and the estimators are discussed in detail in Chapter 2. The analysis of the different estimators is given in Chapter 3 and finally, the performance results are discussed in Chapter 4. The estimates are obtained using a

22 11 Maximum Likelihood (ML) estimator [4], and the performance of different estimators is evaluated using basic rules of expectationlstatistics. Analytical results are corroborated by simulation.

23 Chapter 2 System Model and Overview We consider single carrier direct-sequence spread-spectrum (DS-SS) signaling in a code-division multiple access (CDMA) system. This system model is followed in most of the present commercial and as well as in the proposed third generation (3G) CDMA system standards. These standards include Interim Standard - 95 (IS-95) [13], wideband CDMA (WCDMA) [15], and cdma2000 [16]. As discussed in Chapter 1, the CDMA systems are based on the principle of "interference resistance" as opposed to "interference avoidance" which is applicable in the case of frequency division and time division multiple access systems. This unique resistance capability in CDMA systems is due to several inherent features discussed in the last chapter. Though the CDMA systems are highly suited for multiple access applications, the cost-quality requirements on commercial systems impose additional challenges, since the capacity of the system, in terms of the number of users that can be served per base station, must be maximized. This means that these (CDMA) systems must work "normally" without reducing quality of service (QoS) even with a significant increase in the number of users and hence interference due to these other signals. In such systems, one of the important factors for proper operation and reliable reception of signals in all kind of situations, low and high interference, is good signal quality estimation. As noted, in practice, different systems have been designed using various kinds of signal quality parameters. Signal-to-noise ratio (SNR) and signal-to-interference ratio (SIR) are the most widely used signal quality parameters. Specifically in multiple access

24 13 systems, signal-to-noise-plus-interference ratio (SNIR) is more accurate, since it is more directly related to error rate performance. In this work, we will show that the SNIR can be estimated quickly and reliably with low complexity in terms of length of correlation required. Correlation is done over a relatively small segment of signal bits (training bits) that are known to the receiver in advance. BPSK DS-SS transmitter, I I I I I I rlb,fi) ~'k(q I B~nary Data *Modulator I I I Spread data Sequence Phase Xk AWGN channel I I I Sumof I BPSK DS-SS recelver (user k) I s,o-r/j I I Delayed Code sequence I skit) I I Code sequence I I I I '---/----; Interfering signals and nolse get added to the des~red signal, phase delay & amplitude attenuation takes place in channel Figure 2.1. Block Diagram of K-user asynchronous DS-SS-CDMA system. 2.1 System Description We consider a K user asynchronous DS-SS-CDMA system in an AWGN channel model as shown in F igure 2.1. We have made few assumptions to make the analysis simple and clear. They are as follows: (1) The noise due to the channel is additive white Gaussian noise (AWGN) with two-sided noise power spectral density No I2 W/Hz. (2) Modulation is binary phase-shift keying (BPSK).

25 14 (3) Transmissions are asynchronous with the delay z of any user signal confined to the interval 0 < z < T (modulo T), where T is the time period of a bit. (4) The codes are assumed to be short random codes, i.e., the processing gain I, is L = T IT,= N la, where N is the period after which the deterministic spreading sequence repeats and T,, is the chip period. For short codes a is unity (N is equal to processing gain) whereas for long codes it is a positive integer. (5) The shape of the chip pulse is rectangular, with unit amplitude over Tc. (6) All the users transmit at the same data rate and have equal and constant amplitude (perfect power control). (7) Each user's signal is assumed to consist ofn, bits. The number of packet transmissions it takes to transmit N, bits is P. The size of each packet in bits is N, I P. The baseband representation of the transmitted signal for user k in this system is where h, (n) E (+I } is the nth bit of user k's modulating signal, A, = dx is the signal amplitude, with E,, the bit energy, and T is the bit duration. The symbol 1x1 denotes the greatest integer less than or equal to x. The signature or spreading sequence waveform for the kt" user, with unit-energy over T, is

26 where c, (mi) is the nilh binary spreading code element of user k's N-element spreading code such that c, (m) t {i1 l ~ } p(t), is the chip pulse waveform, rectangular with unit amplitude in 0 I t I Tc. When the desired signal is transmitted through the channel, the other users' signals and AWGN get summed with the desired user's signal. The disturbance due to other users' signals constitutes multiuser interference (MUI) and AWGN represents the channel noise. The resultant received bandpass signal, shown in Figure 2.1, at the receiver front end, is of form where the kth user signal is delayed by r, with 0 I z, I T, and 6, = o,,r, is the carrier phase shift and is modeled as a random variable, uniform on [0,2n) 2.2 Statistical Model for SNIR The asynchronous model, in which different users suffer different channel delays and/or begin transmitting at different instants of time, is considered to emulate the transmission in the reverse link, i.e., from mobile to base-station. The reverse link in the present commercial systems is usually non-coherent, but for all future systems will likely be coherent [2]. We assume that the reception is phase as well as symbol synchronous and the correlator output for the kih user's jth bit is given by

27 where Akbk(j) is user-k's desired signal component, MkG) denotes the multiuser interference imposed on user k's j"' bit, and w(j) is the noise sample, zero mean, with variance No. The MU1 component of (4) is where the first sum is over users whose delay zi < z,, and the second sum is over users whose delay zi > z,, and A, = A, cos(0, -0;). The p 's in (5) are partial-period correlations between the spreading waveforms. These partial correlation terms in (5) result because the signals of different users differ in delay and the spreading waveforms are generally not orthogonal (even at zero delay); hence the data symbols from different users are partially overlapping as shown in Figure 2.2. Generalizing the formulation in [3] to allow for long codes, the partial crosscorrelations in (5) are defined as where a,, = j 1 a,, = ( j - 1) I a], and the notation ik denotes an estimate of the true delay zk

28 Figure 2.2. Diagram showing the partial overlapping of bits between two asynchronous users (i & k) that gives rise to partial correlation SNIR Estimators In the reverse link, the mobile terminal typically sends some bits embedded within the signal called training bits (N, bits per packet), which are known to the basestation (in advance). These bits are included to aid the basestation in synchronization, phase ambiguity resolution, and framing. The training bits typically constitute 10 to 20 % of a packet size or of the total number of bits constituting the signal (N,) [12]. These bits are enough to estimate the SNIR using correlation, instead of doing the time consuming and computationally intensive correlation over the entire errorcorrupted recovered sequence (as is the case with "in-service" estimators). We will show that the SNIR estimate obtained using these known N, bits is quite close to the actual SNIR that is calculated over the whole sequence.

29 18 To compare the goodness of the estimate in simulations we use two other parameters, namely ''True" SNIR and " N, -bit estimate of SNIR. It must be noted here that the computation of these two terms is only possible in simulation and not in a real communication system. This is because to find the True and N, -bit estimate of SNIR, we assume that the receiver knows the original E, l No (to find the True SNIR), the whole block of transmitted data ( Nb bits) in advance and that the correlation is done over the entire N, bits to find the actual (Trtie and N, -hit estimate) SNR. Hence, the N, -bit estimate SNIR is found by using all N, 1 P bits per packet at the output of the matched filter (MF) or correlator while the estimated SNIR uses only N, bits per packet at the output of the MF. In a subsequent section we define these SNIR measures precisely. We can rewrite (4) as vk (j) = Akbk (j) + M,(j) + w, ( j) = Akbk (j) + H, (j) (8) where H,(j) is the sum of the MU1 variable M,O) and the Gaussian noise random variable w,fi). We know that the SNIR of a system is a ratio of the signal energy to MU1 + AWGN energy (which we abbreviate as MUI energy). Generally, the signal energy can be found by squaring of the signal amplitude. The MU1 energy is the mean-square of the sum of MU1 and AWGN. The true SNIR, denoted y,, is a ratio of the true signal energy (2Eb) to the actual computed value of MU1 energy I, = H,' = (M, + w,)', where computation is over the entire data block received. The MU1 energy used in the true SNIR is the square of the computed value of (M, + w,), which is obtained by subtracting the known true

30 amplitude and bit, equal to b,(j)&, from each of the N, bits of the synchronous 19 conelator output (see (8)). The N, -bit estimate of SNIR, fk.,,.h, is calculated from the square of estimated amplitude (4,vh) and sum of MUI+AWGN (A,). The amplitude is estimated by correlating the N, known bits with the synchronous correlator outputs. And the estimate of the sum of MUI+AWGN ( H,) is obtained by subtracting the amplitude estimate from N, synchronous correlator output bits. The SNIR estimate, y,,,, which emulates the real communication system situation, is found using the same method as N, -bit estimate of SNIR except that it only uses N, known training bits which are sent with the signal. These terms are described below The true SNIR y, for kth user is where S, = 2Eb. The N, -bit estimate o f SNIR, *-.. Bk.,v, - ~ k, ~ ~ /AkN, = s ~ I H. ~ -, s ~,,~~ ~ I jk,n, ~ is of the same form as (91, except that the estimated values of the amplitude (ik,nh ) and MUI+AWGN are used to find the SNIR. For the SNIR estimate (f,,, ), we use the sample-variance of MU1 + AWGN. By sample-variance, we mean that we estimate the MU1 energy and the signal energy over the training bits (N,) only for each of the P packets of size N, = N, 1 P bits. That

31 means, for a message length of N, bits, we use onlypn, bits for the estimate, where PN, << N,. The MU1 for N, -hit estimate involves correlation over the complete signal 2 0 length ( N, ). The true MU1 energy (over the entire signal length) is computed as below and the MU1 energy for N, -bit estimate is 2 where and ' are the true and the N, -hit estimate variance of MU1 component 2 respectively. The value Nu is the true noise density and c?,~, is the N, -bit estimate noise density. The term 2(K -1)E,/(3N) is the "standard Gaussian" MU1 energy approximation in a Gaussian channel for K-users with equal energy The sample MU1 + AWGN variance, or MU1 energy estimate is In this work, we have used a Maximum-Likelihood (ML) estimator to find the estimated SNIR. We find both the amplitude and MU1 energy (sample variance of MU1 energy) estimates using ML estimation theory [4]. Then, to find the ML estimate of the SNIR f,, we use the property that the ML estimate of the ratio of two parameters (in this case, S, and j, ) is the ratio of individual ML estimates of the two parameters [9]. This kind of ML estimator for SNIR (DAE) also falls in the category of a special case of squared Signal-to-Noise variance (SNV) estimator [9], which for our study will obviously

32 get modified to Signal-to-Noise-plus-Interference variance (SNIV) estimator. 2 1 The detailed description of these estimators is in the following chapter SNIR Probability Density Functions The characteristics of a stochastic signal can be described with the help of its probability density function (pdf). We assume that the MU1 M, (j) is also Gaussian, with rn ean,l[, and v anance o,,~ ', h ence H, (j) i s also G aussian w ith mean,l[, and variance N,, + o,'. ~ The ~ Gaussian assumption is quite good for a system with a large number of active users K and large processing gain N. This (Gaussian) assumption is mostly appropriate for K/N ratio (,) larger than 0.3 [l 11. The pdf for SNIR can be found in two ways - with or without approximation of the chi-square variable, which we get in the denominator due to the MU1 energy. When H, i s G aussian, i ts s quare i s c hi-squared d istributed [ 71, h ence I, i s the s um o f c hi- squared random variables (see (10~)). We derive pdf using both methods. In the SNIR expression, the denominator (MU1 energy) is a random variable while the numerator is constant (signal energy). Since the numerator A,' is constant, the pdf is dependent on the statistics of the sum of chi-square distributed random variables in the denominator. In the direct, or exact method, we find the pdf of the SNIR by finding the pdf of the reciprocal of the sum of the chi-squared variables. In this case, I, (10a) and f,,,, (10b) are chi-squared variates with N, degrees of freedom, while j,.,%,, is a chi-squared

33 variate with N, degrees of freedom. By doing a simple transformation of the reciprocal of the chi-squared variate [7], the pdf p, (g) of SNIR [7] is 2 2 p, (g) = { (si N~ ) '* g-( 'I')-I 1 or " I 2 " T(N, 12)) exp(- s, N, /2g or ) (I 1 a) where g is the SNIR variate with mean,~r- and variance a,' = N, + Z(K - l )~, /3N, and s, represents the signal energy, equal to A,'. The function ~(x) is the gamma function. The SNIR pdf can be plotted for the true SNIR, the N, -bit estimate of SNIR, as well as the estimated SNIR, by making appropriate substitutions in (1 la). The expression given in (1 la) is the pdf of the true SNIR, when s, = 2E,,, and is the pdf of the N,-bit estimate of SNIR when s, = The pdf of estimated SNIR can be found from (1 la), when s, = k,,,v,' and N, is replaced by N,. In the second method, we approximate the sum of the chi-squared variables as another Gaussian by invoking the Central Limit Theorem, i.e., MU1 energy (I,) is 2 modeled as Gaussian with modified mean and variance given by pt= o,, and ak2'= 2q,4 1 N, respectively. The variance all2 is the variance of the sum of the chi- square distributed variables. Then we do a simple transformation of the reciprocal of a Gaussian random variable to obtain a new pdf for the SNIR estimate given below

34 2 where,urn = o,, and o,,' = 2o,,' 1 N, are the mean and the variance of the Gaussian distributed variate g. The pdf expression of (1 lb) can be used in a way similar to (1 la) to find the pdf of true SNIR, the N, -bit estimate of SNIR, and the estimated SNIR by substituting corresponding values. We will show in Chapter 4 that the pdf using the true value and the estimated value have good agreement. --. SNIK P SNIR pdf(chi') Figure 2.3. Example plot for pdf of true SNIR (using SGA and chi-squared distribution), 2 Rayleigh and Gaussian with N, =I00 bits and og = Z(K - l )~, /(3N) + No where K=10 users, N=15 chipslsample. Y In Figure 2.3, an example true SNIR pdf is plotted using equation (1 la) and (I lb) for N, =I00 bits and variance og2 = Z(K - l )~, /(3N) + No, where K=10 users, processing gain N=15. A comparable Rayleigh and Gaussian distribution are also included on the plot to enable comparison of the nature of the SNLR pdf with respect to these standard distributions. Note from Figure 2.3 that the SNIR pdf is somewhat "Gaussian like," but with a heavy tail. The pdf given by (I lb) shown in Figure 2.3 is

35 referred to as the pdf of average of SGA estimate of SNIR. The pdf of true SNIR is found by averaging I, in (1 Oa). 2 4 We can also find an instantaneozls N, -bit estinzate of SNIR, as follows: 1 (M, (i) + vt,(i))' In (12), the averaging is done on a "per bit" basis. We find the average SNIR by first finding the instantaneous SNIR (per bit), and then average these per-bit estimates to find the resulting SNIR. We can also find SNIR using gsynchronous conelator outputs in place of the synchronous correlator output (8). The SNIR using asynchronous correlations can be found quickly as compared to SNIR using synchronous correlator outputs, but at the cost of accuracy, since the asynchronous correlator outputs can be obtained during signal timing acquisition, before any data detection commences. In Chapter 3, we will discuss the three ML estimators we employ, namely estimators for the signal amplitude, the MU1 energy, and the SNIR. We will also discuss the three different kinds of estimators that are differentiated according to the correlations, synchronous or asynchronous, used to find the SNIR estimates. We, also classify according to the process by which the SNIR is estimated, i.e., average SNIR over a given (fixed) duration or average of the instantaneous (per-bit) SNIR. We will also find the bias of the estimates and analyze how it can be reduced.

36 Chapter 3 Estimation of Signal Quality Estimation involves making inferences from observations that are distorted or corrupted in a manner that is only partially known, or known in a statistical sense. Since the information that is to be extracted from these observations is a fortiori, the estimation problem is solved using a statistical analysis framework. For the same reasons, estimates are also called statistics since they depend upon samples taken from a whole population. As noted, various estimation parameters are used in different systems for defining the signal quality. Most commonly used are signal to noise ratio (SNR), signal to interference ratio (SIR) and signal to noise plus interference ratio (SNIR). Although SNIR is relatively less widely used, partly because of the increased computation time, it is more directly related to error rate performance than the other two (approximate) measures. In this study, we investigated the statistics and characteristics of SNIR estimation based upon correlation, when correlation is done over a training sequence of known symbols. The training sequence is typically 10 to 20 % of a given block of symbols. We use two estimators, namely an amplitude estimator and an MU1 estimator, and use their ratio as the SNIR estimate. More precisely, the SNIR estimate is the square of the amplitude estimate divided by the estimate of MU1 energy, which itself is the square of the sum of MU1 and noise. These quantities will be defined subsequently. We also study the use of different SNIR estimators based on average estimates, instantaneous estimates and for the case where we use asynchronous correlator outputs to obtain coarse estimates of MU1 energy. These three estimators are as follows:

37 26 1. an average SNIR over a given (fixed) duration, with MU1 measured from synchronous correlations, 2. an average of the instantaneous (per-bit) SNIR, 3. an average SNIR over a fixed duration, with MU1 measured from asynchronous correlations. The a verage o f i nstantaneous S NIR (#2) appears primarily u seful for b ounding the former, but is of general theoretical interest as well. The Gaussian model is used for MUI, as described in Chapter 2. The third estimator listed is similar to the first estimator, with the difference being that it uses asynchronous correlations instead of synchronous correlations for estimation of the MU1 energy. This MU1 estimation can be performed during initial acquisition when serial or sequential code acquisition scheme are employed, and hence is slightly more rapid than the estimator using synchronous correlations, at the expense of some accuracy. In general, there are various estimation criteria that can be used, such as least squares estimation (LSE), maximum likelihood estimation (MLE) and minimum meansquare error estimation (MMSE). Different criteria entail different levels of complexity in terms of implementation and usage. We primarily employ ML estimation and approximations to it in this work because they are generally better. The estimate of the SNIR is found from the ratio of the individual ML estimates of the signal energy and MU1 energy. We need to check how "good" our amplitude, MU1 energy, and SNIR estimates are. One measure of the goodness of an estimator is how close its expected value is to the true value of the parameter. An unbiased estimator is one for which E@)= 6', where

38 the expectation of the estimate of the parameter B is equal to parameter itself. The estimator is said to be biased if ~(6)= 6 + B, with bias equal to B Amplitude Estimator We judge the goodness of our amplitude estimator using this simple method of the expectation of the estimate of the parameter and also its consistency. The ML estimate of the amplitude, under the assumption that the MU1 and noise are both Gaussian and constant amplitude, is calculated when the synchronous correlator output (eq. (4), Chapter 2) is correlated with the known (training) bit sequence. The square of the ML estimate of the amplitude gives the signal energy estimate. In estimators that use synchronous correlations, the sum of MU1 and AWGN is calculated by subtracting the amplitude estimate (multiplied by the training bit) from the synchronous correlator output. The square of this quantity gives the MU1 energy. And finally, the signal energy estimate is divided by the ML estimate of the MU1 energy estimate to obtain the SNIR estimate. For clarity, we again write the correlator output y, given by (eq. (4), Chapter 2). (i+l)t+ri y, (i) = 2 Sr(t)s, (t - it - r,) cos(o,t - 8,)dt it+ri = A, b, (i) + Mk (i) + ~ (i) = Ak b, (i) + Hk (i) where A, is the bit amplitude and b, (i) is the ith bit of the user k. The amplitude estimate is calculated as follows

39 where Ai = A since by assumption the amplitudes are constant. The expectation of the amplitude estimate is since the mean of the MU1 and noise terms are both zero. Thus the summation in (14a) is zero and hence the amplitude estimator is unbiased. It can also be shown that (14a) is a consistent estimate, since ~ M, ~, I w, I < m, which means that the estimate variance (around the true value since unbiased) decreases with an increase in the number of samples used for the estimate. Finally, we show that the estimate of (13) is the maximum likelihood (ML) estimate as follows: Taking a derivative with respect to A, we obtain and by setting this derivative to zero, we get

40 which is equal to (1 3), thus our amplitude estimate is ML. 3.2 MU1 Energy Estimator As noted, the MU1 energy estimate or the estimate of the variance of the MU1 + AWGN (i,,), shown in (15a), is found by subtracting the amplitude estimate (13)--the correlation of the synchronous correlator output ( yi) and the actual (known bit) sequence (bi)--from the received signal, and averaging its square. The N, -hit estimate of MU1 energy, shown in e q. 1 5(b), i s analogous to the MU1 energy estimate except that it i s estimated over the complete signal length of N, bits. Thus the MU1 energy estimate (i,) is given by and the N, -bit estimate of MU1 energy is given by For the case when we have the true amplitude A in our estimator of (15a), the MU1 estimate is again an ML estimate (conditioned on the Gaussianity of the MUI). We next find the bias on the MU1 energy estimate. So, we substitute (13) into (15a) and then take expectation to find the bias.