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Rate detection for variable-rate data transmission in CDMA communication systems Yang, Gordon 2001

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RATE DETECTION FOR VARIABLE-RATE DATA TRANSMISSION IN CDMA COMMUNICATION SYSTEMS by Gordon Yang B.Sc, Beijing University of Aeronautics and Astronautics, 1982 M.Sc., Beijing University of Aeronautics and Astronautics, 1984 M.A.Sc., Simon Fraser University, 1991 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING We accept this thesis as conforming to the required standard T H E U N I V E R S I T Y OF BRITISH C O L U M B I A February, 2001 © Gordon Yang, 2001 UBC Special Collections - Thesis Authorisation Form Page 1 of 1 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e for. reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head of my department or by h i s or her re p r e s e n t a t i v e s . I t i s understood, that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department of The U n i v e r s i t y of B r i t i s h Columbia Vancouver, Canada Date O 6 T , 2-, ZsCO j http://www.library.ubc.ca/spcoll/thesauth.html 2001-10-01 Abstract Variable-rate data transmission is one of the key techniques to effectively reduce the mutual interference and as a result increase the link capacity in direct sequence code division multiple access (DS-CDMA) systems. To avoid frame overhead, a blind rate detection scheme that does not explicitly transmit any rate information of transmitted data has been proposed for use in the third-generation DS-CDMA cellular communication systems. In this thesis, a novel joint rate detection and data decoding algorithm (JRDDDA) for variable-rate data transmission in DS-CDMA systems is proposed. Its performance in terms of frame error rate and false rate detection rate is investigated by means of computer simulation in three different, standard channels; namely, the additive white Gaussian noise channel, the frequency-flat Rayleigh fading channel, and the frequency-selective Rayleigh fading channel. The effect of channel estimation error on the system performance is also investigated in the considered channels. Moreover, a novel joint source and channel coding based rate detection algorithm (JSCC-RDA) is proposed, which exploits rate sequence redundancy for combating the effect of the noisy channels. A first-order Markov process is used to model the rate sequence from the vocoder's output in the case of voice transmission. An instantaneous Maximum a posteriori algorithm is employed in our joint source and channel decoder due to the delay constraint on real-time cellular communication systems. The proposed JSCC-RDA is applied to two well-known rate detection algorithms and the JRDDDA as well for performance improvement in terms of false rate detection rate. ii Table of Contents Abstract ii Tables of Contents iii List of Tables vi List of Figures vii Acknowledgment xii Chapter 1 Introduction 1 1.1 Motivations 1 1.2 Research Contributions of this Thesis 4 1.3 Organization of this Thesis 8 Chapter 2 Background 9 2.1 Basic Elements of a Digital Communication System 9 2.1.1 Source Coding 10 2.1.2 Channel Coding 12 2.1.3 Multiple Access 25 2.1.4 Modulation and Channel 28 2.2 Variable-Rate Data Transmission in DS-CDMA 29 2.3 Overview of Blind Rate Detection Techniques , 35 2.3.1 Pre-decoding B lind Rate Detection 37 2.3.2 Post-decoding Blind Rate Detection 40 Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the AWGN Channel 43 3.1 System Model in the AWGN Channel 43 3.2 Joint Rate Detection and Data Decoding Algorithm 46 i i i 3.3 Simulated Results in the AWGN Channel 50 3.3.1 Simulation System 52 3.3.2 FER Performance 59 3.3.3 FRDR Performance 64 3.3.4 Channel EyJNt Mismatch 67 3.4 Conclusions 68 Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 70 4.1 Multipath Propagation Model 70 4.2 Joint Rate Detection and Data Decoding Algorithm 75 4.3 Simulation Results in Multipath Rayleigh Fading Channels 79 4.3.1 Simulation System 81 4.3.2 Simulated Results in the One-path Rayleigh Fading Channel 85 4.3.3 Simulated Results in the Three-path Rayleigh Fading Channel 94 4.4 Complexity 103 4.5 Conclusions 105 Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 107 5.1 Introduction 107 5.2 Background of Joint Source and Channel Coding (JSCC) 108 5.3 A JSCC Based Rate Detection System I l l 5.4 JSCC Encoder - Variable-Rate Vocoder 114 5.4.1 QCELP Vocoder 116 5.4.2 Vocoder Rate Generation Algorithm 121 5.4.3 First-Order Markov Model of Rate Sequences 126 iv 5.5 JSCC Decoder - MAP Decoder for Rate Sequences 130 5.5.1 Sequence MAP Decoder 131 5.5.2 Instantaneous MAP Decoder 132 5.5.3 Rate Delay Constraint 135 5.6 Simulated Results 137 5.6.1 Simulated Results in the AWGN Channel 138 5.6.2 Simulated Results in the One-path Rayleigh Fading Channel'. 140 5.6.3 Simulated Results in the Three-path Rayleigh Fading Channel 143 5.7 Conclusions 148 Chapter 6 Conclusions and Topics for Future Research 150 6.1 Conclusions 150 6.2 Topics for Future Research 151 6.2.1 Channel E\/Nt Estimation 152 6.2.2 Importance Sampling Technique 152 6.2.3 Multiuser Detection Receiver 153 6.2.4 Image and Video Transmission 153 6.2.5 Additional Channel Models 154 Bibliography 155 Glossary 163 V List of Tables Table 2.1 Forward traffic channel frame structure summary 13 Table 2.2 Number of error bits produced by paths with a distance d from the correct path for rate 1/2 code with code generator (753, 561) 19 Table 2.3 Symbol energy and chip energy corresponding to data rate 34 Table 4.1 One path fading channel parameters 86 Table 4.2 Three path fading channel parameters 95 Table 4.3 Complexity of different rate detection schemes 104 Table 5.1 Variable rates provided by QCELP vocoder 116 Table 5.2 Variable traffic channel data rates 117 Table 5.3 Parameter update and bit allocations 120 Table 5.4 Rate transition probability 129 Table 5.5 Complexity of instantaneous MAP decoder 135 vi List of Figures Figure 2.1 Basic elements of a digital communication system 10 Figure 2.2 Convolutional encoder 15 Figure 2.3 Rate 1/2 convolutional code with constraint length K=9 15 Figure 2.4 A communication system employing convolutional codes 16 Figure 2.5 BER performance of the rate 1/2 convolutional code with the code generating polynomial (753, 561) 21 Figure 2.6 Symbol repetition scheme 22 Figure 2.7 Block interleaver 23 Figure 2.8 Three different multiple access schemes: (a) FDMA, (b) TDMA, and (c) CDMA 26 Figure 2.9 Variable-rate data transmission in DS-CDMA 31 Figure 2.10 Frame structure for Radio Configuration 1 32 Figure 2.11 Cohen's blind rate detection algorithm 41 Figure 2.12 Butler's blind rate detection algorithm 42 Figure 3.1 System model in the AWGN channel 44 Figure 3.2 Block diagram of j oint rate detection and data decoding algorithm in the AWGN channel 49 Figure 3.3 Simulation setup for different rate detection algorithms 52 Figure 3.4 CDMA forward channels 54 Figure 3.5 Complex PN spreading and QPSK modulation 55 Figure 3.6 Block diagram of IS-2000 RC1 forward traffic channel 57 Figure 3.7 Matched-filter rake receiver in the AWGN channel 58 Figure 3.8 FER benchmark of IS-2000 CDMA forward link in the AWGN channel 59 vii Figure 3.9 FER in the AWGN channel in the case of all rate frames 61 Figure 3.10 FER in the AWGN channel in the case of 9600 bps frames 62 Figure 3.11 FER in the AWGN channel in the case of 4800 bps frames 62 Figure 3.12 FER in the AWGN channel in the case of 2400 bps frames 63 Figure 3.13 FER in the AWGN channel in the case of 1200 bps frames 63 Figure 3.14 FRDR in the AWGN channel in the case of all rate frames 65 Figure 3.15 FRDR in the AWGN channel in the case of 9600 bps frames 65 Figure 3.16 FRDR in the AWGN channel in the case of 4800 bps frames 66 Figure 3.17 FRDR in the AWGN channel in the case of 2400 bps frames 66 Figure 3.18 FRDR in the AWGN channel in the case of 1200 bps frames 67 Figure 3.19 FER versus channel Eb/Nt mismatch in the AWGN channel (true E j / N ^ dB) . 69 Figure 4.1 Tapped delay line model of a multipath fading channel 72 Figure 4.2 Rake receiver in multipath fading channel 73 Figure 4.3 Block diagram of joint rate detection and data decoding algorithm in multipath fading channels 80 Figure 4.4 Simulation system in multipath fading channel 82 Figure 4.5 Pilot-aided coherent Rake receiver for multipath fading channel 84 Figure 4.6 FER benchmark of IS-2000 CDMA forward link in the three-path Rayleigh fading channel 86 Figure 4.7 FER in the one-path Rayleigh fading channel in the case of all rate frames . . . . 88 Figure 4.8 FER in the one-path Rayleigh fading channel in the case of 9600 bps frames . . 88 Figure 4.9 FER in the one-path Rayleigh fading channel in the case of 4800 bps frames .. 89 Figure 4.10 FER in the one-path Rayleigh fading channel in the case of 2400 bps frames .. 89 Figure 4.11 FER in the one-path Rayleigh fading channel in the case of 1200 bps frames .. 90 v/77 Figure 4.12 FRDR in the one-path Rayleigh fading in the case of all rate frames 90 Figure 4.13 FRDR in the one-path Rayleigh fading in the case of 9600 bps frames 91 Figure 4.14 FRDR in the one-path Rayleigh fading in the case of 4800 bps frames 91 Figure 4.15 FRDR in the one-path Rayleigh fading in the case of 2400 bps frames 92 Figure 4.16 FRDR in the one-path Rayleigh fading in the case of 1200 bps frames 92 Figure 4.17 FER versus channel Eb/Ni mismatch in the one-path Rayleigh fading channel (true Eb/Nt=12 dB) 94 Figure 4.18 FER in the three-path Rayleigh fading channel in the case of all rate frames . . . 96 Figure 4.19 FER in the three-path Rayleigh fading channel in the case of 9600 bps frames . 97 Figure 4.20 FER in the three-path Rayleigh fading channel in the case of 4800 bps frames . 97 Figure 4.21 FER in the three path Rayleigh fading channel in the case of 2400 bps frames . 98 Figure 4.22 FER in the three path Rayleigh fading channel in the case of 1200 bps frames . 98 Figure 4.23 FRDR in the three-path Rayleigh fading in the case of all rate frames 99 Figure 4.24 FRDR in the three-path Rayleigh fading in the case of 9600 bps frames 100 Figure 4.25 FRDR in the three-path Rayleigh fading in the case of 4800 bps frames 100 Figure 4.26 FRDR in the three-path Rayleigh fading in the case of 2400 bps frames 101 Figure 4.27 FRDR in the three-path Rayleigh fading in the case of 1200 bps frames 101 Figure 4.28 FER versus channel Eb/Nt mismatch in the three-path Rayleigh fading channel (true Eb/Nt=4 dB) 102 Figure 5.1 Block diagram of JSCC system based on VQ and MAP decoder 110 Figure 5.2 Variable-rate DS-CDMA communications system for speech transmission . . . 112 Figure 5.3 Block diagram of an equivalent rate transmission system 113 Figure 5.4 Block diagram of a JSCC based rate detection system 114 Figure 5.5 QCELP vocoder structure: (a) Encoder and (b) Decoder 119 ix Figure 5.6 Speech energy, rate thresholds and background noise estimate 122 Figure 5.7 An example of rate generation: (a) speech signal in 5000 ms, (b) speech energy, rate decision thresholds and background noise energy and (c) data rate . . . . . . 127 Figure 5.8 QCELP coding 128 Figure 5.9 Rate trellis diagram 129 Figure 5.10 Graphical representation of rate cross-over probability 131 Figure 5.11 Block diagram of various delay components in the one-way transmission . . . . 136 Figure 5.12 Block diagram of joint source and channel coding based rate detection algorithm 137 Figure 5.13 Simulation setup for different rate detection algorithms with JSCC-RDA . . . . 139 Figure 5.14 FRDR of JSCC-RDA with Cohen's BRDA in the AWGN channel 140 Figure 5.15 FRDR of JSCC-RDA with Butler's BRDA in the AWGN channel 141 Figure 5.16 FRDR of JSCC-RDA with the proposed JRDDDA in the AWGN channel 141 Figure 5.17 FRDR of JSCC-RDA with Cohen's BRDA, Butler's BRDA and the JRDDDA in the AWGN channel 142 Figure 5.18 FRDR of JSCC-RDA with Cohen's BRDA in the one-path Rayleigh fading channel 143 Figure 5.19 FRDR of JSCC-RDA with Butler's BRDA in the one-path Rayleigh fading channel 144 Figure 5.20 FRDR of JSCC-RDA with the proposed JRDDDA in the one-path Rayleigh fading channel 144 Figure 5.21 FRDR of JSCC-RDA with Cohen's BRDA, Butler's BRDA and the proposed JRDDDA in the one-path Rayleigh fading channel 145 Figure 5.22 FRDR of JSCC-RDA with Cohen's BRDA in the three-path Rayleigh fading channel 146 Figure 5.23 FRDR of JSCC-RDA with Butler's BRDA in the three-path Rayleigh fading channel 146 Figure 5.24 FRDR of JSCC-RDA with the proposed JRDDDA in the three-path Rayleigh fading channel 147 Figure 5.25 FRDR of JSCC-RDA with Cohen's BRDA, Butler's BRDA and the proposed JRDDDA in the three-path Rayleigh fading channel 147 x; Acknowledgment I would like to express my sincere gratitude to Dr. Samir Kallel, my research supervisor, for his supervision, guidance and encouragement throughout the course of this research. I would also like to thank Dr. Cyril Leung, one of my supervisory committee members, for his technical discussions and encouragement over the last two years. I am also thankful to Dr. Robert Link, Dr. Jason Dai, Ms. Ying Fang and Mr. Rob Boyes at Philips Semiconductors for their comments on and proofreading of this thesis. I am greatly indebted to my wife, Hong, for her understanding, encouragement and never ending support. I am grateful to my daughter, Sarah, for the happiness she has brought to our family. xii 1 Chapter 1 Introduction 1.1 Motivations Since the introduction of analog cellular communication about two decades ago, cellular communications have experienced an exponential growth [1]. Cellular communication technol-ogy has evolved from the simple first-generation (1G) analog systems [2] to the advanced second-generation (2G) digital systems [3]-[6]. A vision of more advanced third-generation (3G) cellular communication systems is emerging [7]-[ll]. Voice is the primary transmission in the 1G and 2G cellular communication systems. However, the 3G cellular communication systems are aimed at providing users with the ability of timely exchange of not only voice but also image, video, fax, computer data, electronic mail, electronic commerce, etc. [12]. Wireless multimedia services including image or video require much wider channel bandwidth than voice transmission. For cellular radio applications, however, channel bandwidth is always a scarce resource. To increase the bandwidth efficiency or channel capacity in the cellular communication channel, new technol-ogies like digital speech transmission, modulation, network and multiple access are being developed at an unprecedented rate. Direct Sequence Code Division Multiple Access (DS-CDMA) is emerging as the predom-inant radio access technology for the 3G cellular communication systems, due to the fact that DS-CDMA can effectively mitigate multipath distortion, provide a universal frequency reuse and increase the link capacity [13], [14]. It is clear that for the 3G cellular communication systems, the wireless multimedia applications will generate various data rates and require variable-rate data transmission from time to time. The link capacity of a DS-CDMA cellular communication system is mainly limited by the Multiple Access Interference (MAI) from other users transmitting at the Chapter 1 Introduction 2 same carrier frequency in the same and adjacent cells [13]-[15]. Variable-rate data transmission is one of the key techniques to effectively reduce the mutual interference and as a result increase the link capacity of the DS-CDMA cellular communication systems. In the case of speech transmis-sion, for example, the link capacity can be increased by two times because a speaker is, on average, active less than half of the time in a two-way conversation [14], [16]. During the quiet periods, the transmitters could effectively turn off and reduce interference power introduced into the channel. The reduction in interference directly translates into capacity gain of a DS-CDMA system. In principle, Frequency Division Multiple Access (FDMA) and Time Division Multiple Access (TDMA) systems could also take advantage of the speech statistics. However, the implementation is more complicated as radio resources, such as FDMA channels or TDMA time slots, need to be dynamically assigned in real time by the network infrastructure [17]. Variable-rate data transmission systems can be developed to include the explicit rate information in the transmitted data frame. These are known as explicit rate transmission schemes. A simple explicit rate transmission scheme is one in which the rate information is transmitted in a non-variable rate portion of each frame. One of the drawbacks of this is that some extra bits need to be added to represent the rate information. Moreover, since only a few bits are typically needed, these bits cannot be efficiently encoded for error protection without a lot of overhead. Furthermore, the encoded rate information bits are prone to errors in fading communication channels. Another explicit rate transmission scheme is one in which the rate information is transmit-ted on a Dedicated Control Channel (DCCH) in parallel to the data frame transmitted on a traffic channel. This scheme is known as DCCH rate transmission. On the receiver side, the rate information bits are first decoded from the DCCH, and then the data frame is decoded according Chapter 1 Introduction 3 to the decoded rate information from the DCCH. The major disadvantage of this scheme is that a DCCH is always required when a traffic channel is enabled. The additional DCCH introduces an extra interference and as a result reduces the link capacity. Furthermore, since both the DCCH and the traffic channel are required to be demodulated simultaneously, the demodulation complexity is doubled compared to the case where only the traffic channel is being demodulated. Alternatively, variable-rate data transmission systems which do not include explicit rate information can be developed. These are known as implicit rate transmission schemes. One of the implicit rate transmission schemes is that the rate information is embedded in the transmitted signal by the combination of convolutional code, symbol repetition and different levels of symbol energy. The major advantage of such a scheme is that there is no frame overhead and no require-ment for any DCCH to send the rate information. Therefore, the system employing the implicit rate transmission scheme introduces less mutual interference and as a result offers higher link capacity than the one using an explicit rate transmission scheme. As such, the implicit rate transmission scheme has been proposed for use in the 3G DS-CDMA cellular communication systems like the IS-2000 CDMA [7]. In order to decode variable-rate data frames, the rate of the transmitted frames needs to be detected first based on received frames of data on a frame-by-frame basis. Since there are no explicit rate bits transmitted, the rate detection for implicit rate transmission schemes is often referred to as blind rate detection. Also, implicit rate transmission schemes are generally termed blind rate detection schemes. In recent years, it is an active research topic to develop a reliable Blind Rate Detection Algorithm (BRDA) for variable-rate data transmission in DS-CDMA cellular communication systems. Several BRDAs were proposed in the literature. Most of them (see, for example, [18], [19], [20], [23], [25]) were proposed for use in the IS-95 CDMA communication system [6], Chapter I Introduction 4 where voice transmission is the primary application. For voice transmission, relative high Frame Error Rate (FER), say five percent, is tolerable due to the fact that parameter interpolation and error concealment techniques can be applied to voice reconstruction for voice quality improve-ment when frame errors occur. For the 3G DS-CDMA cellular communication systems, however, low FER is required for high quality multimedia services including voice, image, video, and computer data. The BRDAs used for the IS-95 CDMA communication system can hardly meet the new requirements in the 3G DS-CDMA cellular communication systems [7], [66]. Investiga-tion of more reliable BRDAs for the variable-rate data transmission in the 3G DS-CDMA cellular communication systems is the main focus of this thesis. 1.2 R e s e a r c h C o n t r i b u t i o n s o f this T h e s i s A few heuristic approaches exploiting the symbol repetition property [18], [19] and using the Symbol Error Rate (SER) [23], [25] have been explored to devise BRDAs. Some theoretical approaches using matched filtering or Maximum Likelihood (ML) estimation have also been investigated to arrive at BRDAs (see, for example, [20]-[22]). An overview of blind rate detection techniques will be given in Section 2.3 of Chapter 2. In this thesis, a theoretical approach to the blind rate detection problem using hypothesis test theory [27] is used. We derive a novel Joint Rate Detection and Data Decoding Algorithm (JRDDDA) based on the criterion of maximizing the joint a posteriori probability of the transmitted data rate and the information bit sequence, given a frame of received symbols. The proposed JRDDDA is investigated under three different, widely employed, channel models: namely, the Additive White Gaussian Noise (AWGN) channel [30], the frequency-flat Rayleigh fading channel, and the frequency-selective Rayleigh fading channel [31], [32]. The first Chapter 1 Introduction 5 is a simple, standard channel model, in which the received signal is affected only by background noise. The others are more realistic channel models for cellular communication systems. The one-path Rayleigh fading and three-path Rayleigh fading channels standardized in the IS-2000 CDMA specification [66] are used to model the frequency-flat and frequency-selective Rayleigh fading channels, respectively. The forward traffic channel of the Radio Configuration 1 (RC1) in the IS-2000 CDMA standard [7] is used to illustrate the idea of the JRDDDA proposed in this thesis. The system performance of the proposed JRDDDA in terms of FER and False Rate Detection Rate (FRDR) is investigated by means of computer simulation in the considered channels. The system performance of an ideal rate detection system where the rate information is known to the receiver is given as a reference. The system performance of two well-known BRDAs is also included for comparison. The first is the one proposed by Cohen in [19], called Cohen's BRDA, and the other is the BRDA proposed by Butler in [23], called Butler's BRDA. Simulation results show that the proposed JRDDDA significantly outperforms both Cohen's and Butler's BRDAs in all the three channels mentioned above. Particularly in the 1200 bps case, the proposed JRDDDA provides more than 2.5 dB gain over both Cohen's and Butler's BRDAs in terms of the required bit energy to total noise ratio, denoted by EiJNt, at a FER of 10"2, and the FRDR of the JRDDDA is two orders of magnitude lower than that of the other two BRDAs for a given EfJNt in the AWGN channel. In the three-path Rayleigh fading channel and for the same rate case, the proposed JRDDDA provides more than 2.1 dB gain over both Cohen's and Butler's BRDAs in terms of the required EJN, at a FER of 10"2, and the FRDR of the proposed scheme is more than one order of magnitude lower than that of the other two BRDAs for a given EjJN,. An estimation of bit energy E^ and the total noise spectral density Nt is required by the Chapter 1 Introduction 6 joint rate detection and data decoding algorithm. Some effective techniques for estimating Eb and Nt are given in [28], [73]-[76], [102], [103]. Although the study of Eb and Nt estimation algorithms is beyond the scope of this thesis, we investigate the performance degradation in terms of FER due to channel EfJN, mismatch in the AWGN and multipath Rayleigh fading channels by means of computer simulation. It is shown through simulation that there is about 5 dB and 2 dB tolerance in terms of EiJN, mismatch in the AWGN channel and the multipath Rayleigh fading channels, respectively [32]. It is shown in [28] that the channel EfJN, estimation accuracy can be under 0.5 dB, which is well within our channel mismatch tolerance. It has been known for some time that any redundancy in the source can be utilized to combat the effect of channel noise at the receiver. The use of the source statistics by the receiver has been shown to give very significant performance improvement for vector quantization, speech coding and image transmission applications where the bit sequence redundancy is exploited for mitigating the effect of the noisy channel [90], [95], [97]. The technique for utilizing the source statistics by the receiver is usually referred to Joint Source and Channel Coding (JSCC). In this thesis, a novel JSCC based Rate Detection Algorithm (JSCC-RDA) [33] is proposed for further improving the system performance of the basic BRDAs like Cohen's, Butler's and the JRDDDA. This JSCC-RDA is a new application of the JSCC concept to the blind rate detection problem. In the proposed JSCC-RDA, the rate sequence redundancy instead of the traditionally used bit sequence redundancy is exploited for combating the effect of the channel noise. We use voice transmission as an example, and model the rate sequence from the vocoder's output as a first-order Markov process. A long training sequence is used to compute the rate transition probability. Again, the forward traffic channel in the IS-2000 CDMA RC1 [7] is used to illustrate the concept of the JSCC-RDA proposed in this thesis. The 8 kbps Qualcomm Code Excited Linear Predictive Chapter 1 Introduction 7 (QCELP-8) vocoder is used as the source coder, which compresses input digitized speech into data frames at four variable rates depending on the voice activity. It also functions as a channel encoder since its output contains redundancy regarding the rate sequence. Due to the delay constraint on real-time transmission systems, an instantaneous Maximum a posteriori (MAP) decoder [88] is used as the JSCC decoder to exploit the inherent rate redundancy. The proposed JSCC-RDA is applied to three basic BRDAs such as Cohen's BRDA, Butler's BRDA and the JRDDDA for performance improvement in terms of FRDR. It is evident from simulation results that the proposed JSCC-RDA can provide up to 2 dB gain for Cohen's BRDA, 1.5 dB gain for Butler's BRDA and 0.5 dB gain for the JRDDDA in terms of the required Ef/N, in a FRDR range of 10 - 3 to 10 - 2. It will be shown in Chapter 5 that such performance gain is obtained with a negligible complexity increase. In summary, the primary research contributions of this thesis are as follows: 1. A novel joint rate detection and data decoding algorithm (JRDDDA) for variable-rate transmission in DS-CDMA cellular communication systems is proposed. Its perfor-mance in terms of FER and FRDR is investigated by means of computer simulation in the AWGN channel, the frequency-flat Rayleigh fading channel, and the frequency-selective Rayleigh fading channel. The effect of the channel estimation error on the system performance is also investigated. 2. A novel joint source and channel coding based rate detection algorithm (JSCC-RDA) which exploits the rate sequence redundancy is proposed for further improving the FRDR performance of basic BRDAs. The proposed JSCC-RDA is applied to three basic BRDAs such as Cohen's BRDA, Butler's BRDA and the JRDDDA for FRDR Chapter I Introduction 8 performance improvement. 1.3 O r g a n i z a t i o n o f this T h e s i s The remainder of this thesis is organized as follows. The required background knowledge of DS-CDMA communication systems related to this thesis is provided in Chapter 2. A novel joint rate detection and data decoding algorithm for variable-rate data transmission in DS-CDMA systems in the AWGN channel case is proposed in Chapter 3. The joint rate detection and data decoding algorithm in multipath Rayleigh fading channels is investigated in Chapter 4. A novel JSCC based rate detection algorithm is proposed in Chapter 5. Finally, some conclusions and suggested topics for future research are given in Chapter 6. Chapter 2 Background 9 The purpose of this chapter is to present the required background knowledge of DS-CDMA communication systems related to this thesis. Basic elements of a digital communication system are described in Section 2.1. A brief description of source and channel coding techniques employed in the IS-2000 CDMA communication system is also given in Section 2.1. Following this, the variable-rate data transmission in the DS-CDMA communication system is discussed in Section 2.2. Finally, an overview of blind rate detection techniques is given in Section 2.3. 2.1 B a s i c E l e m e n t s o f a D i g i t a l C o m m u n i c a t i o n S y s t e m Figure 2.1 shows the functional block diagram of a typical digital communication system [17], [35]. The source output may be either an analog signal, such as audio, image, video signal, or a digital signal, such as fax data or computer data. The information source is first converted into digital form or a sequence of binary digits by the source encoder function. The sequence of binary digits from the source encoder, called the information sequence, is passed to the channel encoder. The purpose of the channel encoder is to introduce, in a controlled manner, some redundancy in the binary information sequence that can be used at the receiver to overcome the effects of noise and interference encountered in the transmission of the signal through the channel. The binary sequence at the output ofthe channel encoder is passed to the multiple access function, which arranges the binary sequence so that more than one user can share the given spectrum. The binary sequence at the output of the multiple access function is passed to the digital modulator, which serves as the interface to the communication channel. In wireless transmission, the communication channel is the atmosphere. On the receiver side, the signals are first demodu-lated from RF to baseband, then the multiple access function separates the different users that are Chapter 2 Background 10 sharing the particular spectrum. Then, the channel decoder for a particular user attempts to correct the errors that have been introduced by the channel. Finally, the source decoder reconstructs the original source. To provide for the required background knowledge of DS-CDMA communication systems related to this thesis, we will briefly discuss each of these blocks in the following subsections. Source Information Source Encoder Channel Encoder Multiple Access Modulator Channel Reconstructed Source Source Decoder — Channel Decoder Multiple Access Demodulator Figure 2.1 Basic elements of a digital communication system 2.1.1 Source Coding For all the 1G and 2G cellular communication systems, speech transmission is the primary application. Source coding is generally referred to as speech coding for the 2G cellular communi-cation systems, such as the United States Digital Cellular System (IS-54/136) [3], Global System Chapter 2 Background 11 for Mobile (GSM) [4], Personal Digital Cellular (PDC) [5], and CDMA Digital Cellular (IS-95) [6]. For the 3G cellular communication systems, however, image transmission, video conference, fax, electronic mail, internet browsing, and so on are emerging into wireless applications [7]-[12], [36]-[40], A source coder may be a vocoder, image encoder, or video encoder in the 3G cellular communication systems. In wireless communications, channel bandwidth is always a scarce resource. Therefore, low bit rate vocoders like QCELP at 8 kbps (QCELP-8), QCELP at 13 kbps (QCELP-13) and Enhanced Variable Rate Code (EVRC) are standardized for the IS-2000 CDMA [41]-[43]. QCELP-8, QCELP-13 and EVRC fall into the family of code excited linear prediction vocoders [44]. Real-time visual communication is an integral part of multimedia services envisioned for the 3G cellular communication systems. Due to the limitations of the available radio spectrum and the enormous amounts of data involved, the most advanced compression algorithms must be used in the management and delivery of digital video. Many state-of-the-art video compression algorithms adopted as standards like ITU H.261 and H.263 do not work well when used to transmit video over error-prone radio channels [40], [45]. Low bit rate image and video coding for wireless transmission is an active research topic (see, for example, [40], [45]-[48]). However, the detailed discussion of vocoders, image and video coders is beyond the scope of this thesis. In Chapter 3 and Chapter 4, we will assume that the rate sequences from source coders are random processes. Then, the case where the source output contains redundancy with regard to the rate sequence is considered in Chapter 5. We will use voice transmission as an example to study the rate correlation. The QCELP-8 vocoder used in the IS-2000 CDMA [41] will be described in more detail when the JSCC based rate detection algorithm is discussed in Chapter 5. Chapter 2 Background 12 2.1.2 Channel Coding After the source information is coded into a digital format, redundancy needs to be added to this digital baseband signal. This is done to improve performance of the communication system by enabling the signal to better withstand the effects of channel impairments, such as noise and fading. The goal of channel coding is to reduce the required bit energy to noise spectral density ratio, denoted as Ei/N0, given a desired probability of error; or alternatively, to reduce the probability of error given an achievable EjJN0. The cost of this goal is more bandwidth required by the system to transmit. Traditionally, there are two major classes of error-correcting codes: block codes and convolutional codes. Block codes code an information sequence one block at a time. Cyclic Redundancy Check (CRC), one of the most common block codes, is used to indicate the quality of transmitted frames in the IS-2000 CDMA standard. Convolutional codes, on the other hand, have a memory property. In addition to using CRC, the IS-2000 CDMA channel coder uses convolutional coding to further improve the error performance. Turbo coding [49], a new error-correcting technique, is also used in the IS-2000 CDMA for high data rate transmission [7]. However, variable-rate data transmission is not used when Turbo coding is employed. Therefore, Turbo coding will not be discussed in this thesis. In addition to CRC and convolutional codes, we will also briefly describe other channel coding related techniques like symbol repetition and interleaving in this subsection. 2.1.2.1 Cyclic Redundancy Check In the IS-2000 CDMA forward channel, CRCs are used to indicate the quality of a transmitted frame which contains a block of information bits. Different CRCs are used depending on frame rates. In the IS-2000 CDMA RC1, each 20 ms frame at 9600 bps contains 192 bits, Chapter 2 Background 13 which are made up of 172 information bits, 12 frame quality indicator bits and 8 encoder tail bits. The 12 frame quality indicator bits are the redundancy bits that are a function of the 172 informa-tion bits in the frame. The generator polynomial used to generate the redundancy bits for a 9600 bps frame is [7] gx(x) = x l 2 + x n +xl0 + x9 + x* + x4+x+ 1. (2.1) At the 4800 bps, each 20 ms frame contains 96 bits, which are made up of 80 information bits, 8 frame quality bits, and 8 encoder tail bits. In this case, the 8 frame quality bits or CRC bits are generated using the following polynomial: g2(x) = x* + x7+ x4 + x3+x+ 1. (2.2) For the two other lower rates, there are no CRCs. The forward traffic channel frame structure of the IS-2000 CDMA RC 1 is summarized in Table 2.1. Table 2.1 Forward traffic channel frame structure summary Transmission Rate (bps) Number of Bits Per Frame Total Information Frame Quality Indicator Encoder Tail 9600 192 172 12 8 4800 96 80 8 8 2400 48 40 0 8 1200 24 16 0 8 Chapter 2 Background 14 2.1.2.2 Convolutional Codes A convolutional code is generated by passing the information sequence to be transmitted through a linear finite-stage shift register. In general, the shift register consists of K (k-bit) stages and n linear algebraic function generators, as shown in Figure 2.2. Note that © represents the exclusive OR function. The input data to the encoder, which is assumed to be binary, is shifted into and along the shift register k bits at a time. The number of output bits for each A>bit input sequence is n bits. Consequently, the code rate is defined as The parameter AT is called the constraint length of the convolutional code. The channel encoder for the forward link of the IS-2000 CDMA RC1 uses a rate 1/2 convolutional code with a constraint length of K=9. Its structure is shown in Figure 2.3. The code generating polynomial is g0=[753] and gl=[561] in octal notation. This code has a minimum free distance [35], [53] The error probability performance of this rate 1/2 convolutional code using the Viterbi decoding algorithm will be discussed in the next subsection. 2.1.2.3 Viterbi Decoding Algorithm The Viterbi algorithm (VA) was discovered in 1967 by A. J. Viterbi [50], and it was proved by J. K. Omura in 1969 that the Viterbi algorithm is a maximum likelihood decoding rule [51]. The Viterbi decoder for the convolutional code is used throughout this thesis and is briefly described in this section (see [35] and [52] for detail). A communication system employing a convolutional code is shown in Figure 2.4. The input bit sequence is denoted by U=(uj, u2> u^), the encoded symbol sequence by C=(cjj, Rc = k'n. (2.3) 12. (2.4) Chapter 2 Background Figure 2.2 Convolutional encoder Figure 2.3 Rate 1/2 convolutional code with constraint length K=9 Chapter 2 Background 16 c J n , c M 1 , c M n } and the corresponding channel output symbol sequence by Y=(yu, ....,yjn, ••••> yMh •••>)'Mn)> where Mis the length of input bit sequence. The symbol sequence Y is the input to the Viterbi decoder. Assuming an AWGN channel with antipodal signaling, we can represent the soft symbol sequence Fto the decoder as yu = JE~bcki + nki k=l,2,...,M; / = 1 , 2 , . ( 2 . 5 ) where ckl = +1 is an encoded symbol, Eb is the bit energy and nkl is an additive white Gaussian noise with a two-sided spectral density of AV2. Given ckl is transmitted, the pdf of the received symbol yki is ((yk,-jE~bckl)2^ p(yu\cu) = - ? = e x P k = 1 ,2,. . . ,M; / = 1 , 2 , ( 2 . 6 ) U Convolutional Encoder C Y Memoryless Viterbi Channel Decoder A u Figure 2.4 A communication system employing convolutional codes Chapter 2 Background 17 Since the channel is memoryless, the conditional probability of the sequence Y, given C , can be written as M P ( * \ Q = n k=i n ^ e x p [ jro— •l=lJnNo (2.7) In order to minimize the sequence error probability over all possible sequences when all are equiprobable a priori, we must maximize the conditional probability p(Y\C) given in (2.7) over all input sequences C . The maximum then corresponds to the most likely channel input code sequence, and the corresponding encoder input sequence is the most likely information sequence. Equivalently, we may seek the maximum of the logarithm of (2.7), which is an additive function of the symbol log-likelihoods, M f n \ A(C,Y)=lnp(Y\C) = £ £ ln/»(y«|cw) . (2.8) Jk=A/=i J We define the kth branch metric, denoted by \xk, as n Vk = u(ck>yk) = ZM>«|c w ) . (2.9) /= 1 where c# andj^ are -^dimensional vectors, with n being the number of symbols per branch. Then for the channel input sequence C , and its output E the log-likelihood function (2.8) can be written as A ( C , F ) = £ <ck,yk). (2.10) k = all branches The maximum likelihood decoder then seeks the path for which the sum of the branch metrics, as defined by (2.9) and (2.10), is maximized. Substituting (2.6) into (2.9) yields Chapter 2 Background 18 n v-k = S mp(yu\cki) /=! (2.11) ( n n \ The first sum is obviously the same for the Ath branch on all paths, the second term and the last term are constant. Removing the common terms and scaling the result by N0, the branch metric is replaced by n / = I That is, the branch metric is the inner product of its code symbols with the received channel output. Finding the maximum likelihood path thus consists of finding the path for which the sum of its branch metrics is the greatest over all paths. The bit error probability performance of the Viterbi algorithm on the AWGN channel with soft-decision decoding is upper bounded by the expression [35], [53] Pb* Z P<AW)> (2-13) d=df where prf is the total number of error bits produced by paths with a Hamming distance d from the correct path, df is the minimum free distance, and P2(d) is the probability of error in the pairwise comparison of two paths that differ in d bits and given by: Chapter 2 Background 19 P2(d) = Q where Q(.) is the Q-function defined as oo Q(z) = [-^e-y^dy. (2.14) (2.15) For the rate 1/2 convolutional code with the code generating polynomial (753, 561) used in the IS-2000 CDMA, the minimum free distance dj- is 12 and the total number of error bits produced by paths with a distance d from the correct path are given in Table 2.2 [54]. Table 2.2 Number of error bits produced by paths with a distance d from the correct path for rate 1/2 code with code generator (753,561) K df (prf, d=df dj+1, dj+19) 9 12 (33, 0, 281,0, 2179, 0, 15035, 0, 105166, 0, 692330, 0, 4580007, 0,29692894, 0, 190453145, 0, 1208999091, 0) The BER performance bound computed from (2.13) is plotted in Figure 2.5. The simulated BER and the uncoded BER are also included in the same figure. Unquantized, 6-bit and 4-bit quantized soft symbols are considered in the simulation. The decision depth of Viterbi decoding can be chosen to be 5 to 10 times the constraint length without much performance loss. The decoding depth of 96 is chosen in this thesis. The 9600 bps frame in the IS-2000 CDMA RC1, which contains 192 information bits including 8 tail bits, is used to generate the simulated BER curves. The encoding and decoding are done on a frame-by-frame basis. The BER is Chapter 2 Background 20 computed by dividing the total number of bit errors by the total number of information bits transmitted. As observed from Figure 2.5, the BER performance bound is loose in the low EjJNQ range, but is very tight in the high EjJN0 range compared to the simulated BER performance with unquantized soft symbols. It is apparent from Figure 2.5 that the convolutional code using the Viterbi decoder with unquantized soft symbols provides about 5.5 dB coding gain compared to the uncoded scheme at a BER of 10"4. It is also evident that 6-bit quantization virtually results in no performance loss and 4-bit quantization introduces about 0.1 dB loss in terms of the required EfJNg for a BER of 10"4 compared to the unquantized case. Therefore, 6-bit quantized soft symbols to the Viterbi decoder will be used in our simulations in this thesis. 2.1.2.4 Symbol Repetition After convolutional encoding, the encoded data undergoes symbol repetition. This is a simple mechanism to provide a rate match between the input data rate and the modulation symbol rate. For the IS-2000 CDMA forward traffic channel, the modulation symbol rate is kept constant at 19200 symbols per second (sps). A frame of repeated symbols for the four different data rates in the IS-2000 CDMA RC1 is graphically shown in Figure 2.6, where c i k is the Ath coded symbol in the /th frame as an input to the symbol repetition function. There are 384 modulation symbols in a frame duration of 20 ms. A frame of modulation symbol sequence is denoted as ~ (.xii>xa> • • • ' x iw) ' where/represents the frame index and ^=384. As shown in Figure 2.6, coded symbols are not repeated for the 9600 bps data rate. Each code symbol at the 4800 bps data rate is repeated once (each code symbol occurs two consecutive times). Similarly, each code symbol at the 2400 bps and 1200 bps data rate is repeated three times and seven times, respec-tively. To keep the bit energy Eb constant over the different rates, the symbol energy of 4800 bps, Chapter 2 Background Figure 2.5 BER performance of the rate 1/2 convolutional code with the code generating polynomial (753, 561) Chapter 2 Background 22 9600 bps 4800 bps 2400 bps 1200 bps 384 modulation symbols x i l "12 xi3 xi4 xi5 xi6 X i6 »i7 X i 8 M384 ci2 <=i3 ci2 Ci. c i 2 «i3 ci6 ci3 C i 2 ci2 <=i8 <=i2 Symbol Energy E s= Eb/2 E,= Eb/4 Lil92 ci96 ci48 E^Eb/8 E s= Eb/16 Figure 2.6 Symbol repetition scheme 2400 bps and 1200 bps symbol sequences is reduced to 1/2, 1/4 and 1/8 of the symbol energy of the 9600 bps symbol sequence, which is Ef/2 due to the rate 1/2 convolutional encoding. 2.1.2.5 Interleaving Signals traveling through a mobile communication channel are susceptible to fading. The error-correcting codes are designed to combat errors resulting from noisy channels. Most error-correcting codes perform well in correcting random errors. However, during periods of deep fades, long streams of successive or burst errors may render the error-correcting function useless. Interleaving is a technique for randomizing the bits in a message stream so that burst errors Chapter 2 Background 23 introduced by the channel can be converted to random errors. There are two types of interleaving techniques: block interleaving and convolutional interleaving. Block interleaving is known for its ease of implementation, whereas convolutional interleaving has performance advantages. Block interleaving is most commonly employed. An (I, J) block interleaver can be viewed as an array of storage locations which contains I columns and J rows. The data is written into the array by column-wise and read out by row-wise, as depicted in Figure 2.7. This has the effect of separating 2 adjacent symbols in the original symbol sequence by J symbols. At the receiver, the de-interleaver stores the received data in the array by row-wise and reads the data by column-wise. The minimum separation of any two errors in a burst of length B is given by S- J ' * S / (2.16) l l , B>I I Columns Write in by columns Read out by rows Figure 2.7 Block interleaver Chapter 2 Background 24 The block interleaver with a bit reversal technique [7], [55] is used in the IS-2000 CDMA standard. The bit reversal technique can be described using the following example. Suppose a 16-symbol sequence is to be interleaved, and the first symbol is assigned position 0, and the last symbol is assigned position 15. The original ordering is thus 0,1,2, 3,4, 5, 6, 7, 8, 9,10,11, 12,13,14,15. Expressing this ordering in binary format yields 0000, 0001, 0010, 0011, 0100, 0101,0110, 0111, 1000, 1001,1010, 1011, 1100, 1101, 1110,1111. Reversing the order of the bits in each binary number gives 0000, 1000, 0100, 1100, 0010, 1010, 0110,1110, 0001, 1001, 0101, 1101, 0011, 1011, 0111,1111. Converting the binary representation back to decimal form gives the order with which the symbols are read 0, 8,4,12, 2,10, 6, 14,1, 9, 5,13, 3,11, 7,15. Through observation, the minimum spacing for symbols in a burst of length B is S = 4, 5 = 2 2, 3<5<4 (2.17) 1, B>4 In the IS-2000 CDMA RC1, the interleaver for the forward traffic channel uses a charac-teristic of an (1=6, J=64) block interleaver. Using the bit-reversal block interleaving, the mini-mum-separation profile is found to be [55] Chapter 2 Background 25 "64, 32, 16, 3, B<5 B B = 7 8<5<48 = 6 (2.18) 2, 49<B<96 \, B>91 For the conventional (1=6, J=64) block interleaver, the minimum spacing for symbols in a burst of length B is It is seen that the bit reversal technique reduces the minimum separation for B=6 while increases the separation for B>6. 2.1.3 Multiple Access After the baseband signal has been channel coded for error control, the signal is further transformed in order to allow multiple access by different users. Multiple access refers to the sharing of a common resource in order to allow simultaneous communications by multiple users, and this common resource is the RF spectrum. Figure 2.8 depicts the three common multiple access schemes: FDMA, TDMA and CDMA. In the traditional FDMA scheme, each individual user is assigned a particular frequency band in which transmission can be carried out. A portion of the frequency spectrum is divided into different channels as shown in Figure 2.8 (a). Each users' signal is lowpass filtered and modulated onto an assigned carrier frequency of a particular channel. This way, multiple users can simulta-neously share the frequency spectrum. In TDMA, each user is assigned a different time slot in which to transmit, as shown in Figure 2.8 (b). In this case, the division of users occurs in the time B<6 B>6 (2.19) Chapter 2 Background FDMA TDMA CDMA (C) Frequency Figure 2.8 Three different multiple access schemes: (a) FDMA, (b) TDMA, and (c) CDMA Chapter 2 Background 27 domain. In CDMA, each user's narrowband signal is spread over a wider bandwidth. This wider bandwidth is normally substantially greater than the minimum bandwidth required to transmit the information. Each user's narrowband signal is spread by a different wideband code. Each of the codes is orthogonal to one another, and channelization of simultaneous users is achieved by the use of this set of orthogonal codes. All the spread wideband signals are added together to form a composite signal, and the composite signal is transmitted over the air in one common frequency band (see Figure 2.8 (c) ). The receiver is able to distinguish among the different users by using a copy of the original code. The receiver sorts the desired user out of the composite signal by correlating the composite signal with the original code. All other users with codes that do not match the code ofthe desired user are rejected. There are many different orthogonal codes such as Gold codes, Walsh codes, etc. Walsh codes with a set of 64 binary orthogonal sequences are used in the IS-2000 CDMA RC1. These sequences are orthogonal to each other, and they are generated by using the Hadamard matrix [55]. In the absence of multipath, the Walsh codes provide perfect orthogonal channelization for users within the same cell. However, the orthogonality breaks down in a multipath mobile environment where multipath delays introduce inhomogenous auto-correlation and cross-correla-tion characteristics. Furthermore, not all of the Walsh sequences have wideband spectral charac-teristics as desired in spread spectrum systems. These undesirable effects are mitigated by concatenating Walsh sequences with PN sequences in the IS-2000 CDMA standard [7]. The PN sequences used in the IS-2000 CDMA system are m-sequences generated by 15 linear shift registers (see [7] and [55] for detail). The resulting concatenated Walsh/PN codes provide orthog-onality between multiple users within the same cell in a single path propagation environment, Chapter 2 Background 28 while reducing the inhomogenous behavior of Walsh cross-correlation due to non-zero time delays in a multipath environment. In addition, the concatenation scheme reduces interference among users that use the same Walsh code in different cells. 2.1.4 Modulation and Channel As shown in Figure 2.1, the modulator serves as the interface that accepts a digital information sequence at its input and outputs a set of corresponding waveforms. Similarly, the demodulator at the receiving end serves as the interface between the waveform channel and the digital channel decoder. Hence the demodulator accepts waveforms at its input, processes the waveforms, and delivers to the channel decoder a sequence of digital symbols (hard-decision decoding) or discrete-time symbols (soft-decision decoding). Quadrature Phase Shift Keying (QPSK) modulation is employed in the IS-2000 CDMA standard. It is assumed that coherent demodulation and perfect carrier recovery can be achieved at the receiver. Techniques for carrier recovery and coherent QPSK demodulation are well documented in literature (see, for instance, [13] and [35]). In this thesis we have considered three different, widely accepted, channel models, namely: the Additive White Gaussian Noise (AWGN) channel, the frequency-flat Rayleigh fading channel and the frequency-selective Rayleigh fading channel. The first is a simple, standard channel model, in which the received signal is affected only by background noise. The others are more realistic channel models for cellular communication systems. Due to signal scattering and reflection, multipath interference occurs when the transmitted signal simultaneously follows many different paths to the receiver, arriving along each path with different attenuations and propagation delays [64], [65]. If the delay spread of the different paths is relatively small Chapter 2 Background 29 compared to the chip duration, the channel is categorized as frequency-flat fading. On the other hand, if the delay spread of the different paths is greater than the chip duration, the channel is said to undergo frequency-selective fading. In this thesis, the one-path Rayleigh fading and the three-path Rayleigh fading channels standardized in the IS-2000 CDMA specification [66] are used to model the frequency-flat and frequency-selective Rayleigh fading channels, respectively. In other words, the one-path and three-path Rayleigh fading channels are used interchangeable with the frequency-flat and frequency-selective Rayleigh fading channels. The AWGN channel and the multipath Rayleigh fading channels will be discussed in Chapter 3 and Chapter 4, respectively. 2.2 V a r i a b l e - R a t e D a t a T r a n s m i s s i o n i n D S - C D M A The link capacity of a DS-CDMA system is mainly limited by the multiple access interfer-ence from other users transmitting at the same carrier frequency in the same and adjacent cells [15]. The primary reason for variable-rate data transmission is to effectively reduce the mutual interference, and as a result increase the link capacity of the DS-CDMA systems by making use of the nature of variable-rate data sources in wireless multimedia applications, such as voice, image, video, fax, and internet data transmission. In the case of voice transmission, for example, it is possible to reduce the transmission rate when there is no voice, and thereby substantially reduce interference to other users. Since the level of other user interference directly determines the link capacity, the link capacity can be increased by two times because voice activity is, on average, less than half of the time in a two-way conversation [14], [16]. One of the other advantages with the variable-rate transmission is that average mobile station transmit power is reduced and thus the talk time is increased. The system model of a variable-rate DS-CDMA communication system is shown in Chapter 2 Background 30 Figure 2.9. In multimedia-type services, the data rate changes from time to time or frame by frame during communications. Suppose that there are M discrete data rates to be supported. M is a positive integer number. We denote a particular data rate as f" bits per second (bps), where m=l, 2,..., M. It is assumed that data rates are arranged in a descending order, that is, r'>r2>...>rM. At first, the input data at rate r™ is convolutionally encoded using a rate-A/w code for forward error correction, k and n are positive integers and k<n. After convolutional encoding, the encoded data undergoes symbol repetition, which repeats the coded symbols when the input data rate is lower than r1. The number of repeated symbols is 2m~' corresponding to rate r™, where m=l, 2,..., M. After such symbol repetition, the symbol rate is rm-2m~1 symbols per second (sps). The output k of the symbol repetition block is referred as the modulation symbol stream. For a continuous transmission as in the IS-2000 forward traffic channel, the modulation symbol rate is kept constant. The combination of convolutional encoding and symbol repetition can be used to provide various degrees of error protection, and a rate matching mechanism between the input data rate and modulation symbol rate. The signal to noise ratio (SNR) or bit energy to noise spectral density ratio, denoted by EjJNt, is the figure of merit of a well-designed digital receiver for achieving a specified frame error rate (FER). To maintain a particular FER, EfJNt needs to be kept same for various rates. In the DS-CDMA communication system, therefore, the symbol energy denoted by E™ corresponding to the data rate r"1 is decreased by a factor of j2^m~^ relative to the bit energy Eb. As we can see, the rate information is embedded in the transmitted signal by the combination of convolutional code, symbol repetition and symbol energy. After symbol repetition, the data is block interleaved to combat fading. Then, the interleaved data is quadrature spread and QPSK modulated. A QPSK spread spectrum signal is passed through a Chapter 2 Background 31 commvinication channel. The channel and receiver models are described in Chapter 3 and Chapter 4. The output of the rake receiver is block de-interleaved. Finally, the transmitted data rate is blindly detected, and the information data is decoded and passed to the data sink. I-channel PNCode a'k(t) Variable-Rate Data Convolutional Encoder Symbol Repetition i I T Block Interleaver Data Sink Rate and i Block De- — Rake Data Detection interleave Receiver Q-channel PN Code a%(t) Figure 2.9 Variable-rate data transmission in DS-CDMA The forward traffic channel based on the IS-2000 CDMA is used to illustrate the concept of the joint rate detection and data decoding algorithm in this thesis. The forward traffic channel frame structure for Radio Configuration 1 (RC1) is shown in Figure 2.10 [7]. There are M=4 input data rates in the RC1. The input data rates include r/=9600 bps, ^=4800 bps, r5=2400 bps and Chapter 2 Background 32 9600 bps Frame 4800 bps Frame 20 ms frame duration Fy=192 bits Li=172 Information Bits 2^=96 bits L2=80 Information Bits 12 8 8 F T 8 F T 2400 bps Frame 1200 bps Frame F3=48 bits L3=40 Information Bits F =^24 bits Z.4=16 Information Bits Notation: F - Frame Quality Indicator T - Encoder Tail Bits T Figure 2.10 Frame structure for Radio Configuration 1 r*=1200 bps. A frame quality indicator or CRC bits are appended to the input information data according to [7], [66]. The rate-1/2 convolutional code with the generating polynomial (751,563) is used. In order to put the trellis state to the zeroth state, 8 tail bits are padded to each frame prior to the convolutional encoding. Due to the rate-1/2 convolutional encoding and the symbol repeti-tion, the modulation symbol rate is constant at 19200 bps, and the symbol energy Ef correspond-ing to the data rate r™ is reduced by a factor of 2m relative to the bit energy Eb. For example, the Chapter 2 Background 33 symbol energy of the r/=9600 bps frame, denoted by E* , is Efjl, and the symbol energy of the r2=4800 bps frame, denoted by E2, is EjJA, which is only half that of the r/=9600 bps frame and so on. The symbol energy and chip energy for each frame rate is given in Table 2.3, where Eb is the energy per bit and G is the spreading gain which will be defined later in this section. As shown in Figure 2.9, a frame of input bit sequence at rate rt is denoted by where the subscript / represents the frame index and rt - rm>, mi e {1, 2, 3, 4} denotes the input data rate as given in Table 2.3. As defined in Table 2.3, either rm> or mi can be used to represent the input data rate, in other words, rm> and mi are interchangeable in notation. Given a frame duration of Tf=20 ms, the length of input bit sequences corresponding to the four rates, denoted as Fj, F2, F3, and F4, is 192, 96, 48 and 24, respectively (see Figure 2.10). The length of information bit sequences corresponding to the four rates, denoted as Lh L2, L3, and L4, actually is 172, 80, 40 and 16, respectively. The modulation symbol sequence is always ^=384 in length given a frame duration of Ty=20 ms. The coded symbol sequence corresponding to the input bit sequence I, at rate r, is denoted by Ci = (c • c -2,..., c^F)) > where cik is the Ath coded symbol in the /th frame and takes a value cik = ±1 k = 1, ...,2F, (2.20) where Fe {F{,F2,F3,F4}. Let Xt - (xn,xi2, ...,xiN) represent a modulation symbol sequence, where xik is the Ath modulation symbol in the /th frame and takes a value xik = ±1 k = \,...,N. (2.21) Chapter 2 Background 34 Table 2.3 Symbol energy and chip energy corresponding to data rate Rate Frame Rate Symbol Chip Energy Notation m r™ (bps) Energy Ef E« 1 9600 EJ2 EJ2G 2 4800 E,/4 Ef/4G 3 2400 E,J8 Eb/8G 4 1200 Ef/16 ^16G Due to the symbol repetition, the relation between the coded symbol sequence C, = (c n , ci2,c,(2/r)) and the modulation symbol sequence X( = (xn,xi2, ...,xiN) is: V - ' - ' - y ) = °ik k = h -,2Fmi; j = °' •••'2m'"1-1' (2-22) where m,- e {1,2,3,4}. The output of the interleaver is denoted as Ut, which is an interleaved version of Xt. For the desired user, the transmitted QPSK direct sequence spread signal corresponding to the modulation symbol sequence Xt = (xn, xi2,...,xiN) can be written as: s(t) = X(t){Pl(t)cos(2nfct) +/7g(/)sin(27t/cO}, (2.23) where + oo N X ^ = X I jE»*ikPT,(t-*T,) , (2.24) i = -oo k = 1 + 00 Pi(0 = E ajPTe(t-iTe), (2.25) i = -oo Chapter 2 Background 35 and + 00 PQ& = I oQPT{t-iTc). (2.26) i = - O O where { } is the modulation symbol sequence of symbol duration 7^ , and {af }and {a®} are the PN code sequences of chip duration Tc in the I and Q channels, respectively. {xik}, {af} and {aQ} are modeled as mutually independent and identically distributed (i.i.d.) random sequences and take a value of+1 and -1 with equal probability. The symbol pulse function pT (/) is unit in [0, Ts] and zero elsewhere. pT (t) is the impulse response of the chip pulse-shaping filter, which is defined in [7] for the IS-2000 CDMA system. The spreading gain of the system is defined as G = T/Tc. (2.27) In the RC1 of IS-2000 CDMA, the spreading gain G is 64. E™ is the chip energy corresponding to the frame at rate r"7. The relation between the chip energy E™ and the bit energy Eb is: = me {1,2,3,4}. (2.28) c 2mG The carrier frequency fc is assumed to be sufficiently large for the double carrier frequency terms to be safely neglected. 2.3 O v e r v i e w o f B l i n d R a t e Detec t ion T e c h n i q u e s In recent years, several BRDAs have been proposed for variable-rate data transmission systems in DS-CDMA cellular communication systems. They can be classified into two catego-ries: pre-decoding BRDA and post-decoding BRDA. A pre-decoding BRDA performs rate Chapter 2 Background 36 detection prior to channel decoding. The main motivation of the pre-decoding BRDA is to detect the data rate before convolutional decoding and perform Viterbi decoding of a received frame only once. Since only one time Viterbi decoding is required, the system complexity is reduced. The BRDAs proposed in [19]-[22] fall into this category. They consist of estimating the data rate by exploiting the symbol repetition property. Simulation results in [19]-[22] show that these pre-decoding BRDAs provide marginal performance for the IS-95 CDMA systems [6] in terms of FER due to the fact the symbol repetition patterns can be severely distorted by channel noise and fading. A post-decoding BRDA performs rate detection after the channel decoding of all possible rates. The BRDAs proposed in [23], [24] belong to this post-decoding BRDA category. In [23] and [24], all four possible frame rates are decoded using the Viterbi algorithm, and the decoded data of the four rates are re-encoded for calculating the Symbol Error Rate (SER) between the received symbols and the re-encoded symbols. Then, the SER is used to detect the transmitted frame rate. The BRDA proposed in [23] is often referred as the conventional BRDA due to the fact that it is proposed for use in the IS-95 CDMA system by Qualcomm [6]. Since the SER can vary widely with the channel SNR, the SER can be very unreliable in low SNR scenarios. It is found that with this post-decoding BRDA, the FER performance for lower rate frames degrades significantly compared to that in the ideal rate detection case where the transmitted frame rate is known to the receiver (see the simulated results in Chapter 3 and Chapter 4). This degradation is due to high rate detection errors for the lower rate frames. A hybrid of the pre-decoding BRDA in [19] and the post-decoding BRDA in [23] is proposed in [25] for complexity reduction compared to the post-decoding BRDA. Most of the above BRDAs (see, for example, [18]-[20], [23], [25]) have been proposed for use in the early DS-CDMA communication system (IS-95) where voice transmission is the Chapter 2 Background 37 primary application. For voice transmission, relatively high FER, say five percent, is tolerable due to the fact that parameter interpolation and error concealment techniques can be applied to voice reconstruction for voice quality improvement when frame errors occur. For the 3G DS-CDMA cellular communication systems, however, a low FER is required for high quality multimedia services. The BRDAs used for the IS-95 DS-CDMA standard can hardly meet the new require-ments in the 3G DS-CDMA systems. Investigation of more reliable BRDAs for the variable-rate data transmission in the 3G DS-CDMA cellular communication systems is an active research topic. Two well-known BRDAs, namely, the pre-decoding BRDA in [19] and the post-decoding BRDA in [23], will be used for performance comparison with our proposed algorithm in this thesis. A brief description of these two BRDAs is provided in the following. 2.3.1 P r e - d e c o d i n g B l i n d R a t e Detec t ion As described above, several pre-decoding BRDAs were proposed in the past (see, for example, [18]-[20], [23], [25]). The BRDA proposed by Cohen [19], named as Cohen's BRDA, provides relatively superior performance and is easy to implement. A more detailed description of Cohen's BRDA using the IS-2000 CDMA RC1 is given in the following. In the IS-2000 CDMA RC1 as described in the last section, there are four variable data rates, namely, 9600 bps, 4800 bps, 2400 bps and 1200 bps, which are denoted as r1, r2, r3 and r4, respectively. Assume that the de-interleaved soft symbol sequence after the rake receiver (see Figure 2.9) is Y=(yj, y% y^f), where JV=384 is the frame length and is the kth soft symbol, where k = 1 , N . The value of yk is an integer in the range of [-7, +7]. Note that we shall Chapter 2 Background 38 drop the frame index for convenience since the rate detection is done on a frame-by-frame basis. The main idea in Cohen's BRDA is to estimate the data rate by exploiting the symbol repetition property. For example, a 2-tuple of received symbols are added constructively if r2 is sent, a 4-tuple of soft symbols are added constructively if r is sent, a 8-tuple of soft symbols are added constructively if r3 is sent. Based on the tuple structure, the quantities L E M , U E M , EM for a rate hypothesis r™, m=\,2, 3 are first computed as follows: 1. Compute LE,, UEX, E X : N/2 (a)^ = £ \y2k-i+y2k\> k=\ N/2 k= l N/2 (C)UEX = 2h*-J + hJ-*= i 2. Compute L E 2 , UE2, E 2 : N/4 (a) E2 = Y + ^ 2 * - 2 +y*k-1 +y2k\> k= 1 N/4 (b) LE2 = Y\\y*k-3+y2k-2\-\y*k-i+y2k\\> k=l N/4 (c) UE2 = £ | y 4 £ _ 3 + 3>2Jt_2| + h*-1 +y2k\ • k=\ 3. Compute L E 3 , UE3, E 3 : Chapter 2 Background 39 0) £ 3 = X K - 7 + ^ - 6 + ^ - 5 + ^ - 4 + ^ - 3 + ^ - 2 + ^ - 1 + ^ 1 k = 1 N/S (b) LE3 = £ | |y 8 *-7 + J '8*-6 + y*k-5 + yu-4\-\ysk-3 + ysk-2 + ysk-\ + yik\ k=i N/S (C) UE3 = £ ^ - 7 + ^ - 6 + ^ - 5 + ^ - 4 ! + \y»k-3+y&k-2+ysk-*= 1 4. Compute the ratios K j , K 2 , K 3 : (a) K j (b) K 2 (C) K 3 = £ 1 - LEX UEX -LEL' E2- -LE2 UE2 -LE2 E3- LE3 UE3 -LE3 For a given transmitted rate, the following observations can be made: 1. For w= 1,2,3, we have L E M < EM < U E M , that is, L E M is a lower bound and £/£m is an upper bound on the quantity E M . Hence, Km e [0,1 ]. 2. Given r1, the signs of the received symbols are approximately random. Thus, the expected values of K j , K 2 and K 3 are 0.5. 3. Give r2, the signs of every 2-tuple of symbols are approximately random. Then, the expected value of K j approaches 1, and the expected values of K 2 and K 3 are 0.5. 4. Give r , the signs of every 4-tuple of symbols are approximately random. Then, the Chapter 2 Background 40 expected values of Kj and K 2 approach 1, and the expected values of K 3 are 0.5. 5. Give r4, the signs of every 8-tuple of symbols are approximately random. Then, the expected values of K j , K 2 and K 3 approach 1. Cohen's BRDA was motivated by the above observations, and was fine-tuned by extensive simulation. Figure 2.11 depicts the pseudcode of Cohen's BRDA. Simulation results of Cohen's BRDA in the AWGN and multipath Rayleigh fading channels will be given in Chapter 3 and Chapter 4. 2.3.2 P o s t - d e c o d i n g B l i n d R a t e Detec t ion The post-decoding BRDA proposed by Butler in [23], named Butler's BRDA, is the best known BRDA due to the fact that it is proposed for use in the IS-95 CDMA system by Qualcomm [6]. Butler's BRDA is also included in this thesis for comparison reasons. The block diagram of Butler's scheme is shown in Figure 2.12. As shown in Figure 2.12, the input soft symbols are decoded using the Viterbi algorithm four times (four paths as shown in Figure 2.12), each time testing one of the four different frame rate hypotheses. For the hypothesis of 9600 bps, there is no symbol combining. For the hypothesis of 4800 bps, two to one symbol combining is performed. For the hypothesis of 2400 bps, four to one symbol combining is performed. For the hypothesis of 1200 bps, eight to one symbol combining is performed. The four streams of Viterbi decoded data are re-encoded for calculating the SER between the received symbols and the re-encoded symbols. The smaller the SER, the more likely the hypothesis. Thus, the minimum SER is used to determine the transmitted rate. Simulation results of Butler's BRDA in the AWGN and multipath Chapter 2 Background Rayleigh fading channels will be given in Chapter 3 and Chapter 4. if (LEl < 400) AND (K, < 0.6), return rl if (K 3 > 0.8), return r4 if (K 3 ^0.7) 1. if (K 2 £ K 3 + 0.07), return r3 2. if (K, + K 2 < 1.05), return rl 3. if ( K , > K 3 ) AND (K 2 < 0.62), return r2 4. return r4 if (K2>0.73), return r3 if (K2>0.67) 1. if (K, > K 2 + 0.05), return r2 2. if (K 2 < 0.69) AND ( K T < 0.55), return rl 3. return r3 if (K2>0.62) 1. if (K, < 0.6), return r1 2. if (K, > K 2 + 0.07), return r2 3. return r3 if ( K j > 0.64), return r2 return rx Figure 2.11 Cohen's blind rate detection algorithm Chapter 2 Background 42 Convolutionall Encoder 8-Symbol Combiner Viterbi Decoder Convolutional Encoder Hard-Decision Rate Detection Figure 2.12 Butler's blind rate detection algorithm 43 Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the AWGN Channel The objective of this chapter is to present a novel joint rate detection and data decoding algorithm for variable-rate data transmission in the Additive White Gaussian Noise (AWGN) channel. The system model in the AWGN channel is described in Section 3.1. Based on the criterion of maximizing the joint a posteriori probability of the transmitted data rate and the information bit sequence given a frame of received symbols, the novel joint rate detection and data decoding algorithm is derived in Section 3.2. Simulation results are presented in Section 3.3. Finally, some conclusions of this chapter are given in Section 3.4. 3.1 System Model in the AWGN Channel The system model for a variable-rate DS-CDMA communication system in the AWGN channel is shown in Figure 3.1, where all blocks except that of the channel, the rake receiver, and the rate and data detection are described in Section 2.2. The AWGN channel case is considered in this chapter. Multipath Rayleigh fading channels will be considered in the next chapter. Assuming a perfect carrier recovery, the received signal for the desired user in the AWGN channel can be written as: r(f) = X<t){Pl(t)cos(2Tifct) +pe(Osin(27t/cO} + "(0, (3-1) where + 00 N X ^ = E E ^ x i k P T p - * T s ) , (3.2) i = -oo k = 1 where E™' is the chip energy, {xik} is the modulation symbol sequence, pj(t) and PQ(0 are the Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 44 I-channel <\ „ „ R . C0S (Z7l / / ) PNCode ai(t) I C ' Variable-Rate Data Convolutional Encoder Symbol Repetition i 3 Q-channel PN Code a%(t) AWGN —•{+) n(t) ^ Data Sink i Rate and Data Detection Y ; Rake Receiver r(f) Figure 3.1 System model in the AWGN channel PN sequences for I and Q channels, respectively, PT (t) is a pulse function of symbol duration Ts as defined in Section 2.2, and n(t) is an AWGN representing the background noise. It is assumed that the conventional rake receiver which is matched to the reference user's CDMA spreading code is used [35]. In the AWGN channel case, only one active finger is required. The output of the rake receiver is denoted by Yt = (yn^a, • • • » > ' i w ) corresponding to the modulation symbol sequence Xi = (xn,xi2, ...,xjN). Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 45 For a DS-CDMA cellular communication system in the AWGN channel, there are two noise sources: one is the multiple access interference (MAI) and the other is the background noise. It is well known that the MAI can be approximated as a Gaussian process based on the cen-tral limited theorem [15], [67], [68]. It is found that the Gaussian approximation is quite accurate even for a small number of users when the BER is greater than 10"5 [68]. In the AWGN channel, therefore, we can write the rake receiver output as: yik = JOE™' xik + nik k = 1,2, ...,N, (3.3) where G is the spread gain, E™' is the chip energy corresponding to input data rate mh and nik is an AWGN with the two-sided power spectral density of NJ2, which represents both the MAI and the background noise. Using Table 2.3, we can rewrite (3.3) as: yik = jE~nr> xik + nik k = 1,2, ...,N. (3.4) The probability density function (pdf) of the demodulated symbol sequence = Cy/l'^ 12' - ' ^ i w ) conditional on rate mt and information bit sequence denoted by piY^m^ It), is equal to p(F ;|X-) because convolutional coding and symbol repetition are deter-ministic processes. Since nik is a memoryless Gaussian random variable, p(Y^m{,I{) can be expressed as p(Yi\mijt) = n . T ^ e x p v (3.5) The pdf in (3.5) will be used to derive the joint rate detection and data decoding algorithm in the next section. Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 46 3.2 J o i n t R a t e D e t e c t i o n a n d D a t a D e c o d i n g A l g o r i t h m Since rate detection and data decoding is done on a frame-by-frame basis, we shall drop the frame index / for convenience in the remainder of this chapter. The joint rate detection and data decoding algorithm is derived based on the criterion of maximizing the joint a posteriori probability of the transmitted data rate and the information bit sequence, given a frame of received symbols. In other words, given a received symbol sequence Y out of the rake receiver, we want to choose data rate m and data sequence I for which the joint a posteriori probability, denoted by p(m, I\ Y), is maximized over all frame rates and input information sequences. Using Bayes' rule, we can write p(m, I\ Y) as , r i _ P(Y\m, r)P(I\m)P(m) p(m,I\Y)=t-^-i ' 1* V w , / . (3.6) p(Y) It is assumed that different types of data may be supported in the IS-2000 CDMA system and the four rates in the IS-2000 CDMA RC1 are equiprobable a priori. Frame rate detection using rate a priori probability for voice application will be investigated in detail in Chapter 5. Based on the fact that the pdf of the received symbol sequence Y is independent of the decoding process, we need to maximize: p(Y\m,r)P(I\m) \fm,I. (3.7) Due to the fact that I is a random bit sequence of length L m (see Figure 2.10), P(I\m) = \/2L*. (3.8) Substituting P(I\m) and (3.4) into (3.7) and taking the logarithm yield the following form: Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 47 To find the maximum in (3.9), we are only concerned with the differences among all possible symbol sequences. The first and second terms in (3.9) are common given the same received sym-bol sequence and are subtracted from each other during comparison. Equivalently, one needs to maximize the following function: N N 2 jEb i Eb 7 W A Tm Z - TmN Z c " Z > § 2 • NtH2mk±l 2mN, ^ (3.10) Using the fact that x\ = 1, we define a joint rate detection and data decoding metric (called joint metric hereafter) as: N E JV E JM(m,X) = 2- J>Yykxk-*L-±-Lm\og2. Nt^2m nmM mo k= 1 2mNt (3-11) To find the rate m and symbol sequence X which maximize the joint metric (JM), we need to search all possible rates and modulation symbol sequences. Using the symbol repetition property as given in (2.22), we can write the JM for each of the rate hypotheses as follows: Forthecaseof™=l, JMX = 1 S £ ^ - f ^ - Z , ^ . (3.12) N/2 f 1 For the case of m=2, JM2 = 1 k=lKj=0 (3.13) N/4 f 3 For the case of m=3, JMi = A T Z / Y Z I Z > « - y ' k= 1 )' = 0 c k - - - - L 3 l o g 2 , (3.14) • 7V/8 f 7 \ For the case of m=4, JM4 = 1 & £ I £ yu_j ' A = l S =  o (3.15) Given a rate hypothesis m, say m=l, the second and third terms in (3.12) do not change and will Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 48 N, J2m be cancelled out during comparison. By scaling by — I—, the joint metric in (3.12) is simplified 2 V Eb N to the accumulated path metric of the Viterbi algorithm JMX = ^ ykck as given in (2.12). k= l Therefore, we can use the Viterbi algorithm to find the maximum likelihood sequence for a given rate hypothesis. The second and third terms of the joint metric defined in (3.11) are introduced due to variable symbol energy and variable information bit length in variable-rate data transmission. The introduction of the joint metric with these two terms is the key to this joint rate detection and data decoding algorithm. For traditional fixed rate transmission, there is only one rate. As shown above, the joint metric in (3.11) is simplified to the accumulated path metric as given in (2.12). The joint rate detection and data decoding algorithm is shown in Figure 3.2. The symbol combiner is the reverse operation for the symbol repetition at the transmitter. As shown in (3.12) to (3.15), there is no symbol combiner for the rate hypothesis m=\, while 2-symbol, 4-symbol and 8-symbol combiners are required for rate hypotheses m=2,3,4, respectively. Note that DMm in Figure 3.2 is defined as follows: D M * = 2^Nt + L J ° g 2 m = h 2 , 3 , 4 - ( 3 ' 1 6 ) In summary, the joint rate detection and data decoding algorithm is described in the following three steps: 1. Given each of the four rate hypotheses, search for the maximum likelihood (ML) sym-bol sequence in that hypothesis using the Viterbi algorithm. This will give us four Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 49 t Demodulated Soft Symbol Viterbi Decoder 2-Symbol Viterbi Combiner Decoder 4-Symbol Combiner! Vi terbi Decoder 8-Symbol Vi terbi Combiner Decoder JM. DM 1 / , DM, JM, JMi DM. 3 / . DM. JMA Selector Decoded Frame Detected Rate Figure 3.2 Block diagram of joint rate detection and data decoding algorithm in the AWGN channel accumulated path metrics like the first terms in (3.12) to (3.15) and four ML symbol sequences or decoded bit sequences, which are denoted by Im , where m=l,2,3,4. 2. Calculate the four joint metrics, JMm, m=l,2,3,4, defined in (3.12) to (3.15). 3. Choose the rate hypothesis with the maximum joint metric among the four joint metrics and output the corresponding decoded frame of the chosen rate. In Figure 3.2, the detected rate m is defined as m = max JMm and the decoded frame / is given as i = h As seen from (3.11), the bit energy Eb and the total noise power density Nt are required in Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 50 the joint rate detection and data decoding algorithm. In the IS-2000 CDMA standard, the coded forward link data is punctured with power control symbols at the full rate power level or Efjl (see Table 2.3). Thus, the bit energy Eb can be conveniently estimated from these power control symbols. The base stations also broadcast a pilot signal which can be used to estimate the noise power density Nt. Some detailed description of Eb and Nt estimation techniques are given in [73]-[76], [102], [103]. In the IS-2000 CDMA standard, it is required that Eb and N, be estimated for the forward traffic channel power control. In other words, an estimation of Eb and Nt is already available. The proposed joint algorithm makes use of the estimated Eb and Nt for rate detection and data decoding. Throughout this thesis we assume that an estimation of the bit energy Eb and the interference power spectral density Nt is available. However, we will investigate the system performance degradation due to EbINt mismatch in the following section. 3.3 S i m u l a t e d R e s u l t s i n the A W G N C h a n n e l In this section, we describe and present the results of a software simulation of the DS-CDMA system with variable-rate data transmission shown in Figure 3.1, where the blind rate detection and data decoding block is substituted by the joint rate detection and data decoding block shown in Figure 3.2. The IS-2000 forward traffic channel system with Radio Configuration 1 (RC1) is used to simulate the performance of the joint rate detection and data decoding algorithm (JRDDDA) proposed in the previous section. FER is commonly used to measure the overall performance of a receiver. In variable-rate data transmission systems, frame errors include two events: one is that a rate detection error, or a false rate detection occurs and the other is that the decoded frame has one or more bit errors even Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 51 when the detected frame rate is correct. Both FER and false rate detection rate (FRDR) are used to measure the performance of our proposed JRDDDA. The definition of a false rate detection is that the detected rate is different from the transmitted one. When a false rate detection occurs, the number of received bits is different from that of the transmitted bits. That is, when a false rate detection occurs, the received frame is in error. The reason of using the FRDR measure is that a false rate detection may cause more severe damage than bit errors in some applications like speech transmission. For instance, some annoying noise or clicks would be synthesized by the vocoder from a whole frame of erroneous data introduced by a false rate detection. For comparison, we include the FER and FRDR performance of Cohen's BRDA and Butler's BRDA as described in Section 2.3. As a reference, we also include the ideal rate detection scheme where the transmitted frame rate is known to the receiver. For a fair comparison, Cohen's BRDA, Butler's BRDA and the ideal scheme are running in parallel to the proposed JRDDDA, as shown in Figure 3.3. In other words, the FER and FRDR performance of all four schemes is based on the same demodulated symbol sequence out of the rake receiver. The Monte Carlo (MC) technique [99] is used for estimating the FER and FRDR of the DS-CDMA system with variable-rate data transmission shown in Figure 3.1. The input rate and corresponding bit sequence are randomly generated. Each detected rate and the corresponding decoded bit sequence are compared to the transmitted rate and bit sequence to compute the FER and FRDR, respectively. If the detected rate is different from the transmitted one, a rate detection error is counted and a frame error is counted as well. If the detected rate is correct but there is one or more bit errors, only a frame error is counted. The simulated FER is estimated by dividing the number of frame errors by the total number of frames transmitted. Similarly, the simulated FRDR Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 52 Rake Receiver JRDDDA Compute • FER and FRDR Cohen's Compute BRDA FER and FRDR Butler's Compute BRDA FER and FRDR Ideal Compute Scheme FER Figure 3.3 Simulation setup for different rate detection algorithms is estimated by dividing the number of rate errors by the total number of frames transmitted. In the simulation, an adequate number of error events are generated in order to achieve a 95% confidence interval of ±10 % of the average FER or FRDR. 3.3.1 Simulation System The purpose of this subsection is to provide a detailed description of our simulation sys-tem. In addition, a benchmark of our simulation system in terms of FER is given for verifying our implementation of the IS-2000 CDMA transmitter, the AWGN channel, and the rake receiver. Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 53 A commercial simulation software package, Signal Processing WorkSystem (SPW) [83], is used to model the IS-2000 CDMA forward link system [7]. A block diagram ofthe IS-2000 CDMA forward channels in Radio Configuration 1 (RC1) [7] is shown in Figure 3.4 and Figure 3.5. In the IS-2000 CDMA RC1, the forward channels consist of a pilot channel, a synchroniza-tion channel, up to seven paging channels, and up to fifty five forward traffic channels. The pilot channel is used primarily as a coherent phase reference for demodulating the other channels. The pilot channel is easily acquired by the mobile receiver because it has only the quadrature PN codes (no data modulation). The synchronization channel is used to acquire system synchroniza-tion information conveyed by the sync channel message. This message identifies the particular transmitting base station and conveys long PN code synchronization information. The paging channels are used to alert the mobile to incoming calls, to convey channel assignments, and to transmit system overhead information. In our simulation system, a pilot channel, a sync channel, a paging channel, and a traffic channel are implemented. In addition, an Orthogonal Channel Noise Simulator (ONCS) is imple-mented to simulate the interference from the users on other orthogonal channels [66]. Each of these channels is covered by a channel specific Walsh code of length 64, denoted by Wk, k - 0 , 1 , 6 3 . The Walsh-covered symbol sequence of each channel is added together to form a composite CDMA signal, which is then quadrature-spread by the I-channel and Q-channel PN sequences and is QPSK modulated, as shown in Figure 3.5. Note that the traffic channel signal is the desired signal in our simulation, which is described in detail below. The detailed block diagram of a forward traffic channel of the IS-2000 CDMA RC1 is shown in Figure 3.6. The forward traffic channel frame structure for the IS-2000 CDMA RC1 is Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 54 Pilot Channel Data allOs Pilot Sync Channel Data Convolutional Symbol Block Interleaver Encoder Repetition 4. Sync Paging Channel Data Convolutional Symbol Encoder Repetition Paging channel k long code mask -Block Interleaver A Long Code Generator 4 Paging Traffic Channel Data Convolutional Symbol Encoder Repetition User / long code mask Power control bits Block Interleaver i MIDd - Traffic Long Code Generator OCNS Generator • OCNS Figure 3.4 CDMA forward channels Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 55 Pilot Sync Paging Traffic OCNS I-channel PNCode aUt) Q-channel PNCode ag(t) cos(2n/c0 Pulse-Shaping Filter Pulse-Shaping Filter 1 • 0 -i X •in(2n/c0 Figure 3.5 Complex PN spreading and QPSK modulation shown in Figure 2.10. As shown in Figure 2.10 and Figure 3.6, the supported source data rates include 8600 bps, 4000 bps, 2000 bps and 800 bps, corresponding to 172, 80, 40 and 16 informa-tion bits per 20 ms frame, respectively. A frame quality indicator or CRC bits are appended to the input information data according to [7]. The rate-1/2 convolutional code with the generating polynomial (751,563) is used. In order to put the trellis state to the zeroth state, 8 tail bits are padded to each frame prior to the convolutional encoding. After the rate-1/2 convolutional encoding, the data rates become 9600 bps, 4800 bps, 2400 bps and 1200 bps, which are commonly referred as the transmitted data rates. The code symbol repetition rate on the forward traffic channel varies with data rate. Code symbols are not repeated for 9600 bps data rate. Each code symbol at the 4800 bps data rate occurs two consecutive times. Similarly, each code symbol Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 56 at the 2400 bps and1200 bps data rate occurs four times and eight times, respectively. After the symbol repetition, the modulation symbol rate is constant at 19200 bps regardless of the input data rate. In a 20 ms frame duration, there are ^=384 modulation symbols. For the AWGN channel, there is no need for block interleaving. In compliance to the IS-2000 CDMA standard, the bit reversal interleaver given in Subsection 2.1.2.5 is implemented. The interleaved frame is then scrambled with the long code [7] and punctured with power control bits. Every power control bit replaces two consecutive traffic symbols. The scrambled/punctured modulation sequence is covered by an orthogonal Walsh code of length 64, resulting in a spreading gain G=64. Finally, the Walsh-spread sequence is complex PN spread and QPSK modulated as shown in Figure 3.6. The complex AWGN samples in Figure 3.1 are generated using the built-in Gaussian noise generator from the SPW library. The Gaussian noise generator is implemented based on the widely-used Box-Muller method. The conventional matched-filter rake receiver [35] is shown in Figure 3.7. In the AWGN channel case, only one active finger is required. For simplicity, it is assumed that a perfect carrier recovery is achieved, and the rake receiver is matched to the reference user's PN and Walsh codes, and has achieved time synchronization. In Figure 3.7, the receiver filter is a baseband-matched filter that is matched to the transmitter pulse-shaping filter, and the integrate-and-dump block performs accumulating symbol energy over a symbol period or G=64 chips to arrive at demodulated soft symbols. Due to the fact that two power control symbols are inserted into the modulation symbol stream in every power control group at the transmitter, they are extracted from the received Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 57 Information Bits 8.6 kbps 4.0 kbps 2.0 kbps 0.8 kbps Add Frame Add 8-bit Quality Encoder Indicator Tail 9.6 kbpJ Convolutionall Encoder 4.8 kbps 2.4 kbps 1.2 kbps Code Symbol Modulation 19.2 kbps 9.6 kbps 4.8 kbps 2.4 kbps Symbol Repetition Block Interleaver 19.2 kbps Power 800 kbps Control ^ Bits Long Code Mask * A 19.2 kbps Long Code Decimator Decimator Generator 1.2288 Mcps Q-channel Short PN s i D ( 2 K / C O Figure 3.6 Block diagram of IS-2000 RC1 forward traffic channel modulation symbol stream and replaced with the value of zeroes on the receiver side. The Viterbi decoder with a maximum decoding depth of 96 is used in all simulation results presented in the following. As mentioned in Section 3.2, an estimation of Eb and Nt is required for implementing the fast forward channel power control in the IS-2000 CDMA standard. In this thesis, it is assumed that a perfect estimation of Eb and Nt is available. However, the FER performance degradation caused by EfJN, mismatch will be investigated by means of computer simulation in the following. Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 58 C«S{lKfci) r(t). R e c e i v e r F i l t e r P N D e s p r e a d W a l s h D e s p r e a d R e c e i v e r F i l t e r sin(27t/,) I n t e g r a t e -a n d - D u m p Figure 3.7 Matched-filter rake receiver in the AWGN channel In order to verify our implementation of the IS-2000 CDMA transmitter, the AWGN channel, and the rake receiver, a FER benchmark of our simulation system is compared to the published results from [6] and [56]. To benchmark the system, the ideal rate detection scheme is used as in [6] and [56] for the case of 9600 bps frames. The result is shown in Figure 3.8, where the result in [6] is labeled as "Gutierrez", the result in [56] is labeled as "Philips", and our bench-mark is labeled as "This thesis". As shown in Figure 3.8, our FER benchmark is identical to the results in [6] and [56]. This clearly indicates that our simulation system has the correct implemen-tation of the IS-2000 CDMA transmitter, the AWGN channel, and the rake receiver. Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 59 9600 bps in AWGN 1 —*— Gutierrez - B - Philips - © - This thesis -"! \ 2 2 . 5 3 3 . 5 Eb/Nt (dB) Figure 3.8 FER benchmark of IS-2000 CDMA forward link in the AWGN channel 3.3.2 F E R P e r f o r m a n c e Simulated FER performance of the proposed JRDDDA is given in Figure 3.9. Included in the same figure is the simulated FER performance of the ideal rate detection scheme, Cohen's BRDA and Butler's BRDA. Recall that Cohen's BRDA and Butler's BRDA are described in Section 2.3. It is evident from Figure 3.9 that the FER performance of the proposed JRDDDA is virtually the same as that of the ideal scheme, and the JRDDDA can provide 0.4 dB and 0.9 dB gain in terms of the required Ef/Nt at a FER of 10"2 compared with Cohen's BRDA and Butler's BRDA, respectively. For a closer examination of the different rate cases, we group the FER curves of the four BRDAs in each rate case into separate plots as shown in Figure 3.10 to Figure Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 60 3.13. As seen from these four plots, the JRDDDA can achieve virtually the same FER perfor-mance as that of the ideal scheme in all the rate cases. In the 9600 bps case (see Figure 3.10), the FER performance of Butler's BRDA and the JRDDDA overlaps that of the ideal scheme, but Cohen's BRDA has an obvious degradation. It is observed from Figure 3.11 to Figure 3.13 that Butler's BRDA starts to degrade when the data rate reaches 4800 bps or lower. In the 1200 bps case (see Figure 3.13), both Butler's BRDA and Cohen's BRDA suffer from a significant FER performance degradation compared to the proposed JRDDDA. It is clear that the proposed JRDDDA outperforms Cohen's BRDA in all rate cases and Butler's BRDA in the three lower rate cases in terms of the required Ef/N, for a target FER. Particularly in the 1200 bps case, the proposed JRDDDA outperforms both Cohen's BRDA and Butler's BRDA by more than 2.5 dB in terms of the required Ef/N, at a FER of 10"2. The reason why Butler's BRDA suffers from a significant FER performance degradation in the two lower rate cases is due to a high rate detection error rate for the two lower rates, which will be shown in the next subsection. Since the SNR of lower rate frames is reduced by a factor of symbol repetition times compared to the highest data rate frames, the symbol error rate (SER) varies widely with the channel SNR; in other words, the SER is very unreliable in this low SNR range. Basically, this unreliable SER results in the high rate detection error rate for the two lower rate cases. Regarding Cohen's BRDA, there is a FER floor about 10 - 2 for the 9600 bps case. There are two possible explanations. One is that Cohen's BRDA is optimized for the one-path Rayleigh fading channel case, which is considered to be the worst scenario because there is no multipath diversity. The other is that Cohen's BRDA is proposed for use in the IS-95 DS-CDMA standard where voice is the primary service. Since a FER of 5% is rather tolerable for voice Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 61 application, the 10~2 FER floor in Cohen's BRDA may not be a problem for the IS-95 DS-CDMA standard. It is worth mentioning that our implementation of both Cohen's BRDA and Butler's BRDA is verified by comparing our simulated FER with published results of the two BRDAs in [25] and [57]. In other words, our simulated FER performance of the two BRDAs agrees well with the results in [25] and [57]. All rates in AWGN 2.5 Eb/Nt (dB) Figure 3.9 FER in the AWGN channel in the case of all rate frames Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 9600 bps in AWGN . -e- Ideal - B - Cohen - V - Butler —«— Joint j ] i £ i ; [ -; [ -: i Eb/Nt (dB) Figure 3.10 FER in the AWGN channel in the case of 9600 bps frames 4800 bps in AWGN a: m --e^ Ideal - a - Cohen Butler —*— Joint 4 1 • i I i ; i I I I i I i I 1 1.5 2 2.5 3 3.5 4 Eb/Nt (dB) Figure 3.11 FER in the AWGN channel in the case of 4800 bps frames Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 2400 bps in AWGN ui i -e- Ideal : -EH Cohen -- V - Butler " Joint t ; T r r r r ; : i -r^ s- -; ^ S ? ^ • • i 1 1 1.5 2 2.5 3 3.5 4 Eb/Nt (dB) Figure 3.12 FER in the AWGN channel in the case of 2400 bps frames 1200 bps in AWGN - © - Ideal -EH Cohen - V - Butler 1 1.5 2 2.5 3 3.5 4 Eb/Nt (dB) Figure 3.13 FER in the AWGN channel in the case of 1200 bps frames Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 64 3.3.3 FRDR Performance Simulated FRDR performance of the JRDDDA is given in Figure 3.14. Included in the same figure is the simulated FRDR performance of Cohen's BRDA and Butler's BRDA for comparison. It is shown in Figure 3.14 that the FRDR of the JRDDDA is more than one order of magnitude lower than that of Cohen's BRDA and Butler's BRDA for a given Ef/Nt. Cohen's BRDA has a rate detection error floor at around 5 x IO - 3. For a closer examination of the differ-ent rate cases, we group the FRDR curves of each data rate into separate plots as shown in Figure 3.15 to Figure 3.18. It is shown in Figure 3.15 to Figure 3.18 that the proposed JRDDDA signifi-cantly outperforms the other two schemes. Particularly in the 1200 bps case, the FRDR of the proposed JRDDDA is two order of magnitude lower than that of the other two BRDAs for a given Et/N, It is shown in Figure 3.3 that the proposed JRDDDA runs in parallel to the ideal rate detection scheme for comparison. It is observed from our simulation that the proposed JRDDDA seldom makes a rate detection error if the decoded frame of the ideal rate detection scheme has no bit errors. In other words, when the proposed JRDDDA makes a rate detection error on a received frame, it is most likely that the corresponding decoded frame of the ideal rate detection scheme is in error. This means that a frame error would occur even if the proposed JRDDDA would not make that rate detection error. In this case, a frame error occurs in both the proposed JRDDDA and the ideal rate detection scheme. This explains why the proposed JRDDDA can provide virtually the same FER performance as the ideal case, as shown in the previous subsection. Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel All rates in AWGN or Q 2.5 Eb/Nt (dB) Figure 3.14 FRDR in the AWGN channel in the case of all rate frames 9600 bps in AWGN 2.5 Eb/Nt (dB) Figure 3.15 FRDR in the AWGN channel in the case of 9600 bps frames Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 4800 bps in AWGN 2.5 Eb/Nt (dB) Figure 3.16 FRDR in the AWGN channel in the case of 4800 bps frames 2400 bps in AWGN - E H Cohen - V - Butler —*— Joint 2 2.5 3 Eb/Nt (dB) Figure 3.17 FRDR in the AWGN channel in the case of 2400 bps frames Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 67 1200 bps in AWGN 2.5 3 Eb/Nt (dB) 3.5 Figure 3.18 FRDR in the AWGN channel in the case of 1200 bps frames 3.3.4 Channel E^Nf Mismatch We have made the assumption that a perfect estimation of Eb and Nt is available in the pre-vious subsections. In practice, however, this is not the case. We have studied FER performance degradation due to the mismatch between the true Ef/Nt and estimated E//N,. Simulated FER per-formance versus mismatched Ef/N, is plotted in Figure 3.19, where the true Ef/Nt is 2 dB. Any is / Nt value above 2 dB is over-estimated. Conversely, any Ef/N, value below 2 dB is under-esti-mated. If Ef/N, is over-estimated, N, is smaller than the true value for a given Eb. Scaled by N„ the joint metric defined in (3.11) can be written as Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 68 JM(m,X) = 2 U j ] ¥ r ^ r J V < £ B l o g 2 . (3.17) W Z k=i 1 If Ef/Nt is over-estimated, the joint metric in (3.17) for a higher data rate like 9600 bps increases faster than that for a lower date rate like 1200 bps because the higher rate frame has a longer bit sequence or larger Lm than the lower rate frame. Then, the rate decision favors higher rate frames and disfavors lower rate frames. Therefore, we see the FER of the 9600 bps frames decreases and the FER of the 1200 bps frames increases with over-estimated E//Nt. Conversely, if Ej/Nt is under-estimated, Nt is higher than the true value for a given Eb. In this case, the joint metric in (3.17) for a higher data rate like 9600 bps decreases faster than that for a lower rate like 1200 bps. There-fore, the rate decision is more in favor of the lower rate frame. That is why we see that the FER of the 9600 bps frames increases and the FER of the 1200 bps frames decreases with under-esti-mated Ef/Nt. It is observed that 2 dB underestimation of E//Nt is rather tolerable, but degradation becomes large for greater mismatch. Overestimation of Ej/N, is less detrimental than underestima-tion. Figure 3.19 shows that the required accuracy for the Ef/Nt estimation without appreciable FER degradation is between -2 to +3 dB. 3.4 Conclusions We have presented a joint rate detection and data decoding algorithm for variable-rate data transmission in the IS-2000 CDMA communication system in the AWGN channel case. Simula-tion results have shown that the proposed scheme can achieve virtually the same frame error rate performance as that of the ideal case. Performance comparison between the proposed JRDDDA and the two well-known BRDAs is provided in this chapter. It is clear that the proposed JRDDDA Chapter 3 Joint Rate Detection and Data Decoding Algorithm in the A WGN Channel 69 Estimated Eb/Nt (dB) Figure 3.19 FER versus channel E^/N, mismatch in the AWGN channel (true E / N =2 dB) significantly outperforms the other two BRDAs in terms of the required Ef/Nt for a given FER or FRDR. Complexity comparison among the proposed JRDDDA, Cohen's BRDA and Butler's BRDA will be discussed in the next chapter. 70 Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels The joint rate detection and data decoding algorithm (JRDDDA) was proposed for variable-rate data transmission in the AWGN channel in the previous chapter. The focus of this chapter is to investigate the JRDDDA for multipath Rayleigh fading channels, which are more realistic channel models for cellular communication systems. A tapped delay line model of multipath fading channels is described in Section 4.1. Based on the criterion of maximizing the joint a posteriori probability of the transmitted data rate and the information bit sequence given a frame of received symbols, the JRDDDA for the multipath Rayleigh fading channels is derived in Section 4.2. Simulation results are presented in Section 4.3. The complexity of the proposed algorithm is discussed in Section 4.4. Finally, some conclusions of this chapter are given in Section 4.5. 4.1 Multipath Propagation Model The system model for a variable-rate DS-CDMA communication system was described in Section 2.2. The fading channel model and the rake receiver are discussed in detail in this section. Multipath, Rayleigh slow fading channels are considered in this chapter. By slow fading we mean that the channel attenuation and phase shift are essentially constant for the duration of at least one symbol interval. A model of multipath propagation is shown in Figure 4.1, where multipaths are modeled by a tapped delay line with statistically independent time-variant tap weights {c,(r)} [35]. In the figure, {c^t); / = 0, 1, 1} are independent complex stationary random pro-cesses. A base band equivalent impulse, response of the channel is given by: Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 71 L-l c(0 = £ a / 5 ( / - T / ) e - - ' \ (4.1) / = o where 5(0 is the Dirac impulse function, and a/s represent the amplitudes of slowly varying independent stationary Rayleigh random processes with a probability density function given by />«,(«) = -2exv(-T^)> a^°> (4-2> ' af v 2af The 0,'s are i.i.d. random variables uniformly distributed over (0,2 7 i ] . The T^'S are the relative delays of the L resolvable multipath components with T 0 < x t < ... < xL_ j and are assumed to satisfy xl+ j - xl > Tc,l=0, 1 , L - 2 . The received signal for the desired user can be written as: L-l r(t) = ^a /X(/-T /){^ /(r-T /)cos(27r/ c? + 0 /) + 1 = 0 (4.3) jt?e(f-x/)sin(27c/cf + 0,)} + «(0, where X(t) is the modulation symbol sequence, pj(t) and PQ(J) are the PN sequences for I and Q channels, respectively, as defined in Section 2.2, and n(t) is an AWGN representing the background noise, and © ; = (2nfcxl - 0;) mod (27i). To take advantage of the wideband characteristics of spread spectrum signals, a coherent rake receiver is employed by the system to provide multipath diversity. To simplify the mathemat-ical analysis, we will be assuming that perfect knowledge of the channel phase and gain can be obtained. For our computer simulation, however, the perfect knowledge of channel amplitude is not required. Coherent rake combining weights the resolved multipaths in proportion to their instantaneous received signal envelopes and adds the components constructively. Figure 4.2 shows the receiver structure for the reference user, where the number of fingers is equal to the Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 72 total number of multipaths L. The matched filter receiver is matched to the reference user's CDMA spreading code and is assumed to have achieved time synchronization with the initial path of the reference signal. The tap weights {at; /= 0, 1} and phases {Qt; / = 0 , L - 1} are assumed to be perfect estimates of the channel parameters. In practice, the estimation and coherent demodulation may be done using a pilot signal [13]. The de-interleaved output of the matched filter rake receiver is denoted by Yi = (yn,yi2, • ••>.y,jv) corresponding to the modulation symbol sequence X{ = (xn,xi2, ...,xjN). For mobile radio applications, the channel experiences fading distortion in addition to the background noise. Turin [69] analyzed the effects of multipath fading and multiple access noise on the overall average SNR. Similarly, Lehnert and Pursley [70] analyzed SNR performance for a Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 73 multipath combining receiver and determined system performance in terms of parameters of the signature sequences. Kavehrad and McLane [71] considered coherent system performance for a Rician and Rayleigh channel. Eng and Milstein [72] analyzed the BER performance of a coherent DS-CDMA system in Nakagami multipath fading channels. In multipath fading channels, there is one extra noise component due to 'self-interference' from the multipath waveform of the refer-ence signal, in addition to the MAI and the background noise. It is shown in [72] that these three noise components can be approximated as a Gaussian random variable with a mean of zero and a variance conditional on the channel fading amplitude {at; I = 0,..., L - 1}. Based on the results in [72], the de-interleaved output of the rake receiver can be represented as Vtk' jGE?'Pik*ik + nik> (4-4) Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 74 where pik is the maximal ratio combined amplitude of L resolvable independent stationary Ray-leigh random processes given by pik= Z a h ( 4 - 5 ) /=0 where aik l is an independent stationary Rayleigh random process for the /th path corresponding to the &th symbol in the /th frame. In (4.4), nik represents the total channel noise including the 'self-interference', the MAI and the background noise. As shown in [72], nik can be approxi-mated as an AWGN with the two-sided power spectral density conditional on pjk given by: Nik = PikNr (4.6) where Nt is the total noise power spectral density which determines the channel signal to noise ratio or E^N, for a given received bit energy. Using Table 2.3, we can rewrite (4.4) as: y i k = jE^2r>Pilp:ik + nik. (4.7) The pdf of the demodulated symbol sequence F( = (y^y^, conditional on rate m,, information bit sequence 7, and channel fading amplitude p ; = (p n, p / 2 , p / j V ) , denoted by pCYtrjmt, 11, p (), is equal to p(YAXt, p() because convolutional coding, symbol repetition and de-interleaving are deterministic processes. Since nik is a memoryless Gaussian random variable (due to the assumption of infinite interleaving), (T;| w(, It, p() can be expressed as N i . ( (yk-jES2»'P^f] ( 4 8 ) P(Yi\mi>Ti>Pi) = FT ~ F = e x P Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 75 where pik is a maximal ratio combined amplitude of L resolvable independent stationary Ray-leigh random processes given in (4.5). This pdf will be used for deriving the joint rate detection and data decoding algorithm in the multipath fading channels in the next section. 4.2 Joint Rate Detection and Data Decoding Algorithm Similarly as in the last chapter, we shall drop the frame index i for convenience. The de-interleaved symbol sequence out of the rake receiver is denoted by Y = (yx,y2, •••>>>) corre-sponding to the transmitted symbol sequence X = (x v x2, • • •, xN). The deskewed and combined output of the L fingers tracking the L resolvable multipath components is given in (4.7). It is evi-dent from (4.7) that the output is conditioned on the channel fading gain. To simplify the deriva-tion, we will be assuming that perfect knowledge of the channel fading gain is available. Given a received symbol sequence Y out of the rake receiver, and a channel gain vector p = (pj, p 2 , p N ) , we want to choose data rate m and data sequence / for which the joint a posteriori probability, p(m, I\ Y, p), is maximized over all frame rates and input information sequences. It is assumed that the four rates are equiprobable a priori due to the fact that different types of data besides voice data may be supported in the IS-2000 DS-CDMA cellular communica-tion systems [12]. Using the same derivation as in Section 3.2, it is straightforward to show that we need to maximize: p(Y\m,I,p)P(I\m) Vm,/. (4.9) Substituting (4.8) and (3.8) into (4.9) and taking the logarithm yield the following form: i ' o < ^ ) - i | / z | J w t - i - i - | p K - w . (4..o) Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 76 To find the maximum in (4.10), we are only concerned with the differences among all possible symbol sequences. The first and second terms in (4.10) are common given the same received symbol sequence and are subtracted from each other during comparison. Equivalently, we need to maximize the following form: £ £ J j w * - £ £Jjp|*M.log2. (4.11) Substituting (4.2) into (4.11) yields: wM £ £ p^- z >8 2 - ( 4- i 2> k = l i V ' 2 jfc= ! Using the fact that x% - 1, we define a joint rate detection and data decoding metric, called joint metric or JM as: JM(m,X) = (4.13) Compared to the joint metric defined in (3.11) for the AWGN channel case, the difference is that the second term of the joint metric defined in (4.13) for a multipath fading channel case is weighted by a summation of fading amplitudes in a frame, denoted by Fj- (we call i y as a fading factor hereafter), N Ff= £ p t , (4.14) A = 1 where N=384 is the number of symbols in a frame, and pk is the maximal ratio combined ampli-tudes of L independent fading paths defined in (4.5). A technique for estimating the tap weights {a ;; / = 0 , Z - 1} using the pilot channel signal will be described in Section 4.3. For sim-Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 77 plicity, perfect estimates of the tap weights {a,; / = 0 , L - 1} are assumed to be available. Given the tap weights {a{; I = 0,..., L - 1}, the maximal ratio combined amplitudes pk can be determined by (4.5). Other terms in (4.5) are similar to those in the AWGN channel case dis-cussed in Section 3.2. To find the rate m and symbol sequence A" which maximize the joint metric in (4.13), we need to search all possible rates and modulation symbol sequences. Using the symbol repetition property as given in (2.22), we can write the JM for each of the rate hypotheses as follows: JM, F , J | i ^ - ^ - i | l o g 2 -' Jfc= 1 ' (4.15) JM. 2 ft N/2 f 1 2 Z l Z ^ - y ' k = 1 v = 0 J \ (4.16) 2 W JM, = — -N/A ( 3 A T A / T Z I Z * « - y (4.17) N/% f 7 JMA A?Jre £ [ Z J) c * - TeENtFf~ L ^ 2 -' k = 1V=0 J ' (4.18) Given a rate hypothesis m, the second and third terms in (4.15) to (4.18) do not change and will be cancelled out during comparison. By scaling by — /—, the joint metric in (4.13) is 2 >\Eb simplified to the accumulated path metric of the Viterbi algorithm, as given in (2.12). Similarly as in the AWGN case discussed in Section 3.2, we can use the Viterbi algorithm to find the maximum likelihood sequence for a given rate. Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 78 The joint rate detection and data decoding algorithm in the multipath fading channel is shown in Figure 4.3. The symbol combiner performs reverse operation of the symbol repetition at the transmitter. As shown from (4.15) to (4.18), there is no symbol combiner for the rate hypothe-sis m=\, while 2-symbol, 4-symbol and 8-symbol combiners are required for rate hypotheses /M=2,3,4, respectively. In Figure 4.3, DMm is defined as: DMm = ^Ff+LJog2 m = 1,2,3,4, (4.19) where Fj- is defined in (4.14) and L m is given in Figure 2.10. As discussed above, it is assumed that the tap weights corresponding to the Mi received symbol, {a ;; / = 0 , L - 1}, are avail-able. Given the tap weights {o ;^ / = 0 , L - 1}, the multipath fading amplitude combiner block in Figure 4.3 performs the maximal ratio combining of L independent fading path ampli-tudes to compute p^ . given in (4.5) and the fading factor given in (4.14). DMm ,m = 1,2, 3,4, is calculated according to (4.19). In summary, the joint rate detection and data decoding algorithm is described in the following four steps: 1. Given each of the four rate hypotheses, search for the maximum likelihood (ML) sym-bol sequence in that hypothesis using the Viterbi algorithm. This will give us four accumulated path metrics like the first terms in (4.15) to (4.18) and four ML symbol sequences or decoded bit sequences, which are denoted by Im , where m=J,2,3,4. 2. Compute the fading factor defined in (4.14) based on estimated channel tap weights {a,; l = 0,...,L-\}. Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 79 3. Calculate the four joint metrics, JMm, m=],2,3,4, defined in (4.15) to (4.18). 4. Choose the rate hypothesis with the maximum joint metric among the four joint metrics and output the corresponding decoded frame of the chosen rate. In Figure 4.3, the detected rate m is defined as m = max JMm, and the decoded frame / is given as As explained in Section 3.2, the bit energy Eb can be estimated using the power control symbols and the noise power density Nt can be estimated using the pilot signal as proposed in [73]-[76]. In this thesis we assume that an estimation of the bit energy Eb and the interference power spectral density Nt is available. However, we will investigate the FER performance degradation due to channel EjJNt mismatch by means of computer simulation in the next section. It is seen from Figure 4.3 that the structure of the joint rate detection and data decoding algorithm in the fading channel is similar to that in the AWGN channel. In fact, the AWGN channel is a special case of the Rayleigh fading channel where there is only one path and there is no channel attenuation, that is, = 1, and i y = N in the AWGN channel. The joint metrics in (4.15) to (4.18) for the multipath Rayleigh fading case are reduced to those in (3.12) to (3.15) in the AWGN case. 4.3 Simulation Results in Multipath Rayleigh Fading Channels In this section, we describe and present the results of a software simulation of variable-rate data transmission system with the proposed JRDDDA in the case of multipath fading channel. The IS-2000 forward traffic channel system with Radio Configuration 1 (RC1) is used to simulate Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 80 output from Rake receiver Viterbi Decoder JM, 2-Symbol Viterbi Combiner Decoder 4-Symbol Viterbi Combiner Decoder 8-Symbol Viterbi Combiner Decoder Multipath N Fading Amplitude • Combiner k= 1 DM, 1 JM, DM, JM, DM, "IB-JMA DM, 7 Selector Decoded Frame Detected Rate Figure 4.3 Block diagram of joint rate detection and data decoding algorithm in multipath fading channels Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 81 the performance of the JRDDDA in two well-accepted, standardized channel models for DS-CDMA cellular radio environments: namely, the one-path Rayleigh fading channel and the three-path Rayleigh fading channel specified in the IS-2000 CDMA standard [6], [66]. As mentioned in Subsection 2.1.4, the one-path fading channel represents a frequency-flat fading case while the three-path fading channel represents a frequency-selective fading case. Similarly as in the AWGN channel case, both frame error rate (FER) and false rate detection rate (FRDR) are used to measure the performance of our proposed JRDDDA in the fading channel cases. The FER performance and FRDR performance of Cohen's pre-decoding BRDA [19] and Butler's post-decoding BRDA [23] are included for comparison. As a reference, the FER performance of the ideal rate detection scheme where the transmitted frame rate is known to the receiver is also included. In our simulation, Cohen's BRDA, Butler's BRDA and the ideal scheme are run in parallel to the proposed JRDDDA, as shown in Figure 3.3. In all simula-tions, an adequate number of error events are generated in order to achieve a 95% confidence interval of ±10 % of the average FER or FRDR. 4.3.1 Simulation System The purpose of this subsection is to provide a detailed description of our simulation sys-tem in the Rayleigh fading channels. In addition, a benchmark of our simulation system in terms of FER is given for verifying our implementation of the IS-2000 CDMA transmitter, the Rayleigh fading channels, and the rake receiver. The same SPW simulation software package as used in the previous chapter is used to model the IS-2000 CDMA forward link system in the fading environments [7]. A block diagram of our simulation system is shown in Figure 4.4, where the IS-2000 CDMA transmitter in Radio Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 82 AWGN Multipath Fading Rake Receiver Block De-interleave Y/ Rate and Data Detection Figure 4.4 Simulation system in multipath fading channel Configuration 1 (RC1) [7] is shown in Figure 3.4 and Figure 3.5. The detailed description of the IS-2000 CDMA forward channels is given in Section 3.3.1 and thus is omitted here. The multipath fading channel block and the rake receiver block are to be discussed below. For simpli-fying the derivation, we made the assumption of infinite interleaving depth in the last section. In our simulation, however, the finite, bit reversal block interleaver specified in the IS-2000 CDMA standard [7] and [55] is employed. The rate and data detection block is substituted by the JRDDDA shown in Figure 4.3. The multipath fading channel is modeled by a tapped delay line with statistically indepen-dent time-variant tap weights as shown in Figure 4.1. The amplitude of each path is an indepen-dent Rayleigh random process and the phase of each path is randomly distributed over [0, 2TZ ). A built-in Rayleigh fading channel simulator in SPW's communication library is used in our simula-tion. The Rayleigh fading channel simulator is implemented based on Jakes' Rayleigh fading channel model [64]. The AWGN generator is also a built-in function in SPW's communication library as described in Section 3.3.1. The detailed implementation of the pilot-aided coherent rake Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 83 receiver is shown in Figure 4.5. It is assumed that the number of fingers is equal to the total num-ber of multipaths L. It is also assumed that each finger has achieved PN time synchronization with each path of the reference signal. In practice, the time synchronization can be realized by search-ing the pilot PN sequence (see Chapter 3 o f [13] for detail). In Figure 4.5, all fingers are identical i n structure, but only finger / is shown in detail. A s shown in Figure 4.5, the amplitude and phase of each channel path are estimated by Tow-pass filtering the PN despread pilot signal in both I and Q channels. As given in (4.1), the tap weight of the /th path at time / = it, denoted by c / 9 is cl = a/e~-/9/ = a / C o s O j - y ' a / S i n O / . (4.20) Thus, the output from the I channel estimator of the /th path is o c / C o s O / and the output from the Q channel estimator of the /th path is -ot/sinO/. In other words, the estimated channel tap weight is cl = a /cos0/-/a /sin0/ = a/e_-/6'. (4.21) A A A where at and 0/ are the estimated amplitude and phase of the /th tap weight. When al = cc, and 0/ = 0/, the channel is perfectly compensated. As shown in Figure 4.5, the channel compensated signal is then Walsh-code de-spread and integrated over a symbol period. Finally, the symbols from L independent fingers are delay adjusted and coherently combined to arrive at an output symbol o f the rake receiver. Similarly as in the previous chapter, the Viterbi decoder with a maximum decoding depth o f 96 and 6-bit quantization is used in the JRDDDA (refer to Figure 4.3). In compliance to the IS-2000 CDMA standard, two power control symbols are inserted into the modulation symbol Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 84 Figure 4.5 Pilot-aided coherent Rake receiver for multipath fading channel Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 85 stream in every power control group at the transmitter. The power control symbols are extracted from the received modulation symbol stream and replaced with the value of zeroes at the receiver side. As in the AWGN case, it is assumed that a perfect estimation of E b and Nt is available. Some techniques for E b and Nt estimation are given in [73]-[76]. The FER performance degradation caused by EfJNt mismatch is investigated in the following two subsections. In order to verify our implementation of the IS-2000 CDMA transmitter, the multipath Rayleigh fading channel, and the rake receiver, a FER benchmark of our simulation system in the standardized three-path fading channel specified in [66] is compared to the result in [56]. Note that the three-path fading channel will be described in detail in Section 4.3.3. To benchmark the system, the ideal rate detection scheme is used as in [56] for the case of 9600 bps frames. The result is shown in Figure 4.6, where the result in [56] is labeled as "Philips", and our benchmark is labeled as "This thesis". As shown in Figure 4.6, our FER benchmark is very close to the results in [56]. This clearly indicates that our simulation system has a good implementation of the IS-2000 CDMA transmitter, the multipath Rayleigh fading channel, and the rake receiver. 4.3.2 Simulated Results in the One-path Rayleigh Fading Channel The one-path Rayleigh fading channel which represents a frequency-flat Rayleigh fading is modeled according to the IS-2000 CDMA recommendation [7], [66]. The path fading amplitude a, is characterized statistically by an independent Rayleigh distribution:with mean value given in Table 4.1. The vehicle speed is 30 km/h. In the cellular frequency band with a carrier frequency of 880.0 MHz, the resulting Doppler frequency fd is 24.44 Hz. Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 86 9600 bps in the 3-path fading channel Eb/Nt (dB) Figure 4.6 FER benchmark of IS-2000 CDMA forward link in the three-path Rayleigh fading channel Table 4.1 One path fading channel parameters Path Delay (us) Attenuation (dB) 1 0.0 0.0 4.3.2.1 FER Performance Simulated FER performance of the JRDDDA in the one-path Rayleigh fading channel is given in Figure 4.7. Included in the same figure are the FER curves of the ideal rate detection Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 87 scheme, Cohen's BRDA and Butler's BRDA, which are labeled as "Ideal", "Cohen", and "Butler", respectively. As seen from Figure 4.7, the proposed JRDDDA can provide 0.8 dB and 2.1dB gain in terms of the required Ef/N, at a FER of 10"2 compared with Cohen's BRDA and Butler's BRDA, respectively. Compared with the ideal case, the proposed JRDDDA has a negligible FER performance degradation. For a closer examination of the different rate cases, the FER curves of each data rate are grouped into separate plots as shown in Figure 4.8 to Figure 4.11. In the 9600 bps case (see Figure 4.8), the ideal scheme, Butler's BRDA and the JRDDDA have virtually the same FER performance, but Cohen's scheme has an obvious degradation. It is observed in Figure 4.9 and Figure 4.10 that in the 4800 bps and 2400 bps cases, the JRDDDA has a slight FER performance degradation compared with the ideal case. In contrast, the FER perfor-mance of Cohen's BRDA and Butler's BRDA significantly degrades when the data rate gets to 2400 bps or lower. Particularly in 1200 bps case, the proposed JRDDDA outperforms Cohen's BRDA and Butler's BRDA by about 2.2 dB and 5.6 dB in terms ofthe required Ef/N, at a FER of 10"2, respectively. 4.3.2.2 FRDR Performance Simulated FRDR performance of the JRDDDA is given in Figure 4.12. The FRDR curves of each data rate are also grouped into separate plots as shown in Figure 4.13 to Figure 4.16. Included in each figure is the simulated FRDR performance of Cohen's BRDA and Butler's BRDA for comparison. It is evident from these figures that the JRDDDA outperforms Cohen's BRDA and Butler's BRDA in terms of FRDR for a given Ef/N,. Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels All rates In one-path fading - © - Ideal - B - Cohen " - V - Butler —*<— Joint • i 8 10 12 14 16 Eb/Nt (dB) Figure 4.7 FER in the one-path Rayleigh fading channel in the case of all rate frames 9600 bps in one-path fading — - 4 4 A— -e- Ideal - B - Cohen - V - Butler —*— Joint r . - , r "! "1 ; ; ! ; i i . - - - T r ^ ^ c ^ ^ ^ 3 5 ^ _ ! ! ^ ~~~~—~~~—~f 8 10 12 14 16 Eb/Nt (dB) Figure 4.8 FER in the one-path Rayleigh fading channel in the case of 9600 bps frames Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 10 4800 bps in one-path fading 10 -e- Ideal - B - Cohen Butler - * - Joint 12 Eb/Nt (dB) Figure 4.9 FER in the one-path Rayleigh fading channel in the case of 4800 bps frames 10 2400 bps in one-path fading 10 -e- Ideal -E3- Cohen - V - Butler —*— Joint 12 Eb/Nt (dB) Figure 4.10 FER in the one-path Rayleigh fading channel in the case of 2400 bps frames Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 10 10 DC LU 10 10' 1200 bps in one-path fading 10 12 Eb/Nt (dB) [ -I 1.-- - e - Ideal - s - Cohen -- V - Butler " -*— Joint • i i ; ! " ^ i 14 16 Figure 4.11 FER in the one-path Rayleigh fading channel in the case of 1200 bps frames All rates in one-path fading 12 Eb/Nt (dB) Figure 4.12 FRDR in the one-path Rayleigh fading in the case of all rate frames Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 9600 bps in one-path fading - Q - Cohen : - V - Butler -—«— Joint 8 10 12 14 16 Eb/Nt (dB) Figure 4.13 FRDR in the one-path Rayleigh fading in the case of 9600 bps frames 4800 bps in one-path fading L - _ . 1 1 - B - Cohen - V - Butler —x— Joint . ! J • > - • • • • : : ' i Eb/Nt (dB) Figure 4.14 FRDR in the one-path Rayleigh fading in the case of 4800 bps frames Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 2400 bps in one-path fading 12 Eb/Nt (dB) Figure 4.15 FRDR in the one-path Rayleigh fading in the case of 2400 bps frames 1200 bps in one-path fading 12 Eb/Nt (dB) Figure 4.16 FRDR in the one-path Rayleigh fading in the case of 1200 bps frames Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 93 4.3.2.3 Channel EyNt Mismatch In this subsection we present the FER degradation due to Ef/N, mismatch between the true Ef/N, and the estimated Ef/N, in the one-path Rayleigh fading channel. Given the true Ef/N, is 12 dB, simulated FER performance versus mismatched Ef/N, is plotted in Figure 4.17. Any Ef/N, value above 12 dB is over-estimated. Conversely, any Ef/N, value below 12 dB is under-esti-mated. If Ef/N, is over-estimated, Nt is smaller than the true value for a given Eb. By scaling by N„ the joint metric defined in (4.13) can be written as JM(m, A ) - 2 M j ; ykxk - ±Eb £ pk - NJLJogl. (4.22) W / k=\ 1 jfc-i If Ef/N, is over-estimated, the joint metric in (4.22) for a high data rate like 9600 bps increases faster than that for a low date rate like 1200 bps because the higher rate frame has a longer bit sequence or bigger Lm than the lower rate frame. Then, the rate decision is more in favor of higher rate frames and less in favor of lower rate frames. Therefore, we see that the FER of the 9600 bps frames decreases and the FER of the 1200 bps frames increases with over-estimated Ef/N,. Con-versely, if Ef/N, is under-estimated, Nt is higher than the true value for a given Eb. In this case, the joint metric in (4.22) for a high data rate like 9600 bps decreases faster than that for a low rate like 1200 bps. Therefore, the rate decision is more in favor of the lower rate frame because a lower rate frame is more likely to have higher joint metric than a higher rate frame. That is why we see that the FER of the 9600 bps frames increases and the FER of the 1200 bps frames decreases with under-estimated Ef/N,. It is observed from Figure 4.17 that the FER performance does not degrade appreciably if the estimated Ef/N, is within 1.0 dB around the true value. In other words, there is about 2 dB tolerance in terms of Ef/N, mismatch. It is reported in [28] that the signal to interfer-Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 94 ence ratio can be estimated with an error of 0.5 dB, which is within our channel mismatch toler-ance. In the one-path Rayleigh fading channel, the overestimation of Ef/Nt is as detrimental as the underestimation. This is different from the AWGN channel case where overestimation is less det-rimental than underestimation (see Figure 3.19). Estimated Eb/Nt (dB) Figure 4.17 FER versus channel EfJNt mismatch in the one-path Rayleigh fading channel (true EjJN(=\2SS) 4.3.3 S i m u l a t e d Resu l t s i n the T h r e e - p a t h R a y l e i g h F a d i n g C h a n n e l The three-path Rayleigh fading channel according to the IS-2000 CDMA recommenda-tion [66] is used to model a frequency-selective Rayleigh fading case. Each path has a fixed delay with the value given in Table 4.2. The path fading amplitudes a,, 1 < / < 3, are characterized sta-Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 95 tistically by independent Rayleigh distributions with mean values given in Table 4.2. Note that all the three paths are resolvable because the path delays of the second and third paths relative to the first path are greater than one chip duration. The vehicle speed is 100 km/h. In the cellular fre-quency band with a carrier frequency of 880.0 MHz, the resulting Doppler frequency fd is 81.48 Hz. Table 4.2 Three path fading channel parameters Path Delay (us) Attenuation (dB) 1 0.0 0.0 2 2.0 0.0 3 14.5 -3.0 4.3.3.1 F E R Performance Simulated FER performance of the JRDDDA is given in Figure 4.18. Included in the same figure is the simulated FER performance of the ideal rate detection scheme, Cohen's BRDA and Butler's BRDA. It is shown in Figure 4.18 that the FER performance of the proposed JRDDDA is virtually the same as that of the ideal scheme, and the JRDDDA can provide 0.3 dB and 0.7 dB gain in terms of the required Ef/N, at a FER of 10~2 compared with Cohen's BRDA and Butler's BRDA, respectively. The FER curves of each data rate are drawn in separate plots as shown in Figure 4.19 to Figure 4.22. As seen from the four plots in Figure 4.19 to Figure 4.22, the proposed JRDDDA can achieve virtually the same FER performance as that of the ideal scheme in all the rate cases, which is similar to the AWGN channel case. In the 9600 bps case (see Figure 4.19), the Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 96 FER performance of the ideal scheme, Butler's BRDA and the JRDDDA overlaps, but Cohen's BRDA has an obvious degradation. It is observed from Figure 4.19 to Figure 4.22 that Butler's BRDA starts to degrade when the data rate reaches 4800 bps or lower. In the 1200 bps case (see Figure 4.22), both Cohen's BRDA and Butler's BRDA suffer from a significant FER performance degradation compared to the proposed JRDDDA. In the 1200 bps case, the proposed JRDDDA outperforms Cohen's BRDA and Butler's BRDA by 2.3 dB and 2.6 dB in terms of the required Ei/N, at a FER of 10"2, respectively. All rates in three-path fading 3.5 4 Eb/Nt (dB) 4.5 Figure 4.18 FER in the three-path Rayleigh fading channel in the case of all rate frames Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 10 9600 bps in three-path fading -e- Ideal - B - Cohen - V - Butler - M — Joint r ! "! ~* ^ ^ ^ ^ ^ ^ ' ' ' 3.5 4 Eb/Nt (dB) Figure 4.19 FER in the three-path Rayleigh fading channel in the case of 9600 bps frames 4800 bps in three-path fading 3.5 Eb/Nt (dB) -0- Ideal -S - Cohen - V - Butler Joint Figure 4.20 FER in the three-path Rayleigh fading channel in the case of 4800 bps frames Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 10 2400 bps in three-path fading ::::::::::::::::h::::::::::::::h::::::::::::::J:::::::::::::::: -e- Ideal - B - Cohen - v - Butler —*— Joint r ! i ! ! ! : ; ! 3 3.5 4 Eb/Nt (dB) 4.5 Figure 4.21 FER in the three path Rayleigh fading channel in the case of 2400 bps frames 1200 bps in three-path fading 3.5 Eb/Nt (dB) Figure 4.22 FER in the three path Rayleigh fading channel in the case of 1200 bps frames Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 99 4.3.3.2 FRDR Performance Simulated FRDR performance in the three-path fading channel is shown in Figure 4.23. The FRDR performance of Cohen's BRDA and Butler's BRDA is also included in the same figure for comparison. It is shown in Figure 4.23 that the proposed JRDDDA outperforms both Cohen's BRDA and Butler's BRDA in terms of the FRDR. It is observed that in the 9600 bps case, Butler's BRDA provides approximately the same FRDR as the JRDDDA. Similarly as in the case of the AWGN channel, the FRDR performance of Butler's BRDA starts to degrade when the data rate reaches 4800 bps or lower. It is obvious that Cohen's BRDA has a very high FRDR in the 9600 bps case. In the two lower rate cases, the FRDR performance of the proposed JRDDDA is more than an order of magnitude lower than both Cohen's BRDA and Butler's BRDA for a given Ey/N, in the three-path Rayleigh fading channel. All rates in three-path fading -B- Cohen -V- Butler —«— Joint I" r ; ; 1 j L 3^_^_^ . J ::::::::::::::'5i!!rr^ H E^ i i !• > s " j j.TvC^ I^ . i N. i" i ^ i \L i 2 2.5 3 3.5 4 4.5 5 Eb/Nt (dB) Figure 4.23 FRDR in the three-path Rayleigh fading in the case of all rate frames Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 9600 bps in three-path fading 3.5 4 Eb/Nt (dB) Figure 4.24 FRDR in the three-path Rayleigh fading in the case of 9600 bps frames 4800 bps in three-path fading 3 3.5 4 Eb/Nt (dB) Figure 4.25 FRDR in the three-path Rayleigh fading in the case of 4800 bps frames Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 2400 bps in three-path fading - S - Cohen - V - Butler - * - Joint Eb/Nt (dB) Figure 4.26 FRDR in the three-path Rayleigh fading in the case of 2400 bps frames E b / N t ( d B ) Figure 4.27 FRDR in the three-path Rayleigh fading in the case of 1200 bps frames Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 102 4.3.3.3 Channel E/JN, Mismatch In this subsection we present the FER degradation due to Ej/N, mismatch between the true E//N, and the estimated Ef/N, in the three-path Rayleigh fading channel. Simulated FER perfor-mance versus mismatched E/N, is plotted in Figure 4.28. Note that the true Ej/Nt is 4 dB. It can be seen from Figure 4.28 that the FER performance does not degrade appreciably if the estimated Ej/ Nt is within 2.0 dB around the true value. In other words, there is about 4 dB tolerance in terms of Ef/N, mismatch. In the three-path Rayleigh fading channel, overestimation of E//N, is as detrimen-tal as underestimation. This is similar to the one-path Rayleigh fading case but different from the AWGN channel case where overestimation is less detrimental than underestimation (see Figure 3.19). Figure 4.28 FER versus channel E^/N, mismatch in the three-path Rayleigh fading channel (true E^/N,^ dB) Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 103 4.4 C o m p l e x i t y The purpose of this section is to discuss the complexity of the proposed JRDDDA in comparison with the two well-known BRDAs (Cohen's pre-decoding BRDA and Butler's post-decoding BRDA). The JRDDDA proposed in this thesis falls into the post-decoding BRDA, which requires Viterbi decoding of all possible rates. Compared to the Butler's post-decoding BRDA shown in Figure 2.12, the proposed JRDDDA does not require re-encoding the four decoded bit streams, and as a result, the complexity of the proposed scheme is less than that of Butler's BRDA. However, with the post-decoding BRDAs shown in Figure 2.12 and Figure 4.3, the Viterbi decoder invokes most of the computational complexity. Therefore, the proposed JRDDDA has approximately the same order of complexity as Butler's BRDA. The complexity of a Viterbi decoder is mainly due to performing Add-Compare-Select (ACS) operations for updating the surviving paths and the corresponding path metrics [53], [55]. For a convolutional code with a constraint length of K, the complexity of Viterbi decoding of A^ information bits is on the order of Nb2K~l ACS operations. Let Od denote the decoding complexity of the 9600 bps frames in the case of the IS-2000 CDMA RC1. Since the constraint length of the rate 1/2 convolu-tional code employed is K=9 and the number of information bits is A ,^=Fj=192 (see Figure 2.10) for the 9600 bps frames, Od is on the order of 192*29_1=49152 ACS operations. Given the decoding complexity for the 9600 bps frame is Od, the decoding complexity for the 4800 bps, 2400 bps and 1200 bps frames is OJ2, OdIA, and 0/8, respectively. The total decoding complex-ify of the JRDDDA and Butler's BRDA is about \.%150d in terms of ACS operations. A pre-decoding BRDA like Cohen's performs Viterbi decoding of a received frame only once, and thus the complexity of Cohen's BRDA is about Od at the peak1, which is about half the complexity of Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 104 the two post-decoding BRDAs. The complexity of the three rate detection schemes is summarized in Table 4.3. Table 4.3 Complexity of different rate detection schemes Rate Detection Scheme Complexity JRDDDA 1.8750^ Butler's 1.8750rf Cohen's With the advances in VLSI technologies, the complexity of Viterbi decoding can be allevi-ated by an application specific integrated circuit (ASIC), or Viterbi decoder accelerator. Accord-ing to IS-95/IS-2000 CDMA mobile hardware architecture, in fact, the Viterbi decoder is commonly implemented in an ASIC [77] and integrated into a chipset [78], [79]. The current drain for performing Viterbi decoding is typically less than 5 mA. It takes about 6 ms to complete the four-times Viterbi decoding in the case of the IS-2000 CDMA RC1. This power consumption is considered to be insignificant compared to the total current drain by the radio and other components like CPU and DSP chips, which can amount to 300 mA for a class III mobile station or a hand-held device during the talk time. Since the complexity of a pre-decoding BRDA is half of the proposed JRDDDA, the current drain saving using the pre-decoding BRDA is about 5 mA A system design normally accounts for the peak computation requirement. Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 105 in a 3 ms duration out of a 20 ms frame duration, which is negligible compared to the 300 mA total current drain in a 20 ms duration. It should be mentioned that the rate detection algorithm does not operate in standby mode, meaning there is no impact on the standby time at all. For a real-time transmission like voice or video, the end-to-end delay should be minimized. In order to reduce the processing delay at the receiver, the channel decoding should be scheduled to run immediately upon receiving a frame of demodulated symbols, followed by the source decoding. The processing delay at the receiver (the time for completing the four-times Viterbi decoding) in the case of Radio Configuration 1 in the IS-2000 CDMA standard is approximately equal to 6 ms. The allowable processing delay is up to 40 ms. It is clear that the complexity and processing delay of the proposed scheme are not an issue. 4.5 Conc lus ions In this chapter we have investigated the joint rate detection and data decoding algorithm for variable-rate data transmission in DS-CDMA communications systems in the multipath Rayleigh fading channel cases. The standard one-path and three-path Rayleigh fading channels are considered. Simulation results have shown that the proposed scheme can achieve virtually the same FER performance as the ideal case in the multipath fading channels. Performance compari-son between the JRDDDA and two well-known BRDAs (Cohen's and Butler's) are provided in this chapter. Simulation results in the previous chapter and this chapter have shown that the proposed JRDDDA significantly outperforms the two BRDAs in terms of the required Ef/Nt for a given FER or FRDR in both the AWGN and the multipath Rayleigh fading channels. It is also shown that the complexity and processing delay of the proposed JRDDDA are not an issue. In summary, the proposed JRDDDA not only offers a superior performance, but also is viable in a Chapter 4 Joint Rate Detection and Data Decoding Algorithm in Multipath Rayleigh Fading Channels 106 real implementation. It is worthwhile to mention that the proposed JRDDDA is general with regard to the number of data rates although the case of four data rates is used to illustrate the concept of the JRDDDA. In other words, the JRDDDA can be straightforwardly extended to the cases of any number of data rates. 107 Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 5.1 Introduction It has been known for some time that any redundancy in the source can be utilized to combat the effect of channel noise at the receiver. The use of source statistics by the receiver has been shown to give very significant performance improvement for vector quantization, speech coding and image transmission applications where the bit sequence redundancy is exploited for mitigating the effect of the noisy channel [90], [95], [97]. Techniques for utilizing the source statistics by the receiver are usually referred to as joint source and channel coding (JSCC) [89], [92]. Using voice transmission as an example, we have found that the frame rates from a vocoder's output are strongly correlated. The purpose of this chapter is to develop a novel JSCC based Rate Detection Algorithm (JSCC-RDA) for further improving the system performance of the basic BRDAs, such as Cohen's pre-decoding BRDA, Butler's post-decoding BRDA and the JRDDDA proposed in the previous two chapters. Rather than the more usual practice of utilizing bit sequence redundancy, in this JSCC-RDA, the rate sequence redundancy is exploited for combating the effect of the channel noise. This chapter is organized as follows. Firstly, some background on joint source and channel coding is briefly provided in Section 5.2. Secondly, the idea of a JSCC based rate detection scheme is introduced in Section 5.3. Thirdly, the variable-rate QCELP vocoder used in the JSCC scheme is briefly discussed in Section 5.4. A detailed discussion of the rate generation algorithm used by the vocoder is given in the same section. The rate transition probability and modeling of the rate sequence from the QCELP vocoder output based on a long training sequence is also Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 108 discussed in Section 5.4. Following Section 5.4, a JSCC based rate detection algorithm employing an instantaneous maximum a posteriori (MAP) algorithm is proposed in Section 5.5. Simulated results of the proposed JSCC based rate detection with Cohen's BRDA, Butler's BRDA and the JRDDDA are given in Section 5.6. Finally, some conclusions from this chapter are given in Section 5.7. 5.2 B a c k g r o u n d o f J o i n t S o u r c e a n d C h a n n e l C o d i n g ( J S C C ) Traditionally, the source and channel coders are separately designed due to Shannon's famous papers [84], [85], which demonstrate that the source and channel coding functions are fundamentally separable. In other words, the source and channel coders can be separated in such a way that the entropy rate reduction takes place in the source coder and the protection against channel errors in the channel coder. Viterbi and Omura [86] have clearly indicated that in order to achieve optimality, it is necessary to allow the source and channel coders to operate on sequences that are infinitely long. The fundamental fact is that the source and channel coding functions are only asymptotically separable, that is, they can be designed independently of each other and when connected together will not result in a loss in optimality, provided they operate on sequences that are infinitely long. In most practical communication systems like the cellular systems, it is impossible to process infinitely long sequences due to the limitations on system computational complexity and delay. As a result, practical systems based on separate source and channel coding design are not optimal, and may suffer performance degradation or inefficient use of the system power and bandwidth. Joint source and channel coding technique is not new, but recently it has received much attention because there is a new demand for lower complexity systems and/or more efficient use Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 109 of the transmission power and channel bandwidth in mobile communication systems. It has been shown that for a fixed degree of complexity and/or delay, the jointly designed source code/ channel code can outperform the separately designed pair [87]-[95]. In other words, a significant reduction in complexity with the same performance of separately designed systems can be achieved by JSCC systems. Ideally, a source coder removes all redundant information in the source and produces a sequence of independent code bits. However, in practice, limitation on the complexity or lack of exact information about the source results in residual redundancy in the source coder output sequence. A constrained JSCC receiver uses knowledge of this residual redundancy, similarly to the manner in which channel coders use knowledge of explicit redundancy, to protect against channel errors. The idea of a constrained JSCC system is supported by Shannon's celebrated paper [84] stating that in information transmission over a noisy channel, "redundancy must be introduced in the proper way to combat the particular noise structure involved. However, any redundancy in the source will usually help if it is utilized at the receiving point. In particular, if the source already has a certain redundancy and no attempt is made to eliminate it in matching to the channel, this redundancy will help combat noise." This statement forms the foundation of joint source and channel coding techniques. In practice, the source to be transmitted often has a certain memory or redundancy and due to certain constraints on complexity and delay, the transmitter makes no attempt to remove the redundancy. Instead, the source is transmitted directly over the channel. The problem thus is to design a receiver which fully utilizes the source redundancy to combat the effect of channel noise. As an example, a JSCC system based on a Vector Quantizer (VQ) is depicted in Figure Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 110 5.1. The source code is a VQ with block length of k and rate R=(1/k)log2N bits/sample or bits/ dimension, where N is the size of the VQ codebook. The VQ is memoryless in the sense that it operates on a block of k source samples independent of the rest of the data. The source {Xn} is assumed to be correlated from block to block and therefore, the VQ encoder output {/„} is also correlated. The correlation is known as the residual redundancy [92]. As shown in Figure 5.1, the sequence {/„} is transmitted across a discrete memoryless channel (DMC). At the receiver, MAP detection of the received sequence {/„} is performed. The MAP decoder output {/„} is then provided to the VQ decoder to obtain the reconstructed replica of the source {Xn}. VQ n DMC n MAP VQ Encoder Decoder Decoder Figure 5.1 Block diagram of JSCC system based on VQ and MAP decoder Though the purpose of the VQ encoder is to remove all of the source redundancy, it fails to do so mainly due to the limitation on the complexity or the block length k. If the source is highly correlated and k is small, the VQ encoder output is also correlated from one block to the next. The inherent redundancy in the data is exploited by the MAP decoder to combat channel errors. The VQ encoder can be thought of as a joint source and channel encoder. It acts as a source encoder because it reduces the source entropy. It also functions like a channel encoder since its output Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 111 contains redundancy. Although there is no explicit channel encoder in Figure 5.1, the MAP decoder is used to exploit the source residual redundancy for combating the effect of the channel noise. In other words, the MAP decoder can be thought of as a channel decoder. Many JSCC systems for speech transmission have been reported in the literature (see [97] and [98], for example). Recently, the development of constrained JSCC decoders for Differential Pulse Code Modulation (DPCM) transmission of digitized pictures has been an active research topic (see, for example, [92], [94], [95]). The encoder output is modeled by a Markov model, which is defined by the codeword-to-codeword transition probabilities, and the decoder uses the model to increase the probability of making correct decisions as to which codewords are transmit-ted over the noisy channel. The use of the source statistics by the receiver is shown to give very significant performance improvement when transmitting over a binary symmetric channel. As discussed above, JSCC has been applied to vector quantization, speech and image transmission systems. One important fact is that in all these JSCC systems, the bit sequence redundancy has been exploited for mitigating the effect of the noisy channel. In this thesis, we develop a new application of the JSCC concept, that is, a JSCC based rate detection system for variable-rate data transmission in DS-CDMA communication systems. In this new JSCC based system, the rate sequence redundancy instead of the traditionally used bit sequence redundancy is exploited for combating the effect of the channel noise. The idea of JSCC rate detection scheme is explained in the following section. 5.3 A J S C C B a s e d R a t e Detec t ion Sys tem The block diagram of a variable-rate DS-CDMA communication system for speech transmission is shown in Figure 5.2. Because voice transmission is used as an example, the Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 112 variable-rate data block in Figure 2.9 is replaced by a speech encoder which produces compressed speech data sequences at variable rates ri in accordance with speech activity. The decoded data sequence at the detected rate ri is fed to a speech decoder to reconstruct the original speech. All other blocks between the speech encoder and decoder are described in Section 2.2, 3.1 and 4.1. I-channel PNCode a{(t) Speech Encoder Convolutional | Encoder Symbol Repetition i 3 Q-channel PNCode a%(f) Speech Decoder i h Viterbi Y Block De-Decoder interleave I Basic BRDA Rake Receiver Figure 5.2 Variable-rate DS-CDMA communications system for speech transmission Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 113 An equivalent rate transmission system is shown in Figure 5.3, where the equivalent channel represents all the blocks between the speech encoder and decoder shown in Figure 5.2. Basically, the input to the equivalent channel is the source data rate rt, and the output is the detected data rate r(, which may not be same as the transmitted rate due to the channel noise. The cross-over probability between the transmitted and received rates depends on the rate detection error performance or false rate detection rate of a particular blind rate detection algorithm, such as Cohen's BRDA, Butler's BRDA, or the JRDDDA presented in Chapter 3 and Chapter 4. Speech n Equivalent Speech Encoder Channel Decoder Figure 5.3 Block diagram of an equivalent rate transmission system For voice transmission, we have found that there exists a strong correction among neighboring data rates. It will be shown in Subsection 5.4.3 that the rate sequence generated from the QCELP encoder can be modeled as a first order Markov sequence. This rate redundancy can be exploited to combat rate detection errors at the receiver since it is not going to be removed at the transmitter. Based on the equivalent rate transmission model shown in Figure 5.3, a JSCC based rate detection system is shown in Figure 5.4. The speech encoder functions as a joint source and channel coder regarding the rate sequence. A JSCC decoder is used to exploit the inherent rate redundancy for combating the effect of the noisy channel. As discussed in [87], both a Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 114 sequence MAP algorithm and an instantaneous MAP algorithm can be used as the JSCC decoder. However, it will be shown in Subsection 5.5 that only the instantaneous MAP algorithm can be applied here due to the delay constraint. The absence of an explicit channel coder means that there is no change at the transmitter for implementing the joint system. It will be shown that the JSCC decoder can be easily implemented in the existing variable-rate data transmission system at the receiver in Section 5.6. The vocoder and JSCC decoder used for this joint source and channel rate detection system will be described in the next two sections in detail. Speech Equivalent JSCC n Speech Encoder Channel Decoder Decoder Figure 5.4 Block diagram of a JSCC based rate detection system 5.4 JSCC Encoder - Variable-Rate Vocoder A central objective in the design of a cellular network for mobile communication is to maximize the capacity while maintaining an acceptable level of voice quality under varying traffic and channel conditions. Conventional FDMA and TDMA techniques dedicate a frequency channel or time slot to one unidirectional speech signal regardless of the fact that a speaker is silent roughly 50% of the time in a two-way conversation. Furthermore, when speech is present, the short-term rate-distortion trade-off varies quite widely with the changing phonetic character. Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 115 Thus, the number of bits needed to code a speech frame for a given perceived quality varies widely with time. The speech quality of coders operating at a fixed bit rate is largely determined by the worst-case speech segments, i.e., those that are the most difficult to code at that rate. Variable rate coding can achieve a given level of quality at an average bit rate that is substantially less than the bit rate that would be required by an equivalent quality fixed rate coder. CDMA can directly translate this rate reduction into a corresponding increase in network capacity. Variable rate coders can be divided into two main categories: (a) source-controlled variable rate coders, and (b) network-controlled variable rate coders. In source-controlled coding, the coder dynamically allocates bits in response to the short-term character of the speech source. Such coders are intended to maintain a desired level of quality for each short segment of speech with the fewest bits needed. Network-controlled variable rate coders can be viewed as multi-mode variable rate coders, where a different mode of encoding or perhaps an entirely distinct coding algorithm is performed for each bit rate option. A special case of particular interest is an embedded coder which offers a more elegant approach to external rate control. The first embedded coder is an ADPCM based one where a simple and effective method is available for achieving graceful degradation of quality as the rate is dropped. Recently, a method for achieving embedded coding in CELP type coders was introduced by Iacovo and Serno [80]. Source-controlled variable rate coders can readily be modified to include network control of the rate by simply forcing the coder to switch to one of the rates normally selected by source control. The QCELP coder includes both source-controlled and network-controlled rate features. We will use the QCELP variable-rate vocoder to demonstrate our approach to the joint source and channel coding based rate detection concept. The QCELP variable-rate vocoder will be briefly described below. The detailed description is provided in [41], [42]. Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 116 5.4.1 Q C E L P V o c o d e r The QCELP speech coder uses a code excited linear predictive (CELP) coding algorithm, which was first introduced in [44]. This technique uses a codebook to vector quantize the residual signal using an analysis-by-synthesis method. The speech codec produces a variable output data rate based on speech activity. For typical two-way telephone conversations, the average data rate is reduced by a factor of two or more with respect to the maximum data rate. There are two versions of QCELP vocoders: one is at 8 kbits/s and the other at 13 kbits/s. The QCELP vocoder at 13 kbits/s offers a better speech quality than the QCELP at 8 kbits/s. In structure, however, they are basically same. Thus, we will only give a description of the QCELP vocoder at 8 kbits/s, denoted by QCELP-8. This vocoder produces four variable rates based on speech activity. The definition of data rates is given in Table 5.1. For the highest data rate (m=1), for example, 171 bits are produced by the vocoder per 20 ms frame, resulting in a data rate of 8550 bps. The rate notation of /n=l, 2, 3, and 4 corresponds to the vocoder data rates of 8550, 4000, 2000, and 800 bps, respectively. The forward traffic channel frame rates corresponding to the four vocoder rates is summarized in Table 5.2. As shown in Table 5.2, by adding a mixed mode bit, frame quality indicator bits and encoder tail bits, the resulting channel frame rate is 9600, 4800, 2400 and 1200 bps corresponding to the vocoder data rate of 8550, 4000,2000 and 800 bps, respectively. Table 5.1 Variable rates provided by Q C E L P vocoder Rate Vocoder Vocoder Frame Notation m Bits/Frame Rate r™ (bps) 1 171 8550 2 80 4000 3 40 2000 4 16 800 Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 117 Table 5.2 Variable traffic channel data rates Rate Notation m Number of Bits per Frame Channel Data Rate (bps) Mixed Mode Bit Vocoder Bits Frame Quality Indicator Encoder Tail Total 1 1 171 12 8 192 9600 2 0 80 8 8 96 4800 3 0 40 0 8 48 2400 4 0 16 0 8 24 1200 The basic structure of the QCELP coder is depicted in Figure 5.5. The encoder consists of a rate generation function, a short-term format predictor l/A(z), a long-term pitch predictor \IB(z), a weighting filter W(z), and a normalized VQ codebook with a codebook gain G. The input speech signal, denoted by s(n), is sampled at a rate of 8 kHz. This speech signal is segmented into 20 ms frames consisting of 160 samples. The encoder dynamically selects one of four data rates every 20 ms, depending on the speech activity. The four data rates are given in Table 5.1. The rate genera-tion algorithm will be described in detail in Subsection 5.4.2. Based on the selected data rate, a bit allocation to the short-term format predictor \IA(z), long-term pitch predictor \IB(z), normalized VQ codebook and codebook gain G is determined. The bit allocation to the various operations is given in Table 5.3. The format filter \IA(z) of Figure 5.5 models the short-term correlation in the speech signal, that is, the spectral envelope of the speech signal, and has the form Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 118 A(z) = 1 - £ af, (5.1) i= 1 where {a,} are the short-term predictor coefficients, or linear predictive coding (LPC) coefficients and p is the order of the filter, which is chosen to be 10 in the QCELP vocoder. The LPC filter coefficients are updated once per frame, regardless of the data rate selected. The number of bits used to encode the LPC parameters is a function of the selected data rate as shown in Table 5.3. That is, 40,20,10 and 10 bits are allocated to quantize the LPC parameters for rate m=l, 2,3, and 4, respectively. The pitch filter \IB(z) models the long-term correlations in the speech signal, that is, the spectral fine structure, and has the general form r B(z) = 1- £ bfd+i\ (5.2) i = -q where d is the pitch period in samples and {bt} are the long-term predictor coefficients. A one-tap long-term pitch predictor is used in the QCELP vocoder. That is, the long-term filter has the form B(z) = l-b0z~d, (5.3) The pitch period, d, is represented by seven bits and ranges between 17 and 143 inclusive. The pitch gain, bQ, is represented by three bits and ranges from 0 to 2.0. Within each frame, the pitch parameters are updated a varying number of times, where the number of pitch parameter updates is also a function of the selected data rate. As shown in Table 5.3, there are four pitch subframes for a rate m=\ frame, two pitch subframes for a rate m=2 frame, and one pitch subframe for a rate m=3 frame. There are no pitch subframes for a rate m=4 frame. For each pitch subframe, the speech encoder determines and encodes the pitch period, d, and the pitch gain, b0. Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm A Code Book • • J i l l h4-Rate Generation rate r™ W(z) index (a) Encoder rate i Code Book Pseudorandom Vector Generator G A mi ±_ 1 JUL (b) Decoder Figure 5.5 QCELP vocoder structure: (a) Encoder and (b) Decoder Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 120 Table 5.3 Parameter update and bit allocations Parameter Rate m=\ Rate m=2 Rate m=3 Rate m=4 LPC updates per frame 1 1 1 1 Samples per LPC update 160 160 160 160 Bits per LPC update 40 20 10 10 Pitch updates per frame 4 2 1 0 Samples per pitch subframe 40 80 160 N/A Bits per pitch update 10 10 10 N/A Codebook updates per frame 8 4 2 1 Samples per codebook subframe 20 40 80 160 Bits per codebook update 10 10 10 6 The method used to select the pitch parameters is an analysis-by-synthesis method, where encoding is done by selecting parameters which minimize the weighted error between the input speech and the synthesized speech using those parameters. The synthesized speech is the output of the pitch synthesis filter filtered by the format synthesis (LPC) filter. The pitch period, d, is selected from the set {17, 18, . . ., 143}, and the pitch gain, b0, is selected from the set {0, 0.25, 0.5, . . . , 2.0} (linearly quantized between 0 and 2.0 in steps of 0.25). The perceptual weighting filter is of the form: A(z/k) where A(z) is the format prediction error filter and X, which equals 0.8, is a perceptual weighting parameter. The purpose of perceptual weighting of the error signal is to shape the noise spectrum in order to reduce the level of perceived noise. Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 121 The normalized codebook consists of 2M candidate excitation waveforms, where M=l is the codebook dimension. An analysis-by-synthesis technique is used to select the best candidate excitation using a perceptually weighted mean-squared error (MSE) criterion [44]. The codebook parameters are updated a varying number of times, where the number of updates is also a function of the selected data rate. Except for a rate m=4 frame, each pitch subframe consists of two codebook subframes (refer to Table 5.3). For each codebook subframe, the speech codec determines the codebook index, k, and the codebook gain, G. For a rate m=4 frame, only one codebook index and one codebook gain are determined for each frame. The method used to select the codebook vector and gain is an analysis-by-synthesis method similar to that used for the pitch parameters search procedure. In Figure 5.5, the decoder performs an inverse operation of the encoder. First a vector is taken from one of two sources depending on the received data rate. For the rate m=4, a pseudo-random vector is generated. For all other rates, a vector specified by an index is taken from the codebook, which is a table of vectors. This vector is multiplied by a codebook gain, and then is filtered by the long-term pitch synthesis filter whose characteristics are determined by the pitch period and gain. This output is filtered by the format synthesis filter whose characteristics are governed by the LPC coefficients to reconstruct a speech signal. 5.4.2 V o c o d e r R a t e G e n e r a t i o n A l g o r i t h m The QCELP vocoder uses an adaptive algorithm to determine the data rate for each frame. The algorithm keeps a running estimate of the background noise energy, and selects the data rate based on the difference between the background noise energy estimate and the current frame's energy. Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 122 In each frame, the previous estimate of the background noise energy is compared with the current frame's energy. If the previous estimate is higher than the current frame's energy, the estimate is replaced by that energy. Otherwise, the estimate is increased slightly. Figure 5.6 shows the energy in a few sentences of speech, and the background noise estimate for these sentences. When no speech is present, the background noise estimate follows the input signal energy. During active speech, the estimate slowly increases, but fluctuations inherent in the energy of the speech signal cause it to be reset continually. The data rate is then selected based on a set of thresholds Figure 5.6 Speech energy, rate thresholds and background noise estimate. which "float" above the background noise estimate. If the current frame's energy is above all three thresholds, the coder encodes the speech at the full rate (w=l). If the energy is less than all three thresholds, the coder encodes the speech at the lowest rate (w=4). If the energy is between rate thresholds 7 Background Noise Estimate Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 123 the thresholds, the intermediate rates are chosen. With this rate generation algorithm, background noise is almost always coded at the lowest rate (m=A) regardless of its energy. If the background noise suddenly increases, such as when a driver using a car phone opens his window, initially the background noise may be coded at the higher rates. After a few seconds the background noise estimate will rise to the new level of the noise and the background noise will once again be coded at the lowest rate. If the background noise suddenly drops, the estimate immediately drops with it, preventing speech from being coded at the lower rates. The detailed description of the signal energy estimation, the background noise estimation and the three threshold estimation is given below. The energy in a frame is estimated by the autocorrelation, denoted by R(0), which is computed as follows J?(0)= £ s > K ( " ) , (5.5) 71 = 0 where 1^ =160 is the frame size in samples and sw(n) is the windowed speech signal defined as sw(n) = s(n + 60)wH(n) for 0 < n < 160 - 1, (5.6) where wrfn) is the Hamming window whose value is specified in [41]. Note that there is an offset of 60 samples from the center of the current 160 sample frame of speech. The three thresholds are based upon an estimate of the background noise level, Bh com-puted for the current, or /'th frame. They are updated every frame before the rate is determined. First, an estimate of the background noise level Bi is computed for the current, or /'th frame using Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 124 the background noise level estimate Bx.x for the previous, or (i-l)sX frame and R(0)pKV, (which is the value R(0) for the previous frame) as follows: 5, = min(R(0) 5059644, majc(1.005475,_1,5,_1 + 1)), (5.7) where min(x,y,z) is the minimum of x, y, and z, and max(x,y) is the maximum of x and y. At initial-ization, the background noise estimate for the first frame, Bh is set to 5059644. If the audio input to the encoder is disabled, the background noise estimate is re-initialized whenever the audio is re-enabled. This prevents the silence before the audio is connected from being mistaken as unusually low background noise. Then, for 5 , < 160000, the three thresholds are computed as a function of Bj as follows: 7^(5 , ) = -(5.544613 x 10~ 6)5 ( 2 + 4.0471525,. + 362, (5.8) 7/ 2 (5,) = -(1.529733 x 10~ 5)5, 2 + 8.7500455- + 1136, (5.9) 7/3(5,.) = - (3.957050 x 10~ 5)5, 2 + 18.899625,. + 3347. (5.10) For 5 , > 160000, the three thresholds are computed as follows: 7/,(5,) = - (9.043945 x 10~8)52+ 3-5357485,.-62071, (5.11) r,(5,) =-(1.986007 x 10~7)52 +4.9416585.+ 223951, (5.12) 7,(5,) = - (4.838477 x 10~7)5? + 8.630025,. + 64586. (5.13) For the vocoder rate generation, the current speech energy R(0) is compared with the three thresholds: TjfBj), T2(BJ, and T3(Bj). If R(0) is greater than all three thresholds, the full rate (m=l) is selected. If R(0) is greater than only two thresholds, the second rate (m=2) is selected. If R(0) is greater than only one threshold, the third rate (m=3) is selected. If R(0) is below all three Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 125 thresholds, the lowest rate (m=A) is selected. During speech pauses, the acoustic signal is not really "silence". Background noise, at some level, is always present. The task of a rate generation algorithm is complicated because certain speech sounds have a very low energy level and are random in character and hereby often confused with background noise. To avoid detecting extremely brief pauses and to reduce the risk of audible clipping due to premature declaration of a silent interval when the background noise level is very high, some hangover time is desirable. During the hangover time, the rate generation can gracefully reduce the data rate during a transition from active speech to silence. Some constraints on rate selection are implemented in the QCELP vocoder. For example, the data rate is only permitted to decrease by one rate per frame. If the previous frame was encoded at the full rate and the initial rate selection for the current frame is the third rate or the lowest, then the second rate is chosen. Similarly, if the previous frame was encoded at the second rate and the initial selection for the current frame is the lowest rate, then the third rate is chosen. Figure 5.7 shows an example of voice data rate generation. Figure 5.7 (a) represents a 5000 ms speech signal. Figure 5.7 (b) displays the estimated speech energy R(0), the three rate decision thresholds, Th T2, and T3, and the background noise estimate Bt corresponding to the speech signal shown in Figure 5.7 (a). When no speech is present in the first 800 ms, the background noise estimate follows the input signal energy R(0). As seen in Figure 5.7 (b), the estimated signal energy R(0) is below all the three thresholds and as a result the lowest rate (m=A) is selected during this period (see Figure 5.7 (c) in the first 800 ms). When a voiced sentence (from 800 ms to 2000 ms in Figure 5.6) sounds, the signal energy R(0) increases and surpasses the thresholds T}, T2, and T3. In sequence, the selected rates are the third rate (m=3), the lowest rate Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 126 (m=4), the full rate (m=\), and so on, In summary, the function of QCELP coding is to compress the input speech samples into a bit packet at a reduced bit rate. As shown in Figure 5.8, the output of the QCELP coder includes data rate, denoted by mh and data frame, denoted by where / is the frame index. Given 160 samples of input speech, a frame of data is produced per 20 ms. The number of bit per frame is dependent on the data rate selected. For QCELP coding, there are four possible data rates as given in Table 5.1. In this thesis, we have investigated the rate transition probability of the rate sequence to aid the blind rate detection at the receiver side. A Markov model of the rate sequence will be discussed in the next subsection. 5.4.3 F i r s t - O r d e r M a r k o v M o d e l o f R a t e Sequences For an input speech sequence, the QCELP vocoder generates a rate sequence, denoted as r={rh r2, rt, ...}. In the IS-96 8 kbps QCELP vocoder, four discrete data rates are supported. They are 8550 bps, 4000 bps, 2000 bps and 800 bps, which are called rate r1, r2, r3 and r4, respec-tively. Let us denote the encoded rate sequence as r„ where / is the rate index and r^r1, r2, r3 or r4. The rate sequence is generated using the IS-96 8 kbps QCELP vocoder based on two-way conversations. The IS-96 8 kbps QCELP vocoder is implemented using the SPW commercial simulation package [83]. The speech database is sourced from Linguistic Data Consortium, University of Pennsylvania [82]. The training speech data used to generate rate sequences includes 16 minutes of male's and female's conversations or 7,680,000 speech samples (the sampling rate is 8 kHz). In other words, the training sequence consists of 48,000 frames of speech Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 127 Figure 5.7 An example of rate generation: (a) speech signal in 5000 ms, (b) speech energy, rate decision thresholds and background noise energy and (c) data rate Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 128 s(n) QCELP Encoder Figure 5.8 QCELP coding samples, each frame having 160 samples. After speech encoding, the output of the speech encoder includes a rate sequence of 48,000 rates and a data packet sequence of 48,000 packets. With regard to rate detection, we are only interested in the rate sequence. The rate transition probability is the probability of a current rate conditional on a previous rate, denoted by p(r^r(_,). The current rate and the previous rate can be one of the four rates. Therefore, there are 16 entries in the rate transition probability matrix. The rate transition probability of the rate sequence generated from the IS-96 QCELP 8 kbps vocoder is shown in Table 5.4. Our implementation of the vocoder is tested against the reference implementation in C program provided by Qualcomm, Inc. For a given speech sequence, our implementation generates the same rate transition probability as does the Qualcomm's reference. The rate transition can be drawn in a trellis diagram as shown in Figure 5.9. A circle represents a rate and a branch represents a transition from one rate to another. Each branch is labelled with a rate transition probability. In structure, this rate transition diagram is similar to the trellis diagram representing a convolutional or trellis code. Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm Table 5.4 Rate transition probability p ( ' / h - i ) r7=8550 bps ^=4000 bps r5=2000 bps /=800 bps r7=8550 bps 0.9424 0.0576 0.0000 0.0000 ^=4000 bps 0.2881 0.2494 0.4600 0.0000 r5=2000 bps 0.2546 0.1626 0.2393 0.3436 /=800 bps 0.1282 0.1068 0.2479 0.5171 Figure 5.9 Rate trellis diagram Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 130 5.5 J S C C D e c o d e r - M A P D e c o d e r f o r R a t e Sequences The proposed JSCC based rate detection system is depicted in Figure 5.4. The source coder is the 8 kbps QCELP speech encoder with four discrete data rates as described in the last section. The rate transition probability matrix p(r(|r._ j) of the rate sequence is estimated using a long training sequence and is tabulated in Table 5.4. For variable-rate CDMA transmission systems, the channel may be the AWGN channel, or the multipath Rayleigh fading channels considered in the previous two chapters. As described in Section 5.3, the equivalent rate transmis-sion channel can be modeled. Basically, the input to the equivalent rate transmission channel is the source data rate rh and the output is the detected data rate rt, which may not be the same as the transmitted rate due to the channel noise. Its input and output are from the same rate set {r1, r2, r3, r4}. The cross-over rate probability between the transmitted and received rates is provided by a basic blind rate detection algorithm such as Cohen's BRDA, Butler's BRDA and the proposed JRDDDA investigated in the last two chapters. The cross-over rate probabilities of the three basic BRDAs in the AWGN channel, the one-path Rayleigh fading channel, and the three-path Rayleigh fading channel are given in Subsection 3.3, Subsection 4.3.2 and Subsection 4.3.3, respectively. Specifically, the rate cross-over probabilities of the three basic BRDAs in the AWGN channel are shown in Figure 3.15 to Figure 3.18, the rate cross-over probabilities of the three basic BRDAs in the one-path Rayleigh fading channel are shown in Figure 4.13 to Figure 4.16, and the rate cross-over probabilities of the three basic BRDAs in the three-path Rayleigh fading channel are shown in Figure 4.25 to Figure 4.27. We denote the rate cross-over probability of the equivalent rate transmission channel as Q(Y= rAX= r() , where rt, r( e {r1, r2, r 3, r 4 }. The graphical representation of the rate cross-over probability is shown in Figure 5.10. Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 131 Q(Y= rt\X= r,) ^rO r ,1 Figure 5.10 Graphical representation of rate cross-over probability 5.5.1 Sequence M A P D e c o d e r Given the rate transition probability matrix P, the rate channel cross-over probability matrix Q and an observation sequence rn = {rx,rn), the sequence MAP decoder is that of finding the most probable transmitted sequence rn = {rv rn} where R" is all possible rate sequences of length n and R = {rl,r2,r3,r4}. By successively applying rate transition probability and the Markovian property of the rate sequence, the above rn = arg max Pr{rn\rn}Pr{rn}, rneR» (5.14) Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 132 equation can be expressed as rn = arg max U = 1 i = l (5.15) Since the logarithm is monotonic, the above is equivalent to rn = arg max rneR» M i ; i o 8 [e f t i r / ) p ( ' , / i r i - i ) ] + l o 8 [G ( ? i i r i ) / , ( r o)] -i= 1 (5.16) In the above form, the sequence MAP decoder can be implemented straightforwardly using the well-known Viterbi algorithm as described in Subsection 2.1.2.3. The trellis has 5=4 states. There are 5=4 branches entering and leaving each state. The path metric of the branch leaving state rk.j at time £-1 and entering state rk at time k is log[C2(/*,|rJ)P(rIjr/_ j)]. The delay of the sequence MAP decoder is quite large because the sequence MAP decoder must wait to observe the entire sequence rn before making a decision on the value of rn. For a real-time transmission of voice or video, the frame rate needs to be determined with a tolerable delay or no delay. In the following subsection, we are going to discuss an instantaneous MAP decoder to alleviate the delay issue. 5.5.2 Instantaneous MAP Decoder The instantaneous MAP decoder makes a decision on r(ri) as soon as r(n) is received. This problem was studied for vector quantization by Phamdo and Farvardin [88]. The most prob-able transmitted rate at time n is rn - arg max Pr{rn rn). (5.17) rneR» Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 133 (5.17) is equivalent to rn = arg max Pr{rn,rn}. rneR» (5.18) Let us denote the objective function that is to be maximized at time n by nO = Pr{rn,rn} (5.19) f(rn) can be expressed as the sum of the joint probabilities: f(rn)= £ Pr{rn,rn,rn_x} = I Pr{rn,rn}. (5.20) Each term in the summation can be expanded using the definition of rate transition probability f(rn) = X Pr{rn\rn}Pr{rn). (5.21) Given the rate transition matrix P and the rate cross-over probability Q, we can have the follow-ing: f n V n i n^i r/> n / , ^ i r ' - i > p < r i > (5.22) Taking out the common factor Q(rn rn) results in nrn) - Q(rn\rn) £ P(r„\rn_x)x r„^eR fn-l V - 1 s m^h> • rp< r <i r <-i> / , < r i> (5.23) Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 134 Comparing (5.22) and (5.23), we can see that the second summation in (5.23) is just fln ~l^(rn-1) • Hence, the instantaneous MAP decoder can be implemented using the following recursion: T^C/i) = Q(rx\rx)P(rx), (5.24) fn\rn) = Q(rn\rn) £ P<rt\rt_,) x / 0 - »(rH_,) . r„-\tR The most probable transmitted symbol at time n is: rn = arg max /">(/•„). (5.25) rneR Implementation of the instantaneous MAP decoder using the recursion (5.24) requires 2(S2+S) words of memory for storing P(.|.), Q(.\.), /")(.), fn~»)(.), S2+S multiplications, S2-S additions, and S-l comparisons per unit time, where S is the number of data rates. The complexity of the instantaneous MAP decoder in terms of memory locations, multiplications, additions and comparisons is given in Table 5.5 for various state numbers. In our example, there are only four data rates from the speech coder, or S=4. As seen from Table 5.5, the required memory locations are 40 words. If we consider each multiplication, addition or comparison as one operation, the required operations are 35, which is 0.00175 million instructions per second (MIPS) given a 20 ms frame. This complexity is very minimal or negligible compared to the capacity of a digital signal processor (DSP) used in mobile hand-held devices, which commonly has more than 100 kilo words (kword) of memory and over 50 MIPS of processing power. Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 135 Table 5.5 Complexity of instantaneous MAP decoder Number of States S Memory (words) Number of Multiplications Number of Additions Number of Comparisons 2 12 6 2 1 4 40 20 12 3 6 84 42 30 5 8 144 72 56 7 5.5.3 R a t e D e l a y C o n s t r a i n t Historically, the coding delay was never a concern for earlier high-bit-rate speech coders such as the 64 kbit/s pulse code modulation (PCM) or the 32 kbit/s adaptive differential PCM (ADPCM). These coders encode speech sample-by-sample. In contrast, most low bit-rate coders at or below 16 kbit/s encode speech frame-by-frame, where each frame contains many speech samples. A popular frame size for these coders is 20 ms, or 160 samples at the standard 8 kHz sampling rate for telephone-bandwidth speech. Due to frame buffering, such coders have much higher coding delays than PCM and ADPCM coders. Figure 5.11 depicts various delay components in the one-way transmission in a communi-cation system. The total one-way transmission delay is the sum of delays introduced by the speech encoder, channel encoder, channel, channel decoder and speech decoder. Since the speech encoding and channel encoding are done on a frame-by-frame basis, the delay introduced by speech encoder/decoder or channel encoder/decoder is equal to a frame duration. The channel delay is varying dependent on distance. Roughly speaking, the total one-way transmission delay Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 136 is four times the frame duration1 plus the channel delay. For the IS-2000 CDMA RC1, the frame duration is 20 ms and as a result the total delay is on the order of 80 ms, which is about the maximum delay tolerable in good quality voice transmission. Channel Encoder Channel Decoder Speech Decoder Figure 5.11 Block diagram of various delay components in the one-way transmission There are several reasons why a low transmission delay is desirable. First of all, a high transmission delay aggravates echo problems. Echoes with long delay degrade speech quality. Secondly, a long delay is annoying or intolerable in a normal two-way conversation. Speech coders have traditionally been characterized on the basis of three primary criteria: quality, rate, and implementation complexity. Recently delay has also become an important specification for many applications [81]. As discussed in the last subsection, the instantaneous MAP decoder does not introduce any extra delay. Due to the delay constraint, therefore, the instantaneous MAP decoder is used in our JSCC based rate detection scheme shown in Figure 5.4. In practise, the speech decoding delay may be smaller than one frame duration. For example, the reconstructed samples can be immediately delivered to a handset while the speech is being synthesized. Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 137 5.6 Simulated Results In this section, we present the simulated results of the proposed JSCC-RDA in the AWGN channel, the one-path Rayleigh fading channel, and the three-path Rayleigh fading channel discussed in Chapter 3 and Chapter 4. A block diagram of the proposed JSCC-RDA in a variable-rate DS-CDMA communication system is shown in Figure 5.12. The JSCC-RDA is applied to I-channel PNCode a'k(t) COS(2B/,0 • Pulse-p W x ) — • Shaping 1 w Filter Speech Encoder Convolutional Encoder Symbol Repetition ri ! • Block Interleaver Source Decoder Viterbi Decoder Q-channel PN Code a£(f) Y; v i JSCC Basic I Block De- Rake Decoder ~ A BRDA interleave Receiver Figure 5.12 Block diagram of joint source and channel coding based rate detection algorithm Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 138 three basic BRDAs, such as Cohen's BRDA, Butler's BRDA and the JRDDDA for performance improvement in terms of false rate detection rate. The same base station transmitter, channel and rake receiver as described in Chapter 3 and Chapter 4 are used in this simulation. The only change is the addition of JSCC decoder after a basic BRDA compared to the variable-rate DS-CDMA communication system shown in Figure 2.9. Conventionally, the received symbol sequence is decoded according to the detected rate r • of a basic BRDA. In our JSCC-RDA system, the detected rate sequence ri is fed into the JSCC decoder which exploits the rate sequence redundancy for further improving the false rate detection performance. The received symbol sequence is then decoded according to the detected rate sequence ri of the JSCC decoder. For comparison reason, Cohen's BRDA with the JSCC-RDA, Butler's BRDA with the JSCC-RDA and the proposed JRDDDA with the JSCC-RDA are running in parallel as shown in Figure 5.13. In the following simulations, an adequate number of error events are generated in order to achieve a 95% confidence interval of ±10 % ofthe average FRDR. Note that the FRDR performance of Cohen's BRDA without the JSCC-RDA and with the JSCC-RDA is labeled by "Cohen only" and "Cohen + JSCC", respectively, in the following plots. The FRDR performance of Butler's BRDA without the JSCC-RDA and with the JSCC-RDA is labeled by "Butler only" and "Butler + JSCC", respectively. Finally, the FRDR performance of the JRDDDA without the JSCC-RDA and with the JSCC-RDA is labeled by "JRDDDA only" and "JRDDDA + JSCC", respectively. 5.6.1 S i m u l a t e d Resu l t s i n the A W G N C h a n n e l Simulated FRDR performance of the proposed JSCC-RDA with Cohen's BRDA, Butler's Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 139 Rake Receiver Cohen's BRDA JSCC-RDA Compute FRDR Butler's BRDA JSCC-RDA Compute FRDR JRDDDA JSCC-RDA Compute FRDR Figure 5.13 Simulation setup for different rate detection algorithms with JSCC-RDA BRDA and the JRDDDA in the AWGN channel is given in Figure 5.14, Figure 5.15 and Figure 5.16, respectively. It is evident from Figure 5.14 that the proposed JSCC-RDA significantly improves the FRDR performance of Cohen's BRDA. There is about 1.2 dB gain in terms of the required Ef/N, at an FRDR of 10 - 2, and the error floor of Cohen's BRDA is also significantly reduced. It is shown in Figure 5.15 that the proposed JSCC-RDA provides about 0.6 dB gain for Butler's BRDA in terms of the required Eftft at an FRDR of 10~3 to lO" 2. Finally, Figure 5.16 shows that there is up to 0.3 dB gain by applying the JSCC-RDA to the JRDDDA in terms of the required Ej/N, at an FRDR of 10 - 3 to 1Q - 2. The reason why a smaller gain is obtained by applying the JSCC-RDA to the JRDDDA compared to the other two BRDAs can be explained as follows. The transitions from rate m-\ to m=\ and from rate m=4 to m=4 are more probable than other transitions as given in Table 5.4. The false rate detection from rate m=\ to the other rates or from rate m=4 to the other rates of the proposed JRDDDA is very low, while the false rate Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 140 detection from rate m=\ to the other rates or from rate /7*=4 to the other rates of Cohen's and Butler's BRDAs is much higher (see Figure 3.15 and Figure 3.18 of Section 3.3). That is why we can expect a significant improvement by applying the JSCC-RDA to Cohen's and Butler's BRDAs and a smaller improvement by applying the JSCC-RDA to the JRDDDA. For comparison, the FRDR performance of the JSCC-RDA with Cohen's BRDA, Butler's BRDA and the JRDDDA from Figure 5.14, Figure 5.15 and Figure 5.16 is re-drawn in Figure 5.17. It is evident that the JSCC-RDA with the JRDDDA significantly outperforms the other two combined algorithms in the AWGN channel. —*— Cohen only -e- Cohen + JSCC 10 0 . 5 1.5 2 2 . 5 Eb/Nt ( d B ) 3 .5 Figure 5.14 FRDR of JSCC-RDA with Cohen's BRDA in the AWGN channel 5.6.2 S i m u l a t e d Resu l t s i n the O n e - p a t h R a y l e i g h F a d i n g C h a n n e l The same one-path Rayleigh fading channel as described in Section 4.3 is used in this simulation. Simulated FRDR performance of the proposed JSCC-RDA with Cohen's BRDA, Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm Figure 5.15 FRDR of JSCC-RDA with Butler's BRDA in the AWGN channel Figure 5.16 FRDR of JSCC-RDA with the proposed JRDDDA in the AWGN channel Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 142 Figure 5.17 FRDR of JSCC-RDA with Cohen's BRDA, Butler's BRDA and the JRDDDA in the AWGN channel Butler's BRDA and the JRDDDA in the one-path Rayleigh fading channel is given in Figure 5.18, Figure 5.19 and Figure 5.20, respectively. Similarly as in the AWGN channel case, the proposed JSCC-RDA significantly improves the FRDR performance of Cohen's BRDA. For example, there is about 2 dB gain in terms of the required Ef/N, at an FRDR of \0~2. It is shown in Figure 5.19 that the proposed JSCC-RDA provides about 1.5 dB gain for Butler's BRDA in terms of the required Ei/Nt at an FRDR of 10 - 3 to 10 - 2. It is observed from Figure 5.16 that the proposed JSCC-RDA provides about 0.5 dB improvement for the JRDDDA. For comparison, the FRDR curves of the JSCC-RDA with Cohen's BRDA, Butler's BRDA and the JRDDDA from Figure 5.18, Figure 5.19 and Figure 5.20 are plotted together in one graph, as shown in Figure 5.21. It is seen from Figure 5.21 that the JSCC-RDA with the JRDDDA slightly outperforms the JSCC-Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 143 RDA with Butler's BRDA, but significantly outperforms the JSCC-RDA with Cohen's BRDA. 1 1 1 Cohen only Cohen + JSCC . -e-^^"^---^ i J r "—4"——— ^ i T " •—— 8 9 10 11 12 13 14 15 16 Eb/Nt (dB) Figure 5.18 FRDR of JSCC-RDA with Cohen's BRDA in the one-path Rayleigh fading channel 5.6.3 S i m u l a t e d Resu l t s i n the T h r e e - p a t h R a y l e i g h F a d i n g C h a n n e l The same three-path Rayleigh fading channel as described in Section 4.3 is used in this simulation. Simulated FRDR performance of the proposed JSCC-RDA with Cohen's BRDA, But-ler's BRDA, and the JRDDDA in the three-path Rayleigh fading channel is given in Figure 5.22, Figure 5.23 and Figure 5.24, respectively. Similarly as in the AWGN and one-path fading channel cases, the proposed JSCC-RDA significantly improves the FRDR performance of Cohen's BRDA in the three-path fading channel case (see Figure 5.22). For example, there is about 1.5 dB gain in terms of the required Ef/N, at an FRDR of IO - 2 , and the error floor of Cohen's BRDA is also sig-Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 144 Figure 5.19 FRDR of JSCC-RDA with Butler's BRDA in the one-path Rayleigh fading channel Figure 5.20 FRDR of JSCC-RDA with the proposed JRDDDA in the one-path Rayleigh fading channel Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 145 , 1 -Cohen + JSCC - B - Butler + JSCC " -e- JRDDDA + JSCC '. 1 •L : ; : i i ! ; i ! T I i I i Iii i i i I 8 9 10 11 12 13 14 15 16 Eb/Nt (dB) Figure 5.21 FRDR of JSCC-RDA with Cohen's BRDA, Butler's BRDA and the proposed JRDDDA in the one-path Rayleigh fading channel nificantly reduced. It is observed from Figure 5.23 that the proposed JSCC-RDA provides about 0.7 to 1.0 dB gain for Butler's BRDA in terms of the required Ei/N, at an FRDR of 10~3 to 10~2. In the case of the JRDDDA, however, there is a slight performance improvement by applying the JSCC-RDA to the JRDDDA (see Figure 5.24). For comparison, we have also plotted the FRDR curves of the JSCC-RDA with Cohen's BRDA, Butler's BRDA and the JRDDDA from Figure 5.22, Figure 5.23 and Figure 5.24 into one graph, as shown in Figure 5.25. It is seen that the JSCC-RDA with the JRDDDA appreciably outperforms the JSCC-RDA with Butler's BRDA, and significantly outperforms the JSCC-RDA with Cohen's BRDA in the three-path fading chan-nel. Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 146 I —*— Cohen only -e- Cohen + JSCC ; ' \ ; ! 2 2.5 3 3.5 4 4.5 5 Eb/Nt (dB) Figure 5.22 FRDR of JSCC-RDA with Cohen's BRDA in the three-path Rayleigh fading channel Figure 5.23 FRDR of JSCC-RDA with Butler's BRDA in the three-path Rayleigh fading channel Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 147 1 1 1 —+— JRDDD only - e - JRDDD + JSCC ;; I 1 1 ^ _ _ L _ 1 L_ 2 2.5 3 3.5 4 4.5 E b / N t ( d B ) Figure 5.24 FRDR of JSCC-RDA with the proposed JRDDDA in the three-path Rayleigh fading channel Figure 5.25 FRDR of JSCC-RDA with Cohen's BRDA, Butler's BRDA and the proposed JRDDDA in the three-path Rayleigh fading channel Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 148 5.7 C o n c l u s i o n s In this chapter, we have proposed a novel JSCC-RDA for further improving the FRDR performance ofthe basic BRDAs like Cohen's, Butler's and the JRDDDA. In this JSCC-RDA, the rate sequence redundancy instead of traditionally used bit redundancy has been exploited for combating the effect of the channel noise. We have used voice transmission as an example, and modeled the rate sequence from the vocoder's output as a first-order Markov source. The 8 kbps QCELP vocoder was used as the JSCC encoder. Due to the delay constraint on the real-time voice transmission, the instantaneous MAP decoder was used as the JSCC decoder to exploit the inherent rate redundancy. We have investigated the application of the proposed JSCC-RDA to Cohen's, Butler's BRDAs and the JRDDDA for performance improvement in terms of FRDR. Simulation results have shown that the proposed JSCC-RDA can provide up to 2 dB gain for Cohen's BRDA, 1.5 dB gain for Butler's BRDA and 0.5 dB gain for the JRDDDA in terms ofthe required Ej/Nt for an FRDR from 10~3 to 10 - 2. It is shown in Section 5.5.2 that such perfor-mance gain is obtained with a negligible complexity increase. Due to its low complexly, it is generally worthwhile to apply the JSCC-RDA to a basic BRDA for FRDR performance improve-ment. As discussed in Section 5.3, the JSCC-RDA can be viewed as a value-added device to any basic BRDA for improving the system performance in the presence of channel noise. In other words, this JSCC-RDA can be easily added to any basic BRDA for performance gain without changing other parts of the receiver. Both Cohen's BRDA and Butler's BRDA may have been implemented in deployed 2G CDMA systems. It would be very beneficial to incorporate the proposed JSCC-RDA into these systems for performance improvement. Although the proposed JSCC-RDA is only investigated in the case of variable-rate Chapter 5 Joint Source and Channel Coding Based Rate Detection Algorithm 149 transmission for voice, it should be straightforward to apply the JSCC-RDA to variable-rate transmission for image or video. 150 Chapter 6 Conclusions and Topics for Future Research This chapter summarizes the major conclusions in this thesis and presents some suggested topics for future research. 6.1 C o n c l u s i o n s Variable-rate data transmission is one of the key techniques to effectively reduce the mutual interference, and as a result increase the link capacity in DS-CDMA cellular communica-tion systems. We have proposed a novel joint rate detection and data decoding algorithm (JPJDDDA) for variable-rate data transmission in DS-CDMA communication systems. The performance of the proposed JRDDDA has been investigated by means of extensive computer simulation in the three well-employed, standardized channel models: the AWGN channel, the one-path Rayleigh fading channel, and the three-path Rayleigh fading channel. It has been shown that the proposed JRDDDA provides significant FER and FRDR performance improvement over the two well-known BRDAs (Cohen's pre-decoding BRDA and Butler's post-decoding BRDA) in all the three channel cases. The implementation complexity of the proposed JRDDDA is roughly two times that of the pre-decoding BRDA, but same as that of the post-decoding BRDA. As discussed in Chapter 4, the Viterbi decoder requires most of the computational complexity in the proposed JRDDDA. With the advances in VLSI technologies, the Viterbi decoder is commonly implemented in an ASIC and integrated into a chipset; in other words, the complexity of the proposed JRDDDA is not an issue. In summary, the joint rate detection and data decoding algorithm proposed in this thesis not only offers a superior performance, but also is viable in a real implementation. Therefore, it would be an attractive algorithm for the 3G DS-CDMA cellular communication systems. Chapter 6 Conclusions and Topics for Future Research 151 Furthermore, we have proposed a novel joint source and channel coding based rate detection algorithm (JSCC-RDA) which exploits the rate sequence redundancy for combating the effect of the noisy channel. The envisioned 3G cellular communication systems are aimed at providing users with wireless multimedia applications, such as voice, image and video. Using voice transmission as an example, we have found that the data rates from a vocoder's output are strongly correlated, and therefore, we have modeled the rate sequence from the vocoder's output as a first-order Markov process. Bit sequence redundancy has been traditionally exploited for vector quantization, speech coding, and image coding while our proposed JSCC-RDA instead exploits the rate sequence redundancy for combating the effect of the channel noise. Thus, the proposed JSCC-RDA is a new application of the JSCC concept to the blind rate detection problem. It has been shown that up to 2 dB gain in terms of the required Ej/Nt for a FRDR from 10"3 to 10-2 can be obtained using the proposed JSCC-RDA. It is shown in Chapter 5 that such performance gain is obtained with a negligible complexity increase. Moreover, the JSCC-RDA can be viewed as a value-added device to any basic BRDA for improving the system performance in the presence of channel noise. In other words, this JSCC-RDA can be easily added to any basic BRDA for performance gain without changing other parts of the receiver. 6.2 T o p i c s f o r F u t u r e R e s e a r c h Although this thesis presents a thorough investigation of the JRDDDA and the JSCC-RDA for variable-rate data transmission, there are several issues that remain to be explored. In this section, we discuss several important areas which require further study. Chapter 6 Conclusions and Topics for Future Research 152 6.2.1 C h a n n e l E b / N t E s t i m a t i o n The proposed JRDDDA requires an estimation of bit energy Eb and the total noise spectral density Nt. Investigation of channel Eb and Nt estimation in CDMA environments is an active research subject (see, for example, [73]-[76], [102]-[104]). It would be an interesting topic to investigate some channel estimation techniques for use with the proposed rate detection algorithm, and their impact on the system performance. 6.2.2 I m p o r t a n c e S a m p l i n g T e c h n i q u e We have investigated the FER and FRDR performance of our proposed rate detection algorithms by means of computer Monte Carlo simulation. Because of the system complexity in CDMA, the performance evaluation by computer simulation is largely limited by an excessive computational burden. For example, the Monte Carlo estimation of a FRDR on the order of 10 within 95% confidence interval of a 10% precision requires more than 105 independent simula-tion trials, each of which involves processing 384*64 chips in the case of IS-2000 CDMA RC1 [7]. This inefficiency of Monte Carlo is actually more acute for the multiuser detection receivers than for the matched filter receiver used in this thesis. Analytical performance-analysis-based methods are one way to alleviate this problem. However, CDMA cellular communication systems are operating in environments that are characterized by multiple access interference, intersymbol interference, multipath fading, and a host of other degrading effects. This leads to complex systems which make analytical performance-analysis-based method extremely difficult to apply. As a result, Monte Carlo simulations have often become the only feasible approach for CDMA communication systems. To alleviate the excessive computation problem in computer simulation, it would be interesting to study importance sampling (IS) techniques [100], [101] for use in the Chapter 6 Conclusions and Topics for Future Research 153 performance investigation of the proposed algorithms at a low FER and FRDR. 6.2.3 M u l t i u s e r D e t e c t i o n R e c e i v e r A conventional matched-filter receiver was used to illustrate the idea of the proposed blind rate detection algorithms in this thesis. However, the conventional matched-filter receiver follows a single-user detection strategy in which each user is detected separately without regards for the other users. Due to the limitations of the conventional matched-filter receiver, the link capacity of CDMA communication systems is limited by the MAI [14], [105]. To overcome this drawback, several multiuser detection receivers have been proposed in the recent years (see, for example, [105] and [106]). A multiuser detection receiver uses the information about the multiple users to improve detection of each individual user. Unlike the conventional receiver which treats the MAI as if it were the AWGN, multiuser receivers treat the MAI as additional information to aid in detection. It has been shown that significant improvement in the link capacity can be realized using the multiuser detection technique [107]. The performance of the proposed rate detection algorithms in the CDMA communication systems with multiuser detection receivers remains a subject of further research. 6.2.4 I m a g e a n d V i d e o T r a n s m i s s i o n We have used Qualcomm's 8 kbps vocoder to illustrate the idea of our proposed JSCC based rate detection in Chapter 5. It is clear that the wireless multimedia services including voice, image and video will be provided in the 3 G CDMA communication systems. Recently, image and video coding for wireless radio applications has become a very active research topic. 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Glossary 1G first-generation 2G second-generation 3G third-generation ACS Add-Compare-Select AMPS Advanced Mobile Phone System ASIC Application Specific Integrated Circuit BER Bit Error Rate BPSK Binary Phase Shift Keying bps bit per second BRDA Blind Rate Detection Algorithm CDMA Code Division Multiple Access CELP Code Excited Linear Predictive CRC Cyclic Redundancy Check DCCH Dedicated Control Channel DMC Discrete Memoyless Channel DS-CDMA Direct Sequence Code Division Multiple Access DSP Digital Signal Processor Eb Bit Energy Ei/N0 Bit Energy to Noise Spectral Density Ratio Es Symbol Energy FDMA Frequency Division Multiple Access Bibliography FER Frame Error Rate FM Frequency Modulation FRDR False Rate Detection Rate GSM Global System for Mobile communications i.i.d. independent and identically distributed IS Importance Sampling IS-95 TIA/EIA Interim Standard IS-95 IS-2000 TIA/EIA Resolution Version Standard IS-2000 JM Joint Metric JRDDDA Joint Rate Detection and Data Decoding Algorithm JSCC-RDA Joint Source and Channel Coding based Rate Detection Algorithm kbps kilo bits per second ksps kilo symbol per second kHz kilo Hertz LPC Linear Predictive Coefficient MAP Maximum a posteriori MIPS Million Instructions Per Second ML Maximum Likelihood N0 Spectral Density of Thermal Noise Nt Spectral Density of Total Noise OCNS Orthogonal Channel Noise Simulator pdf probability density function PN Pseudorandom Noise Bibliography QCELP Qualcomm Code Excited Linear Predictive QCELP-8 Qualcomm Code Excited Linear Predictive vocoder at 8 kbps QCELP-13 Qualcomm Code Excited Linear Predictive vocoder at 13 kbps QPSK Quadrature Phase Shift Keying SER Symbol Error Rate SNR Signal to Noise Radio TDMA Time Division Multiple Access VQ Vector Quantizer WCDMA Wideband Code Division Multiple Access 

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