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Adaptive Wireless Tranceivers L. Hanzo, C.H. Wong, M.S. Yee Copyright © 2002 John Wiley & Sons Ltd ISBNs: 0-470-84689-5 (Hardback); 0-470-84776-X (Electronic) L 5 1 Tbrbo-Coded and arbo-Equalised Wideband Adaptive Modulation In the previous chapter,we introduced the joint Adaptive Quadrature Amplitude Modulation (AQAM) and equalization scheme, where the pseudo-SNR at the outputof the DFE was used as the modulation mode switching metric in order to mitigate the effects of a wideband fading the channel. In this chapter, the widebandAQAM scheme is extended to incorporate benefits of channel coding. The general motivation for using channel coding is to exploit the error correction and the error detection capability of the channel codesin order to improve the BER and throughput performanceof the wideband AQAM scheme. As we have shown in Chapter 4, the wideband AQAM scheme was capable of yielding an improved BER and BPS performance, when compared to each individual fixed modulation mode. Since the wideband AQAM scheme improves the BER performance, high coding rate channel codes can be utilized in our coded AQAM scheme. The utilizationof these high coding rate channel codes is essential to produce a better coded throughput performance, when compared to the uncoded wideband AQAM scheme, which was discussed in the previous chapter. Since the wideband AQAM scheme always attempts to invoke the appropriate modulation mode in order to combat the wideband channel effects, the probability of encountering a received transmitted burst with a high instantaneous BER is low, when compared to the constituent fixed modulation modes. This characteristic is advantageous, since due to the less bursty error distribution, the coded wideband AQAM scheme canbe implemented without the utilization of high-delay channel interleavers. Consequently we can exploit the error detection capabilityof the channel codes almost instantaneously at the receiver for every received transmission burst. This is essential, since the error detection capability of the channel codes can provide the receiver with extra intelligence,in order to detect the modulation mode that was utilized. The channel codecs’ error detection capability can also be exploited in order to gauge the short term BER of each individual transmitted burst. Hence the short term BER can 123 124 CHAPTER 5. TURBO-CODED AND TURBO-EQUALISED ADAPTIVE MODULATION be used as a modulation mode switching metric, since it can quantify the impactof virtually ISI, etc. For example, to a all channel-induced impairments, such as signal strength variation, certain extent, this metric can incorporate the impactof co-channel interference. In our subsequent discussions the short term BER metric is not exploited, hence the interested reader is referred to the contributionsby Yee and Hanzo [43,44] formore details. In Section 5.1 turbo coding [ I521 is invoked in conjunction with AQAM and its performance is compared to that of the fixed modulation modes as well as to that of the uncoded AQAM scheme presentedin Section 4.3.5. Furthermore, in Section 5.6 channel coding is also exploited for detecting the modulation modes at the receiver. In Section5.7 it is shown that employing adaptive-rate turbo channel coding in conjunction with adaptive modulation results in a higher effective throughput, than fixed-rate channel coding. Our wideband AQAM scheme is then invoked in the context of turbo equalization in Section 5.10, where channel equalization [ 1531 and channel decoding is implemented jointlyand iteratively. The chapter is concluded in Section 5.1 I with a system design example cast in the context of a number of powerful wideband joint coding and modulation schemes, namely Trellis Coded Modulation (TCM), Turbo Trellis Coded Modulation (TTCM) and Bit Interleaved Coded Modulation (BICM). Recent work on combining conventional channel coding with adaptive modulation has been conducted for example by Matsuoka et al. [34], where punctured convolutional coding with and without an outer Reed Solomon (RS) code was invoked in a TDD environment. Convolutional coding was also used in conjunction with adaptive modulation by Lau in reference [52], where results were presentedin a Frequency Division Multiple Access (FDMA) and Time Division Multiple Access (TDMA) environment, when assuming the presenceof a channel feedback path between the receiver and transmitter. Finally, Goldsmith et al. [ 1.541 demonstrated that in adaptive coded modulation the simulation and theoretical results confirmed a 3dBcodinggain at aBER of fora4-statetrelliscode and acodinggain of 4dB was achieved by an 8-state trellis code over Rayleigh-fading channels, while a 128-state code performed within 5dB of the Shannonian capacity limit. Let us now briefly review the concept of turbo coding. 5.1 Turbo Coding Turbo codingis a formof iterative channel decoding that produces excellent results as demonstrated by Berrou et al. [ 152,1551 in 1993. The conceptof turbo coding canbe best explained by referring to its encoder and decoder structures. The schematic of the turbo encoder is in order to produce the shown in Figure 5.1. Explicitly, two component encoders are utilized, [ 152,1561 is placed before the second turbo code, where a so-called random turbo interleaver encoder. The general aim of the turbo encoder is to generate two independent component codes, which encode the same information bits. The role of the turbo interleaver is to ensure that the two encoded bit streams are independent from each other, due to the scramblingof the information bits by the interleaver. The component codesused in the encoder can be either block or convolutional codes.An example of a binary block code, which is amenable to turbo coding is the family of Bose-Chaudhuri-Hocquenghem (BCH) codes [ 1571 that possess multiple error detection and correction capabilities. Explicitly, each BCH code is represented by the notation BCH ( n , k , &in), where n, IC and dm,, denote the number of the encoded 5.1. TURBO CODING 125 Interleaver Figure 5.1: Turbo encoder schematic. bits, the number of information bits and the minimum Hamming distance,respectively. The number of parity bits is equal ton - k and the coding rate is.: The BCH encoder acceptsk information bits and by using a specific polynomial code generator [157], the parity bits are added in order to produce n coded bits. Thus, according to the encoding rules, only certain encoded sequences are legitimate.It is this distinction that enables the decoder to recognize and correct corrupted or illegitimate codewords. We will refrain from discussing the code generation and decoding mechanism, referring the reader to references [13,157-1591. By referring to Figure 5.1, the generated codewords are punctured and multiplexed,in order to produce the turbo code. However, puncturing of the parity bits is not applied to turbo BCH codes as proposed by Hagenauer [l601 and Pyndiah [161]. Consequently, for example, a component codeof BCH (31,26, 3) will yield a turbo block codeof BCH (36,26), where the additional five parity bits of the second encoder are includedin the output turbo block code, while the systematic information bits producedby the second encoder are discarded. The other family of constituent turbo encoders that can be utilized is Recursive Systematic Convolutional (RSC) codes, which is shown in Figure 5.2. Here, the constraint length is set to K = 3, and the generator polynomials are setin octal terms, to7 and 5 [ 1571. Referring to Figure 5.2, a streamof systematic bits, which represents the original information sequence is generated along with the corresponding parity sequence.In forming the convolutional-based turbo code, the systematic bits of the second convolutional encoder are discarded andtwo the sets of parity sequences are punctured accordingly. The puncturing pattern can be varied in order to produce different code rates. The iterative decoding structureof the turbo decoder is shownin Figure 5.3. The component decoders require soft inputs and produce soft outputs. Consequently, special decoding algorithms such as the Maximum A Posteriori (MAP) [ 1621 and the Log-MAP [ 1631 algorithms can be invoked, which were proposed by Bahl and Robertson, respectively. These algorithms are highlighted in Appendix A. 1 [ 1641. Essentially, the soft output generatedby either decoder determines whether the decoded bit aisbinary 1 or 0 as well as the reliability in Figure of the output bit decision. Let us now analyse in detail the decoder structure shown 5.3, where the notations L,1 and La2 represent the so-called a priori information produced by the first and second decoder, respectively. Similarly, L:' and LF2 denote the so-called a posteriori information of the first and second decoders, respectively. Finally, the so-called extrinsic information of the first and second decodersis labelled as L:' and L:2, respectively. At the receiver the soft channel outputs are generated, which consist of the systematic 126 CHAPTER 5. TURBO-CODED AND TURBO-EQUALISED ADAPTIVE MODULATION Systematic Bits Input Bits H . I l Parity Bits Figure 5.2: Recursive Systematic Convolutional (RSC) encoder. ~~ Soft Channel ~ ~. Interlv Parity 2 Decoder 2 . . .. . L, Figure 5.3: Schematic of the turbo decoder. and the parity bits, as illustrated in Figure 5.3. The two parity sequences generated by the turbo encoder are utilized by the corresponding decoders. In this respect, the punctured parity bits are replaced by zeros during the decoding process. In the first iteration, the first component decoder accepts the soft channel outputs by andutilizing the Log-MAP algorithm of Appendix A. 1 [ 1641, the decoder produces the a Posteriori log likelihood ratio (LLR) L:', which is defined as L ( u r L lin ~ )Appendix A.l [164]. Essentially this LLR represents the log-domain probability that the bit was decoded error freely. The polarity of this LLR can also be used in order to determine whether the decoded bit is a binary 1 or 0. Subsequently, the extrinsic information L:', is generated by subtracting the contribution of the channel outputs, as shown in Figure 5.3. This justifies the terminology 'extrinsic', sinceit represents 5.2. SYSTEM 127 the information related to a certain bit carried by sources other than the channel output itself related to this specific bit. Hence the extrinsic information is only influenced by the first decoder, which is then interleaved in order to generate the apriori LLR information L,1. For the sake of presenting the information to the second decoder in the right order, the systematic bits are interleaved in order to form the soft channel outputs as depicted in Figure 5.3. Subsequently, the second decoder utilizes not only the soft channel outputs but also the independent a priori LLR values L,1, from the first decoder in order to produce the a posteriori LLR LF2. This a posteriori LLR value is improved at this stage, since it was influenced by the estimates of both decoders. As before, the extrinsic information of the second decoder L:2, is generated by subtracting the channel information and the a priori information of the first decoder. This essentially removes any contribution generated by the first decoder, when producing the a priori information La2, of the second decoder, which is used in the first decoder for the subsequent iteration. This subtraction process allows us to maintain the independence of the decoding process, which is important for the sake of attaining independent estimates from the two separate decoders for each decoded bit. This process constitutes one turbo decoding iteration and it is repeated, in order to achieve better consecutive estimates of the decoded bits. After each iteration, the output a posteriori LLR is improved, since the decoder can exploit the independent a priori information generated by the other decoder. Consequently, as the number of iterations increases, the estimation of the decoded bit improves. The performance of the turbo decoder will vary depending on the size of the turbo interleaver, where a larger interleaver will provide a higher degree of independence of the a priori information that is being passed from one decoder to another. This high degree of independence is exploited by both decoders in order to yield an improved decoding performance. The number of iterations also plays an important role, where a higher numberof iterations will generally result in a better performance, although at the expense of a higher complexity. However, the gain achieved by each iteration reduces with increasing numbersof iterations, which will be exemplified by Figure 5.4. This is because the two decoders’ information becomes more dependent on each other, diminishing the benefits of acquiring two ’opinions’ concerning a given received bit. In the next section, the implementation of turbo coding in a wideband AQAM scheme is highlighted. 5.2 SystemParameters The system parameters that were used throughout our associated investigations are listed in Table 5.1. The channel coder parameters, which include the turbo interleaver size and code rate will be varied according to the different system requirements as it will be demonstrated at a later stage. The generic setupof the turbo codedAQAM scheme consistsof the modulation switching mechanism, the turbo coding parameters andthe switching thresholds. The modulation mode switching mechanism is identical to that discussed in Section 4.3.2 with the exception thatthe coding rate and the size of the turbo interleaver is varied according to the modulation mode 128 CHAPTER 5. TURBO-CODED AND TURBO-EOUALISED ADAPTIVE MODULATION COST207 TU(see Figure 4.12) Channel Type Normalized Doppler Frequency 3.25 x AQAM (NOTX, BPSK, 4QAM, 16QAM, Data Modulati 64QAM) with perfect channel estimation Receiver Type Decision Feedback Equalizer Number of Forward Taps = 35 Number of Backward Taps = 7 Correct Feedback Turbo Coding Parameters: Number of Iterations 6 Decoding Algorithm Log-MAP Table 5.1: Generic system parameters of the turbo codedAQAM scheme. selected. The modulation mode switching mechanism can be summarized as follows: Modulation Mode = i NOTX B P S K , I o , R0 4QAM, I,, R1 16QAM, 1 2 , R2 64QAM, 1 3 , R3 ~ ~ Y D F5E t; if tf < Y D F E 5 t; if t$ < Y D F E 5 ts if tg < Y D F E 5 tE if Y D F E > ti, (5.1) where I , represents the random turbo interleaver size in terms of the number of bits. The coding rate is denotedby R, and t k represents the coded switching thresholds. The switching thresholds for the codedAQAM scheme are difficult to numerically optimize in order to achieve a certain target BER due to the non-linear BER versus SNR characteristics of the scheme. However, the switching thresholds for the different turbo coded AQAM schemes are intuitively optimised,in order to achieve target BERsof below 1% and High-BER and Low-BER schemes, respectively. These 0.01%, which are termed as the coded schemes will be compared to the uncoded AQAM scheme, where the uncoded switching thresholds are set according to Table 4.8 for target BERs of 1%and 0.01%. The burst and the nonstructures used for theHigh- and Low-BER schemes are the non-spread speech spread data bursts, respectively, which were shown in Figure 4.13. 5.3 'Purbo BlockCodingPerformanceoftheFixed Modes QAM Before we attempt to characterize the Turbo Block Coded AQAM (TBCH-AQAM) scheme, of turbo coding,when applied to the constituent fixed modulation let us study the performance modes. In our experiments the component turbo channel code used was the BCH(3 1, 26, 3) scheme and a random turbo interleaver [l651 of size 9984 bits was chosen. The block channel interleaver size was set to 13824 bits, which corresponded to the channel-coded of the BPSK modulation block-length of the turbo interleaver.The turbo coding performance mode is shown in Figure 5.4, which displayed the BER performance for different number of 5.3. TURBO BLOCK CODING PERFORMANCE OF THE FIXED QAM MODES 129 10-l 5 2 l o-2 5 2 l 1 0 - 35 2 1o -~ 5 2 1o - 0~ \\ \ 15 5 10 Channel SNR(dB) Figure 5.4: Turbo block coded performance of BPSK for different number of iterations with a component code of BCH(31, 26, 3). The system parameters of Table 5.1 and the non-spread speech burstof Figure 4.13 was utilized. The channel interleaver size was set 13824 to bits. turbo iterations. The performance improved, as the numberof turbo iterationswas increased, which illustrated the improvement in estimating the decoded bit as a result of the iterative decoding regime. The iteration gain was approximately 2.ldB after six iterations at a BER of 0.01%. Explicitly, the iteration gain measured the difference between the average channel SNR required in order to achieve a particular BER and the corresponding average channel SNR required after n. iterations for the same BER. However, the improvements achieved upon each iteration decreased, as thenumber of iterations increased, as evidencedby Figure 5.4. The turbo block coded BER performance of the BPSK, 4QAM, 16QAM and 64QAM modes is shown in Figure 5.5 after six iterations using different channel block interleavers, where the uncoded performance is also displayed for comparison. Based on the turbo interleaver size of 9984 bits, the size of the channel interleaver was set to 13824 bits, which of the turbo block encoder. In order to assess corresponded to the channel-coded block-length of size 4 x 13824 was the impact of the channel interleaver size, a larger channel interleaver also utilized. As expected,in Figure 5.5 the BER performance using the larger channel interleaver was superior, when compared to that using the smaller channel interleaver, although at the costof an associated higher transmission delay. Referring again to Figure 5.5, substantial SNR gains were achieved, when comparing 130 CHAPTER 5. TURBO-CODED AND TURBO-EQUALISED ADAPTIVE MODULATION - IO 15 1 x 13824 itlv. 20 25 30 Channel SNR(dB) (a) Turbo block coded performanceof BPSK and 4QAM. d l" 0 5 15 10 20 25 30 35 40 Channel SNR(dB) (b) Turbo block coded performance of I6QAM and 64QAM Figure 5.5: Turbo block coded performance of each individual modulation modes after six turbo iterations utilizing the system parameters of Table 5.1 and the non-spread speech burst of Figure 4.13. A component code BCH(31, 26, 3) was utilized in conjunction with channel interleavers of size 13824 bits and 4x 13824 bits. 5.4. FIXED CODING RATE, FIXED INTERLEAVER SIZE TURBO CODED AQAM 131 the coded and uncoded performance. However the gains achieved at a BER of 0.01% was higher than those achieved at a BER of l%, as evidenced by Figure 5.5. This observation is important in the contextof turbo block codedAQAM scheme, which will be presentedin the next section. 5.4 FixedCodingRateandFixedInterleaver Size Turbo Block Coded Adaptive Modulation In this Fixed Coding Rate and Fixed Interleaver Size Turbo BCH Coded AQAM (FCFITBCH-AQAM) scheme, we utilized a random turbo interleaver of fixed size and a fixed coding rate for all modulation modes[ 1661. The turbo interleaver sizewas set to 9984and a of BCH (3 1, 26, coding rate of 0.7222 was utilized, which corresponds to a component code 3). The switching mechanism describedby Equation 5.1 was utilized in conjunction with the coded switching thresholds shown in Table 5.2 for the target BERs of l%, 0.01% and for a near-error-free system. Target BER < 1% 5 0.01% Near-Error-Free Coded Switching Thresholds (dB) t; ts t; ti 14.1846 Data 17.7589 Burst Type see Figure 4.13 8.1450 2.7258 0.1363 Speech Data 16.7589 9.7980 10.7980 4.4579 2.2458 Table 5.2: The coded switching thresholds, which were experimentally set in order to achieve the target BERs of below l%,0.01% and near-error-free for the FCFI-TBCH-AQAM scheme described in Section 5.4. The corresponding transmission burst types utilized are shown in Figure 4.13 and the switching mechanism was characterized by Equation 5.1. The BER and BPS performance of the FCFI-TBCH-AQAM scheme is shown in Figure 5.6 for the target BERs of 1% and 0.01%. The uncoded FCFI-TBCH-AQAM performance is also depicted for comparison.As expected, the coded BER performance improved signifof 1% and 0.01% icantly, when compared to the uncoded performance, and the target BERs were achieved. Conversely, the coded BPS was reducedby a factor equal to the coding rate. The BPS performance of the turbo block coded AQAM scheme was also compared to that of the fixed modulation modes for different channel interleaver sizes, as illustrated by Figure 5.7, where the throughput values were extracted from Figures5.5 and 5.6. Referring to Figure 5.7(a), where the channel interleaver was set to 13824 bits, the wideband AQAM scheme displayed throughput SNR gains of approximately l.0dB and 5.0dB for target BERs of 1% and 0.01%, respectively, when considering the corresponding BPS curves. However, by referring to Figure 5.7(b), when the larger channel interleaver was size utilized for the fixed modulation modes, the BPS/SNR gain was minimal fora target BER of 1% whilea BPS/SNR gain of approximately 1.5dB was observed for a target BER of 0.01%. The reduction in the AQAM scheme was due to throughput SNR gain achieved by the wideband turbo block coded fixed modulation modes. However, the superior performanceof the larger channel interleaved was incurred. it is important to note that an associated high transmission delay 3 132 CHAPTER 5. TURBO-CODED AND TURBO-EQUALISEDADAPTIVE MODULATION (a) Turbo block coded performancefor a target BER of below 1%. 10' 3 IO-' m , lo-( I od 'o-70 5 10 15 20 * ----- Uncoded BER W -- UncodedBPS 25 30 35 41 Channel SNR(dB) (b) Turbo block coded performancefor a target BER of below 0.01%. Figure 5.6: Turbo block coded and uncoded performance of the FCFI-TBCH-AQAM scheme described in Section5.4, where the generic system parametersof Table 5. l were utilized. The coded switching regime was characterized by Equation 5.1 with the coding rate and turbo interleaver size set to 0.7222 and 9984 bits, respectively. The coded switching thresholds and transmission burst type were set according to Table 5.2.