This paper studies the performance of turbo-coded system in the frequency non-selective correlated Rayleigh fading channels. The turbo-coded system employs a pilot-symbol-aided (PSA) technique for fading compensation and interleaving for spreading the error bursts to reduce the error rate. The PSA technique is also used to provide the decoder with channel side information (CSI) for better performance in fading channel. Two PSA techniques, three normalized Doppler spreads and different interleaving sizes have been investigated. Results of computer simulations have shown that, an improved first-order fading prediction technique can improve the BER performance by a factor of about 62, relative to those obtained using the pilot symbols only. Results have also shown that an interleaving depth equal to one-quarter the reciprocal of normalized Doppler spread can achieve a good BER performance.published_or_final_versionThe IEEE 49th Vehicular Technology Conference (IEEE-VTS 1999), Houston, TX., 16-20 May 1999. In IEEE-VTS Vehicular Technology Conference Proceedings, 1999, v. 3, p. 2413-241

Cheung, SW

Li, KL

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Title Performance of turbo codes with fading compensation inmultipath channelsAuthor(s) Li, KL; Cheung, SWCitationThe IEEE 49th Vehicular Technology Conference (IEEE-VTS1999), Houston, TX., 16-20 May 1999. In IEEE-VTS VehicularTechnology Conference Proceedings, 1999, v. 3, p. 2413-2417Issued Date 1999URL http://hdl.handle.net/10722/165254Rights IEEE-VTS Vehicular Technology Conference Proceedings.Copyright © IEEE.PERFORMANCES OF TURBO CODES WITH FADING COMPENSATION IN MULTIPATH CHANNELS K. L. Li and S .  W. Cheung Communications Research Group Department of Electrical and Electronic Engineering The University of Hong Kong Hong Kong e-mail: klli@eee.hku.hk, swcheung@eee.hku.hk PH: 852-2859-2425 FAX: 852-2559-8738 Abstract - This paper studies the performance of turbo- coded system in the frequency non-selective correlated Rayleigh fading channels. The turbo-coded system employs a pilot-symbol-aided (PSA) technique for fading compensation and interleaving for spreading the error bursts to reduce the error rate. The PSA technique is also used to provide the decoder with channel side information (CSI) for better performance in fading channel. Two PSA techniques, three normalized Doppler spreads and different interleaving sizes have been investigated. Results of computer simulations have shown that, an improved first-order fading prediction technique can improve the BER performance by a factor of about 62, relative to those obtained using the pilot symbols only. Results have also shown that an interleaving depth equal to one-quarter the reciprocal of normalized Doppler spread can achieve a good BER performance. I. INTRODUCTION Turbo codes have been shown to be close to the Shannon’s capacity limit in the additive white Gaussian noise (AWGN) channels [l]. In order to apply this powerful coding technique in wireless channels, more works have to be carried out. Some researchers have already investigated the applications of turbo codes over the fading channels [2-51. However, in these works, one of the important assumptions made is perfect phase tracking of the fading process. This assumption is not realistic because, in the fading environments both phase and amplitude distortions are introduced into the signals. Thus the signals will suffer significant degradation in the error-rate performances. There are different ways to counter fading. This paper proposes to use pilot-symbol-aided (PSA) transmission to counter fading. This is because the PSA process can easily be incorporated with the turbo coding process. In a turbo-coded system, the transmitted data-symbol sequence is turbo coded into frames of data symbols and so the pilot symbols can easily be inserted into these frames without any addition framing process [6]. At the receiver, the fading effects of the data symbols can be estimated and corrected before feeding into the turbo decoder for decoding. In section 2, the system model used in the computer simulations is introduced. Section 3 describes two PSA tecbniques for fading compensation and CSI extraction. Discussion of simulation results is given in section 4. Finally, section 5 summarizes our investigation. 11. SYSTEM MODEL The turbo-coded system studied here is shown in Figure 1. The turbo encoder is half rated and has the generator matrix (1,5/7)8 and a block size of 1000. The turbo encoder encodes the binary data { uk ) (where k is the integer symbol index), into the sequence { x i  , x[ }, where xf , x: E {-1, 1 } and the sequences { xi  } and { x: } represent the systematic sequence and parity- check sequences respectively. The coded symbols are fed to a block interleaver with a buffer of size M rows (depth) by N columns (span) to produce { d, }. The encoded symbols are written in successive M rows and transmitted over the channel in N columns. For every (L-1)-interleaved symbols, a known pilot symbol pr is inserted to form an L-symbol h m e  as shown in Figure 2. The resultant sequence { s k }  are filtered by a premodulation filter and then QPSK modulated. QPSK is used here because it can increase the bandwidth efficiency without increasing the complexity of system, relative to BPSK used in [4,5]. However, in QPSK, 0-7803-5565-2/99/$10.00 0 1999 IEEE 2413 because the systematic information is transmitted together with parity information in the same QPSK symbol(s), they are not corrupted by independent distortion; hence it can be expected that the error rate performance of QPSK is worse. The QPSK signal is then subjected to a time-varying frequency-nonselective Rayleigh fading channel where the signal s, is multiplied by a Rayleigh variable ck = A, + j = I c, I e’’ . The A, and are modeled as a statistically independent, real-valued and zero-mean Gaussian low- pass process whose bandwidth equals the Doppler shift. Without loss of generality we normalize the power of { c, } to unity. The AWGN process’s variables n, ’s are added to the faded symbol, where nk ’s are independent and identically distributed zero-mean complex Gaussian random variables with variance U: . At the receiver, the received sequence { rk‘ } is filtered by a postdemodulation filter which is taken to have the same characteristics as the premodulation at the transmitter. The resultant frequency response of the premodulation filter and postdemodulation filter in cascaded has a raised cosine roll-off of 100%. Assume that perfect carrier and clock recovery has been achieved. Thus, the signal at time t = kT sec can be written as rk = cksk + nk (1) where c, is the effects of fading introduced in the fading channel. By using the pilot symbols, the fading effects can be estimated and then used to compensate the fading effects on the coded symbols within the frame. Two prediction techniques are described in the following section. In Fig. 1, after fading compensation, the received coded symbols are deinterleaved to produce { y i  , ykp }, where { yf } and { y[ ) are the systematic and parity-check sequences fed to the turbo decoder implemented using the log-MAP algorithm. Eight iterations are used in the algorithm to obtain the binary data { i, } in the studies. In the study, it has been assumed that the receiver has a perfect knowledge of the variance U: . 111. PILOT-SYMBOL-AIDED TECHNIQUES First-Order Prediction [6] The sample signal in the i-th position of the k-th received pilot frame can be written as (2) rk,i = ‘k,iSk,i + nk,i where s,,~ is either a pilot symbol or a data symbol, is the change in the i-th symbol of the k-frame, n,,i is the noise sample in the i-th symbol of the k-frame. For i = 0, the sample signal is ‘k.0 = Pk,OCk,O + nk,O (3) where P , , ~  is the pilot symbol in the k-th m e .  Since the pilot symbol P,.~ is known at the receiver, cp,o can be obtained using Eqn. (3) as ‘k.0 ‘k,O Pk.0 PC.0 ck,o = - -- (4) The estimates of the fading effects for the rest of the data symbols { & }  can be obtained by first-order prediction, i.e. fori = 1,2, ..., L-1. The estimated signal effects in the received signal sample, rkai .is used to correct the fading Improved First-Order Prediction [6] For the frame lengths of 4, 8, 16, ..., 2n , a better BER performance can be obtained by the proposed fmt- order prediction using the pilot and data symbols. The changes on the pilot symbols in the k-th frame, & ,  and in the k+l-th frame, 2k+1,0, can be estimated from improved estimate of c,,,,, in the L/2-th symbol of the k-th frame is given by ‘k.07 Pk.09 rk+l,O 9 and Pk+l,O 7 using Eqn* (4)* The which is then used to correct the fading effect in r,,L,, to give an estimate of the data signal The signal F,,, is fed to the threshold detector to produce the data signal dk,L12 which is used as a known 2414 symbol to correct the data symbols r,,,,, and rk,3L14. Since is a possible signal vector on the constellation and r,,L,2 I dkJI2 is closer to c ~ , , , ~  and ck,3L14 in a slowly-faded channel, the better estimates of ck,,,, and can be obtained as, respectively, These signals &L,4 and ck,3L14 are used to correct r,, and rk,3L14 , respectively, to obtain the signals The process continues until all the coded symbols are done. The improved fmt-order prediction makes use of the pilot and data symbols for fading compensation and so has a better accuracy. However it has the constraint that the frame length must be 4,8, 16 . . . or 2”, where n is an integer. Here, a modification is used to remove this constraint as follows. The middle position of data symbols can be re-estimated using the neighbor pilot symbols as described previously. If the number of data symbols is odd, only one data symbol is required to estimate. Otherwise, the two data symbols in the middle positions are re-estimated. Then, the data frame is equally subdivided (e.g. 1000 data symbols divided into two 500 data symbols) and the newly estimated data symbols are used as the new references. The middle positions of divided frames are estimated again. The process is repeated until all data symbols are done. It has been shown that the modification of the channel reliability Lc = (2/0:)Ic,l in the BCJR-MAP algorithm, where Ic,l = ,/- is known as CSI, could greatly improve the BER performance [2]. Here. CSI for each symbol is used in the decoding process in this study. IV. RESULTS AND DISCUSSIONS Intensive Monte Carlo simulations have been carried out to evaluate the BER performance of the system of Figure 1. The signal-to-noise ratio is taken as where Eb is the average transmitted energy per bit (after taking into account the pilot symbols) at the transmitter output of Figure 1 and No is the one-sided power spectral density of the additive white Gaussian noise measured at the same point. The BER performances of the turbo coded signal, at SNR = 15 dB using 5O(depth)x 40(span) block interleaver, with different pilot frame lengths L and normalized Doppler spreads of fdT = 0.01, 0.005 and 0.001 are shown in Fig. 3. It can be seen that with fdT = 0.001, the performances are about the same with L = 10 to 100. However, with fdT = 0.005 and 0.01, degradation occurs from at L = 20 and 50, respectively. This is because in fast fading, the correction of fading has to be made more often than in slow fading. To assess the effective of the two prediction techniques, we define an improvement factor as follows: Improvement factor - (10) BER of system using pilot symbols only BER of system using pilot and data symbols The improvement factors withfdT = 0.01, 0.005 and 0.001, for different pilot kame lengths using 50 x 40 block interleaver, are shown in Figs. 4a, 4b and 4c, respectively. At low SNRs, none of the pilot symbol- aided technique is recommended because the presence of Gaussian noise reduces the accuracy of the estimates Zk,,,Ckj,&. With fdT=O.O1, a S N R  of 15dB and a pilot frame length L of 11, the BER performance can be improved by a factor of about 62. Whereas with fdT = 0.005, a S N R  of 15 dB and a pilot fiarne length L of 11, the improved factor reduces to about 32. With fdT = 0.001, a S N R  at 20dB and a frame length of 101, the improvement factor reduces to 1.6. Figure 4 shows that, if the pilot frame length L is too long, the improvement factor is less than 1 which means that the improved fmt-order prediction is worse than the fmt- order prediction. Ideally, the depth of block interleaver should be infinite to achieve independent fading. However, in a practical system, the interleaving depth M is finite, this implies that, the received symbols remain correlated after 2415 deinterleaving. Paul and Dominic [7] proved that an interleaving depth equivalent to one-fifth to one-quarter the duration of a fade cycle (defmed as the reciprocal of the maximum f d T )  is almost as good as full interleaving using Trellis Coded PSK modulations. On the other hand, the interleaving span is related to the memory of encoder. Thus, a larger span is required if the memory size increases. In this paper, we try to fmd out the optimum depth and span by computer simulations. Figures 5 and 6 show the BER performances using simple first-order interpolation prediction with L = 11 with fdT = 0.005. Figure 5 shows that an increase of interleaving depth from 25 to 50 has about 1.5 dB improvement at BER = 1E-3. An increase of interleaving depth from 50 to 100 has no significant on the BER performance. Figure 6 shows that improvements can be obtained by increasing the interleaving span from 20 to 100. (41 V. CONCLUSION Turbo (2.g) Block Decoder Deinterleaver The performances of a turbo-coded signal incorporated with PSA techniques and interleaving have been studied using computer simulations. Results of computer simulation have shown that, at high SNRs, and in the fast faded channels, the improved first-order prediction has substantial improvements in BER performance. The BER performance can be improved by a factor about 62 by using improved first-order prediction. Results have also shown that an interleaving depth equal to one-quarter the reciprocal of normalized Doppler spread should be enough to produce a good BER performance. REFERENCES (1) C. Berrou, A. Glavieux, and P. Thitimajshima, “Near Shannon limit error-correcting coding and decoding: Turbo-codes”, IEEE International Conference on Communications, ICC ’93, Genva, Switzerland, 23 May 93, Vol, 2. pp. 1064-1070 (2) Eric K. Hall and Stephen G. Wilson, “Design and Analysis of Turbo Codes on Rayleigh Fading Channels”, IEEE Journal on Selected Areas in Communications, Vol. 16, N0.2, February 1998, pp. (3) S .  A. Barbulescu, “Iterative decoding of Turbo Codes and other Concatenated Codes,” PhD Thesis, University of South Australia, 1996 (4) Li-Der Jeng, Yu T. Su and Jung-Tang Chiang,”Performance of Turbo Codes in Multipath 160- 174 Fading Channels”, Vehicular Technology Conference, 1998, VTC 98 48th IEEE Vol. 1 , pp.61-65 (5) Matthew C. Valenti and Brian D. Woerner, “Refined Channel Estimation for Coherent Detection of Turbo Codes over Flat-Fading Channels”, IEE Electronics Letters, Aug 20 1998, Vol. 34, No. 17, (6) H.K. Lau and S.W. Cheung, “Multipath Fading Compensation Techniques Using Pilot and Data Symbols in Mobile Radio Channels”, GLOBECOM ’94 : IEEE Global Telecommunication Conference, 1994, (7) Paul Ho, and Dominic K. P. Fung, “Error Performance of Interleaved Trellis-Coded PSK Modulations in Correlated Rayleigh Fading Channels”, IEEE Transactions on Communications, Vol. 40, No. 12, December 1992, pp.1800-1809 pp. 1648-1 650 pp. 1009- 101 3 1 Information Turbo 1 cg’51 I Block 1 Source Encoder Interleaver Generator Inseltion I I I Premoddation filter I Transmitter  Channel Postdemodulation filter Pilot Symbol Extraction & fading estimation U Figure 1: System model k-th frame Figure 2: Frame structure of transmitted symbol sequence 2416 1 1 .OE+OO +0.001 1 .OE-01 P) d 1.OE-02 ‘f! bij 1.OE-03 1.OE-04 -*c-o.oos -0.01  4 6 8 10 12 14 16 EWNo (a) Figure 4a 0.0 -[ ---.--.- r-_-- , --IT-- - 0 2 4 6 bhlNiyBj2 14 16 18 20 Figure 4c Figure 4: Improvement Factor with a) f d T  = 0.01, b) f d T  = 0.005 and C) f d T  = 0.001 1 ___-__ l.OE+OO r 1 .OE-01 32 2 E w Y .-m .OE-02 .OE-03 .OE-04 0 15 20 ’ Eb/NdPdB) Figure 5: BER performance with improved first-order prediction and different block interleaver sizes Mx40 3 1.OE-01 d 1.OE-02 w a 1.OE-03 Y .- 1 .OE-04 0 10 15 Eb/No(dB) 20  Figure 6: BER performance with improved first-order prediction and block interleaver size of 50 xN 2417 

Performances of turbo codes with fading compensation in multipath channels

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Performance of turbo codes with fading compensation in multipath channels

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