Soft-Output MLSE for IS-136 TDMA

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1 Soft-Output MLSE for IS-136 TDMA ABSTRACT - An inner estimator for concatenated maximum a posteriori decoding of convolutionally encoded DQPSK affected by time- and frequency-selective fading is derived and applied to IS-136 TDMA. The estimator is asymptotically optimal in the sense that the generated soft-decision metric constitutes a sufficient statistic for maximum a posteriori decoding of the convolutionally encoded data in the limit as SNR + -. By imposing a fixed-delay constraint, the estimator may be implemented as a straightforward generalization of the Viterbi Algorithm (VA). The simulation results confirm that gains Of Over db with respect to the hard-decision case can be obtained at high speeds and with significant delay spread. I. INTRODUCTION IS-136 TDMA [l] is one of the standards adopted for both digital cellular and high-tier PCS in the US. In [2], we presented an adaptive receiver based on a 4-state Maximum Sequence Estimator (MLSE) supported by a estimator with per-survivor TorbjiSrn Larsson Torrey Science Corp., San Diego, CA Angel Lozano Rockwell Semiconductor Systems, San Diego, CA George M. Peponides Istari Design, San Diego, CA applicable to non-binary modulation formats [4], such as z/4-dqpsk used in IS-136. Moreover, the work presented in [6-81 suggests the existence of superior algorithms of comparable or smaller complexity. In particular, the authors of [6] established the concept of an asymptotically optimal soft-output algorithm (AOSA), defined as an algorithm for which the soft-decision metric coincides with the a posteriori symbol probability in the limit as SNR+ 00. In this contribution, we present an AOSA for Is-136. Since Is-l 36 employs bit-wise interleaving, it is evident that optimal concatenated decoding will soft bit decisions. This in contrast to the soft-decisibn algorithms for non-binary modulation schemes presented in [6-81, which were designed to deliver soft information on a symbol-by-symbol basis only. 11. SYSTEMMODEL A number of different slot formats exist in IS-136, with distinct interleaving and coding. The interleaving spans only one slot (intra-slot) for the DCCH, two for processing that meets the IS-136 requirements at both the DTC data and the Fast Associated Control 800 MHZ and 1.9 GHZ and is thus suitable for dual- Channel (FACCH) in the DTC, eleven for the slow band operation. This MLSE, however, can only deliver Associated Control Channel (SACCH) in the DTC. The hard decisions because it finds the most probable path convo~ut~ona~ code has a constraint length of 6 and a sequence but it is unable to establish the specific prob- rate of 1/2 except for the FACCH, where the rate is 1/4. ability or reliability of each symbol and bit. Since all of the information transmitted the Digital Control To avoid confusion, we will focus on the DCCH case Channel (DCCH) of the information trans- because it has the most disadvantageous interleaving mitted on the Digital Traffic Channel (DTC) is convolu- fc" (intra-slot exclusively). Accordingly, all our retionally encoded, it would be desirable to modify the sults should only get better with inter-slot interleaving equalizer in order to generate. soft outputs which should especially at low speeds on the DTC. Out of the 296 bits improve the performance of the convolutional decoder composing a 260 are coded bits On the data considerably. corresponding to 125 information bits plus 5 tail bits. Accordingly, our block size will be N = 125 bits and the Word Error Rate (WER) will indicate the probability that one or more of those bits is in error. In our model (Fig. The first soft-output MLSE to appear in the literature was the Soft-Output Viterbi Algorithm (SOVA) [3]. Simplified versions of SOVA have been successfully employed in the GSM system. However, SOVA is less l), a rate 1/2 convolutional encoder maps a block of N source bits U, onto coded bit-pairs (C,,J,C,,~), which are /97/$ IEEE 53

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3 nality of this set. As an illustration, the set of paths in the channel trellis corresponding to the set xk,o(o) (associated with ci = 0) has been indicated in Fig. 2a. Since, according to Eq. (1) and Table 1, the bit ci is carried by the phase shift from xk-1 to xk, the set xk,)(o) contains dl sequences for which either xk = Xk-1 or xk j ' xk-1. Using the Gaussian noise assumption, it is now straightforward to show that 1 pr(rl ci,l= CJ = C zpr(ri x> = X X,,,(I) = zcexp{-t(x)/oi}, i=o,l, Z=O,1 (8) X X,,,(I) where C is a constant, T(x) = Ilr -y1i2 and y is the channel output vector corresponding to input vector x. It is T 3~12 (a) xk-3 xk-2 xk-l xk xktl I I I I c (b) 'k-3 xk-2 xk-l xk I I I I I b (c) xk-3 xk-2 xk-l xk xk+l I, I b Fig. 2. Systematic reduction of the set xk,o(o). (a) Original set. (b) After selection of survivors for time k - 1. (c) After selection of forward survivors for time k. assumed at this point that the receiver has perfect knowledge of the channel impulse response, although in practice the channel response is estimated. The summation in Eq. (8) is over all modulation sequences x for which c;,~ = i. For moderate-to-high SNR, the sum can be approximated by its largest term, as first proposed in [7]. Thus, letting Q(i) denote the particular member of the set xk,l(i) that minimizes r(x), we obtain the approximation 55 pr(rlci,l = 8 Cexp{-r(~k,l(i))/O;}. (9) Finally, substituting Eq. (9) into Eq. (7), the softdecision metric is obtained as The factor 0; is clearly irrelevant under a stationary noise assumption, and will be omitted in the following. Note that by the nature of the approximation in Eq. (9), the quantity in Eq. (10) becomes a sufficient statistic in the limit as 0; 0. Hence, any algorithm that generates pll according to Eq. (10) will be asymptotically optimal. Since the metric contribution in Eq. (6) takes the form of a correlation (with symbol values AA), we can expect the observed variable to exhibit Gaussian statistics. For the asymptotic approximation in Eq. ( 10) it is straightfoward to show that this is indeed the case in the limit as 0; 3 0, More specifically, it can be shown that with a probability that approaches 1 with increasing SNR, the observed soft-decision metric is given by 2 pi,, = (2ci,,-1)dmin + vn (11) where d&, is the minimum squared Euclidean distance of the IS1 channel, vn is a zero-mean Gaussian variable with variance a, = 2dmin.ow and c;,~ is the transmitted code bit. For an arbitrary but fixed two-tap channel, we have dkin = 2)lh112. The effective SNR seen by the outer system (i.e. the convolutional decoder) is therefore SNR,", = d;in /24 = II~II'/~ (12) which is identical to the SNR seen by the inner system at the output of the channel. Clearly, we cannot do better. What now remains is to specify an efficient algorithm for determining I?(&Ji)). We will exemplify the procedure by considering the computation of r(iik,o(o)). To this end, consider again Fig. 2a. Observe that the portion of kk,o(o) leading up to time k-1 must be one of the four survivors selected by the VA for the four states

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5 g loo lo- 10 ~ \ x Uncoded y 1 \\ \. \. frequency-selective channels. The core of the estimation algorithm was shown to consist of the VA with a modified add-compare-select operation. Simulation results indicate that gains of over 4 db in W R (with a word size of 125 bits) can be achieved by replacing the conventional hard-decision VA with the proposed softoutput MLSE algorithm. The price paid for this performance improvement is an increase in the number of arithmetic operations by roughly a factor of three or four (for the two cases D = 0 and D = 1, respectively) as compared to the regular VA. On the other hand, the generation of soft decisions does not require backtracing, which removes the cost associated with survivor memory management EdNO Fig. 4. WERversus Eb/No for a fixed (non-fading) tworay channel. Delay interval = T. a g Ispeed = 100 kmh I I I I I 1 V. CONCLUSIONS A soft-output maximum-likelihood sequence estimator suitable for IS-136 (as well as other systems employing DQPSK) has been presented. The estimator delivers asymptotically optimal soft bit-decisions for decoding of convolutionally encoded data transmitted over References IS- 136-A, TDMA CellularPCS - Radio Interface - Mobile Station - Base Station Compatibility, EIA/TIA, Oct A. Lozano and G. Peponides, Adaptive Equalization for TDMA 1.9 GHz High-Tier Personal Communications, to be presented at PIMRC 97, Helsinki, Finland, Sept J. Hagenauer and P. Hoeher, A Viterbi Algorithm with Soft-Decision Outputs and its Applications, IEEE Globecom 89, pp , Dallas, TX, Nov P. Hoeher, TCM on Frequency-Selective Fading Channels: a Comparison of Soft-Output Probabilistic Equalizers, IEEE Globecom 90, pp , San Diego, CA, Dec G. D. Forney, Concatenated Codes, MIT Press, Cambridge, MA, USA, U. Hansson and T. M. Aulin, Soft Information Transfer for Sequence Detection with Concatenated Receivers, IEEE Trans. Comm., Vol. 44, pp , Sept W. Kock and A. Baier, Optimum and Sub- Optimum Detection of Coded Data Disturbed by Time-Varying Intersymbol Interference, ZEEE Globecom 90, pp , Y. Li, B. Vucetic and Y. Sato, Output Detection for Channels Interference, IEEE Trans. In$ pp , May Optimum Softwith Intersymbol Theory, Vol. 41, 57