IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 52, NO. 4, JULY 2003 1173 [12] A. Svensson and C. Sundberg, “Optimum MSK-type receivers for CPM on Gaussian and Rayleigh fading channels,” Proc. Inst. Elect. Eng., pt. F, vol. 131, no. 5, pp. 480–490, 1984. [13] P. Galko and S. Pasupathy, “Linear receivers for correlatively coded MSK,” IEEE Trans. Commun., vol. COM-33, pp. 338–347, Apr. 1985. [14] P. Laurent, “Exact and approximate construction of digital phase modu- lations by superposition of amplitude modulated pulses (AMP),” IEEE Trans. Commun., vol. COM-34, pp. 150–160, Feb. 1986. [15] P. Jung, “Laurent’s representation of binary digital continuous phase modulated signals with modulation index 1/2 revisited,” IEEE Trans. Commun., vol. 42, pp. 221–224, Feb./Mar./Apr. 1994. [16] J. G. Proakis, Digital Communications, 3rd ed. New York: McGraw- Hill, 1995. [17] M. V. Eyuboglu and S. U. H. Qureshi, “Reduced-state sequence estima- tion with set partitioning and decision feedback,” IEEE Trans. Commun., vol. 36, pp. 13–20, Jan. 1988. [18] A. Svensson, C.-E. Sundberg, and T. Aulin, “A class of reduced com- plexity Viterbi detectors for partical response continuous phase modula- tion,” IEEE Trans. Commun., vol. COM-32, pp. 1079–1087, Oct. 1984. [19] S. Lin and D. J. Costello, Error Control Coding: Fundamentals and Ap- plications. Englewood Cliffs, NJ: Prentice-Hall, 1983. Per-Survivor Processing-Based Decoding for Space–Time Trellis Code Yisheng Xue and Xuelong Zhu Abstract—The problem of adaptive decoding of space–time trellis code on the time-variant wireless channels is considered in this paper. We show that per-survivor processing (PSP) can be adopted to obtain approximated adaptive maximum-likelihood sequence detection (MLSD) of space–time trellis code when there is no periodically inserted orthogonal pilot sequence. Then we propose a self-tuning least mean square (LMS)-based PSP decoder and a second-order LMS-based one. The former has the advantage that there are only fading rate-independent parameters to be predetermined, while the latter can offer fairly good performance on the moderately fast time-varying channels. Index Terms—Maximum-likelihood sequence detection (MLSD), per-survivor processing (PSP), space–time trellis code, Viterbi algorithm. I. INTRODUCTION Multiple-antenna transmission-reception has recently drawn inten- sive attention for its impressive capability in improving wireless spec- trum efficiency in the radio-link level (see [2] and [3], especially [4], and reference therein). Space–time trellis code is one such promising method and is believed to be able to improve the bandwidth efficiency as high as twice to four times of that of today’s wireless communica- tion system [5]. One problem in the application of space–time trellis code is the channel estimation at the receiver, because it is designed with the as- sumption that the decoder has perfect knowledge of the channel state information (CSI). To deal with this problem, the method of periodi- cally inserted orthogonal pilot sequence was proposed in [1] and [6]. In this way, the transmitter periodically inserts orthogonal pilot sequence into the transmission burst, while at the receiver an interpolation filter, Manuscript received May 2000; revised October 24, 2001. The authors are with the Department of Electronic Engineering, TsingHua University, Beijing, P. R. China (e-mail: xueys98@mails.tsinghua.edu.cn; xlzhu@mail.tsinghua.edu.cn). Digital Object Identifier 10.1109/TVT.2003.808807 Fig. 1. The considered wireless communication system. Fig. 2. The employed four-state QPSK-based space–time trellis code [5]. e.g., the Wiener interpolation filter (WIF) or the low-pass interpolation filter (LPIF) [1] is used to obtain a smoothed estimate of the CSI. Ob- viously, the power and bandwidth efficiencies are reduced due to the inserted pilot sequences, especially when the number of transmitter an- tennas is large. To reduce the channel estimation overhead, we study adaptive de- coding of space–time trellis code in this paper. When an adaptive de- coder is employed at the receiver, the pilot sequence is needed only at the beginning of each transmission burst for the receiver to get an ini- tial CSI estimate; then, in the data mode, the receiver tracks the channel with the aid of feedback decisions. By analyzing the maximum-likeli- hood sequence detection (MLSD)-based adaptive decoding, we show that per-survivor processing (PSP) [7] can be adopted to obtain prac- tical adaptive space–time trellis-code decoder with rational implemen- tation complexity. By “rational implementation complexity,” we mean that the well-known Viterbi algorithm can be used. Then, based on PSP, we propose two adaptive decoders: the self-tuning least mean square (LMS) [10]-based PSP decoder and the second-order LMS-based PSP decoder [13], [14]. The former has the advantage in that there are only channel-fading rate-independent parameters to be determined, while simulation results show that the latter can offer fairly good performance on moderately fast time-varying fading channels. By the way, some insightful discussions on the PSP-based MLSD can be found in the literature [8]. The paper is organized as follows. In Section II, we present the system model. Then, the PSP-based adaptive decoding of space–time trellis code is derived in Section III, followed by the development of the self-tuning LMS-based PSP decoder and the second-order LMS-based PSP decoder in Section IV. Section V presents the simulation results. This paper is concluded in Section VI. Throughout the paper, the super- scripts , , and denote transpose, Hermitan, and complex conju- gate, respectively; Pr represents probability distribution; Re de- notes the real part of ; denotes a unit matrix; and is a 2 1 zero vector. 0018-9545/03$17.00 © 2003 IEEE