Iterative Receivers for Space-time Block Coded OFDM Systems in Dispersive Fading channels Ben Lu, Xiaodong Wan Ye( Geoffrey)Li Department of Electrical Engineering School of Electrical and Computer Engineering Texas a&M Universit Georgia Institute of Technology College Station, TX 77843 Atlanta GA 30332 i benlu, wang @ee. tamu. edu liye(@ece gatech.edu Abstract- We consider the design of iterative receivers for drawback to any decision feedback system, when the decisions are space-time block coded orthogonal frequency-division multiplex ad. not accurate(e.g, in very fast fading channels ), the receivers in ing(STBC-OFDM) systems in unknown wireless dispersive fad- [5, 6] show error floors. In this paper, we approach the problem ing channels, with or without outer channel coding. First, we of receiver design without CSI by using iterative techniques, in- propose a maximum-likelihood(ML) receiver for STBC-OFDM cluding the expectation-maximization(E)algorithm [7 and the By assuming that the fading processes remain constant over the for sequence estimation in uncoded and coded systems. More re- duration of one STBC code word, and by exploiting the orthog- cently, in [9, 10], a receiver employing the Em algorithm, which onality property of the STbC as well as the OFDM modulation, exhibits a good performance but on the other hand a relatively high we show that the eM-based receiver has a very low computation complexity, is proposed for STC systems complexity, and that the initialization of the EM receiver is based In this paper, we focus on the design of iterative receivers on the linear minimum mean-square-error(MMSE) channel esti- for STBC-OFDM systems in unknown wireless dispersive fading mate for both the pilot and the data transmission. Since the ac- channels. We first derive the maximum likelihood(ML)receiver tual fading processes may vary within one STBC code word, we based on the EM algorithm for STBC-OFDM systems, under the also analyze the effect of a modelling mismatch on the receiver assumption that the fading processes remain constant over the du- performance, and show both analytically and through simulations ration of one STBC code word (or equivalently across several that the performance degradation due to such a mismatch is neg- jacent OFDM words contained in one STBC code word).Based ligible for practical Doppler frequencies We further propose a on such an assumption and the orthogonality property of the StB Turbo receiver based on the maximum a posteriori(MAP)EM as well as the OFDM modulation, we show that no matrix inver- algorithm for STBC-OFDM systems with outer channel coding. sion is needed in the EM algorithm. Therefore, the computational Compared with the previous non-iterative receiver employing a cost for implementing the EM-based ML receiver is low and the decision-directed linear channel estimator. the iterative receivers proposed here significantly improve the receiver performance and computation is numerically stable. Moreover, we show that the an approach the ML performance in typical wireless channels can achieve its minimum for both the pilot transmission mode and the data transmission mode(assuming correct decision feedback) well suited for real-time implementations Since the actual fading processes may vary over the duration of ne sTBC code word, we also analyze the effect of a modelling L INTRODUCTION imse as well as an upper bound on the instantaneous MSE Recently several studies addressing the design and applications of of the channel estimate in the initialization of the em algorithm ace-time coding(STC)have been conducted, e.g., [ 1, 2].Mean- ye show that the average mse due to a modelling mismatch is while, from the signal processing perspective, research on receiver ne negligible for practical Doppler frequencies. To further impre design for STC systems is also active. With ideal channel state the quality of the initialization step of the EM algorithm(andor to information(CSI), the iterative receivers based on the Turbo prin- reduce the computational complexity), following [5, 11, 12], the are al n concatenated STC systems [4]. When the CSI is not available poral filtering are adopted in the proposed EM-based mLreceiver [5, 6], the design of channel estimators and training sequences Finally, for STBC-OFDM systems employing outer channel cod vere studied and receiver structures based on the decision-directed g, we propose a Turbo receiver, which iterates between the max ast-square channel estimator or its simplified variant were pro- imum a posteriori(MAP)-EM STBC decoding algorithm and the sed for space-time trellis coded orthogonal frequency-division MAP channel decoding algorithm to successively improve the re- multiplexing (STTC-OFDM) systems. However, as a com ceiver performance in part by the U.s. National Science lation under grant CAREER CCR-98753 14 and grant CCR-9980599. The STBC-OFDM system is described. In Section Ill, an EM-based work of B. Lu was also supported in part by the Texas Telecommunications ML receiver for STBC-OFDM systems without outer channel cod Engineering Consortium(TxTEC) ing is developed In Section IV, an MAP-EM-based Turbo receiverIterative Receivers for Space-time Block Coded OFDM Systems in Dispersive Fading Channels Ben Lu, Xiaodong Wang Department of Electrical Engineering Texas A&M University College Station, TX 77843. ￾ benlu,wangx✁ @ee.tamu.edu Ye (Geoffrey) Li School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta, GA 30332. liye@ece.gatech.edu Abstract – We consider the design of iterative receivers for space-time block coded orthogonal frequency-division multiplex￾ing (STBC-OFDM) systems in unknown wireless dispersive fad￾ing channels, with or without outer channel coding. First, we propose a maximum-likelihood (ML) receiver for STBC-OFDM systems based on the expectation-maximization (EM) algorithm. By assuming that the fading processes remain constant over the duration of one STBC code word, and by exploiting the orthog￾onality property of the STBC as well as the OFDM modulation, we show that the EM-based receiver has a very low computational complexity, and that the initialization of the EM receiver is based on the linear minimum mean-square-error (MMSE) channel esti￾mate for both the pilot and the data transmission. Since the ac￾tual fading processes may vary within one STBC code word, we also analyze the effect of a modelling mismatch on the receiver performance, and show both analytically and through simulations that the performance degradation due to such a mismatch is neg￾ligible for practical Doppler frequencies. We further propose a Turbo receiver based on the maximum a posteriori (MAP)-EM algorithm for STBC-OFDM systems with outer channel coding. Compared with the previous non-iterative receiver employing a decision-directed linear channel estimator, the iterative receivers proposed here significantly improve the receiver performance and can approach the ML performance in typical wireless channels with very fast fading, at a reasonable computational complexity well suited for real-time implementations. I. INTRODUCTION Recently several studies addressing the design and applications of space-time coding (STC) have been conducted, e.g., [1, 2]. Mean￾while, from the signal processing perspective, research on receiver design for STC systems is also active. With ideal channel state information (CSI), the iterative receivers based on the Turbo prin￾ciple [3] are shown to be able to provide near-optimal performance in concatenated STC systems [4]. When the CSI is not available [5, 6], the design of channel estimators and training sequences were studied and receiver structures based on the decision-directed least-square channel estimator or its simplified variant were pro￾posed for space-time trellis coded orthogonal frequency-division multiplexing (STTC-OFDM) systems. However, as a common This work was supported in part by the U.S. National Science Foun￾dation under grant CAREER CCR-9875314 and grant CCR-9980599. The work of B. Lu was also supported in part by the Texas Telecommunications Engineering Consortium (TxTEC). drawback to any decision feedback system, when the decisions are not accurate (e.g., in very fast fading channels), the receivers in [5, 6] show error floors. In this paper, we approach the problem of receiver design without CSI by using iterative techniques, in￾cluding the expectation-maximization (EM) algorithm [7] and the Turbo processing method [3]. In [8], EM receivers are studied for sequence estimation in uncoded and coded systems. More re￾cently, in [9, 10], a receiver employing the EM algorithm, which exhibits a good performance but on the other hand a relatively high complexity, is proposed for STC systems. In this paper, we focus on the design of iterative receivers for STBC-OFDM systems in unknown wireless dispersive fading channels. We first derive the maximum likelihood (ML) receiver based on the EM algorithm for STBC-OFDM systems, under the assumption that the fading processes remain constant over the du￾ration of one STBC code word (or equivalently across several ad￾jacent OFDM words contained in one STBC code word). Based on such an assumption and the orthogonality property of the STBC as well as the OFDM modulation, we show that no matrix inver￾sion is needed in the EM algorithm. Therefore, the computational cost for implementing the EM-based ML receiver is low and the computation is numerically stable. Moreover, we show that the mean-square-error (MSE) in the initialization of the EM algorithm can achieve its minimum for both the pilot transmission mode and the data transmission mode (assuming correct decision feedback). Since the actual fading processes may vary over the duration of one STBC code word, we also analyze the effect of a modelling mismatch on the receiver performance, by considering the aver￾age MSE as well as an upper bound on the instantaneous MSE of the channel estimate in the initialization of the EM algorithm. We show that the average MSE due to a modelling mismatch is negligible for practical Doppler frequencies. To further improve the quality of the initialization step of the EM algorithm (and/or to reduce the computational complexity), following [5, 11, 12], the techniques of significant-tap-catching linear estimation and tem￾poral filtering are adopted in the proposed EM-based ML receiver. Finally, for STBC-OFDM systems employing outer channel cod￾ing, we propose a Turbo receiver, which iterates between the max￾imum a posteriori (MAP)-EM STBC decoding algorithm and the MAP channel decoding algorithm to successively improve the re￾ceiver performance. The rest of this paper is structured as follows. In Section II, the STBC-OFDM system is described. In Section III, an EM-based ML receiver for STBC-OFDM systems without outer channel cod￾ing is developed. In Section IV, an MAP-EM-based Turbo receiver