MIMO DETECTION USING MARKOV CHAIN MONTE CARLO TECHNIQUES FOR NEAR-CAPACITY PERFORMANCE Haidong Zhu ∗ , Zhenning Shi + , and Behrouz Farhang-Boroujeny ∗ ∗ ECE Department, University of Utah, USA, e-mails: haidongz@eng.utah.edu and farhang@ece.utah.edu + Wireless Signal Processing Group, NICTA, Australia, email: zhenning.shi@nicta.com.au ABSTRACT In this paper, we develop a new soft-in soft-out (SISO) multiple-input multiple-output (MIMO) detection algorithm using the Markov chain Monte Carlo (MCMC) simulation techniques and study its performance when applied to a MIMO communication system. Comparison with the best MIMO detection algorithm in the current literature, the sphere decoding, show that the proposed detection algo- rithm can improve the gap between the present results and the capacity by as much as 2 dB. 1. INTRODUCTION Transmission through multiple transmit and receive anten- nas, known as multiple-input multiple-output (MIMO) com- munication, has been widely studied in recent years [1, 2, 3]. MIMO communication promises an increase in the chan- nel capacity proportional to the minimum of the number of transmit and receive antennas. Furthermore, because of presence of alternative channel paths, MIMO channels are very reliable and robust to fading effects. The challenge in realizing the very high capacity of MIMO communica- tion systems lies in development of effective detection al- gorithms. Among many detection algorithms that have been proposed in the past, the sphere decoding method of Hochwald and ten Brink [4] is the one with the closest per- formance to the channel capacity. In this paper, we present a novel detection algorithm based on the Markov chain Monte Carlo (MCMC) simu- lation techniques [5], and through simulations show that it outperforms the sphere decoding of [4] by as much as 2 dB. 2. CHANNEL MODEL We consider a flat fading channel model whose input and output are related according to the equation y = Hd + n (1) ———————- Z. Shi is with National ICT Australia and affiliated with the Australian Na- tional University. National ICT Australia is funded through the Australian Government’s Backing Australia’s Ability initiative and in part through the Australian Research Council. where d is the vector of transmit symbols, n is the chan- nel additive noise vector, y is the received signal vector, and H is the channel gain matrix. The elements of H are the channel gains between transmit and receive antennas. Assuming that there are N t transmit and N r receive anten- nas, d has a length of N t , y and n have a length of N r and H is an N r × N t matrix. We assume that each ele- ment of d is an L-ary symbol and takes values from the the alphabet A = {α 1 ,α 2 , ··· ,α L }. We assume that n is an iid Gaussian sequence with the autocorrelation matrix E[nn H ]= σ 2 n I, where I is the identity matrix. Through out this paper, we assume that the channel gain matrix H and the noise variance σ 2 n are perfectly known to the receiver. We note that the channel model (1) repeats for transmis- sion of the successive values of d. Hence, there should be a time index attached to all terms in (1). We avoid such a time index here for brevity. 3. ITERATIVE MIMO DETECTION We consider an iterative MIMO detector similar to the one discussed in [4]. Fig. 1 presents the block diagram of such a detector. It consists of a soft-in soft-out (SISO) MIMO detector and a SISO channel decoder. The MIMO detector generates a set of soft output sequences for the data symbols d 1 , d 2 , ··· , d Nt (the elements of d) based on the observed input vector y and the a priori (soft) information from the latest iteration of the channel decoder. After subtracting the a priori information from the output of the MIMO detec- tor, the remaining information which is new (extrinsic) to the channel decoder is passed over for further processing. Similarly, the soft input information to the channel decoder is subtracted from its output to generate the new (extrinsic) information before being fed back to the MIMO detector. The soft information that is exchanged between the MIMO detector and the channel decoder are the likelihood values (L-values) of transmitted information bits or symbols. The L-values are the ratios of the symbol probabilities as com- monly defined in the literature [6]. We continue our discus- sion with an evaluation of symbol probabilities and through that demonstrate the challenge of estimating L-values in the III - 1017 0-7803-8874-7/05/$20.00 ©2005 IEEE ICASSP 2005 ➠ ➡