1086 IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 53, NO. 3, MARCH 2005 Bayesian Detection for BLAST Yufei Huang, Member, IEEE, Jianqiu (Michelle) Zhang, Member, IEEE, and Petar M. Djuric ´ , Senior Member, IEEE Abstract—This work demonstrates the use of the Bayesian methodology for detection in Bell Laboratories Layered Space-Time (BLAST) systems. First, we introduce a procedure for constructing prior distributions and propose the use of two types of prior distributions for the problem. From the corresponding posterior distributions, we obtain the Bayesian linear and deci- sion-feedback detectors and show their equivalence to the popular zero forcing and minimum mean square error (MMSE)-based detectors. Then, we establish an equivalent whitening filter output system model whose unique structure lends itself to constructing a dynamic state space model (DSSM) for BLAST systems, which evolves in space. This DSSM allows for the application of sequen- tial Monte Carlo sampling, or particle filtering (PF), for detection in BLAST systems. We introduce two different particle filtering detectors: the generic particle filtering detector and the stochastic algorithm. The stochastic algorithm exploits the discrete nature of the problem in the implementation and, therefore, is much more efficient. Overall, a distinct advantage of the PF detec- tors is that they can greatly reduce error propagation and thereby achieve near optimum performance. In addition, since they aim at the approximation of the posterior distribution using weighted samples, they can provide soft (probabilistic) information about the unknowns. Index Terms—Bell Laboratories Layered Space-Time (BLAST) systems, Gibbs sampling, Monte Carlo sampling, particle filtering, Space-time processing, Stochastic M-algorithm. I. INTRODUCTION R ECENT studies on bandwidth efficient transmission for broadband wireless communications have been focused on the exploitation of spatial diversity of antennas. It has been shown that the use of multiple transmitting and receiving an- tennas in rich scattered multipath communication environments can provide enormous capacity gain over the state-of-the-art systems. Much of the recent work on bandwidth efficient trans- mission was propelled with the architecture called Bell Labora- tories Layered Space-Time (BLAST) [1], [2]. In BLAST systems, different data streams are transmitted on different transmitting antennas simultaneously. At the receiver, detection is performed by separating and extracting the streams from the received signals. Although the maximum likelihood Manuscript received January 4, 2003; revised January 23, 2004. This work was supported by the National Science Foundation under Awards CCR-9903120 and CCR-0082607. The associate editor coordinating the review of this manu- script and approving it for publication was Prof. Zhi Ding. Y. Huang is with the Department of Electrical Engineering, University of Texas at San Antonio, San Antonio, TX 78249-0669 USA (e-mail: yhuang@utsa.edu). J. Zhang is with the Department of Electrical and Computer Engi- neering, University of New Hampshire, Durham, NH 03824 USA (e-mail: jianqiu.zhang@unh.edu). P. M. Djuric ´ is with the Department of Electrical and Computer Engineering, State University of New York at Stony Brook, Stony Brook, NY 11794 USA (e-mail: djuric@ece.sunysb.edu). Digital Object Identifier 10.1109/TSP.2004.842210 (ML) criterion provides optimum performance, its complexity increases exponentially with the number of transmitting an- tennas. Thus, its practical implementation is prohibitive for systems with large number of transmitting antennas. To achieve manageable complexity, linear and recursive decision feedback algorithms have been proposed, most of which are based on either zero-forcing (ZF) or the minimum mean square error (MMSE) principle. A notable algorithm based on ZF and the use of ordered successive interference cancellation (OSI) has been developed and named vertical BLAST (V-BLAST) [3]. The V-BLAST system is rather simple for implementation, but its performance is limited due to error propagation. To alleviate the error propagation, various new schemes based on hard deci- sion have been proposed, but the performance improvement has often been only marginal [4]–[6]. New algorithms based on soft decision as in [7], [8], however, show promising improvement over those based on hard decisions. Note that all these methods assume that the channels are estimated through, for example, pilot transmissions, and so is the case in this work. In our paper, we study the detection problem under the Bayesian paradigm. The advantage of the Bayesian method- ology is its ability to combine prior knowledge with information collected from the data. We introduce a procedure for con- structing of prior distributions for VBLAST systems and propose the use of two types of priors. From the corresponding posterior distributions, we obtain the Bayesian linear and decision feedback (DF) detectors and show their equivalence to the ZF and MMSE based detectors. Moreover, we establish an equivalent whitening filter output (WFO) system model. Based on the WFO model, we develop Bayesian decision feedback detectors as well as an -detector, which is based on the principle of the -algorithm. Particularly, the unique structure of the model enables the construction of a dynamic state space model (DSSM) for BLAST systems that evolves in space. This DSSM allows for the application of sequential Monte Carlo sampling, or particle filtering (PF) [9]–[11], for detection in BLAST systems. We introduce two different PF detectors: the generic particle filtering detector and the stochastic algorithm. The stochastic algorithm exploits the discrete nature of the problem in the implementation and therefore is much more efficient. A distinct advantage of detection by PF is that the error propagation is greatly reduced and that near-op- timum performance is achieved. In addition, since PFs aim at the approximation of the posterior distribution using weighted samples, they can provide soft (probabilitic) information about the unknowns, which can be used in turbo BLAST algorithms [12], [13]. The remaining of the paper is organized as follows. In Sec- tion II, we describe the system model and state the detection objective. We derive the posterior distributions and discuss 1053-587X/$20.00 © 2005 IEEE Authorized licensed use limited to: SUNY AT STONY BROOK. Downloaded on April 30,2010 at 18:01:40 UTC from IEEE Xplore. Restrictions apply.