Generalized Feedback Detection for MIMO Systems Tao Cui and Chintha Tellambura Department of Electrical and Computer Engineering University of Alberta Edmonton, AB, Canada T6G 2V4 Email: {taocui, chintha}@ece.ualberta.ca Abstract—In this paper, we present a unified detection frame- work for spatial multiplexing multiple-input multiple-output (MIMO) systems. We propose a generalized feedback detector (GFD) by modifying the classical feedback decoding algorithm for convolutional codes. When the three controlling parameters of the GFD vary, the diversity order of the GFD varies between 1 and N and the SNR gain also varies. Many previous MIMO detectors are special cases of our GFD. The connection between MIMO detectors and tree search algorithms is also established. To reduce redundant computations in the GFD, a shared computation technique is proposed using a tree data structure. The complexity of the GFD varies between those of maximum-likelihood (ML) detection and zero-forcing decision feedback detector (ZF-DFD). Our proposed GFD provides a flexible performance-complexity tradeoff. I. I NTRODUCTION Multiple-input multiple-output (MIMO) systems over a rich scattering wireless channel are capable of providing enormous capacity improvements without increasing the bandwidth or transmitted power. Because of that promise, MIMO techniques have attracted considerable interest in the wireless research community and are under consideration for future high-speed wireless applications including wireless LAN and wireless cellular systems. The Bell-Labs layered space-time (BLAST) architecture is such a MIMO system [1]. In uncoded MIMO systems, the complexity of the maximum-likelihood detector (MLD) increases exponentially with the number of transmit antennas, making the MLD infeasible. Several reduced-complexity suboptimal detectors have thus been proposed in the literature. The zero-forcing (ZF) decision feedback detector (DFD) with optimal ordering or the V-BLAST detector is proposed in [1] using nulling and interference cancellation (also known as the VBLAST detector). Using nulling based on the minimum mean square error (MMSE) principle, the ZF-DFD is extended to the MMSE-DFD [2], and this detector makes a trade-off between interference suppression and noise enhancement. The perfor- mance of these simple detectors is significantly inferior to that of the MLD. The large gap in both performance and complexity between the MLD and suboptimal detectors has motivated alternative detectors. In [3], a combined detector (ML-DFD) is proposed to detect the first few symbols using a MLD and the remaining symbols using a ZF-DFD, which prevents the error propagation resulting in a higher diversity order. In [4], sphere decoding (SD) is proposed as a near- optimal detection method, which has low complexity in high SNR. However, in low SNR or for systems with a large number of transmit antennas, the complexity of SD is also high. The Chase decoding algorithm for linear block codes has been adopted for MIMO detection in [5]. The Chase detector generates a list for the first detected symbol. For each element from the list, a subdetector is applied to the remaining symbols. The vector with the minimum mean square error is chosen as the output. Depending on the type of subdetector, the performance of the Chase detector varies between those of ML and ZF-BLAST. Different SNR gains can be achieved with different list sizes. But the Chase detector achieves a diversity order of 1 or N in an N × N system, but nothing in between. In this paper, we develop a unified framework for detecting spatial multiplexing systems such as V-BLAST. We generalize the feedback decoder of Heller [6] for convolutional codes as a new generalized feedback detector (GFD) with three characteristic parameters: window size, step size and branch factor. With different values for these parameters, the GFD achieves different diversity orders between 1 and N and differ- ent SNR gains, as well as a performance-complexity tradeoff. Choosing different parameter values also yields many well- known algorithms such as ZF-BLAST [1], SD [4], combined ML and ZF-DFD [3] and the B-Chase detector [5] as special cases of our GFD. Moreover, all such detection algorithms can be explained as tree search problems. A reduced-complexity shared computation technique is proposed, making the com- plexity of the GFD varies between those of ZF-DFD and MLD. Using the union bound (UB) approach for the symbol error probability of the GFD, we obtain the diversity order and SNR gain achievable by modifying the three parameters. This paper is organized as follows. Section II describes the system model and review feedback decoding for convolutional codes. In Section III, we propose the new GFD and present the computation sharing technique. The diversity order and SNR gain of the GFD are also analyzed. Simulation results and conclusions are given in Section IV and in Section V. Notation: Bold symbols denote matrices or vectors. (·) T ,(·) H and (·) ∗ denote transpose, conjugate transpose and conjugate, respectively. (·) † denotes pseudo-inverse. ‖(·)‖ 2 is 2-norm of (·). E{(·)} is the expectation of (·). P [(·)] is the probability of (·). The set of all complex K × 1 vectors is C K . A circularly complex Gaussian random variable with mean μ and variance σ 2 is denoted by z ∼ CN (μ, σ 2 ). The complement of event A is A c . The N × N identity matrix is matter experts for publication in the IEEE GLOBECOM 2005 proceedings. This full text paper was peer reviewed at the direction of IEEE Communications Society subject IEEE Globecom 2005 3077 0-7803-9415-1/05/$20.00 © 2005 IEEE Authorized licensed use limited to: UNIVERSITY OF ALBERTA. Downloaded on December 21, 2009 at 19:38 from IEEE Xplore. Restrictions apply. "©2005 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE."