Near-Optimum Soft Decision Equalization for Frequency Selective MIMO Channels

Abstract

Abstract-In this paper, we develop soft decision equalization (SDE) techniques for frequency selective multiple-input multiple-output (MIMO) channels in the quest for low-complexity equalizers with error performance competitive to that of maximum likelihood (ML) sequence detection. We demonstrate that decision feedback equalization (DFE) based on soft-decisions, expressed via the posterior probabilities associated with feedback symbols, is able to outperform hard-decision DFE, with a low computational cost that is polynomial in the number of symbols to be recovered and linear in the signal constellation size. Building on the probabilistic data association (PDA) multiuser detector, we present two new MIMO equalization solutions to handle the distinctive channel memory. The first SDE algorithm adopts a zero-padded transmission structure to convert the challenging sequence detection problem into a block-by-block least-square formulation. It introduces key enhancement to the original PDA to enable applications in rank-deficient channels and for higher level modulations. The second SDE algorithm takes advantage of the Toeplitz channel matrix structure embodied in an equalization problem. It processes the data samples through a series of overlapping sliding windows to reduce complexity and, at the same time, performs implicit noise tracking to maintain near-optimum performance. With their low complexity, simple implementations, and impressive near-optimum performance offered by iterative soft-decision processing, the proposed SDE methods are attractive candidates to deliver efficient reception solutions to practical high-capacity MIMO systems. Simulation comparisons of our SDE methods with minimum-mean-square error (MMSE)-based MIMO DFE and sphere decoded quasi-ML detection are presented.Index Terms-Efficient reception algorithms, equalization for frequency selective MIMO channels, overlapping sliding windowing, soft decision.

A Generalized Probabilistic Data Association Detector for Multiple Antenna Systems

“…When the full number of probabilities 3 are evaluated by the GPDA detector, the complexities for the aforementioned parts per iteration is and complex operations, respectively. By comparison, the PDA implementation of [3] has a worst case complexity of complex operations for updating the inverse of the covariance matrix per iteration, and complex operations for evaluating the symbol probabilities per iteration. Hence for , the PDA implementation used in this paper is more efficient than that of [3].…”

“…The GPDA detector is presented for the special case of square/rectangular (sqr/rect) QAM, but extension to other constellations is straightforward and follows the basic PDA implementation of [3] which requires the computation of probabilities for each transmit symbol, where is the size of the constellation.…”

“…In the case of sqr/rect -QAM, the new algorithm differs from the direct PDA approach of [3] by reducing the number of probabilities associated with each transmit symbol. As an apparent consequence of reducing the number of probabilities (hypotheses) for sqr/rect QAM, the new detector shows an improved error probability over the direct PDA approach used in [3].…”

“…As an apparent consequence of reducing the number of probabilities (hypotheses) for sqr/rect QAM, the new detector shows an improved error probability over the direct PDA approach used in [3]. A further advantage of this method is that it offers a reduced computational cost over that of [3] for the case when the number of receive antennas is greater than or equal to the number of transmit antennas; this advantage, which is true for any complex modulation scheme, is achieved by returning to the formulation of the original PDA algorithm, which works from the "decorrelated signal model" [2]. Computer simulations show that the proposed algorithm significantly outperforms the V-BLAST optimal order detector [1] and has a computational complexity that is cubic in the number of transmit antennas.…”

A Novel Probabilistic Data Association Based MIMO Detector Using Joint Detection of Consecutive Symbol Vectors

“…It is easy to find the advantage of the PDA-JD detector over the conventional PDA algorithm. When 8 d = and 2 d = , the BER performance of the proposed PDA-JD detector is nearly 2 dB and more than 1 dB better than that of the conventional PDA detector respectively at BER= 3 10 − . Unfortunately, it can observed that unlike the reported performance of the PDA in BPSK systems, in QPSK, the ML detector is still considerably better than the PDA based detectors.…”