Soft quasi-maximum-likelihood detection for multiple-antenna channels

The paper addresses soft maximum-likelihood (ML) detection for multiple-antenna wireless channels. We propose a soft quasi-ML detector which maximizes the log-likelihood function by deploying a semi-definite relaxation (SDR). Given perfect channel state information at the receiver, the quasi-ML SDR detector achieves the performance of the optimal ML detector in both coded and uncoded multiple-input, multiple-output (MIMO) channels with quadrature phase-shift keying modulation and frequency-flat Rayleigh fading. The complexity of the quasi-ML SDR detector is much less than that of the optimal ML detector, and, thus, the quasi-ML detector offers more favorable performance/complexity trade-off. Compared to the existing sphere decoder the quasi-ML detector enjoys low polynomial worst-case complexity, as well as guaranteed near capacity performance.