Efficient Near Maximum-Likelihood Detection for Underdetermined MIMO Antenna Systems Using a Geometrical Approach

Maximum-likelihood (ML) detection is guaranteed to yield minimum probability of erroneous detection and is thus of great importance for both multiuser detection and space-time decoding. For multiple-input multiple-output (MIMO) antenna systems where the number of receive antennas is at least the number of signals multiplexed in the spatial domain, ML detection can be done efficiently using sphere decoding. Suboptimal detectors are also well known to have reasonable performance at low complexity. It is, nevertheless, much less understood for obtaining good detection at affordable complexity if there are less receive antennas than transmitted signals (i.e., underdetermined MIMO systems). In this paper, our aim is to develop an effcient detection strategy that can achieve near ML performance for underdetermined MIMO systems. Our method is based on the geometrical understanding that the ML point happens to be a point that is "close" to the decoding hyperplane in all directions. The fact that such proximity-close points are much less is used to devise a decoding method that promises to greatly reduce the decoding complexity while achieving near ML performance. An average-case complexity analysis based on Gaussian approximation is also given.