Maximum Likelihood detection of quasi-orthogonal space-time block codes: Analysis and simplification

In this paper, we propose a low complexity Maximum Likelihood (ML) decoding algorithm for quasi-orthogonal space-time block codes (QOSTBCs) based on the real-valued lattice representation and QR decomposition. We show that for a system with rate r = n(s)/T, where n(s) is the number of transmitted symbols per T time slots; the proposed algorithm decomposes the original complex-valued system into a parallel system with n(s) 2 x 2 real-valued components, thus allowing for a simple joint decoding of two real symbols. For a square QAM constellation with L points (L-QAM), this algorithm achieves full diversity by properly incorporating two-dimensional rotation using the optimal rotation angle and the same rotating matrix for any number of transmit antennas (N >= 4). We further show that for N = 8 and 16-QAM modulation scheme, the new approach achieves > 98% reduction in the overall complexity compared to conventional ML detection, and > 93% reduction compared to the most competitive reported algorithms in the literature. This complexity gain becomes greater when N or L becomes larger. We also show that the complexity of the proposed algorithm is linear with L and n(s).