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 = ns/T , where ns is the number of transmitted symbols per T time slots; the proposed algorithm decomposes the original complex-valued system into a parallel system with ns 2 × 2 real-valued components, thus allowing for a simple joint decoding of two

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... 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 ns.