This paper presents a family of rate-one quasi-orthogonal space-time block codes (QO-STBCs) for any number of transmit antennas. Full diversity of the proposed QO-STBCs is achieved via the use of constellation rotation. When the number of transmit antennas is even, these codes are delay "optimal." This property along with the quasi-orthogonality one allows the codes to have low decoding complexity. Besides, by applying lookup tables into the detection methods presented in [1] and generalizing them, two low-complexity maximum-likelihood (ML) decoders for the proposed QO-STBCs and for other existing QO-STBCs, called PMLD and QMLD, are obtained. Simulation results are provided to verify the bit error rate (BER) performances and complexities of both the proposed QO-STBCs and the proposed decoders.

This letter proposes two very-low-complexity maximum-likelihood (ML) detection algorithms based on QR decomposition for the quasi-orthogonal space-time code (QSTBC) with four transmit antennas [3]-[5], called VLCMLDec1 and VLCMLDec2 decoders. The first decoder, VLCMLDec1, can be used to detect transmitted symbols being extracted from finite-size constellations such as phase-shift keying (PSK) or quadrature amplitude modulation (QAM). The second decoder, VLCMLDec2, is an enhanced version of the VLCMLDec1, developed mainly for QAM constellations. Simulation results show that both of the proposed decoders enable the QSTBC to achieve ML performance with significant reduction in computational load.

Orthogonal space-time block codes (STBCs) appear to be a very fascinating means of enhancing reception quality in quasi-static MIMO channels due to their full diversity, and especially their simple maximum-likelihood (ML) decoders. However, full-rate full-diversity orthogonal STBCs do not exist for more than two transmit antennas. Vertical layered space-time architecture (so-called the V-BLAST) with a nulling- and cancelling-based detection algorithm, in contrast, has an ability of achieving high transmission rates at the cost of having very low diversity gain, an undesirable consequence caused by the interference nulling and cancelling processes. The uncoded V-BLAST system is able to reach its ML performance with the aid of the sphere decoder algorithm at the expense of higher detection complexity. Undoubtedly, the tradeoff between transmission rates, diversity, and complexity is inherent in designing space-time codes. This paper investigates a method to increase the "nulling diversity gains" for a general high-rate space-time code and introduces a new design strategy for high-rate space-time codes detected based on interference nulling and cancelling processes, thanks to which high-rate quasi-orthogonal space-time codes for MIMO applications are proposed. We show that when nT transmit and nR=nT receive antennas are deployed, the first code offers a transmission rate of (nT-1) with a minimum nulling diversity order of 3, whereas the second one offers a transmission rate of (nT-2) with a minimum nulling diversity order of 5. Therefore, the proposed codes significantly outperform the V-BLAST as nR=nT. Simulation results and discussions on the performance of the proposed codes are provided.