Quasi-orthogonal space-time block codes with full diversity

Space-time block codes from orthogonal designs proposed by Alamouti, and Tarokh-Jafarkhani-Calderbank have attracted much attention lately due to their fast maximum-likelihood (ML) decoding and full diversity. However, the maximum symbol transmission rate of a space-time block code from complex orthogonal designs for complex constellations is only 3/4 for three and four transmit antennas. Recently, Jafarkhani, and Tirkkonen-Boariu-Hottinen proposed space-time block codes from quasi-orthogonal designs, where the orthogonality is relaxed to provide higher symbol transmission rates. With the quasi-orthogonal structure, these codes still have a fast ML decoding algorithm, but do not have the full diversity. The performance of these codes is better than that of the codes from orthogonal designs at low SNR, but worse at high SNR. This is due to the fact that the slope of the BER-SNR curve depends on the diversity. In this paper, we design quasi-orthogonal space-time block codes with full diversity by properly choosing the signal constellations. In particular, we propose that half of the symbols in a quasi-orthogonal design are from a signal constellation A and another half of them are optimal selections from the rotated constellation e^jφ A. The optimal rotation angles φ are obtained for some commonly used signal constellations. The resulting codes have both full diversity and fast ML decoding. Simulation results show that the proposed codes outperform the codes from orthogonal designs at both low and high SNRs.