Signal constellations for quasi-orthogonal space-time block codes with full diversity

• Published in: IEEE transactions on information theory 2004-10, Vol.50 (10), p.2331-2347
• Main Authors: Weifeng Su, Xia, Xiang-gen
• Format: Article
• Language: English
• Subjects: Antennas; Applied sciences; Block codes; Codes; Coding, codes; Constellation diagram; Exact sciences and technology; Gallium nitride; Information, signal and communications theory; Maximum likelihood decoding; Modulation coding; Receiving antennas; Signal and communications theory; Signal design; Signal to noise ratio; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Transmission and modulation (techniques and equipments); Transmitting antennas; Wireless communication; Wireless communications
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2004.834740

Space-time block codes (STBCs) from orthogonal designs proposed by Alamouti, and Tarokh-Jafarkhani-Calderbank have attracted considerable attention lately due to their fast maximum-likelihood (ML) decoding and full diversity. However, the maximum symbol transmission rate of an STBC from complex orthogonal designs for complex signals is only 3/4 for three and four transmit antennas, and it is difficult to construct complex orthogonal designs with rate higher than 1/2 for more than four transmit antennas. Recently, Jafarkhani, Tirkkonen-Boariu-Hottinen, and Papadias-Foschini proposed STBCs from quasi-orthogonal designs, where the orthogonality is relaxed to provide higher symbol transmission rates. With the quasi-orthogonal structure, the quasi-orthogonal STBCs still have a fast ML decoding, but do not have the full diversity. The performance of these codes is better than that of the codes from orthogonal designs at low signal-to-noise ratio (SNR), but worse at high SNR. This is due to the fact that the slope of the performance curve depends on the diversity. It is desired to have the quasi-orthogonal STBCs with full diversity to ensure good performance at high SNR. In this paper, we achieve this goal by properly choosing the signal constellations. Specifically, we propose that half of the symbols in a quasi-orthogonal design are chosen from a signal constellation set A and the other half of them are chosen from a rotated constellation e/sup j/spl phi// A. The resulting STBCs can guarantee both full diversity and fast ML decoding. Moreover, we obtain the optimum selections of the rotation angles /spl phi/ for some commonly used signal constellations. Simulation results show that the proposed codes outperform the codes from orthogonal designs at both low and high SNRs.