Space-Time Block Codes for Multi-Input Single-Output Channels and Simple Maximum Likelihood Detection

Abstract

<p>Multi-input multi-output (MIMO) technology has been used to improve wireless communications systems over the past several years. The multiple antennas of MIMO systems are used to increase data rates through multiplexing gain and/or increase the reliability of the system through diversity gain. It is known that an optimum trade-off between diversity gain and multiplexing gain can be achieved by having proper space-time block code (STBC) designs. The current STBC designs minimizing the pair-wise error probability (PEP) of the maximum likelihood (ML) detector are based mainly on the rank and the determinant criteria.</p> <p>In this thesis, we study a special case of the MIMO system. This consists of a coherent communication system equipped with Mt transmitter antennas and a single receiver antenna, i.e., a multi-input single-output (MISO) system. Such systems are often encountered in mobile down-link communications for which a MIMO realization may be expensive or for which the mobile receiver may not be able to support multiple antennas (e.g. a mobile phone). Given a full-rate data transmission, the PEP of the ML detector for such systems can be minimized by using the rotated quasi-orthogonal STBC design, which enables full diversity and optimal coding gains for the system. The efficiency of fast ML decoding for orthogonal STBC is also largely preserved for such quasi-orthogonal STBC. However, for large constellations, the performance of such "optimum" codes deteriorates due to the increase of the number of the nearest neighbours per symbol.</p> <p>To correct such a deficiency of the code, in this thesis, we propose to include the number of nearest neighbors in the design criterion. We show that for the current optimal rotated quasi-orthogonal code, the number of nearest neighbours tends to infinity when the size of constellation becomes infinite. However, we show that by having a particular value of rotation, not only full diversity and maximum coding gain will be achieved, but also a small number of nearest neighbours will be maintained even for very large constellations.</p> <p>Also, at present, STBC designs in a MIMO system are mainly based on the PEP (or its upper bound). This is because the geometrical structure of the decision regions for a general MIMO channel, equipped with the ML detector, is so irregular that it would be impossible to obtain an exact error probability formula for the ML receiver. This means that the error probability formula cannot be utilized as a criterion for the design of the optimal transmitter for the MIMO systems and the current STBC designs may not be truly optimum in terms of the exact error probability. To rectify this problem, in this thesis, we first find a closed form algorithm for ML detection, for a 4 x 1 MISO system equipped with a ML detector, transmitting signals from a four signal quadrature amplitude modulation (4-QAM) constellation. This algorithm is derived such that given a received signal and the channel, the transmitted signal can be obtained using a threshold decision. Then, using this ML detection algorithm, a closed form of the exact error probability of this system is derived. This closed form decoding algorithm is then applied to the 4-group decodable STBC, in order to obtain the optimal rotation angle to minimize the ML error probability.</p>