Space- Time block codes with low maximum likelihood decoding complexity and large coding gain

Abstract

Space-time block coding has been an extensively researched technique to combat multipath fading in multiple-input, multiple-output (MIMO) systems when the channel-state information is available at the receiver but not at the transmitter. A suitably designed space-time block code (STBC) exploits completely the diversity provided by the Rayleigh-fading MIMO channel, but among such full-diversity STBCs, additional desirable attributes include high coding gain and low maximum likelihood (ML)-decoding complexity. Coding gain signifies the saving in transmission power while transmitting data at a target bit rate and at a chosen error rate, while low-ML-decoding-complexity (low-MLDC) STBCs are desirable from the perspective of MIMO receivers that have limited computational capabilities. In this thesis, the problem of designing linear STBCs (LSTBCs) with lower ML-decoding complexity than that of the best existing LSTBCs is considered, and methods to enhance their coding gain are explored. Since any LSTBC is characterized by weight matrices that determine its ML-decoding complexity, the issue of designing LSTBCs with low ML-decoding complexity is addressed by utilizing irreducible matrix representations of Clifford algebras, and their products, as weight matrices of LSTBCs in an appropriate manner so that low ML-decoding complexity is achieved. The problem of obtaining LSTBCs with high coding gain is tackled using tools from number theory and cyclic division algebra. The restriction to LSTBC design is due to the existence of efficient sphere decoding algorithms that perform ML-decoding with a much lower average ML-decoding complexity than that required by exhaustive search. The main results of this thesis are as follows. An achievable upper bound on the rate of single-symbol-decodable (SSD) STBCs with unitary weight matrices is obtained and the characteristic structure of all unitary-weight, SSD STBCs is presented along with methods to achieve optimum coding gain. Next, a general design methodology to obtain two-group-ML-decodable STBCs with symbol rate greater than 1 complex symbol per channel use is proposed. Following this, a technique to obtain fast ML-decodable STBCs that are full-rate, i.e., have a symbol rate equal to the lesser of the number of transmit antennas and the number of receive antennas, is explained, and the resulting STBCs are shown to have the least ML-decoding complexity among known comparable STBCs. All the aforementioned results are obtained for the case where the number of transmit antennas is a power of two. Diversity-multiplexing gain tradeoff (DMT) is a fundamental performance measure of STBC-schemes, and STBC-schemes that optimally trade off diversity gain and multiplexing gain are desirable. The existing sufficient criterion for achievability of DMT-optimality does not capture many STBC-schemes that either have multi-group ML-decodability or fast-decodability. In this thesis, a stronger sufficient criterion is obtained using which the DMT-optimality of these low-MLDC STBC-schemes for certain asymmetric MIMO systems, i.e., MIMO systems with lesser number of receive antennas than transmit antennas, is established. Following this, a modified shaping criterion is proposed using which STBCs for 4 and 6 transmit antennas with coding gains larger than that of the well-known perfect codes, which hitherto had the best known coding gains, are presented. Finally, a new method to obtain fast-decodable, full-rate STBCs with large coding gain for multiple-input, double-output (MIDO) systems is proposed, and the STBCs obtained for 4 × 2, 6 × 2, 8 × 2 and 12 × 2 MIDO systems have the least ML-decoding complexity among known comparable STBCs with large coding gain. Additional results on low-MLDC precoding schemes for MIMO systems with perfect channel-state information also available at the transmitter are presented. In particular, a full-rate, full-diversity precoding scheme whose ML-decoding complexity as a function of the input constellation size M is only of the order of ?M is proposed, and this precoding scheme has the least ML-decoding complexity among known full-rate, full-diversity yielding precoding schemes.