| Telatar in 1995 presented a powerful scheme that utilizes multiple transmit and receive antennae and translates the conventional single antenna channel into a multiple-input-multiple-output (MIMO) channel. He showed that the ergodic MIMO channel capacity increase linearly as the minimum number of transmit and receive antennae. To exploit this enormous capacity through channel coding, Guey et al. and Tarokh et al. treated the channel codes, termed space-time codes, as code matrices. To minimize the pairwise error probability (PEP) of codewords, based on Chernoff bound, they propose that the difference matrix between all distinct pairs of codewords must have full matrix rank so that all available diversities can be completely realized.; In this dissertation, we first provide a more robust design criterion derived from a closed-form expression of the PEP. Based on this criterion, several best BPSK space-time codes are presented in the case of small number of transmit antennae and short coherence time.; There is also an interesting class of codes, termed orthogonal-design-based space-time (ODST) codes, by Tarokh et al. We show that ODST codes represent an instance of orthogonal signaling and the exact symbol error probabilities of these codes are therefore derived. We also show the nonexistence of new orthogonal designs even when the constellation is a constrained subset of the complex numbers.; For a fixed, finite signal constellation, the full rank criterion inherently draws a limitation of maximal achievable transmission rate. To attain higher rate, the degree of desirable diversities must be compromised. We show that there is a trade-off between the desirable rate and rank. Several classes of block and convolutional codes that achieve this optimal tradeoff over a variety of constellations including PAM, QAM and 2K-ary PSK, are presented for any number of transmit antennae and arbitrary duration of channel coherence time.; We finally show that by applying coding to several consecutive fading blocks simultaneously, this yields another rate-diversity-tradeoff where large diversities and high rate can be simultaneously obtained. Systematic constructions of codes that achieve this new tradeoff are also provided. |
