The application of orthogonal designs to wireless communication

We introduce space-block coding, a new paradigm for transmission over Rayleigh fading channels using multiple transmit antennas. Data is encoded using a space-block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas. The received signal at each receive antenna is a linear superposition of the n transmitted signal perturbed by noise. Decoding is achieved in a simple way using the orthogonal structure of the space-block code and the maximum likelihood decoding algorithm is totally based on linear processing at the receiver. Space-block codes are designed to achieve the maximum diversity gain of transmit and receive antennas with the constraint of having a simple decoding algorithm. It is shown that the classical mathematical framework of orthogonal designs can be applied to construct channel codes which have a simple decoding algorithm, while providing the full spatial diversity order. Space-block codes constructed in this way only exist for few sporadic values of n and therefore there is a need for a new mathematical theory. We introduce the theory of generalized designs which provides codes for both real and complex constellations for any number of transmit antennas. Using this theory, we construct space-block codes that achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as PAM. For any arbitrary complex constellation such as PSK and QAM, we construct space-block codes that achieve half of the maximum possible transmission rate for any number of transmit antennas. For the specific cases of two, three and four transmit antennas, we provide space-block codes that achieve respectively the whole, 3/4 and 3/4 of maximum possible transmission rate using arbitrary complex constellations.