Space-time block codes from orthogonal designs

We introduce space-time block coding, a new paradigm for communication over Rayleigh fading channels using multiple transmit antennas, Data is encoded using a space-time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas. The receiv ed signal at each receive antenna is a linear superposition of the n transm itted signals perturbed by noise. Maximum-likelihood decoding is achieved i n a simple way through decoupling of the signals transmitted from different antennas rather than joint detection. This uses the orthogonal structure o f the space-time block code and gives a maximum-likelihood decoding algorit hm which is based only on linear processing at the receiver. Space-time blo ck codes are designed to achieve the maximum diversity order for a given nu mber of transmit and receive antennas subject to the constraint of having a simple decoding algorithm. The classical mathematical framework of orthogonal designs is applied to co nstruct space-time block codes. It is shown that space-time block codes con structed in this way only exist for few sporadic values of n, Subsequently, a generalization of orthogonal designs is shown to provide space-time bloc k codes for both real and complex constellations for any number of transmit antennas. These codes achieve the maximum possible transmission rate for a ny number of transmit antennas using any arbitrary real constellation such as PAM, For an arbitrary complex constellation such as PSK and QAM, space-t ime block codes are designed that achieve 1/2 of the maximum possible trans mission rate for any number of transmit antennas. For the specific cases of two, three, and four transmit antennas, space-time block codes are designe d that achieve, respectively, all, 3/4, and 3/4 of maximum possible transmi ssion rate using arbitrary complex constellations. The best tradeoff betwee n the decoding delay and the number of transmit antennas is also computed a nd it is shown that many of the codes presented here are optimal in this se nse as well.