Space-Time Convolutional Codes Over GF(p) for the Quasi-Static, Flat Rayleigh Fading Channel

In this paper, we consider a space-time coded system consisting of a rate R = 1/ n linear convolutional encoder over GF( p ), p a prime, followed by n mappers from GF( p ) into a p -ary signal constellation, and by a transmitter with n transmit antennas. At each time, the n p -ary coded symbols are transmitted simultaneously from the n antennas. The convolutional codes are designed to provide the best error performance in the quasi-static, flat Rayleigh fading channel, according to the rank and the determinant criteria derived by Tarokh et al. A spectral efficiency of log 2 ( p ) b/s/Hz is achieved. Simple conditions on the generator matrices of a rate R = 1/2 convolutional code are given so that maximum diversity advantage is guaranteed. The linear structure of these convolutional codes reduces significantly the computer search effort with respect to the determinant criterion. In this regard, some properties of reciprocal STC's are derived. New space-time codes with two transmit antennas are presented for the 5-PSK and 7-PSK modulations, with spectral efficiencies 2.32 and 2.81 b/s/Hz, respectively. Simulation results in the form of frame error rate versus signal-to-noise ratio are reported for these codes, showing agreement with the theoretical results.