Space-time trellis codes over GF(p) for p-PSK modulation

In this paper, we consider a space-time coded system composed of an encoder over GF(p), where p can be any prime number, followed by a serial-to-parallel converter, n mappers from GF(p) into a p-PSK signal constellation, and a transmitter with n antennas. The 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. We present two theorems by which we can simplify the design of full diversity space-time trellis codes (STTCs), for any number of transmit antennas. A spectral efficiency of Iog₂(p) b/s/Hz is achieved. Such non-integral rates can be useful to serve a wider range of multimedia applications. New STTCs with n = 2, 3, and 4 transmit antennas are presented for the 5-PSK, 7-PSK, and 11-PSK modulations.