Full-diversity group space-time-frequency (GSTF) codes from cyclic codes

It is known that multi-antenna transmissions over frequency-selective channels can provide a diversity gain that is product of the number of transmit antennas, the receive antennas and the length of the channel impulse response. Liu, Xin and Giannakis have studied multi-antenna orthogonal frequency division multiplexing (OFDM) through frequency-selective Rayleigh-fading channels and have introduced the concept of space-time frequency (STF) coding to enable maximum diversity and high coding gains. It is known that under some conditions, an n-length cyclic code C over F_qm (n|q^m - 1, and m les n) can have fullrank i.e Rank_q(C) = m. Designs for space-time codes suitable for both quasi-static fading channels and block-fading channels have been derived from n length cyclic codes over F_qm. In this paper, we present a simplified design of STF codes using designs derived from cyclic codes to obtain group space-time-frequency (GSTF) codes for frequency selective Rayleigh fading channels. These codes achieve maximum diversity gain