Properties of space-time codes for frequency selective channels and trellis code designs

This paper derives some properties of the diversity gain and the coding gain of space-time codes (STCs) for frequency selective channels. It is shown that additional diversity order can be obtained by STCs when they are employed in frequency selective channels rather than in flat fading channels. It is demonstrated that spatial dependence, correlated taps and non-uniform power delay profile will cause coding gain penalty. The optimum codes designed for spatial independence with uncorrelated taps and uniform power distribution are shown to be the optimum codes for the other channels scenarios with the same number of taps. A systematic design procedure is applied to search for the best space-time trellis code (STTC) for frequency selective channels. At an FER of 0.01, our example 16-state BPSK STTC outperforms the delay diversity code by 3.4 dB for a channel with 3 uncorrelated uniform taps. It is demonstrated that a STC designed for a channels with the maximum expected memory, will guarantee good performance if a channel with less memory is encountered.