Properties of space-time codes for frequency-selective channels

Some important properties are derived for the diversity gain and the coding gain of space-time codes (STCs) for frequency-selective channels. It is proven that the diversity gain of a STC that provides maximum diversity gain for channels with a given number of taps is robust to a decrease in the number of taps. For coding gain analysis, we categorize the possible types of correlation matrices into several classes based on the type of power delay profile, spatial correlation, and tap correlation. It is proven that optimum STCs found for spatially independent and frequency-selective channels with uncorrelated taps and uniform power delay profile have coding gains that are robust against a mismatch in correlation structure if the number of taps is fixed. Thereafter, a systematic design procedure is applied to search for the best space-time trellis codes (STTCs) for frequency-selective channels. At a frame error rate (FER) of 0.01, our example 16-state binary phase-shift keying (BPSK) STTC outperforms the delay diversity code by 3.4 dB for a channel with three uncorrelated uniform taps. Further, the example STC designed for a channel with a given number of taps is shown to provide good performance for channels with fewer taps.