On the "high SNR" assumption in space-time codes designs

Space-time codes designs commonly rely on the assumption of a high SNR. In this communication, we investigate the impact of this assumption when the channel is correlated. Therefore, we discuss the impact of transmit and receive correlations on the performance of space-time codes as a function of the SNR and the diversity achieved by the codes on independent and identically distributed channels. Full diversity codes are shown not to interact with the channel at high SNRs while at realistic SNRs, interactions occur and affect the coding gain. For non-full diversity codes, interactions with the channel occur whatever the SNR. At realistic SNRs, every space-time code interacts with the channel. While it might be reasonable on independent and identically distributed channels, we show that on correlated channels, the ´high SNR´ assumption is totally unrealistic and may lead to bad code designs.