Multipath diversity and coding gains of cyclic-prefixed single carrier systems

The multipath diversity and coding gain metrics for cyclic-prefixed single-carrier (SC-CP) systems, which characterize the bit error rate (BER) at high SNR, have not been carefully studied in the literature. We first show that, unlike OFDM, the diversity and coding gains for SC-CP are data-realization-dependent. Then, we show that there is a signal-to-noise ratio (SNR) threshold beyond which the dominant diversity order starts deviating from the maximum diversity order to eventually reduce to one at higher SNRs. Using the averaged pairwise probability, we derive an analytical expression for this SNR threshold. The latter is shown to increase with the block length and to be unrealistically high for moderate/high block lengths. Comparisons of SC-CP with rotated constellations and zero-padded SC systems are also provided.