Capacity of Frequency Selective Slowly Fading Channels with Correlated Coefficients

Capacity of frequency selective slowly fading channels has usually been treated by assuming that the channel coefficients are non-correlated. Under this assumption, capacity of frequency selective Rayleigh fading channel is equal to capacity of frequency non-selective Rayleigh fading channel. Here, we assume that channel coefficients are correlated. This results in a different distribution of the squared channel gain at each frequency. We investigate the impact of coefficient correlation on the capacity. We treat two cases: side information to receiver only (RSI), and side information to transmitter and receiver (TRSI). We derive capacity formulas for both cases. When there is correlation, in the RSI case we prove that there is performance loss for any SNR, and in the TRSI case we prove that there is performance loss in the high SNR region and performance gain in the low SNR region, compared to the non-correlated case. We determine the asymptotic performance loss in the high SNR region and the asymptotic performance gain in the low SNR region.