Multipath Rayleigh Fading Channels in the Low SNR Regime

The multipath block Rayleigh fading channel with a uniform energy spread in the low SNR regime is studied in both coherent and non-coherent scenarios. In the coherent reception case, a closed form expression of the wideband slope of the multipath Rayleigh fading channel is derived as a function of the channel coherence time and the channel delay spread. In the non-coherent reception case, when the input signal is under a fourth moment constraint, theoretical analysis shows that the non-coherent mutual information is proportional to the channel coherence time and inversely proportional to the channel delay spread in the low SNR regime.