Non-coherent Mutual Information of the Multipath Rayleigh Fading Channel in the Low SNR Regime

Multipath Rayleigh block fading channel with uniform energy spread in the low signal to noise ratio (SNR) regime is studied. Theoretical analysis shows that in the low SNR regime, the non-coherent mutual information is proportional to the channel coherence time and inversely proportional to the channel delay spread when the input signal is under the fourth moment constraint. Besides, due to the lack of the channel knowledge, the non-coherent mutual information degrades significantly to a value which is asymptotically quadratic in SNR while the frequency selectivity and the channel coherence contribute only linear terms to the non-coherent mutual information.