The information theoretic reliability function for multipath fading channels with diversity

With the emergence of wireless and mobile communication systems and technology new channel models and impairment phenomena have appeared. We derive the information theoretic reliability function for a number of ideal fading channels with diversity. It has been shown by Buz (see Ph.D. Dissertation, Dept. of Elec. and Comp. Eng., Queen's University, Kingston) that the asymptotic SNR loss in the capacity, relative to the AWGN channel, for ideal Rayleigh fading is no more than 2.51 dB, which is not very dramatic. By looking at the reliability function, we have found, on the other hand, that the loss in the cutoff rate due to Rayleigh fading is monotonically increasing with SNR and considerably longer codes are required for transmission over the Rayleigh channel at rates below capacity. Nevertheless, this loss can be regained by means of diversity, where it has been found that most of the loss can be reclaimed with the use of 2 or 3 antennas.