Asymptotic Performance of Digital Communication Over Fading Channels

This paper presents a simple way to obtain the asymptotic performance of various digital communications systems operating over fading channels. The resulting expression for performance contains only the inverse average SNR raised to the system´s diversity order, by averaging the conditional error probability (conditioned on the fading) with the dominant term in the fading density function. The proposed approach often renders simple closed-form asymptotic error probabilities (ASEPs), even when the corresponding closed-form actual error probabilities (ACEPs) are too difficult to find, such as those in generalized selection combining, denoted by GSC (m,L), where the strongest m branches from L (1lesmlesL) total branches are selected and combined Using the proposed approach, the paper derives simple closed-form ASEPs for GSC (m,L) which show its diversity order and SNR gaps among different m, over both iid and non-iid Rayleigh fading channels for both MPSK and QAM. It is found that the SNR gaps of GSC (m,L) are not a function of modulation type or orders. In addition, the paper also presents simple closed-form ASEPs for a Nakagami-m fading channel with both MPSK and QAM in conjunction with maximal ratio combining (MRC).