Asymptotic Performance of Composite Lognormal-X Fading Channels

It is challenging to derive closed-form performance expressions for composite channels considering both the large-scale lognormal fading and small-scale fading, thus most existing analyses on the composite channels are based on numerical approaches such as the Gauss-Hermite quadrature. In this paper, we develop a simple framework to achieve closed-form asymptotic expressions for the outage probabilities and the error rates of the composite lognormal-X fading channels, where the “X” can be Rayleigh, Rician, Nakagami-m or any other fading channels that have finite diversity orders. It is proved that the lognormal fading contributes an exponential factor to the asymptotic expressions, and the exponential factor is related to the diversity order of the X channel and the lognormal parameters. The new analytical tool is shown to be versatile in evaluating the performance of radio-frequency communications suffering both the large-scale and small-scale fading, including diversity reception systems, relaying systems, and distributed antenna systems. It is also shown to be useful in evaluating free-space optical communication systems with pointing error, and in deriving asymptotic signal-to-noise ratio gaps between different modulation formats over lognormal fading channels. The elegant asymptotic expressions reveal insights into the composite fading channels and can be a criterion for various system designs.