Outage Probability Bounds of EGC Over Correlated Lognormal Fading Channels

Lognormal fading channel is an important channel model for wireless communications and free-space optical communications, but it is much more mathematically intractable than Rayleigh, Rician, and Nakagami fading channels. The cumulative distribution function of a sum of lognormal random variables does not yield a closed-form expression, thus it is challenging to approximate the outage probability of a diversity system over lognormal fading channels. In this work, we obtain the closed-form expressions of outage probability bounds for dual-branch equal-gain combining (EGC) system over correlated lognormal fading channels. A detailed proof and numerical results verify the tightness of the bounds from low to high signal-to-noise ratio (SNR) regimes. The new analytical tool provides an efficient way to compare two EGC systems over correlated lognormal fading channels, and shows that correlation can cause an infinite SNR loss to the EGC system.