Asymptotic Outage Analysis on Dual-Branch Diversity Receptions Over Non-Identically Distributed Correlated Lognormal Channels

Abstract

It is challenging to quantify the left tail behavior of the cumulative distribution function of a sum of lognormal random variables, especially when they are correlated and non-identically distributed. The mathematical intractability hampers the analysis on diversity receptions over lognormal fading channels. In this paper, a novel asymptotic technique is exploited to study non-identically distributed dual-branch lognormal fading channels with correlation. Closed-form asymptotic outage probability expressions are derived for maximum-ratio combining (MRC), equal-gain combining (EGC), and selection combining (SC). Three counterintuitive facts are revealed: 1) one of the two channels contributes no asymptotic performance gain to the diversity reception systems under certain conditions, implying that a link can be discarded without causing asymptotic performance loss; 2) SC outperforms EGC under certain conditions; and 3) the outage probability of SC is arbitrarily close to that of MRC under certain conditions. The new result reveals insights into the long-standing problem of asymptotic analysis for correlated lognormal fading channels, paving the way for analysis on more general channel models. This paper also provides an efficient approach to evaluate the non-identically distributed lognormal fading channels at a high signal-to-noise ratio. Practically, the analytical results prevent some redundant units that contribute no performance gain.