A New Asymptotic Analysis Technique for Diversity Receptions Over Correlated Lognormal Fading Channels

TL;DR

This paper introduces a novel asymptotic analysis framework for evaluating the outage probabilities of diversity combining schemes over correlated lognormal fading channels, overcoming limitations of traditional methods.

Contribution

It presents a new analytical approach for correlated lognormal channels, providing closed-form asymptotic outage probability expressions where previous methods failed.

Findings

EGC and MRC outperform SC at high SNR

Channel correlation causes significant performance loss

Analysis avoids complex simulations and integrations

Abstract

Prior asymptotic performance analyses are based on the series expansion of the moment-generating function (MGF) or the probability density function (PDF) of channel coefficients. However, these techniques fail for lognormal fading channels because the Taylor series of the PDF of a lognormal random variable is zero at the origin and the MGF does not have an explicit form. Although lognormal fading model has been widely applied in wireless communications and free-space optical communications, few analytical tools are available to provide elegant performance expressions for correlated lognormal channels. In this work, we propose a novel framework to analyze the asymptotic outage probabilities of selection combining (SC), equal-gain combining (EGC) and maximum-ratio combining (MRC) over equally correlated lognormal fading channels. Based on these closed-form results, we reveal the followings: i) the outage probability of EGC or MRC becomes an infinitely small quantity compared to that of SC at large signal-to-noise ratio (SNR); ii) channel correlation can result in an infinite performance loss at large SNR. More importantly, the analyses reveal insights into the long-standing problem of performance analyses over correlated lognormal channels at high SNR, and circumvent the time-consuming Monte Carlo simulation and numerical integration.