Outage Probability of MRC Diversity over Correlated Shadowed Fading Channels

Abstract

In this letter, the outage probability of an L-branch Maximal Ratio Combining (MRC) diversity system is evaluated under non-identical correlated lognormal shadowed Rayleigh fading channels by extending the Moment Generation Function (MGF) method to approximate the output signal-to-noise ratio (SNR) by a new lognormal random variable, whose cumulative distribution function (cdf ) is obtained by numerically solving for its mean and standard deviation. This cdf is then utilized to obtain the outage probability at a specific threshold. Extensive Monte Carlo simulations verify that the proposed approach is an accurate and efficient method to evaluate the desired outage probability, which would greatly facilitate the design and analysis of such systems.

Approximating bivariate Suzuki distribution with bivariate Lognormal distribution

“…For trackable analysis, equal μ and σ are assumed for both of two diversity branches, which means μ 1 = μ 2 = μ and σ 1 = σ 2 = σ. The parameters of interest can be look up in Table I. Those original values, i.e, the cdf of max(x 1 , x 2 |ρ; μ 1 , σ 1 ; μ 2 , σ 2 ) based on original bivariate Suzuki distribution, are numerically calculated by [5,7]…”

“…, can be mathematically expressed in equation 1 [3,5,7], where z t = (10 log 10 ω t − μ t )/ √ 2σ t , μ t and σ t (both in decibel) are the mean and standard deviation of the Lognormal component 10 log 10 ω t , respectively, t = 1, 2. ρ is the correlation coefficient between the lognormal components. ξ = 10/ ln 10 = 4.3429 is the scaling constant.…”

“…With the growing interest in channel modeling and corresponding wireless applications, a great deal of attention has been devoted to more accurate performance evaluations of diversity systems over Suzuki channels [3,4,5,6,7,8,9]. In such diversity systems, more than one Suzuki RV are involved, and these Suzuki RVs are indeed possible to be correlated with each other [3,5,7]. Similar to the univariate Suzuki distribution, the joint pdf of multivariate Suzuki distribution was presented as multiple fold integral with correlation matrix, and consequently, the system performance was derived or numerically calculated in strenuous manners.…”

On the Bivariate Nakagami-Lognormal Distribution and Its Correlation Properties

“…The effect of the correlated shadowing or correlated fast fading on the performance parameters in wireless communication diversity has attracted the attention of several researches [14][15][16][17][18][19]. Nevertheless, all the above works have assumed either correlated fast fading with independent shadowing or correlated shadowing with independent fast fading.…”

Outage probability of composite microscopic and macroscopic diversity over correlated shadowed fading channels

“…Recently, Shankar [15,18] presented an analytical expression for the outage probability of MRC microdiversity and SC macrodiversity over correlated shadowed fading channels, where the multipath fading is modelled by Nakagami-m distribution and the shadowing is approximated by Gamma distribution with equal correlation. In our previous work [19], a Moment Generation Function (MGF) based method was extend to evaluate the outage probability of L-branch macroscopic MRC diversity system over non-identical correlated lognormal shadowed Rayleigh fading channels. Generally, if the joint probability density function (pdf) of the interested performance measure over all branches is known, the outage probability can readily be obtained by the cumulative density function (cdf) at a specific threshold.…”