Outage Probabilities in the Presence of Correlated Lognormal Interferers

Several approaches that can be used to compute the distribution of a sum of correlated lognormal RVs are investigated. Specifically, Wilkinson's approach, an extension to Schwartz and Yeh's approach, and a cumulants matching approach are studied. The aim is to determine which method is best for computing the complementary distribution function (CDF) of a sum of correlated lognormal RVs considering both accuracy and computational effort. Then, using these techniques, we compute the outage probability of a desired lognormal shadowed signal in the presence of multiple correlated lognormal co-channel interferers. The outage results are presented as a function of the reuse factor. The reuse factor is defined as the distance between the centers of the two nearest cells using the same frequencies divided by the cell radius. It is a key parameter in the design of any frequency reuse system. Simulation results are used for verification and comparison. Overall, the results obtained in this paper show that among the three methods considered in this paper Wilkinson's approach may be the best method to compute the CDF of sums of correlated lognormal RVs (and hence the outage probability in correlated lognormal shadowed mobile radio environments). This is due to both its accuracy and computational simplicity over the range of parameters valid for practical applications.