Outage analysis of cellular systems in an arbitrary lognormal shadowed Rician environment

Current techniques used to tackle the outage problem in a lognormal shadowed (LNS) Rician environment follow the philosophy of using the chain rule in probability. The crucial issue is to determine the probability density function (pdf) of the total power of the co-channel interferers (CCI), ending up with a mathematically intractable integral of multiple fold. Results available in the literature, all based on certain explicit or hidden assumptions, apply only to some special cases. The purpose of this paper is to present an exact solution to outage performance for cellular or microcellular systems operating in an arbitrary lognormal shadowed Rician environment without any restrictions. We formulate the outage event as an inequality in terms of a decision variable and directly determine the outage probability from the characteristic function of the decision variable. The integrand so obtained is in a simple factored form, so that all integrals can be determined individually. As a result, the expression for the outage probability takes the form of a two-fold integral, which can accurately be evaluated by using Hermite and Gaussian quadrature.