New approximations to the lognormal characteristic function

Abstract

Computation of the lognormal characteristic function (CF) is required in analysis of many wireless communication systems. No closed-form expression exists for the lognormal CF. In this paper, two approximations to the lognormal CF are derived. The approximations are accurate over specified ranges of parameters. The first approximation is in terms of elementary mathematical functions and is useful for parameters typical in optical communication applications. The second approximation is a finite series in terms of the generalized hypergeometric functions and can be used to evaluate the lognormal CF with parameters motivated by both optical and wireless communication applications. Theoretical results are corroborated by computer simulations.