Simple precise approximations to Weibull sums

Simple and precise closed-form approximations to the probability density function and cumulative distribution function of the sum of independent identically distributed Weibull variates are derived. The new approximations find applicability in several wireless communications issues such as equal-gain combining, signal detection, linear equalizers, outage probability, intersymbol interference, and phase jitter

I. Introduction

Sums of fading variates occur in several wireless communications issues, such as equal-gain combining, signal detection, linear equalizers, outage probability, intersymbol interference, and phase jitter. However, the evaluation of the probability density function (PDF) and cumulative distribution function (CDF) of these sums for the well-known fading models can be rather cumbersome [1]–[7]. Even for the simplest condition of independent identically distributed (i.i.d.) summands, only for the bivariate Nakagami- case the sum statistics are known in exact closed form [2]. For the general case, numerical convolution can be used, but its computation becomes rapidly critical as the number of summands increases.