On the sum of multiplicative chi-square-lognormal random variables

In order to analyze the performance of the DS-CDMA cellular forward channel with convolutional encoding and soft-decision decoding operating in a Rayleigh-fading and lognormal-shadowing environment, we require the probability distribution function for a sum of d multiplicative chi-square (with two degrees of freedom)-lognormal random variables. We approximate the sum using a multiplicative chi-square(with 2d degrees of freedom)-lognormal random variable which is developed in this paper. We further investigate the usefulness of the approximation as it applies to the performance analysis of the DS-CDMA cellular forward channel.