On the achievable diversity orders over non-severely faded lognormal channels

Abstract

We propose to approximate the distribution of the sum of identically-distributed lognormal random variables by an Erlang distribution. The advantage of the proposed approximation over the lognormal and non-lognormal approximations proposed in the literature resides mainly in the fact that it results in simple closed-form expressions of the average bit-error-rate (BER) thus offering clear insights on the performance of diversity combining techniques over correlated and uncorrelated lognormal fading channels. For instance, the proposed approach shows that, for typical values of the BER, the diversity order in the case of non-severe lognormal fading can be accurately approximated by the order of the approximating Erlang distribution