Application of the Mixture of Lognormal Distribution to Represent the First-Order Statistics of Wireless Channels

In a wireless channel, shadow fading along with multipath effect causes random fluctuations of the received signal strength at the receiver. Several composite fading distributions are available for modeling the randomness. Among them, Lognormal-based models are unable to give a closed-form expression of the composite distribution, but Gamma-based model overcomes the problem faced by the former one. However, the Gamma-based model comes with a complicated mathematical function. To get rid of that, mixture of Lognormal (MoLN) distribution is used in this article. Maximum-likelihood approach is used for parameters estimation with the help of the expectation maximization algorithm. Simulation results have been provided in order to show the accuracy of the proposed mixture model. The first-order statistics of both the envelope and signal-to-noise ratio of a wireless channel are represented by a simple mathematical form. Several performance metrics, used in a wireless system, are expressed in a closed form for the MoLN distribution. The fitness of MoLN distribution is tested. Quantitatively, by measuring metrics like mean square error and Kullback-Leibler divergence, it has been shown that MoLN distribution is a suitable candidate to represent the composite wireless channel accurately.