In wireless communication systems (WCSs), fading and shadowing of signals are the most frequently encountered phenomena which lead to degradation in the performance of communication channels. Several multipath distribution models like Weibull, Rayleigh, and Nakagami-m models have been extensively used for statistically capturing the fading signals in large-scale propagation scenarios. Several studies have emphasized on exploiting the log-normal model which efficiently characterizes the shadowing signals, or large-scale effects of the propagation channel. However, the conventional log-normal model suffers through some limitations, due to the lack of mathematical tractability in its analytical expression for characterizing shadowed multipath fading signals. In this perspective, the present work proposes a novel adaptive generalized stochastic differential equation (SDE) in context to Tsallis non-extensive sense, which leads to q-Lognormal distribution under a suitable initial condition corresponding to Fokker-Planck equation for effectively capturing the rapid fluctuations in composite signals. The closed form expressions corresponding to the probability density function (PDF) and cumulative distribution function (CDF) are obtained in terms of Gauss-Hypergeometric function F12[a,b,c;z] for the proposed distribution model. Finally, several performance measures like average channel capacity, higher order moments, and coefficient of variation (CV) are estimated for proposed q-Lognormal model by employing extensive Monte-Carlo simulations. The corresponding results obtained by using the above techniques are presented to understand the applicability of the proposed model for modeling WCS and multipath composite signals.
Read full abstract