Analytical approach to performance analysis for channel subject to shadowing and fading

In this paper a unified analytical approach to performance analyses in a gamma-shadowed Nakagami-m fading channel is presented. Specifically, a lognormal probability density function (PDF) of shadowing is approximated by a gamma PDF. The approximation is based on the moment matching method. The accuracy of the approximation is examined. A mathematical framework is developed for deriving key statistical parameters such as the PDFs, as well as performance metrics including outage probability and average bit-error rate of different noncoherent digital modulation schemes. These formulas are validated by specialising the general results to some particular cases whose solutions are known and by means of comparing our graphically presented results (based on the closed-form expressions) with corresponding known results evaluated by numerical techniques. In this way, one can conclude that presented results are reliable for lognormal shadowing spread <9 dB (note that, the shadowing spread actually observed in macrocells has a typical value that lies between 4 and 9 dB). The final results are remarkably simple and can serve as a quick way of assessing performance. In addition, presented analytical expressions are suitable for asymptotic analyses, which is a significant feature for both theoretical and practical aspects of their applications.