A Simple Approximation for the Sum of Fading Random Variables via a Nakagami-m Distribution

Most of the classic fading variables can be obtained through Nakagami-m distribution and the sum of them has a pivotal role in the analytical performance evaluation of many practical wireless applications. However, the exact probability density function (PDF) of this sum of fading variables could be difficult to obtain. In this paper, we investigate the performance of the Maximum Likelihood Estimation to find a simple accurate approximation to the probability density function of the sum of Nakagami-m random variables. This approach provides expressions that can be used straightforwardly in the performance analysis of a number of wireless communication systems including multibranch receivers such as Maximal Ratio Combining and Equal Gain Combining, for which we present the application of the proposed framework. Numerical simulations show that our proposed method outperforms the well- known approach based on moment-matching method in terms of accuracy and simplicity. Moreover, the easiness of our proposal makes it suitable to be incorporated in network simulators to model and configure several wireless environments without additional computational complexity.