An Improved Closed-Form Approximation to the Sum of Arbitrary Nakagami- $m$ Variates

The aim of this paper is threefold: 1) to propose a simple accurate closed-form approximation to the probability density function of the sum of arbitrarily distributed Nakagami-$m$ random variables; 2) to propose a simple accurate closed-form approximation to the level crossing rate for the sum of Nakagami-$m$ random processes; and 3) to show some possible applications for the proposed formulations. With such an aim, we choose the $\alpha$–$\mu$ distribution for which the parameters are estimated from the sum of the Nakagami- $m$ envelopes. As shall be shown from sample representative examples, the proposed approximations are simple, versatile, and highly accurate. The approach used here can easily be extended to other applications such as bit error rate and channel capacity calculations among others.