Highly Accurate Approximations for the Sum of Double-Nakagami-m Envelopes

The sum of cascade envelopes is prevalent in a diverse range of applications, techniques, and scenarios within wireless communication systems. However, the intricate nature of the sum renders it challenging to obtain an exact statistical characterization, fostering a growing interest in the pursuit of precise yet approximate formulations. In this work, we provide simplified yet accurate approximations for the probability density function and cumulative distribution function of the sum of independent but not identically distributed (i.n.i.d.) double-Nakagami-m (Generalized-K) envelopes. Furthermore, leveraging these statistical insights, we investigate the performance of an equal gain combining receiver operating over i.n.i.d. double-Nakagami-m fading channels and propose performance metrics accordingly. We also derive asymptotic expressions and quantify the diversity and coding gains. Finally, we validate our findings through Monte-Carlo simulations.