Accurate simple closed-form approximations to the distributions and densities of a sum of independent Rayleigh random variables

The statistical distribution of a sum of Rayleigh random variables is often required when analyzing the performance of wireless communication systems. A closed-form expression does not exist for the sum distribution and consequently, it is approximated or calculated numerically. A widely used small argument approximation for the density is shown to be inaccurate for medium and large values of the argument. Highly accurate, simple closed-form approximations to the distributions and densities of Rayleigh sum random variables are presented in this paper. These approximations are valid for a wide range of probability values and number of summands.