New analytical framework for the products of independent RVs with wireless applications

A novel analytical framework for evaluating the statistics of the products of independent random variables is proposed. Compared with other methods which use either an infinite series or a special function, the new method provides simple and efficient closed-form approximations in terms of elementary functions, such as powers and exponentials, and therefore, is very easy to implement. The accuracy of the new approximation is examined. Numerical results show that it is quite accurate in most regions of interest. As an application, these new approximations are used in wireless communications theory to derive novel closed-form expressions for the outage probability of cascaded fading channels. Numerical examples show that the newly derived closed-form expressions provide insights on the behavior of important performance metrics as the outage probability, the bit error rate and the channel capacity.