Statistics of the Product of Two α-ℱ Variates With Applications

In this letter, we consider the product of two independent and not identically distributed α-
F
variates. Specifically, novel closed-form expressions for the probability density function, the cumulative distribution function, and the n-th moments for the envelope as well as the instantaneous signal-to-noise ratio (SNR) are derived. Subsequently, closed-form expressions for the outage probability, the average bit error rate, and the ergodic channel capacity are derived alongside their asymptotic ones. The analytical expressions are validated through numerical and Monte-Carlo simulations, where excellent agreements are observed over a wide range of SNR values. Furthermore, the asymptotic curves follow the slope of the exact curves at high SNR values.