Product of Squared SR Random Variables: Application to Satellite Communication

Abstract

We investigate the problem associated with the statistics of the product of two squared Shadowed Rician (SR) random variables (RVs). Both SR RVs are independent and nonidentically distributed. The distribution of the product of two squared SR RVs is very important from the satellite communication perspective. We derive approximate expressions of the probability density function (p.d.f.), the moment generating function (m.g.f.), and the cumulative distribution function (c.d.f.) in terms of Meijer-G functions. Furthermore, exact closed-form expressions for higher order moments, channel quality estimation index, and amount of fading are derived. The outage probability is also discussed by utilizing the expression of the c.d.f. An approximate closed-form expression of channel capacity is also derived with the help of the p.d.f. expression. Furthermore, the performance of satellite communication system is discussed in terms of the approximate symbol error rate by using the derived results. Specifically, the derived expression of the p.d.f. is used to develop an approximate closed-form expression of the m.g.f. for an amplify-and-forward-based satellite communication system.