New Findings on the Sum of Squared Fluctuating Two-Ray Random Variables and Applications

The fluctuating two-ray (FTR) fading model has proven to effectively characterize small-scale fading in gigahertz and terahertz frequency bands. In these wireless scenarios, one can enhance the system performance by exploiting multiple communication links, where sums of random variables (RVs) commonly arise and, therefore, need to be statistically addressed to evaluate the system behavior. Unfortunately, the statistical analysis of such sums is rather challenging, which has motivated further research to find exact solutions. In this paper, we characterize the exact statistics of sums of independent and identically distributed squared FTR RVs. Specifically, we derive novel improved expressions for the probability density function (PDF) and the cumulative distribution function (CDF). Our expressions demonstrated to be lighter, faster, and more manageable than the state-of-the-art solutions. More importantly, we show that the sum PDF and the sum CDF can be written as a random mixture of not necessarily identically distributed gamma PDFs and CDFs, respectively. Capitalizing on our findings, we assess the performance of multi-branch maximal-ratio combining receivers operating over FTR fading channels, considering three essential metrics: average bit error rate, outage probability, and ergodic capacity. Simulation results confirm the validity and efficiency of our analytical derivations.