Statistics of the Sum of Double Random Variables and Their Applications in Performance Analysis and Optimization of Simultaneously Transmitting and Reflecting Reconfigurable Intelligent Surface-Assisted Non-Orthogonal Multi-Access Systems

For the future of sixth-generation (6G) wireless communication, simultaneously transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) technology is emerging as a promising solution to achieve lower power transmission and flawless coverage. To facilitate the performance analysis of RIS-assisted networks, the statistics of the sum of double random variables, i.e., the sum of the products of two random variables of the same distribution type, become vitally necessary. This paper applies the statistics of the sum of double random variables in the performance analysis of an integrated power beacon (PB) energy-harvesting (EH)-based NOMA-assisted STAR-RIS network to improve its outage probability (OP), ergodic rate, and average symbol error rate. Furthermore, the impact of imperfect successive interference cancellation (ipSIC) on system performance is also analyzed. The analysis provides the closed-form expressions of the OP and ergodic rate derived for both imperfect and perfect SIC (pSIC) cases. All analyses are supported by extensive simulation results, which help recommend optimized system parameters, including the time-switching factor, the number of reflecting elements, and the power allocation coefficients, to minimize the OP. Finally, the results demonstrate the superiority of the proposed framework compared to conventional NOMA and OMA systems.