Statistical Analysis of the Sum of Double Random Variables for Security Applications in RIS-Assisted NOMA Networks with a Direct Link

Abstract

Next- generation wireless communications are projected to integrate reconfigurable intelligent surfaces (RISs) to perpetrate enhanced spectral and energy efficiencies. To quantify the performance of RIS-aided wireless networks, the statistics of a single random variable plus the sum of double random variables becomes a core approach to reflect how communication links from RISs improve wireless-based systems versus direct ones. With this in mind, the work applies the statistics of a single random variable plus the sum of double random variables in the secure performance of RIS-based non-orthogonal multi-access (NOMA) systems with the presence of untrusted users. We propose a new communication strategy by jointly considering NOMA encoding and RIS's phase shift design to enhance the communication of legitimate nodes while degrading the channel capacity of untrusted elements but with sufficient power resources for signal recovery. Following that, we analyze and derive the closed-form expressions of the secrecy effective capacity (SEC) and secrecy outage probability (SOP). All analyses are supported by extensive Monte Carlo simulation outcomes, which facilitate an understanding of system communication behavior, such as the transmit signal-to-noise ratio, the number of RIS elements, the power allocation coefficients, the target data rate of the communication channels, and secure data rate. Finally, the results demonstrate that our proposed communication can be improved significantly with an increase in the number of RIS elements, irrespective of the presence of untrusted proximate or distant users.