Performance Analysis of Downlink Double-IRS Systems Relying on Non-Orthogonal Multiple Access

The intelligent reflecting surface (IRS) has emerged as a promising solution to enhance the quality of radio transmission by allowing flexible control over the direction of reflection and phase shift of electromagnetic waves. In this study, we present a downlink wireless network considering non-orthogonal multiple access (NOMA) and two IRSs to improve performance for a group of user equipment (UE) at the cell edge, when the UEs cannot reach out direct links from the base station (BS). We start by discussing the framework to design a wireless system relying on both IRS and NOMA, and then calculate the link channel statistics between the BS, IRS, and UEs with Rayleigh fading distributions using the probability density function (PDF) and cumulative distribution function (CDF). Based on these distributions, we derive closed form expressions for the outage probability (OP) for evaluating the performance of the user pair. Additionally, we compute the bit error rate (BER), the ergodic rates (ER) of the UE as functions of the signal-to-interference-plus-noise ratio (SINR) using the Chebyshev-Gauss quadrature method, and hence the complete the overall evaluation of the system's performance can be achieved. Finally, we verify the mathematical analysis through comparing with Monte-Carlo simulations and indicate that the number of IRS meta-surfaces elements as the main limiting factor to achieve better OP, ER and BER performance.