Error Probability Analysis of Intelligent Reflecting Surface-Enabled Non-Orthogonal Multiple Access Systems

We analyze the error performance of intelligent reflecting surface (IRS)-aided non-orthogonal multiple access (NOMA) systems. We deduce novel approximate analytical expressions for average symbol error probability (SEP) for PAM and QAM. We also analyze the multi-user scenario by deriving the novel approximate analytical expressions for (i) the average SEP for multicast transmission and (ii) the average pairwise error probability (PEP) for unicast transmission. We consider Rayleigh fading direct path and independently Rician fading reflected paths from access point to users via IRS. We also formulate and solve a constrained optimization problem to determine the fraction of elements to be activated at any IRS in order to guarantee near-identical SEP performance for both the users. We present results to elucidate that adding few extra IRS elements yields SNR gain for both users, requires allocation of lower power to weaker user and supports communication with higher-order constellation without significant increase in SEP/PEP. Furthermore, a 3-bit programmable IRS yields near-identical performance as an IRS with infinite precision phase-shift. Impact of estimation error on average SEP is also investigated.