Capacity Characterization of Intelligent Reflecting Surface Assisted NOMA Systems

This paper investigates intelligent reflecting surface (IRS)-assisted systems, where an access point sends independent information to multiple users with the aid of one IRS. Our goal is to characterize the capacity region of the IRS-assisted multiuser communication systems. We jointly optimize the discrete phase-shift matrix of the IRS and resource allocation with the capacity-achieving non-orthogonal multiple access (NOMA) transmission scheme. The Pareto boundary of the capacity region is characterized by maximizing the average sum rate of all users, subject to a set of rate-profile constraints, total transmit power and discrete IRS phase shift constraints. Though the formulated problem is non-convex, we derive the globally optimal solutions by invoking the Lagrange duality method. It is shown that the optimal transmission strategy is alternating transmission among different user groups by dynamically adjusting the IRS phase shifts. We further propose a Hadamard codebook based scheme, which serves as a lower bound on the optimal performance gains. Numerical results demonstrate that: i) the IRS is capable of significantly improving the capacity region; ii) the capacity region achieved by the Hadamard codebook based scheme is close to that of discrete phase shifts for a small number of IRS elements.