Max-Min Rate Optimization for Uplink IRS-NOMA With Receive Beamforming

Abstract

This letter addresses an intelligent reflecting surface (IRS) to the uplink nonorthogonal multiple access (NOMA) served by a multiantenna receiver for effective data collection from massive devices. We aim to achieve max-min fairness of the network by optimizing receive beamforming, IRS reflection, and transmit power allocation (PA) of the devices. For this purpose, first, we design a block coordinate descent (BCD) algorithm that reduces the complexity of a conventional IRS reflection optimization. Next, we design a nonlinear optimization (NLO) problem solvable with the limited-memory Broyden-Fletcher-Goldfarb-Shanno bounded (L-BFGS-B) algorithm, which is renowned for handling large-scale problems, to cope with large IRS elements and devices. The problem is formed with a smooth but complex objective function that depends on the IRS phase shift and PA vectors for which the gradient is derived in a computationally efficient form. The results reveal that the proposed BCD and proposed NLO with the L-BFGS-B outperform the conventional BCD in performance and complexity, where the NLO approach offers a substantial complexity reduction.