Abstract- This letter addresses an intelligent reflecting surface (IRS) to the uplink nonorthogonal multiple access (NOMA) served by a multiantenna receiver for more efficient data collection from massive devices. For rate fairness, we formulate a problem of maximizing the minimum rate of the devices by optimizing receive beamforming (BF), IRS reflection, and transmit power allocation (PA) of the devices jointly. We first design a block coordinate descent (BCD) algorithm optimizing receive BF, IRS reflection, and PA iteratively. We then reformulate the problem as a nonlinear optimization (NLO) problem with a smooth objective function of the IRS phase and PA vectors by incorporating the optimal receive BF into the objective and using an approximate minimum. To handle massive IRS elements and devices efficiently, we solve the NLO problem with the limited-memory Broyden-Fletcher-Goldfarb-Shanno bounded (L-BFGS-B) algorithm using the gradient derived in a closed form. The results show that the L-BFGS-B optimizing the IRS phase and PA vectors concurrently reduces the computational complexity of the BCD algorithm significantly at a slight performance gain.

In this letter, we consider intelligent reflecting surface (IRS) aided nonorthogonal multiple access (NOMA) for the uplink employing multiple receive antennas in order to achieve high spectral efficiency and massive connectivity. In particular, the phase shifts of the IRS are optimized under a generalized reflection model to maximize the sum rate. For the unit modulus reflection, a determinant-maximization problem is formulated and solved through extended semidefinite relaxation (max-det). For the practical reflection, we apply the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm by deriving the gradient of the complicated objective function. Based on the results, we observe that the max-det solution provides a near-optimal performance but at high complexity for a large number N of IRS elements, while the L-BFGS relieves the complexity issue for a large N and provides a performance comparable to or better than a conventional sequential optimization at a reduced computational time.