Joint Beamforming Design in Multi-Cluster MISO NOMA Reconfigurable Intelligent Surface-Aided Downlink Communication Networks

Considering reconfigurable intelligent surfaces (RISs), we study a multi-cluster multiple-input-single-output (MISO) non-orthogonal multiple access (NOMA) downlink communication network. In the network, RISs assist the communication from the base station (BS) to all users by passive beamforming. Our goal is to minimize the total transmit power by jointly optimizing the active beamforming matrices at the BS and the reflection coefficient vector at the RISs. Because of the constraints on the RIS reflection amplitudes and phase shifts, the formulated quadratically constrained quadratic problem is highly non-convex. For the aforementioned problem, the conventional semidefinite programming (SDP) based algorithm has prohibitively high computational complexity and deteriorating performance. Here, we propose an effective second-order cone programming (SOCP)-alternating direction method of multipliers (ADMM) based algorithm to obtain the locally optimal solution. To reduce the computational complexity, we also propose a low-complexity zero-forcing based suboptimal algorithm. It is shown through simulation results that our proposed SOCP-ADMM based algorithm achieves significant performance gain over the conventional SDP based algorithm. Furthermore, when the target transmission rates of central and cell-edge users are 0.5 bps/Hz, our proposed NOMA RIS-aided system with 32 RIS elements has about 2.5 dB performance gain over the conventional massive multiple-input-multiple-output system with 64 transmit antennas.