Joint Design of Reconfigurable Intelligent Surfaces and Transmit Beamforming Under Proper and Improper Gaussian Signaling

This paper considers a network consisting of a multiple antenna array access point serving multiple single antenna downlink users with the assistance of a reconfigurable intelligent surface (RIS). The reflecting coefficients of the RIS can be programmed to ensure that the signals reflected from the RIS elements add coherently at the users. The joint design of these programmable reflecting coefficients and transmit beamforming to maximize the users' worst rate is addressed. Under either proper Gaussian signaling (PGS) or improper Gaussian signaling (IGS), the design poses a very computationally challenging nonconvex problem. Based on their exactly penalized optimization reformulation, which incorporates the computationally intractable unit-modulus constraints on the reflecting coefficients into the optimization objectives, new iterative algorithms of low computational complexity, which converge at least to a locally optimal solution, are developed. The provided simulations show not only the benefit of using the RIS, but also the advantage of IGS over PGS in delivering higher rates to users.