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

Abstract

This paper considers a network of a multiple antenna array access points 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 RIS, but also the advantage of IGS over PGS in delivering higher rates to users.

Maximizing the Geometric Mean of User-Rates to Improve Rate-Fairness: Proper vs. Improper Gaussian Signaling

“…Following [36], we have (27). We thus solve the following problem at the κ-th iteration to generate θ (κ+1) :…”

“…In the end, the convergence of alternating optimization-based algorithms to a locally optimal solution is not guaranteed. Our recent work [27] has been the first one that addressed the spectral efficiency of RIS-aided communication via maxmin user-rate optimization. Instead of alternating optimization, we proposed an alternating descent at the first stage and then a joint descent at the second stage to confirm the optimality of the solutions computed.…”

“…While the descent iterations in the beamformers generate a sequence of better feasible points, the descent iterations in the PREs generate a sequence of better infeasible points, which converges to a feasible point. Moreover, it has been also shown in [27] that using widely linear beamformers for facilitating improper Gaussian signaling (IGS) improves the users' max-min rate. To sum up, we provide a brief comparison of the related literature in Table I.…”

“…Thus, the proposed alternating descent method is purely based on closed forms and hence it is computationally efficient. • Like in [27], here we also use improper Gaussian signaling (IGS) in the BS signal transmission, which has been shown to substantially improve the users' max-min rates (see e.g. [28]- [32]) thanks to its ability to mitigate the severe interferences in interference-limited systems.…”

Analytical Performance Assessment of Beamforming Efficiency in Reconfigurable Intelligent Surface-Aided Links

“…The authors in [23] explore the optimization of the number of elements and the phase shifts of the RIS, in order to maximize the data rate, the energy efficiency and their trade-off. The authors in [24] address the problem of joint design of the reflection coefficients of the RIS and the transmit beamforming under proper and improper Gaussian signalling to optimize the data rate at the receiver. Moreover, in [25] the authors explore the optimization of the RIS-AP distance and the orientation of the RIS in order to maximize the received SNR with the help of a coverage maximization algorithm.…”