Uni-polarized RIS Beamforming for Improving Connectivity of Multi-RIS-Assisted D2D Networks

TL;DR

The paper tackles improving connectivity in multi-RIS assisted D2D networks by proposing uni-polarized RIS beamforming to generate multiple narrow beams toward reliable UEs. It introduces a joint optimization of RIS beamforming, link selection, and RIS positioning, solved via two subproblems: a GA-based design of RIS phase shifts to maximize the minimum PDAF toward target azimuths and an Adam-based optimization for RIS placement, with an iterative refinement between them. Connectivity is quantified using the graph-theoretic algebraic connectivity lambda2 of the network Laplacian, augmented by RIS-aided links, and a reliability-based QoS constraint guided by node criticality R v = lambda2(G minus v). Numerical results show significant connectivity gains over baselines including distributed small RISs, validating the effectiveness of generating multiple RIS-aided links per RIS and the accuracy of the SINR approximation used in the design.

Abstract

This paper introduces a novel method to enhance the connectivity of multi-reconfigurable intelligent surface-assisted device-to-device networks, referred to as multi-RIS-assisted D2D networks, through a unique phase shift determination. The proposed method aims to optimize the power-domain array factor (PDAF), targeting specific azimuth angles of reliable user equipments (UEs) and enhancing network connectivity. We formulate an optimization problem that jointly optimizes RIS beamforming design, RIS-aided link selection, and RIS positioning. This problem is a mixed-integer non-binary programming. The optimization problem is divided into two sub-problems, which are solved individually and iteratively. The first sub-problem of RIS-aided link selection is solved using an efficient perturbation method while developing genetic algorithm (GA) to obtain RIS beamforming design. The GA optimizes the RIS phase shift to generate multiple RIS-aided narrowbeams that exhibit significant PDAF towards azimuth angles of interest while minimizing PDAF towards undesired azimuth angles. The second sub-problem of RIS positioning is addressed using the Adam optimizer. Numerical simulations verify the superiority of the proposed scheme in improving network connectivity compared to other schemes, including those utilizing distributed small RISs, each generating one RIS-aided link.

Figures (5)

• Figure 1: Network configuration of a multi-RIS assisted D2D model, clarifying the connections of the transmitting UE$_u$ and RIS$_m$ for $U_m=2$.
• Figure 2: The flowchart for the iterative solution.
• Figure 3: The PDAF of the uni-polarized RIS narrowband beamforming designed using the proposed GA for (a) $\text{UE}_1 \xrightarrow{\text{RIS}} \text{UE}_{2}$, (b) $\text{UE}_1 \xrightarrow{\text{RIS}} \text{UE}_{2,3}$, (c) $\text{UE}_1 \xrightarrow{\text{RIS}} \text{UE}_{2, 3, 4}$, and (d) $\text{UE}_1 \xrightarrow{\text{RIS}} \text{UE}_{2,3,4,5}$.
• Figure 4: Approximated and exact sum rates for (a) $U_m=1$ with $\text{UE}_1 \xrightarrow{\text{RIS}_1} \text{UE}_{3}$ and $\text{UE}_2 \xrightarrow{\text{RIS}_2} \text{UE}_{4}$ and (b) $U_m=2$ with $\text{UE}_1 \xrightarrow{\text{RIS}_1} \text{UE}_{3, 6}$ and $\text{UE}_2 \xrightarrow{\text{RIS}_2} \text{UE}_{4, 5}$.
• Figure 5: Average network connectivity versus (a) number of UEs $U$ and (b) number of RIS elements $N$.