T3DRIS: Advancing Conformal RIS Design through In-depth Analysis of Mutual Coupling Effects

TL;DR

This work addresses the challenge of designing conformal RIS on non-planar surfaces while accounting for mutual coupling. It introduces T3DRIS, an alternating optimization framework that jointly tunes the RIS impedances and the 3D placement of unit cells using an impedance-based, discrete-dipole model and a Neumann-series approximation for fast inverses, complemented by projected gradient updates on feasible shapes. The approach supports multiple 3D geometries (sphere, plane, sphere, cylinder) and proves convergence to a stationary point with manageable complexity, making it suitable for offline design. Full-wave CST validation demonstrates gains over conventional designs, confirming the practicality and performance benefits of conformal RIS deployment in dynamic smart radio environments.

Abstract

This paper presents a theoretical and mathematical framework for the design of a conformal reconfigurable intelligent surface (RIS) that adapts to non-planar geometries, which is a critical advancement for the deployment of RIS on non-planar and irregular surfaces as envisioned in smart radio environments. Previous research focused mainly on the optimization of RISs assuming a predetermined shape, while neglecting the intricate interplay between shape optimization, phase optimization, and mutual coupling effects. Our contribution, the T3DRIS framework, addresses this fundamental problem by integrating the configuration and shape optimization of RISs into a unified model and design framework, thus facilitating the application of RIS technology to a wider spectrum of environmental objects. The mathematical core of T3DRIS is rooted in optimizing the 3D deployment of the unit cells and tuning circuits, aiming at maximizing the communication performance. Through rigorous full-wave simulations and a comprehensive set of numerical analyses, we validate the proposed approach and demonstrate its superior performance and applicability over contemporary designs. This study-the first of its kind-paves the way for a new direction in RIS research, emphasizing the importance of a theoretical and mathematical perspective in tackling the challenges of conformal RISs.

Figures (8)

• Figure 1: Reflection properties of curved surfaces ($a$) planar, ($b$) cylindrical and ($c$) super-cylindrical).
• Figure 2: Graphical description of the proposed T3DRIS approach.
• Figure 3: Four different structures (black color) with their corresponding non-planar element arrangements, optimally designed with T3DRIS in the unconstrained case (green color), whose performance in terms of versus algorithm iterations is shown on the right-hand side.
• Figure 4: Four different structures (black color) with their corresponding non-planar element arrangements, optimally designed with T3DRIS in the constrained case (green color), whose performance in terms of versus algorithm iterations is shown on the right-hand side.
• Figure 5: Bar plot of the maximum SNR obtained with the conventional and optimized shapes.