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Flexible RISs: Learning-based Array Manifold Estimation and Phase-shift Optimization

Mohamadreza Delbari, Ehsan Mohammadi, Mostafa Darabi, Arash Asadi, Alejandro Jiménez-Sáez, Vahid Jamali

TL;DR

The paper tackles RIS deployments on non-planar surfaces where planar beamforming is ineffective due to geometry mismatch. It introduces a learning-based framework that uses a low-dimensional quadratic surface model for surface depth $x=g(y,z)$ and a neural regressor to estimate the five curvature coefficients from sparse power measurements, enabling rapid phase-shift optimization without full CSI. The key contributions are a second-order Taylor surface model to reduce dimensionality, a power-measurement–driven NN that infers the geometry, and a phase-shift design that achieves coherent reflection as if the surface were planar. Results show fast convergence, improved performance over planar designs, and robustness to curvature and localization errors, indicating practical viability for flexible RIS deployments.

Abstract

Reconfigurable intelligent surfaces (RISs) are envisioned as a key enabler for next-generation wireless networks, offering programmable control over propagation environments. While extensive research focuses on planar RIS architectures, practical deployments often involve non-planar surfaces, such as structural columns or curved facades, where standard planar beamforming models fail. Moreover, existing analytical solutions for curved RISs are often restricted to specific, pre-defined array manifold geometries. To address this limitation, this paper proposes a novel deep learning (DL) framework for optimizing the phase shifts of non-planar RISs. We first introduce a low-dimensional parametric model to capture arbitrary surface curvature effectively. Based on this, we design a neural network (NN) that utilizes a sparse set of received power measurements to estimate the surface geometry and derive the optimal phase configuration. Simulation results demonstrate that the proposed algorithm converges fast and significantly outperforms conventional planar beamforming designs, validating its robustness against arbitrary surface curvature. We also analyze the impact of the measurement location error on the algorithm's performance.

Flexible RISs: Learning-based Array Manifold Estimation and Phase-shift Optimization

TL;DR

The paper tackles RIS deployments on non-planar surfaces where planar beamforming is ineffective due to geometry mismatch. It introduces a learning-based framework that uses a low-dimensional quadratic surface model for surface depth and a neural regressor to estimate the five curvature coefficients from sparse power measurements, enabling rapid phase-shift optimization without full CSI. The key contributions are a second-order Taylor surface model to reduce dimensionality, a power-measurement–driven NN that infers the geometry, and a phase-shift design that achieves coherent reflection as if the surface were planar. Results show fast convergence, improved performance over planar designs, and robustness to curvature and localization errors, indicating practical viability for flexible RIS deployments.

Abstract

Reconfigurable intelligent surfaces (RISs) are envisioned as a key enabler for next-generation wireless networks, offering programmable control over propagation environments. While extensive research focuses on planar RIS architectures, practical deployments often involve non-planar surfaces, such as structural columns or curved facades, where standard planar beamforming models fail. Moreover, existing analytical solutions for curved RISs are often restricted to specific, pre-defined array manifold geometries. To address this limitation, this paper proposes a novel deep learning (DL) framework for optimizing the phase shifts of non-planar RISs. We first introduce a low-dimensional parametric model to capture arbitrary surface curvature effectively. Based on this, we design a neural network (NN) that utilizes a sparse set of received power measurements to estimate the surface geometry and derive the optimal phase configuration. Simulation results demonstrate that the proposed algorithm converges fast and significantly outperforms conventional planar beamforming designs, validating its robustness against arbitrary surface curvature. We also analyze the impact of the measurement location error on the algorithm's performance.
Paper Structure (15 sections, 7 equations, 5 figures, 2 tables)

This paper contains 15 sections, 7 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. System, Channel and RIS Model
  3. System Model
  4. Channel Model
  5. RIS Element Location Model
  6. Problem formulation and Solution
  7. Data Collection and Measurement Point Spacing
  8. Network Architecture and Training
  9. Preprocessing and Data Partitioning
  10. Architecture and Hyperparameters
  11. RIS Phase Shift Design
  12. Performance Evaluation
  13. Simulation Setup
  14. Simulation Results
  15. Conclusion

Figures (5)

  • Figure 1: Schematic illustration of the considered RIS-assisted downlink communication system.
  • Figure 2: The required minimum distance for the spatial density of the measurements.
  • Figure 3: Training loss and validation loss versus the number of epochs.
  • Figure 4: power at the versus the geometric parameter variance.
  • Figure 5: The power in versus the variance of the localization error.