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Optimal RIS Placement in Multi-User MISO Systems with User Randomness

Abhishek Rajasekaran, Mehdi Karbalayghareh, Xiaoyan Ma, David J. Love, Christopher G. Brinton

TL;DR

The paper addresses RIS placement in MU-MISO networks under user randomness by formulating a max-min SINR objective averaged over user realizations. It introduces a hierarchical two-stage approach: an inner optimization that jointly optimizes RIS phases and BS beamformers, and an outer optimization that searches discrete RIS locations via obstacle-informed candidate sets, then refines the deployment region with a recursive coarse-to-fine clustering. The core contributions are (i) transforming the inner problem with Lagrangian dual and quadratic transforms and solving via AO and WMMSE-like updates, (ii) constructing candidate RIS locations from obstacle configurations and evaluating performance across PPP-based user distributions, and (iii) a recursive clustering framework that yields a final deployment region despite randomness. The results demonstrate substantial improvements in coverage and average WSR compared to baselines, validating the practical viability of the proposed method for realistic RIS deployment scenarios.

Abstract

It is well established that the performance of reconfigurable intelligent surface (RIS)-assisted systems critically depends on the optimal placement of the RIS. Previous works consider either simple coverage maximization or simultaneous optimization of the placement of the RIS along with the beamforming and reflection coefficients, most of which assume that the location of the RIS, base station (BS), and users are known. However, in practice, only the spatial variation of user density and obstacle configuration are likely to be known prior to deployment of the system. Thus, we formulate a non-convex problem that optimizes the position of the RIS over the expected minimum signal-to-interference-plus-noise ratio (SINR) of the system with user randomness, assuming that the system employs joint beamforming after deployment. To solve this problem, we propose a recursive coarse-to-fine methodology that constructs a set of candidate locations for RIS placement based on the obstacle configuration and evaluates them over multiple instantiations from the user distribution. The search is recursively refined within the optimal region identified in each stage to determine the final optimal region for RIS deployment. Detailed numerical results are presented to corroborate our findings.

Optimal RIS Placement in Multi-User MISO Systems with User Randomness

TL;DR

The paper addresses RIS placement in MU-MISO networks under user randomness by formulating a max-min SINR objective averaged over user realizations. It introduces a hierarchical two-stage approach: an inner optimization that jointly optimizes RIS phases and BS beamformers, and an outer optimization that searches discrete RIS locations via obstacle-informed candidate sets, then refines the deployment region with a recursive coarse-to-fine clustering. The core contributions are (i) transforming the inner problem with Lagrangian dual and quadratic transforms and solving via AO and WMMSE-like updates, (ii) constructing candidate RIS locations from obstacle configurations and evaluating performance across PPP-based user distributions, and (iii) a recursive clustering framework that yields a final deployment region despite randomness. The results demonstrate substantial improvements in coverage and average WSR compared to baselines, validating the practical viability of the proposed method for realistic RIS deployment scenarios.

Abstract

It is well established that the performance of reconfigurable intelligent surface (RIS)-assisted systems critically depends on the optimal placement of the RIS. Previous works consider either simple coverage maximization or simultaneous optimization of the placement of the RIS along with the beamforming and reflection coefficients, most of which assume that the location of the RIS, base station (BS), and users are known. However, in practice, only the spatial variation of user density and obstacle configuration are likely to be known prior to deployment of the system. Thus, we formulate a non-convex problem that optimizes the position of the RIS over the expected minimum signal-to-interference-plus-noise ratio (SINR) of the system with user randomness, assuming that the system employs joint beamforming after deployment. To solve this problem, we propose a recursive coarse-to-fine methodology that constructs a set of candidate locations for RIS placement based on the obstacle configuration and evaluates them over multiple instantiations from the user distribution. The search is recursively refined within the optimal region identified in each stage to determine the final optimal region for RIS deployment. Detailed numerical results are presented to corroborate our findings.

Paper Structure

This paper contains 17 sections, 17 equations, 5 figures, 2 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Overview of Methodology and Contributions
  4. System Model
  5. Problem Formulation
  6. Proposed Solution
  7. The Inner Optimization Problem
  8. Transformed Problem
  9. Iterative Optimization
  10. The Outer Optimization Problem
  11. Recursive Clustering
  12. Time Complexity and Efficient Implementation
  13. Simulation Results
  14. Simulation Setup
  15. Optimal RIS Placement
  16. ...and 2 more sections

Figures (5)

  • Figure 1: RIS-assisted MU-MISO system with obstacles.
  • Figure 2: Optimal RIS placement in different scenarios.
  • Figure 3: Recursive Clustering for Optimal RIS placement in Scenario 1.
  • Figure 4: Conventional Performance analysis of proposed algorithm in Scenario 2.
  • Figure 5: Further analysis of proposed algorithm for Scenario 2.

Theorems & Definitions (2)

  • Remark 1
  • Remark 2