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Power Minimization with Rate Constraints for Multi-User MIMO Systems with Large-Size RISs

Silvia Palmucci, Giulio Bartoli, Andrea Abrardo, Marco Moretti, Marco Di Renzo

Abstract

This study focuses on the optimization of a single-cell multi-user multiple-input multiple-output (MIMO) system with multiple large-size reconfigurable intelligent surfaces (RISs). The overall transmit power is minimized by optimizing the precoding coefficients and the RIS configuration, with constraints on users' signal-to-interference-plus-noise ratios (SINRs). The minimization problem is divided into two sub-problems and solved by means of an iterative alternating optimization (AO) approach. The first sub-problem focuses on finding the best precoder design. The second sub-problem optimizes the configuration of the RISs by partitioning them into smaller tiles. Each tile is then configured as a combination of pre-defined configurations. This allows the efficient optimization of RISs, especially in scenarios where the computational complexity would be prohibitive using traditional approaches. Simulation results show the good performance and limited complexity of the proposed method in comparison to benchmark schemes.

Power Minimization with Rate Constraints for Multi-User MIMO Systems with Large-Size RISs

Abstract

This study focuses on the optimization of a single-cell multi-user multiple-input multiple-output (MIMO) system with multiple large-size reconfigurable intelligent surfaces (RISs). The overall transmit power is minimized by optimizing the precoding coefficients and the RIS configuration, with constraints on users' signal-to-interference-plus-noise ratios (SINRs). The minimization problem is divided into two sub-problems and solved by means of an iterative alternating optimization (AO) approach. The first sub-problem focuses on finding the best precoder design. The second sub-problem optimizes the configuration of the RISs by partitioning them into smaller tiles. Each tile is then configured as a combination of pre-defined configurations. This allows the efficient optimization of RISs, especially in scenarios where the computational complexity would be prohibitive using traditional approaches. Simulation results show the good performance and limited complexity of the proposed method in comparison to benchmark schemes.
Paper Structure (16 sections, 54 equations, 10 figures, 1 table, 2 algorithms)

This paper contains 16 sections, 54 equations, 10 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. State-of-the-art
  3. Main Contributions
  4. Paper Organization and Notation
  5. System Model
  6. Basis Vector Design
  7. Problem Formulation
  8. Precoding Optimization
  9. Tiles Configuration Optimization
  10. Convergence Analysis
  11. A Low Complexity Solution for TO1
  12. Computational Complexity
  13. Numerical Results
  14. Conclusion and Future Research
  15. Deriving the Lagrange Dual Function
  16. ...and 1 more sections

Figures (10)

  • Figure 1: Example of system model for $Q = 2$, $C = 2$, $K = 4$, $N_u = 3$, with $i = 1, \ldots, N_u$, $k = 1, \ldots, K$.
  • Figure 2: Computational complexity comparison for $P = 800$ and different values of $N_u$ (\ref{['fig:ComputationalComplexity']}a) and for $N_u = 6$ and different values of $P$ (\ref{['fig:ComputationalComplexity']}b). As for the existing approaches, the lower bound $N_r^3$ is considered.
  • Figure 3: FF case: system performance for different values of $K$, the SINR target is $0$ and $10 ~\deci\bel$, $N_u = 6.$
  • Figure 4: NF case: system performance for different values of $K$, the SINR target is $0$ and $10 ~\deci\bel$, $N_u = 3.$
  • Figure 5: Comparison for the case studies with and without projection on the unitary circle, assuming the SINR target of 0 $\deci\bel$ and $K = Q = 6$.
  • ...and 5 more figures

Theorems & Definitions (2)

  • proof
  • proof