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RIS with Coupled Phase Shift and Amplitude: Capacity Maximization and Configuration Set Selection

Seyedkhashayar Hashemi, Masoud Ardakani, Hai Jiang

TL;DR

This work develops an efficient method for capacity maximization by finding the optimal reflection coefficients of the RIS elements by finding the optimal reflection coefficients of the RIS elements given a configuration set.

Abstract

A reconfigurable intelligent surface (RIS) is a planar surface that can enhance the quality of communication by providing control over the communication environment. Reflection optimization is one of the pivotal challenges in RIS setups. While there has been lots of research regarding the reflection optimization of RIS, most works consider the independence of the phase shift and the amplitude of RIS reflection coefficients. In practice, the phase shift and the amplitude are coupled and according to a recent study, the relation between them can be described using a function. In our work, we consider a practical system model with coupled phase shift and amplitude. We develop an efficient method for achieving capacity maximization by finding the optimal reflection coefficients of the RIS elements. The complexity of our method is linear with the number of RIS elements and the number of discrete phase shifts. We also develop a method that optimally selects the configuration set of the system, where a configuration set means a discrete set of reflection coefficient choices that a RIS element can take.

RIS with Coupled Phase Shift and Amplitude: Capacity Maximization and Configuration Set Selection

TL;DR

This work develops an efficient method for capacity maximization by finding the optimal reflection coefficients of the RIS elements by finding the optimal reflection coefficients of the RIS elements given a configuration set.

Abstract

A reconfigurable intelligent surface (RIS) is a planar surface that can enhance the quality of communication by providing control over the communication environment. Reflection optimization is one of the pivotal challenges in RIS setups. While there has been lots of research regarding the reflection optimization of RIS, most works consider the independence of the phase shift and the amplitude of RIS reflection coefficients. In practice, the phase shift and the amplitude are coupled and according to a recent study, the relation between them can be described using a function. In our work, we consider a practical system model with coupled phase shift and amplitude. We develop an efficient method for achieving capacity maximization by finding the optimal reflection coefficients of the RIS elements. The complexity of our method is linear with the number of RIS elements and the number of discrete phase shifts. We also develop a method that optimally selects the configuration set of the system, where a configuration set means a discrete set of reflection coefficient choices that a RIS element can take.

Paper Structure

This paper contains 19 sections, 3 theorems, 33 equations, 15 figures, 2 tables.

Table of Contents

  1. Introduction
  2. System Model and Practical RIS Reflection Coefficient Model
  3. System Model
  4. Practical RIS Reflection Coefficient Model
  5. Optimal Solution for Capacity Maximization
  6. Determining $\theta_n^*$ by Assuming $\angle h^*$ is Known
  7. Converting Infinite Possibilities of $\angle h^*$ to a Finite Number of Possibilities
  8. Determining Active Intervals of One RIS Element
  9. Determining the Active Intersections of All Elements
  10. Determining Overall Optimal Reflection Coefficients
  11. Configuration Set Selection
  12. Integral Maximization Based (IMB) Configuration Set Selection
  13. Search Space Compression (SSC)
  14. Numerical Results
  15. Capacity Maximization
  16. ...and 4 more sections

Key Result

Theorem 1

If $\langle h^*,g_{n,i}\rangle$ is the maximum among $\{\langle h^*,g_{n,1}\rangle,\langle h^*,g_{n,2}\rangle,...,\langle h^*,g_{n,K}\rangle\}$, then the optimal reflection coefficient of the $n$th RIS element, denoted as $g_n^*$, is $g_{n,i}$.

Figures (15)

  • Figure 1: The system model consisting of a transmitter, a receiver, and a RIS.
  • Figure 2: Relationship between the phase shift and the amplitude.
  • Figure 3: $\hat{\beta}_i\cos(\angle h^*-\angle g_{n,i})$ versus $\angle h^*\in [0,2\pi)$ for the $n$th RIS element.
  • Figure 4: Demonstration for the nine cases in Table \ref{['CRC_table']}.
  • Figure 5: An example demonstrating $F_n(\angle h^*)$
  • ...and 10 more figures

Theorems & Definitions (6)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Theorem 3
  • proof