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Achievable Rate Analysis and Optimization of Double-RIS Assisted Spatially Correlated MIMO with Statistical CSI

Kaizhe Xu, Jiajia Guo, Jun Zhang, Shi Jin, Shaodan Ma

TL;DR

This paper investigates a general double-RIS assisted multiple-input multiple-input multiple-output (MIMO) wireless communication system under spatially correlated non line-of-sight propagation channels, where the cooperation of the double RISs is also considered.

Abstract

Reconfigurable intelligent surface (RIS) is a novel meta-material which can form a smart radio environment by dynamically altering reflection directions of the impinging electromagnetic waves. In the prior literature, the inter-RIS links which also contribute to the performance of the whole system are usually neglected when multiple RISs are deployed. In this paper we investigate a general double-RIS assisted multiple-input multiple-output (MIMO) wireless communication system under spatially correlated non line-of-sight propagation channels, where the cooperation of the double RISs is also considered. The design objective is to maximize the achievable ergodic rate based on full statistical channel state information (CSI). Specifically, we firstly present a closed-form asymptotic expression for the achievable ergodic rate by utilizing replica method from statistical physics. Then a full statistical CSI-enabled optimal design is proposed which avoids high pilot training overhead compared to instantaneous CSI-enabled design. To further reduce the signal processing overhead and lower the complexity for practical realization, a common-phase scheme is proposed to design the double RISs. Simulation results show that the derived asymptotic ergodic rate is quite accurate even for small-sized antenna arrays. And the proposed optimization algorithm can achieve substantial gain at the expense of a low overhead and complexity. Furthermore, the cooperative double-RIS assisted MIMO framework is proven to achieve superior ergodic rate performance and high communication reliability under harsh propagation environment.

Achievable Rate Analysis and Optimization of Double-RIS Assisted Spatially Correlated MIMO with Statistical CSI

TL;DR

This paper investigates a general double-RIS assisted multiple-input multiple-input multiple-output (MIMO) wireless communication system under spatially correlated non line-of-sight propagation channels, where the cooperation of the double RISs is also considered.

Abstract

Reconfigurable intelligent surface (RIS) is a novel meta-material which can form a smart radio environment by dynamically altering reflection directions of the impinging electromagnetic waves. In the prior literature, the inter-RIS links which also contribute to the performance of the whole system are usually neglected when multiple RISs are deployed. In this paper we investigate a general double-RIS assisted multiple-input multiple-output (MIMO) wireless communication system under spatially correlated non line-of-sight propagation channels, where the cooperation of the double RISs is also considered. The design objective is to maximize the achievable ergodic rate based on full statistical channel state information (CSI). Specifically, we firstly present a closed-form asymptotic expression for the achievable ergodic rate by utilizing replica method from statistical physics. Then a full statistical CSI-enabled optimal design is proposed which avoids high pilot training overhead compared to instantaneous CSI-enabled design. To further reduce the signal processing overhead and lower the complexity for practical realization, a common-phase scheme is proposed to design the double RISs. Simulation results show that the derived asymptotic ergodic rate is quite accurate even for small-sized antenna arrays. And the proposed optimization algorithm can achieve substantial gain at the expense of a low overhead and complexity. Furthermore, the cooperative double-RIS assisted MIMO framework is proven to achieve superior ergodic rate performance and high communication reliability under harsh propagation environment.
Paper Structure (22 sections, 2 theorems, 38 equations, 11 figures, 1 table, 2 algorithms)

This paper contains 22 sections, 2 theorems, 38 equations, 11 figures, 1 table, 2 algorithms.

Table of Contents

  1. introduction
  2. Contributions
  3. Outline
  4. Notations
  5. System Model And Problem Formulation
  6. Large System Analysis
  7. Ergodic Rate Optimization
  8. Optimization of ${\bf Q}$ with Fixed ${\bf \Theta}_1$ and ${\bf \Theta}_2$
  9. Optimization of ${\bf \Theta}_1$ and ${\bf \Theta}_2$ with Fixed ${\bf Q}$
  10. Proposed AO Algorithm
  11. Numerical Results
  12. Verification of the Large System Analysis
  13. Performance of the Proposed AO Algorithm 2
  14. Effectiveness of the Proposed Double-RIS Assisted MIMO Framework
  15. Conclusion
  16. ...and 7 more sections

Key Result

proposition 1

The asymptotic achievable ergodic sum-rate $I$ for double-RIS assisted MIMO in (ergodic_rate_after_replacement) can be given by where the auxiliary variables are the unique solutions of the following system of equations$^{1, 2}$Due to the tedious expressions of the equation system, the dimension indicators of identity matrices and the parantheses following Tr are omitted.By using an iterative alg

Figures (11)

  • Figure 1: A cooperatively double-RIS assisted MIMO system.
  • Figure 2: Ergodic rate versus number of transceiver antennas.
  • Figure 3: Ergodic rate versus distance of RIS elements.
  • Figure 4: Ergodic rate versus number of RIS elements.
  • Figure 5: Convergence performance of the proposed algorithm.
  • ...and 6 more figures

Theorems & Definitions (7)

  • proposition 1
  • remark 1
  • remark 2
  • remark 3
  • remark 4
  • remark 5
  • proposition 2