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Joint MIMO Transceiver and Reflector Design for Reconfigurable Intelligent Surface-Assisted Communication

Yaqiong Zhao, Jindan Xu, Wei Xu, Kezhi Wang, Xinquan Ye, Chau Yuen, Xiaohu You

TL;DR

This work addresses maximizing the achievable rate in RIS-assisted MIMO by jointly designing the BS pre coder, UE combiner, and RIS phase shifts. It converts the nonconvex rate objective to a tractable WMSE problem via a WMMSE reformulation and derives closed-form transceiver updates under fixed RIS, enabling an alternating-optimization framework. Two RIS reflection design methods, SDR and SCF, are developed and analyzed for convergence, with SCF proven to converge to a KKT point. Numerical results demonstrate significant rate/NMSE improvements, robustness to coarse RIS quantization, and practical implications for deploying RIS in high-frequency MIMO systems.

Abstract

In this paper, we consider a reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output communication system with multiple antennas at both the base station (BS) and the user. We plan to maximize the achievable rate through jointly optimizing the transmit precoding matrix, the receive combining matrix, and the RIS reflection matrix under the constraints of the transmit power at the BS and the unit-modulus reflection at the RIS. Regarding the non-trivial problem form, we initially reformulate it into an considerable problem to make it tractable by utilizing the relationship between the achievable rate and the weighted minimum mean squared error. Next, the transmit precoding matrix, the receive combining matrix, and the RIS reflection matrix are alternately optimized. In particular, the optimal transmit precoding matrix and receive combining matrix are obtained in closed forms. Furthermore, a pair of computationally efficient methods are proposed for the RIS reflection matrix, namely the semi-definite relaxation (SDR) method and the successive closed form (SCF) method. We theoretically prove that both methods are ensured to converge, and the SCF-based algorithm is able to converges to a Karush-Kuhn-Tucker point of the problem.

Joint MIMO Transceiver and Reflector Design for Reconfigurable Intelligent Surface-Assisted Communication

TL;DR

This work addresses maximizing the achievable rate in RIS-assisted MIMO by jointly designing the BS pre coder, UE combiner, and RIS phase shifts. It converts the nonconvex rate objective to a tractable WMSE problem via a WMMSE reformulation and derives closed-form transceiver updates under fixed RIS, enabling an alternating-optimization framework. Two RIS reflection design methods, SDR and SCF, are developed and analyzed for convergence, with SCF proven to converge to a KKT point. Numerical results demonstrate significant rate/NMSE improvements, robustness to coarse RIS quantization, and practical implications for deploying RIS in high-frequency MIMO systems.

Abstract

In this paper, we consider a reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output communication system with multiple antennas at both the base station (BS) and the user. We plan to maximize the achievable rate through jointly optimizing the transmit precoding matrix, the receive combining matrix, and the RIS reflection matrix under the constraints of the transmit power at the BS and the unit-modulus reflection at the RIS. Regarding the non-trivial problem form, we initially reformulate it into an considerable problem to make it tractable by utilizing the relationship between the achievable rate and the weighted minimum mean squared error. Next, the transmit precoding matrix, the receive combining matrix, and the RIS reflection matrix are alternately optimized. In particular, the optimal transmit precoding matrix and receive combining matrix are obtained in closed forms. Furthermore, a pair of computationally efficient methods are proposed for the RIS reflection matrix, namely the semi-definite relaxation (SDR) method and the successive closed form (SCF) method. We theoretically prove that both methods are ensured to converge, and the SCF-based algorithm is able to converges to a Karush-Kuhn-Tucker point of the problem.
Paper Structure (16 sections, 78 equations, 12 figures, 2 algorithms)

This paper contains 16 sections, 78 equations, 12 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model
  4. Problem Formulation
  5. Low-Complexity Algorithm Design
  6. Problem Reformulation
  7. Optimal Transceiver Design
  8. Design of the RIS Reflection Matrix
  9. Semi-Definite Relaxation
  10. Sequence of Closed Forms
  11. Computational Complexity
  12. Convergence and Optimality Analysis
  13. Simulation Results
  14. Conclusion
  15. Proof of Lemma 1
  16. ...and 1 more sections

Figures (12)

  • Figure 1: System model for a RIS-assisted MIMO system.
  • Figure 2: Convergence behavior of Algorithm 1 and Algorithm 2.
  • Figure 3: Achievable rate performance of different schemes versus SNR.
  • Figure 4: NMSE performance versus SNR.
  • Figure 5: Achievable rate versus the number of reflecting elements.
  • ...and 7 more figures