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Joint Downlink and Uplink Optimization for RIS-Aided FDD MIMO Communication Systems

Gyoseung Lee, Hyeongtaek Lee, Donghwan Kim, Jaehoon Chung, A. Lee. Swindlehurst, Junil Choi

TL;DR

This work introduces a joint optimization framework for RIS-aided frequency-division duplexing MIMO systems to simultaneously enhance downlink and uplink performance. By decoupling RIS phase design from transmit precoding and applying alternating optimization, it develops two RIS phase-shift strategies: a high-performance manifold optimization method operating on the complex circle manifold, and a low-complexity AO approach with closed-form per-element updates. The methods converge rapidly to local optima and substantially outperform benchmark schemes in weighted-sum-rate and rate-region analyses, validating the benefits of joint DL/UL optimization in FDD RIS systems. The approach provides practical, scalable solutions suitable for RIS-enabled FDD networks, with potential extensions to multi-user and imperfect CSI scenarios.

Abstract

This paper investigates reconfigurable intelligent surface (RIS)-aided frequency division duplexing (FDD) communication systems. Since the downlink and uplink signals are simultaneously transmitted in FDD, the phase shifts at the RIS should be designed to support both transmissions. Considering a single-user multiple-input multiple-output system, we formulate a weighted sum-rate maximization problem to jointly maximize the downlink and uplink system performance. To tackle the non-convex optimization problem, we adopt an alternating optimization (AO) algorithm, in which two phase shift optimization techniques are developed to handle the unit-modulus constraints induced by the reflection coefficients at the RIS. The first technique exploits the manifold optimization-based algorithm, while the second uses a lower-complexity AO approach. Numerical results verify that the proposed techniques rapidly converge to local optima and significantly improve the overall system performance compared to existing benchmark schemes.

Joint Downlink and Uplink Optimization for RIS-Aided FDD MIMO Communication Systems

TL;DR

This work introduces a joint optimization framework for RIS-aided frequency-division duplexing MIMO systems to simultaneously enhance downlink and uplink performance. By decoupling RIS phase design from transmit precoding and applying alternating optimization, it develops two RIS phase-shift strategies: a high-performance manifold optimization method operating on the complex circle manifold, and a low-complexity AO approach with closed-form per-element updates. The methods converge rapidly to local optima and substantially outperform benchmark schemes in weighted-sum-rate and rate-region analyses, validating the benefits of joint DL/UL optimization in FDD RIS systems. The approach provides practical, scalable solutions suitable for RIS-enabled FDD networks, with potential extensions to multi-user and imperfect CSI scenarios.

Abstract

This paper investigates reconfigurable intelligent surface (RIS)-aided frequency division duplexing (FDD) communication systems. Since the downlink and uplink signals are simultaneously transmitted in FDD, the phase shifts at the RIS should be designed to support both transmissions. Considering a single-user multiple-input multiple-output system, we formulate a weighted sum-rate maximization problem to jointly maximize the downlink and uplink system performance. To tackle the non-convex optimization problem, we adopt an alternating optimization (AO) algorithm, in which two phase shift optimization techniques are developed to handle the unit-modulus constraints induced by the reflection coefficients at the RIS. The first technique exploits the manifold optimization-based algorithm, while the second uses a lower-complexity AO approach. Numerical results verify that the proposed techniques rapidly converge to local optima and significantly improve the overall system performance compared to existing benchmark schemes.
Paper Structure (28 sections, 6 theorems, 41 equations, 5 figures, 3 algorithms)

This paper contains 28 sections, 6 theorems, 41 equations, 5 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. Problem Formulation and Algorithm Design
  4. Problem formulation
  5. Optimization of ${\mathbf{F}}_{\mathrm{D}}$ and ${\mathbf{F}}_{\mathrm{U}}$ with given ${\pmb{\Theta}}$
  6. Optimization of ${\pmb{\Theta}}$ with given ${\mathbf{F}}_{\mathrm{D}}$ and ${\mathbf{F}}_{\mathrm{U}}$
  7. Proposed Phase Shift Optimization Techniques
  8. Manifold optimization
  9. Compute Riemannian gradient
  10. Transport
  11. Retraction
  12. Low-complexity AO
  13. Diagonalizable ${\mathbf{A}}_{\mathrm{D},\ell}^{-1} {\mathbf{B}}_{\mathrm{D},\ell}$ and ${\mathbf{A}}_{\mathrm{U},\ell}^{-1} {\mathbf{B}}_{\mathrm{U},\ell}$
  14. Non-diagonalizable ${\mathbf{A}}_{\mathrm{D},\ell}^{-1} {\mathbf{B}}_{\mathrm{D},\ell}$ or ${\mathbf{A}}_{\mathrm{U},\ell}^{-1} {\mathbf{B}}_{\mathrm{U},\ell}$
  15. Summary
  16. ...and 13 more sections

Key Result

Proposition 1

The Euclidean gradient $\nabla_{{\mathbf{H}}_{\mathrm{eff,D}}} R_{\mathrm{D}}$ is

Figures (5)

  • Figure 1: An example of an RIS-aided FDD SU-MIMO communication system with $N$ BS antennas, $K$ UE antennas, and $L$ RIS elements.
  • Figure 2: The convergence behavior of proposed algorithms according to the outer iterations.
  • Figure 3: Weighted sum-rate versus the number of RIS elements.
  • Figure 4: Weighted sum-rate versus the downlink transmit power.
  • Figure 5: The downlink and uplink rate regions for the proposed algorithms.

Theorems & Definitions (10)

  • Proposition 1
  • proof
  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Proposition 2
  • proof
  • Theorem 1
  • Lemma 3