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Transmission Design for XL-RIS-Aided Massive MIMO System with Visibility Regions

Luchu Li, Kangda Zhi, Cunhua Pan

TL;DR

This work tackles XL-RIS aided massive MIMO by introducing a two-timescale transmission framework where BS beamforming relies on instantaneous CSI and RIS phase shifts are set from statistical CSI, accommodating VR-induced non-stationarity and near-field effects. A closed-form approximate uplink rate under spatially correlated Rician fading is derived, and a VR-based dimension reduction reduces computational burdens while preserving performance. A gradient-based RIS phase-shifts design with acceleration is proposed to maximize the minimum user rate, and is shown to rival GA in performance but with much lower runtime. Simulations confirm the benefits of VR-aware modeling, demonstrating substantial complexity reductions and effective RIS optimization for practical XL-RIS deployments in massive MIMO systems.

Abstract

This paper proposes a two-timescale transmission scheme for extremely large-scale (XL)-reconfigurable intelligent surfaces (RIS)-aided massive multi-input multi-output (MIMO) systems considering visibility regions (VRs). The beamforming of base stations (BS) is designed based on rapidly changing instantaneous channel state information (CSI), while the phase shifts of RIS are configured based on slowly changing statistical CSI. Specifically, we first formulate a system model with spatially correlated Rician fading channels and introduce the concept of VRs. Then, we derive a closed-form approximate expression for the achievable rate applicable to any number of BS antennas and RIS elements, and analyze the impact of VRs on system performance and complexity. Next, we solve the problem of maximizing the minimum user rate by optimizing the phase shifts of RIS through an algorithm based on accelerated gradient ascent. Finally, we present numerical results to demonstrate the performance of the gradient algorithm from different aspects and reveal the low system complexity of deploying XL-RIS in massive MIMO systems with the help of VRs.

Transmission Design for XL-RIS-Aided Massive MIMO System with Visibility Regions

TL;DR

This work tackles XL-RIS aided massive MIMO by introducing a two-timescale transmission framework where BS beamforming relies on instantaneous CSI and RIS phase shifts are set from statistical CSI, accommodating VR-induced non-stationarity and near-field effects. A closed-form approximate uplink rate under spatially correlated Rician fading is derived, and a VR-based dimension reduction reduces computational burdens while preserving performance. A gradient-based RIS phase-shifts design with acceleration is proposed to maximize the minimum user rate, and is shown to rival GA in performance but with much lower runtime. Simulations confirm the benefits of VR-aware modeling, demonstrating substantial complexity reductions and effective RIS optimization for practical XL-RIS deployments in massive MIMO systems.

Abstract

This paper proposes a two-timescale transmission scheme for extremely large-scale (XL)-reconfigurable intelligent surfaces (RIS)-aided massive multi-input multi-output (MIMO) systems considering visibility regions (VRs). The beamforming of base stations (BS) is designed based on rapidly changing instantaneous channel state information (CSI), while the phase shifts of RIS are configured based on slowly changing statistical CSI. Specifically, we first formulate a system model with spatially correlated Rician fading channels and introduce the concept of VRs. Then, we derive a closed-form approximate expression for the achievable rate applicable to any number of BS antennas and RIS elements, and analyze the impact of VRs on system performance and complexity. Next, we solve the problem of maximizing the minimum user rate by optimizing the phase shifts of RIS through an algorithm based on accelerated gradient ascent. Finally, we present numerical results to demonstrate the performance of the gradient algorithm from different aspects and reveal the low system complexity of deploying XL-RIS in massive MIMO systems with the help of VRs.
Paper Structure (10 sections, 2 theorems, 99 equations, 12 figures, 1 table, 1 algorithm)

This paper contains 10 sections, 2 theorems, 99 equations, 12 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model
  3. Achievable Rate Analysis
  4. Visibility Region Analysis
  5. RIS Phase Shifts Design
  6. Simulation and Results
  7. Conclusion
  8. The derivation of noise term $E_{VR,k}^{\mathrm{noise}}(\boldsymbol{\Phi})$
  9. The derivation of signal term $E_{VR,k}^{\mathrm{signal}}(\boldsymbol{\Phi})$
  10. The derivation of signal term $I_{VR,ki}(\boldsymbol{\Phi})$

Key Result

Theorem 1

In the XL-RIS-aided massive MIMO systems, the uplink ergodic achievable rate of user $k$ can be approximated as where the first, second, and third items are the desired signal received by the BS, the multi-user interference, and the thermal noise, respectively. The values of $E_{VR,k}^{\mathrm{noise}}(\boldsymbol\Phi)$, $E_{VR,k}^\mathrm{signal}(\boldsymbol{\Phi})$ and $I_{VR,ki}(\boldsymbol{\Phi

Figures (12)

  • Figure 1: An XL-RIS-aided massive MIMO system.
  • Figure 2: The 2D geometry of an RIS with VR consisting of $N_2$ elements per row and $N_1$ elements per column.
  • Figure 3: Minimum user rate versus BS antennas number $M$
  • Figure 4: Minimum user rate versus RIS elements number $N$
  • Figure 5: Max-min achievable rate versus $N$ when $\delta=\varepsilon_k=0$ or $\delta\rightarrow\infty$ and $\varepsilon_k\rightarrow\infty$
  • ...and 7 more figures

Theorems & Definitions (2)

  • Theorem 1
  • Lemma 1