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Robust Beamforming for Multiuser MIMO Systems with Unknown Channel Statistics: A Hybrid Offline-Online Framework

Wenzhuo Zou, Ming-Min Zhao, An Liu, Min-Jian Zhao

TL;DR

Addresses robust MU-MIMO beamforming under unknown channel statistics via a two-phase offline-online learning framework. It learns channel-error covariance offline with a shared DNN, augments accuracy and efficiency with a sparse augmented low-rank representation, and enables rapid online adaptation through MB-MAML-based meta-initializations. The approach yields strong robustness and generalization, outperforming state-of-the-art baselines in weighted sum-rate under imperfect CSI while maintaining low online complexity. This framework offers a practical path to distribution-shift-robust, real-time beamforming in dense wireless networks.

Abstract

Robust beamforming design under imperfect channel state information (CSI) is a fundamental challenge in multiuser multiple-input multiple-output (MU-MIMO) systems, particularly when the channel estimation error statistics are unknown. Conventional model-driven methods usually rely on prior knowledge of the error covariance matrix and data-driven deep learning approaches suffer from poor generalization capability to unseen channel conditions. To address these limitations, this paper proposes a hybrid offline-online framework that achieves effective offline learning and rapid online adaptation. In the offline phase, we propose a shared (among users) deep neural network (DNN) that is able to learn the channel estimation error covariance from observed samples, thus enabling robust beamforming without statistical priors. Meanwhile, to facilitate real-time deployment, we propose a sparse augmented low-rank (SALR) method to reduce complexity while maintaining comparable performance. In the online phase, we show that the proposed network can be rapidly fine-tuned with minimal gradient steps. Furthermore, a multiple basis model-agnostic meta-learning (MB-MAML) strategy is further proposed to maintain multiple meta-initializations and by dynamically selecting the best one online, we can improve the adaptation and generalization capability of the proposed framework under unseen or non-stationary channels. Simulation results demonstrate that the proposed offline-online framework exhibits strong robustness across diverse channel conditions and it is able to significantly outperform state-of-the-art (SOTA) baselines.

Robust Beamforming for Multiuser MIMO Systems with Unknown Channel Statistics: A Hybrid Offline-Online Framework

TL;DR

Addresses robust MU-MIMO beamforming under unknown channel statistics via a two-phase offline-online learning framework. It learns channel-error covariance offline with a shared DNN, augments accuracy and efficiency with a sparse augmented low-rank representation, and enables rapid online adaptation through MB-MAML-based meta-initializations. The approach yields strong robustness and generalization, outperforming state-of-the-art baselines in weighted sum-rate under imperfect CSI while maintaining low online complexity. This framework offers a practical path to distribution-shift-robust, real-time beamforming in dense wireless networks.

Abstract

Robust beamforming design under imperfect channel state information (CSI) is a fundamental challenge in multiuser multiple-input multiple-output (MU-MIMO) systems, particularly when the channel estimation error statistics are unknown. Conventional model-driven methods usually rely on prior knowledge of the error covariance matrix and data-driven deep learning approaches suffer from poor generalization capability to unseen channel conditions. To address these limitations, this paper proposes a hybrid offline-online framework that achieves effective offline learning and rapid online adaptation. In the offline phase, we propose a shared (among users) deep neural network (DNN) that is able to learn the channel estimation error covariance from observed samples, thus enabling robust beamforming without statistical priors. Meanwhile, to facilitate real-time deployment, we propose a sparse augmented low-rank (SALR) method to reduce complexity while maintaining comparable performance. In the online phase, we show that the proposed network can be rapidly fine-tuned with minimal gradient steps. Furthermore, a multiple basis model-agnostic meta-learning (MB-MAML) strategy is further proposed to maintain multiple meta-initializations and by dynamically selecting the best one online, we can improve the adaptation and generalization capability of the proposed framework under unseen or non-stationary channels. Simulation results demonstrate that the proposed offline-online framework exhibits strong robustness across diverse channel conditions and it is able to significantly outperform state-of-the-art (SOTA) baselines.

Paper Structure

This paper contains 23 sections, 38 equations, 8 figures, 1 table, 2 algorithms.

Table of Contents

  1. INTRODUCTION
  2. SYSTEM MODEL AND PROBLEM FORMULATION
  3. System Model
  4. Problem Formulation
  5. Related Work
  6. Hybrid Offline-Online Robust Beamforming Framework
  7. Proposed Framework
  8. Offline Learning Phase
  9. Online Adaptation Phase
  10. Neural Network Design
  11. Neural Network Architecture
  12. Sparse Augmented Low-Rank Approximation
  13. MB-MAML-Based Offline Learning and Online Adaptation
  14. Offline Training Stage
  15. Inner-loop fine-tuning
  16. ...and 8 more sections

Figures (8)

  • Figure 1: Massive MU-MIMO system model.
  • Figure 2: The complete pipeline of the proposed hybrid offline-online robust beamforming framework.
  • Figure 3: Proposed MB-MAML-based offline training and online adaptation scheme.
  • Figure 4: Convergence behavior of the proposed hybrid approach.
  • Figure 5: Performance Comparison of Offline, Online, and Hybrid approach.
  • ...and 3 more figures