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Computationally Efficient Unsupervised Deep Learning for Robust Joint AP Clustering and Beamforming Design in Cell-Free Systems

Guanghui Chen, Zheng Wang, Hongxin Lin, Yongming Huang, Luxi Yang

TL;DR

This work addresses robust joint AP clustering and beamforming in cell-free systems under imperfect CSI. It introduces RJAPCBN, a computationally efficient unsupervised deep learning framework that maps estimated CSI to sparse yet effective beamforming, while satisfying power and sparsity constraints. The method combines problem transformation via the S-procedure and Sign-Definiteness to convert semi-infinite constraints into LMIs, with a differentiable, adaptive AP clustering module and a residual CNN for beamforming, all trained end-to-end in a closed loop. Experiments show RJAPCBN delivers higher worst-case sum rates with a smaller average number of serving APs and significantly lower computational complexity compared to WMMSE, CNN-based, and related baselines, highlighting its practical impact for scalable cell-free deployments.

Abstract

In this paper, we consider robust joint access point (AP) clustering and beamforming design with imperfect channel state information (CSI) in cell-free systems. Specifically, we jointly optimize AP clustering and beamforming with imperfect CSI to simultaneously maximize the worst-case sum rate and minimize the number of AP clustering under power constraint and the sparsity constraint of AP clustering. By transformations, the semi-infinite constraints caused by the imperfect CSI are converted into more tractable forms for facilitating a computationally efficient unsupervised deep learning algorithm. In addition, to further reduce the computational complexity, a computationally effective unsupervised deep learning algorithm is proposed to implement robust joint AP clustering and beamforming design with imperfect CSI in cell-free systems. Numerical results demonstrate that the proposed unsupervised deep learning algorithm achieves a higher worst-case sum rate under a smaller number of AP clustering with computational efficiency.

Computationally Efficient Unsupervised Deep Learning for Robust Joint AP Clustering and Beamforming Design in Cell-Free Systems

TL;DR

This work addresses robust joint AP clustering and beamforming in cell-free systems under imperfect CSI. It introduces RJAPCBN, a computationally efficient unsupervised deep learning framework that maps estimated CSI to sparse yet effective beamforming, while satisfying power and sparsity constraints. The method combines problem transformation via the S-procedure and Sign-Definiteness to convert semi-infinite constraints into LMIs, with a differentiable, adaptive AP clustering module and a residual CNN for beamforming, all trained end-to-end in a closed loop. Experiments show RJAPCBN delivers higher worst-case sum rates with a smaller average number of serving APs and significantly lower computational complexity compared to WMMSE, CNN-based, and related baselines, highlighting its practical impact for scalable cell-free deployments.

Abstract

In this paper, we consider robust joint access point (AP) clustering and beamforming design with imperfect channel state information (CSI) in cell-free systems. Specifically, we jointly optimize AP clustering and beamforming with imperfect CSI to simultaneously maximize the worst-case sum rate and minimize the number of AP clustering under power constraint and the sparsity constraint of AP clustering. By transformations, the semi-infinite constraints caused by the imperfect CSI are converted into more tractable forms for facilitating a computationally efficient unsupervised deep learning algorithm. In addition, to further reduce the computational complexity, a computationally effective unsupervised deep learning algorithm is proposed to implement robust joint AP clustering and beamforming design with imperfect CSI in cell-free systems. Numerical results demonstrate that the proposed unsupervised deep learning algorithm achieves a higher worst-case sum rate under a smaller number of AP clustering with computational efficiency.
Paper Structure (18 sections, 37 equations, 11 figures, 2 tables)

This paper contains 18 sections, 37 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. System Model
  4. AP Clustering
  5. CSI Error Model
  6. Problem Formulation
  7. Problem Transformation
  8. Proposed RJAPCBN
  9. CSI Conversion $\mathcal{C}\left( \cdot\right)$
  10. Residual Network $\mathcal{R}\left(\cdot,\theta \right)$
  11. Adaptive AP Clustering $\mathcal{A}\left(\cdot,\theta \right)$
  12. Beamforming Conversion $\mathcal{V}\left( \cdot\right)$ and Power Constraint $\mathcal{P}\left( \cdot\right)$
  13. Updating Slack Variable Module $\mathcal{U}\left( \cdot\right)$
  14. Experimental Results
  15. Parameter Settings of RJAPCBN
  16. ...and 3 more sections

Figures (11)

  • Figure 1: The model architecture of the proposed RJAPCBN.
  • Figure 2: Differentiable threshold function (\ref{['eq23']}) at different $k$.
  • Figure 3: Differentiable threshold function (\ref{['eq23']}) at different $t_i^q$.
  • Figure 4: Worst-case sum rate and $Q_{\text{ave}}$ at different $\lambda$.
  • Figure 5: Worst-case sum rate at different imperfect CSI error levels.
  • ...and 6 more figures