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Joint Transmit and Pinching Beamforming for Pinching Antenna Systems (PASS): Optimization-Based or Learning-Based?

Xiaoxia Xu, Xidong Mu, Yuanwei Liu, Arumugam Nallanathan

TL;DR

This work proposes a PASS-enabled downlink multi-user MISO framework where pinching antennas (PAs) along long dielectric waveguides reconfigure path loss and phases to enable pinching beamforming. It develops an optimization-based MM-PDD algorithm to jointly design pinching and transmit beamforming, with convergence to a stationary point, and a learning-based KDL-Transformer that reconstructs KKT-satisfying solutions via dual variables and attention mechanisms. The KDL-Transformer exploits inter-PA/inter-user and CSI-beamforming dependencies to achieve substantial gains, reportedly over 20% relative to MM-PDD with millisecond-level inference on GPUs. Across extensive simulations, PASS outperforms conventional massive MIMO architectures even with a fraction of PAs, highlighting its potential for flexible, high-capacity wireless systems. The work also provides detailed complexity analyses and constraint-guarantee procedures, outlining practical pathways for real-time, adaptive PASS deployments.

Abstract

A novel pinching antenna system (PASS)-enabled downlink multi-user multiple-input single-output (MISO) framework is proposed. PASS consists of multiple waveguides spanning over thousands of wavelength, which equip numerous low-cost dielectric particles, named pinching antennas (PAs), to radiate signals into free space. The positions of PAs can be reconfigured to change both the large-scale path losses and phases of signals, thus facilitating the novel pinching beamforming design. A sum rate maximization problem is formulated, which jointly optimizes the transmit and pinching beamforming to adaptively achieve constructive signal enhancement and destructive interference mitigation. To solve this highly coupled and nonconvex problem, both optimization-based and learning-based methods are proposed. 1) For the optimization-based method, a majorization-minimization and penalty dual decomposition (MM-PDD) algorithm is developed, which handles the nonconvex complex exponential component using a Lipschitz surrogate function and then invokes PDD for problem decoupling. 2) For the learning-based method, a novel Karush-Kuhn-Tucker (KKT)-guided dual learning (KDL) approach is proposed, which enables KKT solutions to be reconstructed in a data-driven manner by learning dual variables. Following this idea, a KDL-Transformer algorithm is developed, which captures both inter-PA/inter-user dependencies and channel-state-information (CSI)-beamforming dependencies by attention mechanisms. Simulation results demonstrate that: i) The proposed PASS framework significantly outperforms conventional massive multiple input multiple output (MIMO) system even with a few PAs. ii) The proposed KDL-Transformer can improve over 20% system performance than MM-PDD algorithm, while achieving a millisecond-level response on modern GPUs.

Joint Transmit and Pinching Beamforming for Pinching Antenna Systems (PASS): Optimization-Based or Learning-Based?

TL;DR

This work proposes a PASS-enabled downlink multi-user MISO framework where pinching antennas (PAs) along long dielectric waveguides reconfigure path loss and phases to enable pinching beamforming. It develops an optimization-based MM-PDD algorithm to jointly design pinching and transmit beamforming, with convergence to a stationary point, and a learning-based KDL-Transformer that reconstructs KKT-satisfying solutions via dual variables and attention mechanisms. The KDL-Transformer exploits inter-PA/inter-user and CSI-beamforming dependencies to achieve substantial gains, reportedly over 20% relative to MM-PDD with millisecond-level inference on GPUs. Across extensive simulations, PASS outperforms conventional massive MIMO architectures even with a fraction of PAs, highlighting its potential for flexible, high-capacity wireless systems. The work also provides detailed complexity analyses and constraint-guarantee procedures, outlining practical pathways for real-time, adaptive PASS deployments.

Abstract

A novel pinching antenna system (PASS)-enabled downlink multi-user multiple-input single-output (MISO) framework is proposed. PASS consists of multiple waveguides spanning over thousands of wavelength, which equip numerous low-cost dielectric particles, named pinching antennas (PAs), to radiate signals into free space. The positions of PAs can be reconfigured to change both the large-scale path losses and phases of signals, thus facilitating the novel pinching beamforming design. A sum rate maximization problem is formulated, which jointly optimizes the transmit and pinching beamforming to adaptively achieve constructive signal enhancement and destructive interference mitigation. To solve this highly coupled and nonconvex problem, both optimization-based and learning-based methods are proposed. 1) For the optimization-based method, a majorization-minimization and penalty dual decomposition (MM-PDD) algorithm is developed, which handles the nonconvex complex exponential component using a Lipschitz surrogate function and then invokes PDD for problem decoupling. 2) For the learning-based method, a novel Karush-Kuhn-Tucker (KKT)-guided dual learning (KDL) approach is proposed, which enables KKT solutions to be reconstructed in a data-driven manner by learning dual variables. Following this idea, a KDL-Transformer algorithm is developed, which captures both inter-PA/inter-user dependencies and channel-state-information (CSI)-beamforming dependencies by attention mechanisms. Simulation results demonstrate that: i) The proposed PASS framework significantly outperforms conventional massive multiple input multiple output (MIMO) system even with a few PAs. ii) The proposed KDL-Transformer can improve over 20% system performance than MM-PDD algorithm, while achieving a millisecond-level response on modern GPUs.

Paper Structure

This paper contains 24 sections, 3 theorems, 66 equations, 7 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Signal Radiation Model
  4. Problem Formulation and Conversion
  5. Optimization Based Joint Transmit and Pinching Beamforming
  6. WMMSE-based Reformulation
  7. The Proposed MM-PDD Algorithm
  8. Algorithm Design and Theoretical Analysis
  9. Learning-Based Joint Transmit and Pinching Beamforming
  10. Preliminaries on Learning to Optimize
  11. End-to-end learning
  12. Deep unfolding-based optimization
  13. The Proposed KKT-guided Dual Learning Approach
  14. Fundamentals of KDL
  15. KDL Based Joint Transmit Beamforming and Pinching Beamforming
  16. ...and 9 more sections

Key Result

Lemma 1

The optimal solution of the constrained sum rate maximization problem (P1) is equivalent to the following WMMSE problem: where $\alpha_{k}$ denotes the weighting factor. By fixing other variables, the optimal solution of $\alpha_{k}$ and $v_{k}$ can be given by where $J_{k}\triangleq\sum\limits_{i\in\mathcal{K}}\!\mathbf{h}_{k}^{H}\!\left(\mathbf{X}\right)\!\mathbf{G}\!\left(\mathbf{X}\right) \m

Figures (7)

  • Figure 1: PASS-enabled downlink multi-user MIMO framework.
  • Figure 2: Diagram of the proposed KDL-Transformer.
  • Figure 3: Convergence behaviors of the developed MM-PDD algorithm. $K=4$, $P=10$ dBm, $S_{\mathrm{x}}=20$ m.
  • Figure 4: Comparisons of convergence performance of the proposed KDL-Transformer with other learning-based algorithms. $K=4$, $L=8$, $P=10$ dBm, $S_{\mathrm{x}}=20$ m.
  • Figure 5: Performance comparisons of different algorithms under different $P$. $K=4$, $S_{\mathrm{x}}=20$ m.
  • ...and 2 more figures

Theorems & Definitions (11)

  • Lemma 1
  • proof
  • Definition 1: Lipschitz gradient surrogate
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Remark 1
  • Remark 2
  • Remark 3
  • ...and 1 more