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

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.

💡 Research Summary

The paper introduces a novel downlink multi‑user multiple‑input single‑output (MISO) framework that leverages a Pinching Antenna System (PASS). PASS consists of long dielectric waveguides populated with low‑cost dielectric particles called Pinching Antennas (PAs). By mechanically “pinching” or releasing each PA along the waveguide, both large‑scale path loss and the phase of the radiated signal can be reconfigured, thereby creating a new degree of freedom termed “pinching beamforming.”

The authors formulate a sum‑rate maximization problem that jointly optimizes conventional digital transmit beamforming vectors and the continuous positions of all PAs. The resulting problem is highly coupled and non‑convex because the channel model contains complex exponential terms that depend on PA locations. To tackle this challenge, two complementary solution approaches are proposed.

1. Optimization‑Based Approach (MM‑PDD).
The original problem is first transformed into an equivalent weighted minimum mean‑square error (WMMSE) formulation. The non‑convex complex exponential terms are approximated by a Lipschitz‑continuous surrogate using a majorization‑minimization (MM) technique, which yields an upper bound that can be minimized iteratively. The coupled variables are then decoupled via Penalty Dual Decomposition (PDD). Within each PDD iteration, block coordinate descent (BCD) updates the digital beamforming vectors in closed form and updates the PA positions by solving a convex sub‑problem derived from the surrogate. The algorithm is proven to converge to a stationary point.

2. Learning‑Based Approach (KDL‑Transformer).
Instead of directly learning the high‑dimensional primal variables, the authors exploit the Karush‑Kuhn‑Tucker (KKT) conditions of the original optimization problem. Only the dual variables (Lagrange multipliers) are learned from data; the primal variables (beamformers and PA positions) are then reconstructed analytically from the learned duals, preserving the structure of the optimal solution while drastically reducing the learning burden. A sequence‑to‑sequence transformer network is designed: the input sequence encodes the channel state information (CSI) together with the current PA configuration, while the output sequence predicts the optimal dual variables and the corresponding updates for beamforming and PA locations. Multi‑head attention captures both inter‑user interference patterns and inter‑PA dependencies.

Performance Evaluation.
Simulations are conducted at 60 GHz mmWave frequencies with N = K = 4 waveguides, each hosting L = 8 PAs (total M = 32). Compared with a conventional massive MIMO baseline (64 antennas), PASS achieves 15 %–25 % higher sum‑rate even when only a few PAs are active, thanks to its ability to reshape large‑scale fading. The MM‑PDD algorithm reaches a stationary solution after several hundred iterations, which is computationally intensive for real‑time operation. In contrast, the KDL‑Transformer, trained on a large synthetic dataset, attains more than 20 % sum‑rate improvement over MM‑PDD and produces inference results in sub‑millisecond latency on a modern GPU (≈0.8 ms on an RTX 4090). The learned dual variables closely satisfy the KKT conditions (average absolute error ≈ 0.03 after normalization), confirming that the network effectively captures the optimality structure.

Key Insights and Contributions.

• PASS provides a physical mechanism to jointly manipulate path loss and phase, extending the design space far beyond traditional RIS or movable antenna concepts.
• The MM‑PDD algorithm offers a rigorous, provably convergent method for solving the highly non‑convex joint beamforming problem.
• The KDL‑Transformer demonstrates how optimization theory can guide deep learning, achieving both superior performance and real‑time feasibility by learning only a low‑dimensional set of dual variables.
• Extensive simulations validate that PASS with only a modest number of PAs can outperform large‑scale massive MIMO deployments, highlighting its potential for cost‑effective 6G high‑frequency (mmWave/THz) networks.

Future Directions.
The authors suggest extending the framework to multi‑waveguide cooperation, hardware prototyping, and dynamic adaptation to user mobility. Moreover, integrating reinforcement learning for online PA repositioning and exploring hybrid analog‑digital architectures could further enhance the practicality of PASS in next‑generation wireless systems.