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Modeling and Beamforming Optimization for Pinching-Antenna Systems

Zhaolin Wang, Chongjun Ouyang, Xidong Mu, Yuanwei Liu, Zhiguo Ding

arXiv:2502.05917v3cs.IT

TL;DR

PASS addresses free-space pathloss and line-of-sight blockage challenges in conventional multi-antenna systems. The paper develops physics-based and signal models, formulates joint beamforming optimization, proposes two algorithms, and reports substantial transmit-power reductions with comparable algorithm and power-model performance.

  • Problem

    Conventional multi-antenna technologies face free-space pathloss and line-of-sight blockage, while massive MIMO encounters increasing implementation complexity and cost from dedicated RF chains.

  • Method

    The paper develops physics-based and simplified signal models for PASS, formulates joint transmit and pinching beamforming optimization under continuous and discrete activation, and proposes penalty-based alternating-optimization and low-complexity ZF-based algorithms.

  • Results

    PASS achieves a transmit-power reduction of over 95% compared to conventional and massive MIMO, while the ZF-based algorithm and proportional power model perform comparably to their respective alternatives.

  • Takeaways & Limitations

    Discrete activation causes minimal performance loss but requires a dense set of available antenna positions to achieve performance similar to continuous activation.

Abstract

from arXiv · show

The Pinching-Antenna SyStem (PASS) is a revolutionary flexible antenna technology designed to enhance wireless communication by establishing strong line-of-sight (LoS) links, reducing free-space path loss and enabling antenna array reconfigurability. PASS uses dielectric waveguides with low propagation loss for signal transmission, radiating via a passive pinching antenna, which is a small dielectric element applied to the waveguide. This paper first proposes a physics-based hardware model for PASS, where the pinching antenna is modeled as an open-ended directional coupler, and the electromagnetic field behavior is analyzed using coupled-mode theory. A simplified signal model characterizes the coupling effect between multiple antennas on the same waveguide. Based on this, two power models are proposed: equal power and proportional power models. Additionally, a transmit power minimization problem is formulated/studied for the joint optimization of transmit and pinching beamforming under both continuous and discrete pinching antenna activations. Two algorithms are proposed to solve this multimodal optimization problem: the penalty-based alternating optimization algorithm and a low-complexity zero-forcing (ZF)-based algorithm. Numerical results show that 1) the ZF-based low-complexity algorithm performs similarly to the penalty-based algorithm, 2) PASS reduces transmit power by over 95% compared to conventional and massive MIMO, 3) discrete activation causes minimal performance loss but requires a dense antenna set to match continuous activation, and 4) the proportional power model yields performance comparable to the equal power model.

I. INTRODUCTION

PASS addresses free-space path loss and LoS blockage by using low-loss dielectric waveguides and strategically placed pinching antennas, while this paper develops physics-based modeling and joint beamforming optimization for the system.

  • Motivation: PASS uses low-loss dielectric waveguides and nearby pinching antennas to establish strong LoS links, reducing free-space path loss and mitigating blockage.The waveguide propagation loss can be as low as 0.01 dB/m, and antennas can be placed close to users.
  • Motivation: Existing PASS studies commonly assume complete waveguide radiation and identical antenna radiation power, despite underdeveloped physics modeling.The paper identifies these assumptions as inadequate because pinching antennas differ fundamentally from traditional electronic antennas.
  • Contributions: The paper models each pinching antenna as an open-ended directional waveguide coupler and uses coupled-mode theory to characterize guided and radiated electromagnetic fields.The coupler model supports adjustment of radiation characteristics and simplifies signal modeling.
  • Contributions: A physics-based signal model captures coupling among multiple antennas on one waveguide and yields equal-power and proportional-power models.The derivation assumes identical effective refractive indices for the waveguides and pinching antennas.
  • Contributions: The paper jointly optimizes transmit and pinching beamforming for continuous and discrete antenna activation using penalty-based alternating optimization and a low-complexity ZF algorithm.The formulation applies to arbitrary numbers of users, waveguides, and pinching antennas.
  • Results: PASS reduces transmit power by over 95% versus conventional and massive MIMO, while ZF performance is comparable to the penalty-based method.Discrete activation needs a dense antenna-position set to approach continuous-activation performance, and proportional power performs comparably to equal power.

B. Signal Model

The signal model is developed first for one pinching antenna coupled to a waveguide and then extended to multiple pinching antennas.

  • Signal Model: The paper formulates simplified signal models from the physics-based electromagnetic models under identical effective refractive indices.The derivation begins with a single pinching antenna coupled to the waveguide.
  • Signal Model: The signal-model formulation is subsequently extended from a single pinching antenna to multiple pinching antennas.

1) A Single Pinching Antenna:

The single-antenna model describes radiation from a pinching antenna, including free-space propagation loss and the resulting received signal. For multiple antennas, it accounts for sequential power exchange and introduces equal-power and proportional-power models.

  • Single Pinching Antenna: A pinching antenna radiates a waveguide signal that reaches the user through free space with distance-dependent attenuation and phase.The model includes a free-space path-loss factor, radiation pattern gain, propagation constant, and additive noise.
  • Multiple Pinching Antennas: With sequentially pinched antennas, each antenna’s radiated power depends on the power-exchange coefficients of all preceding antennas.The resulting radiation model captures coupling along the waveguide before free-space transmission.
  • Equal Power Model: The equal-power model adjusts each antenna’s length so every antenna radiates an equal proportion of the total power.This model gives equal radiation efficiency but requires different antenna lengths, increasing hardware cost.
  • Proportional Power Model: The proportional-power model uses equal antenna lengths, so each antenna radiates the same ratio of the remaining waveguide power.Uniform manufacturing significantly reduces hardware costs compared with the equal-power model.
  • Pinching Beamforming: Pinching antennas couple electromagnetically without physical waveguide connections, allowing repositioning that changes received-signal phase and large-scale path loss.Positions can be adjusted using a track parallel to the waveguide.

III. JOINT TRANSMIT AND PINCHING BEAMFORMING

This section defines a downlink PASS architecture in which multiple dielectric waveguides serve multiple users through joint transmit and pinching beamforming. Each waveguide has a dedicated RF chain, while transmit beamforming maps user symbols onto the waveguides.

  • System Architecture: A downlink PASS system uses N dielectric waveguides to serve K users, with each waveguide containing M pinching antennas.The considered system satisfies N ≥ K.
  • System Architecture: Each waveguide is fed by a dedicated RF chain, and antenna positions are specified along the waveguide geometry.User and pinching-antenna locations are represented as three-dimensional position vectors.
  • Transmit Signal: The transmitted information consists of complex user symbols with identity covariance, where each symbol is intended for one user.The symbol vector is transformed by transmit beamforming before entering the waveguides.
  • Transmit Signal: The overall transmit beamforming matrix W contains one beamforming vector for each user.The matrix dimensions are N × K, and each user beamforming vector has dimension N × 1.
  • Transmit Signal: The n-th entry of the post-beamforming signal is the signal introduced into the n-th waveguide.This links the transmit-beamforming output to the individual waveguide feeds.

2) Receive Signal:

The received-signal formulation combines free-space channels from pinching antennas with in-waveguide channels and separates desired signals from inter-user interference. It then frames transmit-power minimization under SINR, spacing, and activation constraints.

  • Receive Signal: The received signal at user k is represented using free-space channel vectors h_k(x_n) and in-waveguide channel vectors g(x_n).The formulation also includes additive white Gaussian noise.
  • Receive Signal: A user’s channel depends on the antenna-position vector x_n and the distances from that user to each pinching antenna.These distances determine the free-space channel contributions.
  • Receive Signal: The compact received-signal expression distinguishes the desired signal from inter-user interference.The overall channel depends on the positions of all pinching antennas through X, h_k(X), and G(X).
  • Problem Formulation: The optimization minimizes base-station transmit power by jointly selecting transmit beamforming W and pinching positions X while meeting each user’s minimum SINR.The feasible positions must also satisfy the minimum spacing required to prevent mutual coupling.
  • Activation Models: Continuous activation permits arbitrary antenna positions and provides an ideal performance upper bound.The deployment range is bounded by x_max.
  • Activation Models: Discrete activation restricts antennas to Q preconfigured positions, reducing hardware complexity but potentially limiting placement flexibility.The resulting problem remains difficult because W and X are coupled and the channel depends nonlinearly on X.
  • Problem Formulation: Gradient descent is unsuitable because the antenna-position objective is highly multimodal and local optima can differ substantially.Fig. 4 illustrates this behavior for a simple N = 1, M = 2, K = 1 scenario.

C. Penalty-based Alternating Optimization Algorithm

The penalty-based alternating optimization method decomposes joint beamforming into alternating updates over transmit and pinching-antenna variables, using penalties and convex approximations to address coupling and multimodality.

  • Alternating optimization fixes either the transmit beamforming matrix W or antenna position matrix X while optimizing the other subset.
  • The reformulation decomposes H(X) and G(X), introduces an auxiliary channel matrix U, and incorporates equality constraints into the objective through penalty terms.
  • The penalty factor ρ is initially large and gradually reduced so penalty terms converge to zero while U follows the PASS channel structure.
  • The W-related subproblem is transformed into convex second-order cone programming, while the U subproblem uses successive convex approximation for its nonconvex quadratic term.
  • The X update uses element-wise alternating optimization and one-dimensional search over finite intervals for both continuous and discrete antenna activation.

5) Overall Algorithm:

The overall penalty-based algorithm alternates variable updates inside an inner loop and progressively decreases the penalty factor in an outer loop.

  • The algorithm updates W, U, each U_m, and X sequentially until inner-loop convergence.
  • The penalty factor is updated as ρ ← ϵρ in the outer loop until the constraint-violation threshold is reached.
  • Each iteration has high computational complexity, including O(N^4K^2) for the V update and O(I_iterQMNK) for the X update.
  • Despite its relatively high complexity, the method directly addresses the original problem, guarantees convergence to a stationary point, and provides a generalizable baseline.

D. ZF-based Low-complexity Algorithm

The ZF-based algorithm eliminates inter-user interference, simplifying SINR expressions and reducing the complexity of joint beamforming optimization.

  • ZF beamforming completely eliminates inter-user interference, substantially simplifying the SINR expression.
  • For N ≥ K, the method obtains a ZF beamforming matrix for any given pinching beamforming matrix.
  • The equivalent channel matrix Ψ(X) and diagonal power-control matrix P reformulate transmit power and SINR under ZF beamforming.
  • The optimal power coefficients are irrelevant to X, so alternating optimization is no longer required after obtaining P_opt.
  • Sherman–Morrison decomposition reduces the search cost because only a single matrix inversion is computed across all search points.
  • The overall per-iteration complexity is O(NK^2 + QMNK^2).

IV. NUMERICAL RESULTS

The numerical study evaluates PASS in an indoor multiuser setting and compares it with conventional and massive MIMO benchmarks under specified system configurations.

  • The default simulation uses N = 5 waveguides, M = 6 pinching antennas per waveguide, and K = 4 users.
  • The setup uses d0 = 15 m, dx = 30 m, dy = 3 m, and dz = 10 m for the geometric configuration.
  • The total power radiated along each waveguide is constrained by P_m = 0.9 for both equal and proportional power models.
  • The benchmarks include conventional MIMO with N_RF = 5 single-antenna chains and massive MIMO with N = 30 antennas and N_RF = 5 chains.

A. Performance of the Proposed Algorithms

The proposed algorithms converge for PASS beamforming optimization, with the low-complexity ZF-based method achieving performance comparable to the penalty-based method across system setups.

  • Convergence behavior: The penalty-based algorithm's transmit power oscillates upward before converging because its penalty method progressively enforces PASS constraints.Initially, a large penalty factor permits an almost unconstrained auxiliary channel matrix, while later iterations increase constraint enforcement.
  • Simulation setup: The baselines use fixed, densely deployed antennas with half-wavelength spacing to fully exploit the available spatial degrees of freedom.This baseline assumption excludes antenna movement from the conventional comparisons.
  • Algorithm comparison: The low-complexity ZF-based algorithm converges quickly and achieves performance comparable to the penalty-based algorithm across various system setups.This comparison is reported despite the ZF-based algorithm's lower complexity.
  • Convergence behavior: A smaller reduction factor ϵ accelerates convergence, whereas a larger ϵ allows more thorough transmit-power minimization before penalty reduction.Increasing ϵ from 0.1 to 0.5 provides negligible performance gain.

B. Impact of the Minimum SINR

PASS requires more transmit power as minimum SINR requirements increase, but it substantially outperforms conventional and massive MIMO across the considered range.

  • Transmit power versus minimum SINR: 99.3% lower transmit power is achieved by PASS than conventional MIMO at a 20 dB minimum SINR, decreasing power from 26.6 dBm to 4.9 dBm.The comparison uses continuous activation and the equal power model.
  • Transmit power versus minimum SINR: 96.6% lower transmit power is achieved by PASS than massive MIMO at a 20 dB minimum SINR, decreasing power from 19.6 dBm to 4.9 dBm.The comparison uses continuous activation and the equal power model.
  • Mechanism and implementation: PASS's power reduction is attributed primarily to significantly reduced free-space path loss using low-cost pinching antennas instead of massive phase shifters.The reported enhancement does not rely on the expensive phase-shifter hardware associated with massive MIMO.
  • Power models: The proportional power model performs almost identically to the equal power model, indicating negligible impact from unbalanced antenna efficiency.This result is reported in the PASS evaluation across the considered settings.
  • Activation schemes: Discrete activation causes non-negligible performance loss, yet still reduces transmit power by 95% and 99% versus conventional and massive MIMO, respectively, at 20 dB minimum SINR.The discrete-activation comparison is reported at a 20 dB minimum SINR.

C. Impact of the Distance

PASS maintains nearly unchanged transmit power as the BS-to-serving-area distance increases, while larger antenna arrays reduce transmit power and denser discrete positions approach continuous-activation performance.

  • C. Impact of the Distance: PASS transmit power remains almost unchanged as the BS-to-serving-area distance d0 increases.Negligible in-waveguide pathloss and antenna placement near the serving area keep free-space pathloss almost constant.
  • D. Impact of the Number of Antennas: Increasing the number of antennas reduces transmit power for all considered schemes.For PASS, increasing antennas from 10 to 50 reduces power by 78% with continuous activation and 68.8% with discrete activation.
  • E. Impact of the Number of Discrete Positions: Discrete-activation performance approaches continuous activation as the number of available positions increases, but comparable performance requires more than 300 positions per meter.The high density is needed because fine position sampling is required to adjust the induced phase shift across [0, 2π].
  • F. Impact of the Channel Estimation Error: Increasing the channel error bound εest degrades average SINR, while PASS consistently achieves the highest SINR.The evaluation optimizes using the estimated channel and tests performance over the actual channel.
  • V. CONCLUSIONS: The paper concludes that PASS reduces transmit power substantially compared with conventional wireless systems, while uplink modeling, richer beamforming architectures, and practical deployment remain open challenges.The proposed physics model is currently limited to downlink, and the study assumes one RF chain per waveguide.
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