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Pinching-Antenna Systems with In-Waveguide Attenuation: Performance Analysis and Algorithm Design

Yanqing Xu, Zhiguo Ding, Robert Schober, Tsung-Hui Chang

arXiv:2506.23966v1eess.SPcs.IT

TL;DR

Existing pinching-antenna studies provide limited analysis of in-waveguide attenuation, although this effect matters for realistic downlink design. The paper incorporates attenuation into single-user placement analysis and MU-MIMO optimization, finding that the proposed algorithms are effective and that pinching-antenna systems consistently outperform fixed-position systems across evaluated scenarios.

  • Problem

    Prior pinching-antenna studies commonly overlook in-waveguide attenuation and provide little theoretical analysis of its impact on system performance.

  • Method

    The paper derives a globally optimal closed-form placement for a single user and develops WMMSE- and MRC-based joint beamforming and antenna-placement methods for MU-MIMO.

  • Results

    The proposed two-stage WMMSE-MRC algorithm achieves performance comparable to the WMMSE-based method while reducing computational complexity, and pinching antennas consistently outperform fixed-position antennas.

  • Takeaways & Limitations

    The analysis provides design guidelines for when attenuation can be safely ignored and supports pinching antennas as a practical flexible-wireless architecture.

Abstract

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Pinching-antenna systems have emerged as a promising flexible-antenna architecture for next-generation wireless networks, enabling enhanced adaptability and user-centric connectivity through antenna repositioning along waveguides. However, existing studies often overlook in-waveguide signal attenuation and in the literature, there is no comprehensive analysis on whether and under what conditions such an assumption is justified. This paper addresses this gap by explicitly incorporating in-waveguide attenuation into both the system model and algorithm design, and studying its impact on the downlink user data rates. We begin with a single-user scenario and derive a closed-form expression for the globally optimal antenna placement, which reveals how the attenuation coefficient and the user-to-waveguide distance jointly affect the optimal antenna position. Based on this analytical solution, we further provide a theoretical analysis identifying the system conditions under which the in-waveguide attenuation has an insignificant impact on the user achievable rate. The study is then extended to the multi-user multiple-input multiple-output setting, where two efficient algorithms are developed, based on the weighted minimum mean square error method and the maximum ratio combining method, to jointly optimize beamforming and antenna placement. Simulation results validate the efficacy of the proposed algorithms and demonstrate that pinching-antenna systems substantially outperform conventional fixed-antenna baselines, underscoring their potential for future flexible wireless communications.

I. INTRODUCTION

Pinching-antenna systems address limitations of fixed-position antennas by dynamically repositioning or activating antennas along waveguides for user-centric service. This paper incorporates in-waveguide attenuation into single-user analysis and MU-MIMO algorithm design, deriving placement results and evaluating proposed methods against fixed-position baselines.

  • Fixed-position antenna deployments can be suboptimal under spatial channel variation, user mobility, and limited coverage flexibility.
  • Pinching antennas can be mechanically repositioned or activated along waveguides to serve users at tailored positions and establish strong LoS channels.
  • Prior pinching-antenna studies commonly overlook in-waveguide attenuation and provide little theoretical analysis of its performance impact.
  • For the single-user case, the paper derives a globally optimal closed-form antenna position depending on the attenuation coefficient and user-to-waveguide distance.
  • Neglecting attenuation causes negligibly small degradation when waveguide height, attenuation coefficient, and communication-region size satisfy mild, practically realizable conditions.
  • For MU-MIMO, the paper develops WMMSE- and MRC-based approaches for jointly optimizing beamforming and pinching-antenna positions.

B. Problem Formulation

The formulation maximizes downlink data rate by positioning a pinching antenna along a waveguide while accounting for the trade-off between waveguide attenuation and free-space path loss. The resulting analysis characterizes optimal placement across attenuation and user-distance regimes and evaluates rate effects across communication-region widths.

  • B. Problem Formulation: Maximizing data rate is equivalent to maximizing received SNR under a transmission-power constraint and feasible antenna-position region.The effective channel denominator combines waveguide attenuation with free-space path loss.
  • B. Problem Formulation: Moving the antenna away from the feed point increases exponential waveguide attenuation while decreasing free-space path loss, creating a placement trade-off.The optimal position balances these opposing effects in the effective channel gain.
  • C. Derivation and Analysis of the Optimal Solution of Problem (4): Lemma 1 gives the globally optimal antenna position in closed form as a piecewise solution determined by attenuation and user-to-waveguide distance.The derivation minimizes the effective-channel denominator over the feasible interval.
  • C. Derivation and Analysis of the Optimal Solution of Problem (4): When attenuation is small, the optimal position balances waveguide attenuation and free-space path loss rather than simply minimizing propagation distance.As α approaches zero, placement converges to the user-aligned position [¯x, 0, dv], which minimizes free-space path loss.
  • C. Derivation and Analysis of the Optimal Solution of Problem (4): When the user is near the waveguide, the optimal antenna position approaches the user’s horizontal coordinate, reducing attenuation’s influence on placement.This follows from the convergence of x2 toward ¯x as C decreases.
  • C. Derivation and Analysis of the Optimal Solution of Problem (4): When C ≥ 1/(4α^2), the optimal antenna is placed at the feed point because free-space path loss dominates or attenuation makes shifts costly.The same feed-point placement applies for sufficiently large C or sufficiently large α.
  • C. Derivation and Analysis of the Optimal Solution of Problem (4): For moderate parameters, free-space path loss dominates before x2, whereas waveguide attenuation dominates after x2 because attenuation grows exponentially with antenna distance from the feed.This identifies the two regions governing effective-channel sensitivity.
  • C. Derivation and Analysis of the Optimal Solution of Problem (4): Average achievable rates decrease with communication-region width D, while ignoring attenuation causes a modest rate loss that grows with D.Scheme 3 closely tracks Scheme 2 and provides a reliable upper-bound approximation of the optimal scheme; Fig. 3 compares the corresponding rate gap analytically and numerically.

D. Average Data Rate Analysis and System Design Insights

The paper quantifies the average rate loss from optimizing antenna placement without in-waveguide attenuation and derives a communication-region design rule for limiting that loss. The analytical approximation closely matches simulations and supports practical choices of region width, waveguide height, and attenuation coefficient.

  • D. Average Data Rate Analysis and System Design Insights: The analysis quantifies average data-rate loss from ignoring in-waveguide attenuation across communication-region width D, waveguide height dv, and attenuation coefficient α.The loss is defined as the difference between achievable rates with and without attenuation-aware placement.
  • D. Average Data Rate Analysis and System Design Insights: Proposition 1 provides a closed-form approximation for the average rate loss caused by attenuation-unaware antenna placement.The proposition is used to derive a practical constraint on communication-region size.
  • D. Average Data Rate Analysis and System Design Insights: The analytical rate-loss expression closely matches simulation results across the considered communication-region widths.This comparison is shown in Fig. 3.
  • D. Average Data Rate Analysis and System Design Insights: Corollary 1 gives a condition on communication-region side length D that keeps average rate loss below a prescribed threshold ϵ.The rule links allowable region size to attenuation level and waveguide height.
  • D. Average Data Rate Analysis and System Design Insights: For dv = 10 m and α = 0.0092 m−1, keeping average rate loss below 0.1 bps/Hz requires D ≤ approximately 92.88 m.This numerical example illustrates the design rule’s use for deployment planning.

E. Extension to the MISO Scenario

The MISO extension jointly uses N pinching antennas on parallel waveguides to serve one user, with antenna positions optimized through separable per-antenna problems. MRC beamforming reduces the received-SNR maximization to the same position problem as the SISO case.

  • System model: N pinching antennas on N parallel waveguides jointly serve a single-antenna user in the MISO setting.The waveguides are separated by dh = D/(N−1) ≫ λ and positioned at height dv.
  • Beamforming: MRC beamforming sets v = h/||h||2 and yields SNR = ρ||h||2 for the single-user channel.The resulting design problem optimizes the antenna positions under this beamformer.
  • Antenna placement: The MISO position objective decomposes across pinching antennas, allowing each antenna position to be optimized separately.Each per-antenna problem is identical to the SISO position problem.
  • Antenna placement: The optimal position of antenna n is given by the closed-form expression in Corollary 2.The supplied corollary states the optimal position, with the displayed expression continuing across the cited passages.

III. PINCHING-ANTENNA SYSTEM DESIGN WITH IN-WAVEGUIDE LOSS: THE MULTI-USER CASE

The multi-user formulation accounts for in-waveguide attenuation while jointly optimizing beamformers and antenna positions to maximize sum rate under a total transmit-power constraint. The problem is difficult because antenna positions affect channel vectors, which are coupled with beamformers in the objective.

  • System model: The multi-user setting deploys N pinching antennas on N waveguides to jointly serve M single-antenna users.Users are represented by positions ψm = [xm, ym, 0], with M ≤ N.
  • System model: The channel model retains in-waveguide attenuation even though its impact can be insignificant under mild system-parameter conditions.This preserves the attenuation-aware model for the multi-user design.
  • Optimization problem: The paper maximizes system sum rate by jointly optimizing user beamformers and pinching-antenna positions under a total transmit-power constraint.V collects the beamformers and ˜x collects antenna positions.
  • Optimization problem: The optimization is challenging because channel vectors depend intricately on antenna positions and are coupled with beamforming vectors in the objective.Both channel geometry and transmission design therefore vary jointly during optimization.

1) Reformulation by Using WMMSE Method:

The WMMSE reformulation converts nonconvex sum-rate maximization into weighted MSE minimization and enables block-coordinate updates of receivers, weights, beamformers, and antenna positions. The antenna-position subproblem remains difficult because phase, path loss, and attenuation create highly oscillatory objectives, so linear search is used for each one-dimensional update.

  • WMMSE reformulation: WMMSE reformulates the nonconvex sum-rate problem as a more tractable weighted MSE minimization problem.The reformulation defines each estimated source signal using an MMSE receiver.
  • Iterative optimization: The reformulated problem supports block-coordinate descent updates because its variable constraints are uncoupled.Beamformers, receivers, weights, and antenna positions are updated iteratively.
  • Iterative optimization: Receiver and weight updates have closed-form solutions, while the beamformer update is convex and can be solved with standard convex optimization tools.The antenna-position update remains the difficult block.
  • Antenna-position update: Antenna positions are coupled through cumulative phase shift, free-space path loss, and in-waveguide attenuation.These dependencies make the position subproblem nonconvex and difficult to solve.
  • Antenna-position update: Rapid phase variation causes severe objective oscillations as an antenna moves along the waveguide.The behavior is illustrated in Fig. 5 for the stated system parameters.
  • Antenna-position update: Because the position subproblem has one real variable, linear search discretizes the feasible interval and exhaustively evaluates candidate positions.The WMMSE algorithm repeats these block updates until convergence.

B. Low-Complexity Scheme via MRC-Based Approximation

The MRC-based scheme reduces joint beamforming and antenna-placement optimization to a lower-complexity two-stage procedure, while addressing oscillatory position objectives through phase removal and gradient projection.

  • Motivation: Linear position searches become computationally prohibitive for long waveguides or high operating frequencies.The position-dependent phase, path loss, and in-waveguide attenuation create pronounced objective oscillations.
  • MRC-Based Scheme: The proposed MRC scheme fixes beamformer directions to users’ channels and alternates antenna-position optimization with power-allocation optimization.The position update uses fixed power coefficients, followed by power allocation under the transmit-power constraint.
  • Approximation: A phase-removal approximation produces a more stable objective, enabling a low-complexity gradient projection algorithm for antenna-position optimization.This approximation mitigates severe oscillations caused by rapidly varying phase terms.

2) Pinching-Antenna Position Optimization:

The position-optimization stage removes rapidly varying phase terms, decomposes the resulting objective across antennas, and updates positions and power allocations iteratively using gradient projection.

  • Pinching-Antenna Position Optimization: The antenna-position subproblem is challenging because cross terms cause the channel magnitude objective to oscillate significantly as positions change.The oscillations arise from the position dependence of the channel cross terms.
  • Pinching-Antenna Position Optimization: A phase-removal approximation yields a more stable, decomposable objective that can be solved across antenna positions using block coordinate descent.The resulting objective is simpler because rapidly varying phase terms are removed.
  • Pinching-Antenna Position Optimization: Gradient projection updates each antenna position while keeping it within [0, xmax], with the step size selected by backtracking line search.Each update consists of computing the derivative and projecting the new position onto the feasible interval.
  • Algorithm 1: The MRC-based algorithm alternates antenna-position updates and power-allocation updates until convergence, starting from equal power allocation.Both update stages use gradient projection with backtracking line search.
  • Algorithm 2: The two-stage WMMSE-MRC algorithm first obtains antenna positions with MRC, then refines beamformers using WMMSE without repeating linear position searches.This design significantly reduces overall computational complexity.

IV. NUMERICAL SIMULATIONS

The numerical study evaluates the proposed pinching-antenna algorithms through computer simulations under specified attenuation, noise, frequency, geometry, and averaging settings.

  • Simulation Setup: Algorithm 2 is evaluated as a two-stage WMMSE-MRC procedure that obtains antenna positions first and then refines beamformers with WMMSE.The final outputs are optimized pinching-antenna positions and beamformers.
  • Simulation Setup: The simulations use α = 0.08 dB/m, noise power −70 dBm, fc = 28 GHz, dv = 3 m, and nneff = 1.4.Results are averaged over 20 random user-position realizations.

A. Pinching-Antenna System Versus Conventional Antenna System

Pinching-antenna systems consistently outperform fixed-position antenna systems across transmit powers and coverage areas. The proposed WMMSE-MRC algorithm achieves comparable rates to WMMSE with substantially lower execution time, while accounting for in-waveguide attenuation improves placement and becomes increasingly important in larger deployments.

  • A. Pinching-Antenna System Versus Conventional Antenna System: Pinching-antenna systems consistently outperform fixed-position antenna systems across transmit powers and coverage-area side lengths.The reported advantage is attributed to stronger LoS links and reduced inter-user interference.
  • B. Performance of the Proposed Algorithms: The WMMSE-MRC scheme achieves sum rates very close to the full WMMSE algorithm across considered transmit powers and coverage-area sizes.Its MRC-based initialization balances in-waveguide and free-space loss while avoiding iterative position searches.
  • B. Performance of the Proposed Algorithms: WMMSE-MRC reaches near-optimal performance within a few iterations and much lower execution time than conventional WMMSE.WMMSE becomes increasingly time-consuming as antenna count and search-grid resolution grow, whereas WMMSE-MRC avoids exhaustive search.
  • C. Performance of the Pinching-Antenna System for Different System Parameters: Accounting for in-waveguide attenuation yields slightly higher sum rates than optimizing antenna positions without attenuation.The improvement reflects a more accurate trade-off between minimizing waveguide loss and reducing free-space path loss.
  • C. Performance of the Pinching-Antenna System for Different System Parameters: Relative rate loss increases with both entry length L and communication-region size D when the feed point lies outside the user region.Overall sum rate also decreases as entry length increases because of higher propagation loss along the waveguide.
  • C. Performance of the Pinching-Antenna System for Different System Parameters: The study combines a closed-form single-user placement solution, rate-loss analysis, and MU-MIMO algorithms based on WMMSE and MRC approximations.The conclusion reports that simulations validate these analyses and show substantial gains over conventional fixed-antenna designs.

APPENDIX A PROOF OF PROPOSITION 1

The appendix derives rate-loss expressions for schemes with and without in-waveguide attenuation and approximates the optimal antenna position under small attenuation. It uses first-order approximations to complete the averaged rate-loss analysis.

  • APPENDIX A PROOF OF PROPOSITION 1: The attenuation-aware scheme's instantaneous SNR is introduced through a lemma and compared with the no-attenuation SNR.The appendix states the relation SNR_wo = SNR_w(1 − α^2C).
  • APPENDIX A PROOF OF PROPOSITION 1: The instantaneous rate loss is derived from the SNR relation, followed by a high-SNR approximation and an averaged rate-loss expression.The proof explicitly invokes a first-order Taylor approximation for the averaged loss.
  • APPENDIX A PROOF OF PROPOSITION 1: For small attenuation α, the optimal antenna position is approximated by replacing √(1−4α^2C) with 1−2α^2C.The appendix then substitutes this position into an approximate received-SNR expression.
  • APPENDIX A PROOF OF PROPOSITION 1: The proof uses the inequality e^(2α^2C) ≤ 1 + α^2C/(1−α^2C) for 0 ≤ α^2C < 1.This inequality supports the bound used in the approximate received-SNR derivation.
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