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Discrete Coupling and Localized Motion for Pinching-Antenna Systems (PASS)

Jie Jiang, Xiaoxia Xu, Chan-Tong Lam, Yuanwei Liu, Arumugam Nallanathan

arXiv:2609.16293v1eess.SP

TL;DR

Practical PASS implementation is constrained by limited antenna movement and difficulty continuously adjusting radiation power. The paper combines localized discrete movement, quantized coupling control, and waveguide attenuation in a joint power-minimization framework, reporting lower power consumption than conventional PASS and MIMO architectures.

  • Problem

    Existing PASS designs commonly assume unrestricted or continuous PA movement and equal or continuously adjustable radiation, while integrating these hardware constraints with waveguide attenuation remains underexplored.

    Source: §I · p. 2

  • Method

    The framework jointly optimizes localized discrete PA positions, discrete coupling spacing, and transmit beamforming under SINR and motion constraints, using BnB for MWSU and GA-PSO for MWMU.

    Source: §I · p. 2

  • Results

    The proposed PASS reduces power consumption by up to 42.2% versus equal-power DM-PASS, 39.7% versus adjustable-coupling DA-PASS, and 99% versus conventional MIMO and hybrid MIMO.

    Source: B. Multi-User Scenario · pp. 10–11

  • Takeaways & Limitations

    The simulations support the framework's use of radiation-power control and PA-position optimization to improve power consumption relative to the compared PASS and MIMO schemes.

    Source: §I · p. 3

    The MWMU GA-PSO search over discrete PA positions and coupling spacings is heuristic, so global optimality is not claimed for that scenario.

    Source: D. GA-Assisted Offspring Generation · p. 9

Abstract

from arXiv · show

The practical implementation of pinching-antenna systems (PASS) is challenging due to hardware limitations in large-scale antenna movement and continuous radiation power adjustment. This paper proposes a practical PASS-enabled downlink multi-user multiple-input multiple-output communication framework that enables discrete radiation power control and localized discrete antenna movement. Specifically, a discrete coupling strength model is exploited to tune the radiation power at each pinching antenna (PA) through quantized coupling spacing levels. Moreover, each PA can only move among discrete locations within a limited region determined by the movement speed and duration. Based on the proposed framework, a joint optimization problem of the PA positions, coupling strength, and transmit beamforming is formulated. Considering waveguide attenuation, the total average power consumption is minimized, subject to each user's minimum SINR requirement and localized motion constraints. To address this coupled mixed-integer nonconvex optimization problem, a globally optimal branch-and-bound-based algorithm is first developed for the multi-waveguide single-user scenario. To further reduce complexity, a scalable genetic algorithm-assisted particle swarm optimization (GA-PSO) method is developed for the multi-waveguide multi-user scenario, where GA operations are incorporated to preserve population diversity and alleviate premature convergence. Simulation results demonstrate that the proposed design significantly reduces the power consumption compared with the conventional PASS schemes and MIMO architectures.

I. INTRODUCTION

The paper addresses practical PASS constraints by combining localized discrete PA movement with discrete coupling control and in-waveguide attenuation in a joint power-minimization framework. It reports lower power consumption than conventional PASS schemes and MIMO architectures, and models coupling control through quantized spacing levels.

I. INTRODUCTION

  • Existing designs leave discrete coupling states and the joint treatment of localized PA movement, discrete radiation control, and waveguide attenuation underexplored.Practical motion is limited by speed, latency, energy, and mechanical resolution; continuous coupling-spacing control is difficult to realize.Source: §I · p. 2
  • The proposed framework jointly optimizes localized discrete PA positions, quantized coupling spacing, and transmit beamforming to minimize transmit and motion power under SINR and motion constraints.The model incorporates in-waveguide attenuation and phase rotation.Source: §I · p. 2
  • For MWSU, the BnB method eliminates the continuous beamforming variable in closed form using the MRT structure and converges to the global optimum within a prescribed tolerance.The resulting optimization is over discrete structure variables.Source: §I · pp. 2–3
  • For MWMU, GA-PSO searches discrete PA positions and coupling levels while SOCP optimally solves beamforming for each candidate configuration.GA operations preserve population diversity and alleviate premature convergence.Source: §I · p. 3
  • Simulations verify the proposed practical PASS framework and algorithms, showing consistent outperformance over conventional and hybrid MIMO, while baseline comparisons highlight coupling-strength control and localized PA movement.Source: §I · p. 3

A. Coupling Strength Control for Adjustable Power Radiation

  • In the coupling model, each PA selects a spacing from finitely many predefined levels, which determines its coupling strength and local radiation factor.The final radiation ratio also depends on residual guided power after preceding PAs on the same waveguide.Source: A. Coupling Strength Control for… · p. 4

B. Discrete PA Movement Model

PA movement is limited to discrete mounting points within a local region determined by the motion bound. The model also accounts for the frame's repositioning phase, minimum PA separation, and exclusive mounting-point assignment.

B. Discrete PA Movement Model

  • Each PA can move only within the bounded range allowed by its maximum speed during the repositioning phase, rather than continuously along the entire waveguide.The frame has a repositioning phase followed by downlink transmission.Source: B. Discrete PA Movement Model · p. 4
  • Each PA selects one mounting point from its locally feasible set, with binary assignment variables encoding that choice.Positions are selected from uniformly spaced discrete mounting points.Source: B. Discrete PA Movement Model · p. 4
  • Adjacent PAs must maintain minimum separation, and each mounting point can host at most one PA per waveguide.Source: B. Discrete PA Movement Model · p. 4

C. Signal Model

The signal model defines user-directed symbols and beamforming over the waveguide-connected PAs. It accounts for guided-signal attenuation and phase rotation before forming the in-waveguide channel matrix.

C. Signal Model

  • The baseband signal injected into each waveguide is formed from user information symbols and the transmit beamforming matrix.Each beamforming vector corresponds to a user.Source: 1) In-Waveguide Propagation · p. 5

1) In-Waveguide Propagation:

  • Guided signals accumulate phase rotation and lose power as they propagate from the feed point to each PA.The model attributes these propagation effects to material properties and fabrication imperfections.Source: 1) In-Waveguide Propagation · p. 5
  • The in-waveguide channel matrix is assembled as a block diagonal matrix from the per-waveguide channel vectors.The propagation factor includes an attenuation coefficient and waveguide wavelength.Source: 1) In-Waveguide Propagation · p. 5

2) Free-Space Propagation:

The section specifies a spherical-wave free-space channel model for LoS-dominant PA-to-user propagation and describes the frame-average power accounting for transmission and PA motion.

2) Free-Space Propagation:

  • The PA-to-user channel assumes LoS-dominant propagation and uses a spherical-wave free-space expression.Source: 2) Free-Space Propagation · p. 5
  • The received-signal description separates desired signal, multi-user interference, and additive white Gaussian noise for defining each user's SINR.Source: 2) Free-Space Propagation · p. 5

D. Power Consumption for PASS

  • Total average power over a frame comprises average transmit power and average PA movement power.PA motion is driven by electric motors with constant power Pm and supported movement speed v.Source: D. Power Consumption for PASS · p. 5

E. Problem Formulation

The formulation minimizes average power while meeting user QoS under discrete PA-placement, coupling, and movement constraints. For the MWSU case, closed-form MRT removes the continuous beamforming variable, leaving a discrete structural optimization.

E. Problem Formulation

  • The objective minimizes average power while satisfying each user's SINR requirement through joint optimization of PA positions, coupling-spacing selections, and transmit beamforming.Source: E. Problem Formulation · p. 5
  • Each PA selects one feasible mounting point and one coupling-spacing level, while mounting points cannot host multiple PAs on a waveguide.Source: E. Problem Formulation · p. 5
  • PA movement is limited by mechanical capability within a frame, and adjacent PAs on each waveguide must satisfy a minimum separation.Source: E. Problem Formulation · p. 6

III. BNB-BASED ALGORITHM FOR THE MWSU SCENARIO

  • For the MWSU scenario, BnB optimizes discrete PA movement and coupling spacing, with a closed-form MRT solution for beamforming at fixed choices.Source: §III · p. 6

A. Problem Formulation

  • With fixed PA positions and coupling spacings, the beamforming subproblem is reduced using an equivalent channel vector c(x, s).Source: A. Problem Formulation · p. 6
  • The equivalent channel is assembled from per-waveguide effective channels, with cascaded radiation and position-dependent propagation coefficients for each PA.Source: A. Problem Formulation · p. 6
  • The SNR constraint is expressed using the equivalent channel, and the MRT solution eliminates continuous beamforming so only discrete movement and spacing remain.Source: A. Problem Formulation · p. 6

B. Branch-and-Bound Algorithm

The BnB lower-bound procedure works over each node's remaining PA-position and coupling-spacing choices, bounding its objective optimistically to support pruning.

B. Branch-and-Bound Algorithm

1) Lower Bound:

  • For each waveguide, enumerating remaining coupling-spacing combinations gives an optimistic upper bound on the magnitude of its effective channel.Source: 1) Lower Bound · p. 6
  • The effective-channel bound yields an upper bound on MRT channel gain, from which the method derives a valid lower bound on the objective over the node.Source: 1) Lower Bound · p. 6

2) Upper Bound:

The MWSU BnB procedure constructs feasible upper bounds and terminates with an ϵ-optimality guarantee, although worst-case search may become exhaustive. For MWMU, GA-PSO searches discrete configurations while SOCP reconstructs beamforming.

2) Upper Bound:

  • A feasible upper bound is built by projecting the incumbent into a node's domains, refining it by coordinate descent, and testing random feasible starts.The best feasible configuration supplies the bound, and its transmit beamformer is recovered afterward.Source: 2) Upper Bound · p. 6
  • The BnB algorithm converges to an ϵ-optimal solution in finite iterations.Source: 2) Upper Bound · p. 7
  • Worst-case BnB search may degenerate into exhaustive enumeration, though lower-bound pruning usually keeps explored nodes below the full configuration count.Source: 2) Upper Bound · p. 7

IV. GA-PSO-BASED ALGORITHM FOR THE MWMU

  • For MWMU, the outer GA-PSO searches discrete PA positions and radiation-control choices, while an inner SOCP reconstructs beamforming for each configuration.Source: §IV · p. 7

A. SOCP-Based Transmit Beamforming Optimization

  • Fixing a PASS configuration yields a standard SOCP; thus the MWMU method heuristically searches discrete structure but optimally reconstructs continuous beamforming per candidate.Phase-rotation invariance permits the desired signal term to be constrained as real without loss of optimality.Source: A. SOCP-Based Transmit Beamforming… · pp. 7–8

B. Particle Encoding and Discrete Decoding

The algorithm represents PA positions and radiation control with continuous latent blocks, then decodes them into feasible discrete PASS configurations. It updates these blocks with PSO and evaluates each configuration using SOCP-based beamforming.

B. Particle Encoding and Discrete Decoding

  • Each particle uses continuous latent blocks for PA positions and radiation control, decoded into discrete configuration variables Φ and V.The position and radiation-control blocks are represented separately.Source: B. Particle Encoding and Discrete… · p. 8
  • Position proxies are clipped to each PA’s local movement interval, mapped to the nearest mounting point, then repaired to satisfy waveguide minimum spacing.The decoded position index determines the binary position variable.Source: B. Particle Encoding and Discrete… · p. 8
  • For radiation control, the maximum-score criterion selects a coupling spacing level, which determines the coupling spacing, coefficient, and cascaded radiation ratio.The selected level is encoded in a binary radiation-control variable.Source: B. Particle Encoding and Discrete… · p. 8

C. Block-Structured PSO Update

  • PSO updates the position and radiation-control latent blocks separately using their respective velocities, personal-best blocks, and global-best blocks.The updates use inertia, cognitive and social coefficients, and random matrices.Source: C. Block-Structured PSO Update · p. 8
  • After decoding, the algorithm constructs the cascaded channel and solves an SOCP to obtain beamforming; total average power consumption is the particle’s fitness.Infeasible SOCPs or configurations violating discrete feasibility constraints receive a large penalty.Source: C. Block-Structured PSO Update · p. 8

D. GA-Assisted Offspring Generation

A periodic GA module generates and evaluates offspring alongside PSO to counter premature convergence in the discrete PASS search. Its search is heuristic for the multi-waveguide multi-user scenario, although beamforming is solved optimally for each fixed configuration.

D. GA-Assisted Offspring Generation

  • After a warm-up period, the GA periodically selects parents by tournament and generates offspring through crossover and mutation.The module is activated every TGA iterations.Source: D. GA-Assisted Offspring Generation · p. 8
  • Position crossover inherits a whole waveguide’s position vector, while radiation-control crossover inherits an individual PA’s spacing-score vector.The two blocks therefore use waveguide-level and gene-level crossover, respectively.Source: D. GA-Assisted Offspring Generation · p. 8
  • Position mutation perturbs proxies with Gaussian noise, while radiation-control mutation can promote an alternative coupling spacing level.Mutated positions are clipped and decoded; offspring are repaired when necessary.Source: D. GA-Assisted Offspring Generation · pp. 8–9
  • Decoded offspring are evaluated through SOCP-based beamforming, and an offspring replaces the swarm’s worst particle only when its fitness is lower.The fitness is based on total average power consumption.Source: D. GA-Assisted Offspring Generation · p. 9
  • Elitist global-best updates make the recorded objective non-increasing and convergent, but the discrete MWMU search remains heuristic and has no global-optimality claim.SOCP optimally solves beamforming for each decoded discrete configuration.Source: D. GA-Assisted Offspring Generation · p. 9
  • The complexity estimate accounts for one SOCP evaluation per particle per iteration and additional SOCP evaluations for offspring at each GA activation.The supplied passage does not specify the completed complexity expression.Source: D. GA-Assisted Offspring Generation · p. 9

TGA NGACSOCP

The simulations use a resource-limited three-waveguide setting and compare the proposed adjustable-coupling, discrete-motion PASS with PASS, MIMO, and hybrid-MIMO baselines.

V. SIMULATION RESULTS

  • The simulations consider N = K = 3, four PAs per waveguide, a 20 m × 10 m deployment region, and a minimum SINR requirement of 24 dB.The carrier frequency is 28 GHz, and movement and transmission durations are 0.2 s and 0.8 s, respectively.Source: §V · p. 9
  • The proposed AC-DM-PASS jointly optimizes localized discrete PA positions, adjustable coupling strength, and transmit beamforming.Discrete coupling spacing levels tune radiation power at each PA.Source: §V · pp. 9–10
  • DM-PASS uses equal radiation power across PAs while optimizing localized discrete positions and beamforming with the proposed GA-PSO.The equal allocation is βl,n = 1/L.Source: §V · p. 10
  • DA-PASS fixes PAs at pre-mounted discrete positions and adjusts coupling for activation, while hybrid MIMO uses N RF chains connected to L antennas through phase shifters.The MIMO baseline uses N RF chains, each connected to a single antenna.Source: §V · p. 10

A. Single-User Scenario

The simulations compare the proposed PASS design across single-user and multi-user settings, and the conclusion summarizes its discrete control framework and algorithms. In the multi-user scenario, it consistently uses less power than the compared architectures across the reported conditions.

A. Single-User Scenario

  • For the MWSU setup, branch-and-bound converges in approximately 3.5 × 10^4 iterations versus approximately 5.31 × 10^17 feasible configurations for exhaustive search.The bound-pruning strategy reduces search complexity, though branch-and-bound complexity still grows rapidly with the number of PAs, candidate positions, and coupling levels.Source: A. Single-User Scenario · p. 10
  • In the MWSU comparison, the proposed PASS uses the least power, outperforming equal-power DM-PASS and adjustable-coupling DA-PASS, especially at high SNR requirements.Conventional and hybrid MISO require substantially more power than the proposed design.Source: A. Single-User Scenario · p. 10

B. Multi-User Scenario

  • The proposed PASS reduces average power by up to 99% versus conventional and hybrid MIMO, 42.2% versus equal-power DM-PASS, and 39.7% versus adjustable-coupling DA-PASS.The reported 42.2% and 39.7% gains concern the minimum-SINR comparison; the 99% comparison is against conventional and hybrid MIMO.Source: B. Multi-User Scenario · pp. 10–11
  • The proposed design reduces average power by up to 53.78% versus adjustable-coupling DA-PASS as the number of PAs per waveguide varies.Power falls as PA count increases across PASS schemes, but gains gradually saturate; position optimization matters more when PA counts are limited.Source: B. Multi-User Scenario · p. 11
  • At DW = 30 m, the proposed design reduces power by approximately 20.3% versus equal-power DM-PASS and 25.8% versus adjustable-coupling DA-PASS.Power consumption rises with spatial range for all schemes, while the proposed design’s gain becomes more significant as range increases.Source: B. Multi-User Scenario · p. 11

VI. CONCLUSION

  • The conclusion combines discrete coupling-spacing control and localized discrete PA movement with joint optimization of positions, coupling strength, and beamforming under SINR and motion constraints.It proposes globally optimal branch-and-bound for MWSU and GA-PSO for MWMU.Source: §VI · p. 12

APPENDIX

The appendix establishes the branch-and-bound bounds and pruning rule, shows finite termination, and characterizes the stopping criterion’s solution guarantee.

A. Proof of Theorem 1

  • For every active node, the lower bound is no greater than the local optimum and the feasible-solution upper bound is no less than it, yielding GLB ≤ f⋆ ≤ GUB.The global lower bound is the minimum lower bound over active nodes, while GUB is the best feasible objective value found so far.Source: A. Proof of Theorem 1 · p. 12
  • Because position and coupling-spacing domains are finite, repeated branching has finitely many leaves and the algorithm terminates after finitely many iterations.Each iteration either prunes a node or branches it into smaller finite subsets.Source: A. Proof of Theorem 1 · p. 13
  • When the relative gap is at most ϵ, the incumbent is ϵ-optimal for P′S, and its recovered MRT beamforming solution is ϵ-optimal for PS.The stated bound is fϵ − f⋆ ≤ ϵ max{1, |fϵ|}.Source: A. Proof of Theorem 1 · p. 13
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