Pinching-Antenna Systems (PASS): A Tutorial

Yuanwei Liu; Hao Jiang; Xiaoxia Xu; Zhaolin Wang; Jia Guo; Chongjun Ouyang; Xidong Mu; Zhiguo Ding; Arumugam Nallanathan; George K. Karagiannidis; Robert Schober

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Pinching-Antenna Systems (PASS): A Tutorial

Yuanwei Liu, Hao Jiang, Xiaoxia Xu, Zhaolin Wang, Jia Guo, Chongjun Ouyang, Xidong Mu, Zhiguo Ding, Arumugam Nallanathan, George K. Karagiannidis, Robert Schober

arXiv:2508.07572v4Aug 11, 2025eess.SP

TL;DR

PASS addresses practical and operational challenges in highly reconfigurable antenna systems. This tutorial surveys PASS fundamentals, beamforming, CSI acquisition, and learning-based operation, finding that GPASS approaches FP-BCD performance with lower execution complexity and outperforms conventional MIMO.

Problem
PASS requires CSI methods that account for dynamically changing antenna positions, while conventional fixed-antenna estimators cannot be directly applied.
Method
The tutorial synthesizes PASS signal and hardware models, beamforming strategies, CSI acquisition methods, and machine-learning approaches for system operation.
Results
GPASS achieves performance close to FP-BCD, with much lower execution complexity, and substantially outperforms conventional MIMO beamforming.
Takeaways & Limitations
PASS combines spatial flexibility with optimization and learning methods that can improve beamforming performance relative to conventional MIMO.
Takeaways & Limitations
Current PASS machine-learning models often fail to generalize across arbitrary numbers of users, antennas, waveguides, network scales, layouts, and mobility patterns.

Abstract

from arXiv · show

Pinching antenna systems (PASS) present a breakthrough among the flexible-antenna technologies, and distinguish themselves by facilitating large-scale antenna reconfiguration, line-of-sight creation, scalable implementation, and near-field benefits, thus bringing wireless communications from the last mile to the last meter. A comprehensive tutorial is presented in this paper. First, the fundamentals of PASS are discussed, including PASS signal models, hardware models, power radiation models, and pinching antenna activation methods. Building upon this, the information-theoretic capacity limits achieved by PASS are characterized, and several typical performance metrics of PASS-based communications are analyzed to demonstrate its superiority over conventional antenna technologies. Next, the pinching beamforming design is investigated. The corresponding power scaling law is first characterized. For the joint transmit and pinching design in the general multiple-waveguide case, 1) a pair of transmission strategies is proposed for PASS-based single-user communications to validate the superiority of PASS, namely sub-connected and fully connected structures; and 2) three practical protocols are proposed for facilitating PASS-based multi-user communications, namely waveguide switching, waveguide division, and waveguide multiplexing. A possible implementation of PASS in wideband communications is further highlighted. Moreover, the channel state information acquisition in PASS is elaborated with a pair of promising solutions. To overcome the high complexity and suboptimality inherent in conventional convex-optimization-based approaches, machine-learning-based methods for operating PASS are also explored, focusing on selected deep neural network architectures and training algorithms. Finally, several promising applications of PASS in next-generation wireless networks are highlighted.

I. INTRODUCTION … A. Signal Model

PASS is introduced as a scalable flexible-antenna technology for 6G that enables meter-scale antenna reconfiguration, line-of-sight creation, near-field operation, and customized wireless channels. The tutorial develops PASS fundamentals and signal models while surveying capacity, beamforming, channel acquisition, machine learning, and applications.

I. INTRODUCTION: Advanced MIMO forms face high computational complexity, heavy channel-estimation overheads, and manufacturing challenges, motivating flexible-antenna technologies for 6G.
B. PASS: From “Last Mile” to “Last Meter” Communications: PASS uses dielectric waveguides and separate dielectric pinching antennas to carry signals over tens of meters with low attenuation before radiating them into free space.
A. The Road to Flexible-Antenna Systems: Flexible-antenna research spans antenna selection, RISs, CAPAs, FAS, MAs, RHS, and DMA, which reshape transmission conditions through diversity, reflection, continuous apertures, position flexibility, or waveguide propagation.
1) Large-Scale Antenna Reconfiguration:: PASS reconfigures antenna positions on a meter scale, allowing signals to be emitted near receivers and thereby enhancing received signal power and energy efficiency.
2) Line-of-Sight Creation:: PASS can create LoS propagation conditions that are a hundred times stronger than NLoS links, helping address blockage and limited multipath at high frequencies.
3) Scalable Implementation:: Adding or removing dielectric PAs at selected waveguide positions provides PASS with scalable implementation without altering the antenna’s inner structure.
4) Near-Field Advantage:: Tens-of-meter waveguides create extremely large apertures, extending PASS near-field operation according to the Rayleigh-distance boundary 2D^2/λ.
C. Motivations and Contributions: The tutorial covers PASS models, activation methods, capacity, beamforming, channel acquisition, machine learning, and applications; its signal model considers a narrowband single-waveguide system with N PAs whose positions customize the aggregated channel.

B. Hardware and Power Radiation Model · 1) Directional Coupler-based Model:

PASS hardware depends on non-destructive, movable coupling between pinching antennas and waveguides. In the directional-coupler model, near-field coupling transfers controllable power to each PA, with radiation governed by coupling coefficients, lengths, spacing, and preceding PAs.

B. Hardware and Power Radiation Model: PASS flexibility relies on non-destructive coupling that extracts waveguide energy without cutting, soldering, or permanently altering the waveguide.The coupling must remain effective as the PA moves along the waveguide.
1) Directional Coupler-based Model:: A directional coupler uses closely spaced transmission lines whose overlapping electromagnetic fields transfer part of the main-waveguide signal through near-field evanescent coupling.The coupled signal propagates in the same direction as the main-waveguide signal, enabling PA implementation with a short waveguide connected to a radiator.
1) Directional Coupler-based Model:: The coupling region begins at x = 0, where only the main waveguide is excited with AG,m = 1 and AP,m = 0.The coupling length Lm denotes the region where the waveguide and m-th PA are adjacent.
1) Directional Coupler-based Model:: sin2(κmLm) is the fraction of normalized input power radiated by the m-th PA, while cos2(κmLm) continues along the waveguide.For sequentially positioned PAs, each PA’s radiated power also depends on the power-exchange coefficients of all preceding PAs.
1) Directional Coupler-based Model:: Complete power coupling (PG,m = 1) occurs at Lm = π/(2κm).Power oscillates periodically between the waveguide and PA as coupling length increases.
1) Directional Coupler-based Model:: Coupled power is regulated through the waveguide–PA spacing and coupling length, with smaller spacing producing stronger coupling.The coupling coefficient depends on waveguide and PA modes, wavelength λ, and spacing Sm; a 2 mm spacing is described as stronger than 7 mm.
1) Directional Coupler-based Model:: The equal power radiation model configures each PA for identical radiation efficiency, whereas the proportional model applies identical configurations to reduce manufacturing complexity.The proportional model is easier to implement because all PAs use the same configuration.

2) Multiport Network-based Model: … 2) Continuous Activation:

The paper develops a multiport network model that captures nonideal hardware effects and cascaded reflections, highlights the unresolved challenge of physically consistent multi-PA uplink modeling, and compares PASS activation strategies. Continuous activation offers the highest spatial resolution and differentiable optimization but is most suitable for slowly varying environments because mechanical delays can cause outdated configurations.

2) Multiport Network-based Model:: The multiport network model accounts for manufacturing and material imperfections, impedance mismatch, signal reflection, and hardware designs beyond a single directional-coupler implementation.For a single PA, the model represents a three-port network connecting two waveguide ports and one free-space radiation port.
2) Multiport Network-based Model:: Cascaded reflections and interactions among multiple PAs can make the multiport model exponentially more complex, with each PA’s radiated power depending on reflected power from other PAs.A cascaded three-port analysis framework was proposed to simplify performance evaluation under these interactions.
2) Multiport Network-based Model:: The scattering matrix S characterizes PA behavior; analytical derivations support theoretical analysis, while full-wave electromagnetic simulation is used to obtain accurate numerical values for real-world systems.For an ideal directional coupler, S31 = −j sin(κLc), where Lc denotes the coupling length.
3) Discussion on Uplink Signal Model:: PASS downlink signals can be characterized with coupler-based or multiport formulations, but no tractable and physically consistent uplink model for multi-PA PASS has been established.The difficulty stems from PAs passively receiving electromagnetic signals from free space into the waveguide and from inter-antenna reception effects.
3) Discussion on Uplink Signal Model:: SWAN addresses the multi-PA uplink challenge by using multiple short, physically disconnected dielectric waveguide segments, each with its own feed point and wired connection to the base station.Signals are injected into or extracted from each segment and relayed through wired connections such as optical fibers or high-quality cables.
C. PA Activation Method: PASS activation methods determine PA placement and participation in the wireless link, while multiple activated PAs require accounting for cascaded reflection and interaction effects.The paper categorizes current activation methods into three distinct modes.
1) Discrete Activation:: Discrete activation uses uniformly spaced, pre-installed PAs and activates a small subset, enabling fast reconfiguration, low hardware complexity, and scalable implementation but limited spatial resolution.Programmable electrical control can adjust PA-to-waveguide spacing and thereby change coupling strength without mechanical modules.
2) Continuous Activation:: Continuous activation mounts each PA on a slide track, providing the highest spatial resolution and fully differentiable optimization but requiring closed-loop actuation and favoring slowly varying environments.Mechanical or electronic delays may produce outdated configurations under fast channel variations, so indoor, manufacturing, and IIoT settings are preferred.

3) Semi-Continuous Activation: … Single-Pinch Case:

The paper presents semi-continuous activation as a hybrid PASS strategy that combines segment-level control with local refinement, then characterizes PASS information-theoretic limits and practical rate regions. In the single-pinch uplink case, PASS capacity depends on the activated PA position and exceeds fixed-antenna performance in achievable and capacity regions.

3) Semi-Continuous Activation:: Semi-continuous activation divides the waveguide into M −1 uniform segments, pre-locates one PA per segment, and permits local offsets um ∈[0, umax].This hybrid balances continuous activation’s resolution with discrete activation’s lower complexity.
3) Semi-Continuous Activation:: The hybrid scheme enables fast segment-level control with local refinement while reducing activation latency and hardware cost relative to fully continuous activation.Its coordination complexity and physical integration, including actuation precision, require system-level co-design.
III. INFORMATION-THEORETIC LIMITS AND PERFORMANCE ANALYSIS OF PASS: PASS information-theoretic analysis characterizes multiuser capacity regions and TDMA/FDMA achievable rate regions under equal power allocation and continuous PA activation.Capacity is determined by the activated PA positions rather than fixed antenna locations.
A. Information-Theoretic Limits: The analyzed multiuser scenario uses one pinched waveguide serving two single-antenna users with M activated PAs along its aperture.The waveguide is aligned along the x-axis.
1) Uplink PASS:: For a given pinching beamformer, the two-user uplink capacity region forms a pentagon and can be achieved through successive interference cancellation or joint decoding at the base station.Time sharing over feasible PA configurations yields the overall capacity region as the convex hull of those configurations.
1) Uplink PASS:: For M = 1, varying the pinched position x1 over [0, xmax] gives the capacity region, with the capacity-achieving position lying within [xR,1, xR,2].This result directly characterizes the single-pinch capacity region.
Single-Pinch Case:: In the single-pinch case, TDMA and FDMA eliminate inter-user interference, while PASS provides larger achievable rate regions and an expanded capacity region than fixed-antenna systems.The comparison is presented for capacity and TDMA/FDMA rate regions.
Single-Pinch Case:: For M > 1, exhaustive search over the feasible set X is computationally infeasible at large M, so SIC characterizes Pareto-optimal rate pairs before time sharing completes the capacity region.The procedure first takes the union of SIC-achievable Pareto-optimal pairs over x ∈X.

Multiple-Pinch Case: · M. Additionally, an outer bound CU · 2) Downlink PASS:

The multiple-pinch analysis characterizes Pareto-optimal rate tuples, derives tight capacity bounds, and finds TDMA and FDMA nearly capacity-achieving. Downlink PASS capacity regions follow from uplink-downlink duality and significantly outperform fixed-antenna systems.

Multiple-Pinch Case:: For a fixed decoding order and rate-profile factor α, the Pareto-optimal two-user rate tuple is (αRsum, (1−α)Rsum).The rate-profile method obtains boundary points as intersections between rays with direction [α, 1−α]T and the Pareto boundary.
Multiple-Pinch Case:: The multiple-pinch capacity region is evaluated using an element-wise alternating optimization method that provides an achievable inner bound for the non-convex, NP-hard problem.The method is used to obtain a high-quality solution, while an outer bound is derived using the Cauchy-Schwarz inequality.
M. Additionally, an outer bound CU: TDMA and FDMA are nearly capacity-achieving in multiple-pinch PASS, demonstrating their near-optimality for practical implementations.TDMA uses antenna position refinement, whereas FDMA uses the rate-profile approach with element-wise alternating optimization.
M. Additionally, an outer bound CU: The derived inner bound closely aligns with the outer bound, indicating that both bounds are tight for multiple-pinch PASS.The capacity and achievable rate regions are illustrated in Fig. 7.
M. Additionally, an outer bound CU: Increasing the number of PAs significantly enlarges the capacity and achievable rate regions in the multiple-pinch case.This comparison is made between the multiple-pinch and single-pinch results shown in Fig. 7 and Fig. 6.
2) Downlink PASS:: Downlink PASS capacity regions are obtained from dual uplink channels under identical effective channels, equal noise power, and power allocations satisfying P1 + P2 = P.The overall downlink capacity region additionally incorporates time sharing among pinching configurations x ∈ X.
2) Downlink PASS:: DPC achieves the two-user downlink capacity region, while superposition coding with SIC decoding can achieve it through power-domain NOMA.The result applies to the considered downlink channel under the stated dual-channel setup.
2) Downlink PASS:: PASS significantly outperforms conventional fixed-antenna systems in downlink achievable rate regions, while TDMA and FDMA are nearly capacity-achieving.These relationships are consistent with the corresponding uplink capacity and rate-region relationships.

B. Performance Analysis · 1) Ergodic Rate: · 2) Coverage Probability:

PASS performance is evaluated through ergodic rate and coverage probability for users randomly located within a service region. Both metrics show advantages over conventional fixed-antenna systems, with gains becoming more pronounced as the service area enlarges.

B. Performance Analysis: Performance analysis evaluates PASS using typical metrics under a single-antenna, single-resource-block scenario without inter-user interference.This setup captures standalone PASS performance.
B. Performance Analysis: PASS’s performance advantage derives from waveguide-enabled extended coverage and flexible PA placement, motivating stochastic-geometry analysis under random user distributions.The random-user setting is central to evaluating average network performance.
1) Ergodic Rate:: Ergodic-rate analysis assumes a user uniformly distributed within a service region and compares PASS’s average network performance with conventional fixed-antenna systems.The comparison quantitatively demonstrates gains enabled by PASS.
1) Ergodic Rate:: With one waveguide spanning a D×D square region and one activated PA, PASS places the antenna at p = [xR, 0, zG]T to maximize received SNR.The waveguide is oriented along the y-axis and the region is centered at the origin.
1) Ergodic Rate:: At high SNR, PASS’s ergodic-rate advantage over the conventional fixed-antenna system is strictly positive and increases monotonically with D.The conventional antenna is positioned at pcon = [0, 0, zG]T, while the conventional ergodic-rate expression generally lacks a closed form.
1) Ergodic Rate:: PASS outperforms conventional fixed-antenna systems in ergodic rate because flexible PA positioning creates strong LoS links and reduces large-scale path loss.Simulation results also show that the performance gap widens as D increases, highlighting scalability over larger service areas.
2) Coverage Probability:: Coverage probability is the likelihood that a typical user achieves target SNR γ0, equivalently the spatially averaged success probability of a transmission or link.For PASS, a closed-form expression can be obtained, whereas an explicit conventional expression is challenging.
2) Coverage Probability:: Simulations show that PASS provides higher network coverage than conventional fixed-antenna systems, with the advantage becoming more pronounced as the service region enlarges.A rigorous theoretical comparison between PcCON remains an open problem.

3) LoS Blockage and Outage Probability: · C. Discussion and Outlook

PASS reduces LoS blockage and outage probability by dynamically positioning antennas to shorten transceiver distances, while the paper identifies broader capacity, multiuser, and EM-coupling-aware analyses as open directions.

3) LoS Blockage and Outage Probability:: PASS inherently lowers LoS blockage probability by reducing the transceiver distance, thereby enhancing wireless-link reliability.
3) LoS Blockage and Outage Probability:: LoS blockage is modeled with a binary indicator ε, where Pr(ε = 1) = e−β∥p−r∥.Here, ε = 1 denotes an existing LoS link and ε = 0 denotes blockage.
3) LoS Blockage and Outage Probability:: The SNR-maximizing pinch remains at the user’s projection along the waveguide, p = [xR, 0, zG]T.This location minimizes the relevant PA-to-user distance under the stated single-pinch setting.
3) LoS Blockage and Outage Probability:: In the high-SNR regime, PASS has a strictly lower outage probability than a conventional fixed-antenna system, with performance gap ∆b > 0.The gap ∆b increases monotonically with Dx, and PASS’s advantage becomes more pronounced as the service rectangle length increases.
C. Discussion and Outlook: The analytical framework shows that PASS reduces transceiver distances, large-scale path loss, and LoS-blockage likelihood, but its capacity and performance analysis remains limited to specific settings.The paper’s baseline analysis includes single-user, single-waveguide performance and a two-user, single-pinched-waveguide capacity framework.
C. Discussion and Outlook: Future work should extend information-theoretic analysis to arbitrary-user and multiple-waveguide settings through rate profiles, decoding orders, and joint baseband–pinching beamforming.
C. Discussion and Outlook: Multiuser and multiple-waveguide PASS requires analysis of ergodic rates, coverage probabilities, and outage probabilities under ZF, MRT, and MMSE beamforming.
C. Discussion and Outlook: EM-coupling-aware PASS performance is an open challenge because coupling may enable super-directive and super-wideband beams that enhance array performance and operational bandwidth.The paper notes that minimum inter-antenna spacing is typically used to mitigate EM coupling, despite these potential benefits.

IV. PINCHING BEAMFORMING OPTIMIZATION … 1) Sub-connected Architecture:

The section develops PASS pinching-beamforming optimization from single-waveguide principles and power scaling to multi-waveguide joint design. It shows that PA-position optimization has a non-monotonic antenna-number effect, while sub-connected architecture decomposes into independently solvable single-waveguide problems.

A. Pinching Beamforming Basis and Power Scaling Law: Pinching beamforming maximizes array gain by optimizing PA positions x and, when possible, the power allocation vector ρ.The maximum rate is γ = log2(1 + Pr/σ2).
A. Pinching Beamforming Basis and Power Scaling Law: The analysis focuses on PA-position optimization under a fixed power radiation model, while power-radiation optimization can further improve communication performance.The feasible PA positions and power allocations depend on the selected activation and radiation models.
A. Pinching Beamforming Basis and Power Scaling Law: Under equal power radiation and continuous activation, Theorem 1 tightly approximates the maximum received power, yielding PASS’s power scaling law as M →∞.The equal-radiation condition is Pm = 1/M.
A. Pinching Beamforming Basis and Power Scaling Law: As M increases, received power eventually tends to zero because per-antenna power decreases and distant PAs contribute ineffectively, implying an optimal PA count.The approximation and simulations show that maximum received power is non-monotonic in the number of antennas.
A. Pinching Beamforming Basis and Power Scaling Law: General pinching-beamforming optimization is non-convex and difficult because PA positions are coupled in both the objective and constraints, with many local optima.Search methods are used to avoid convergence to poor local optima.
B. Joint Beamforming Design for the Single-user Case: For single-user multi-waveguide PASS, two joint transmit-and-pinching structures are proposed according to RF-chain connectivity: sub-connected and fully connected.The system uses NRF RF chains, with connectivity determining the transmission structure.
1) Sub-connected Architecture:: In the sub-connected architecture, each RF chain feeds one waveguide, so NRF = N, and MRT is the optimal transmit beamforming solution for the single-user system.The transmit vector is w = [w1, . . . , wN]T, with wn associated with the n-th RF chain.
1) Sub-connected Architecture:: The sub-connected joint optimization decomposes into N independent single-waveguide pinching-beamforming problems, eliminating the need for high-complexity search algorithms.For general cases, the multiple SISO problems can be solved individually, significantly reducing optimization complexity.

2) Fully-connected Architecture: · C. Joint Beamforming Design for the Multi-user Case · 1) Waveguide Switching:

The fully-connected PASS architecture supports more RF chains than waveguides but creates coupled beamforming optimization challenges, motivating joint design. For multi-user communications, waveguide switching eliminates inter-user interference through time-slot allocation while jointly optimizing shared pinching parameters.

2) Fully-connected Architecture:: Each RF chain connects to all waveguides through phase shifters, enabling NRF ≠ N in the fully-connected PASS architecture.The architecture uses baseband beamforming and phase-shifter-based analog beamforming vectors.
2) Fully-connected Architecture:: Unlike conventional hybrid beamforming, fully-connected PASS can operate with more RF chains than waveguides, making larger pinching-antenna deployments practical with fewer waveguides.Increasing waveguides is challenging because each occupies substantial space.
2) Fully-connected Architecture:: Coupling between baseband and phase-shifter-based analog beamforming complicates fully-connected design, especially when NRF > N.Decoupled optimization can substantially lose performance because both the free-space channel and overall beamformer depend on PA positions.
C. Joint Beamforming Design for the Multi-user Case: For K users served by N waveguides with M PAs each and NRF RF chains, PASS beamforming must enhance desired signals while mitigating inter-user interference.The paper introduces three beamforming protocols that exploit PASS characteristics.
1) Waveguide Switching:: Waveguide switching serves different users in distinct time slots, eliminating inter-user interference and supporting both sub-connected and fully-connected architectures.The discussion focuses on the sub-connected architecture for clarity.
1) Waveguide Switching:: A single PA-position configuration is shared across users because individually adjusting positions per user and time slot would require excessively rapid changes.Time is assumed equally allocated among users, and the resulting objective is weighted sum-rate maximization.
1) Waveguide Switching:: With one user served per time slot, each user’s transmit beamformer can be designed as an MRT beamformer under an individual transmit-power constraint.Positive user weights ωk support resource allocation that prioritizes different users.
1) Waveguide Switching:: Shared pinching parameters must be jointly optimized for balanced WSR performance, and element-wise one-dimensional search can address the resulting multi-modal problem.The multi-user optimization is more multi-modal than in the single-user case.

2) Waveguide Division: · 3) Waveguide Multiplexing: · D. Wideband OFDM Beamforming

Waveguide division assigns one user per waveguide, whereas waveguide multiplexing sends all users through each waveguide and jointly optimizes transmit and pinching beamforming. PASS wideband OFDM systems are analyzed through available bandwidth, waveguide dispersion, and frequency-selective-fading considerations.

2) Waveguide Division:: Waveguide division feeds each waveguide with one user’s signal, schedules K = N users, and applies only to sub-connected beamforming.User k is assigned to the k-th waveguide.
2) Waveguide Division:: Waveguide division reduces transmit beamforming to power allocation, but inter-user interference creates a challenging weighted sum-of-logarithms fractional optimization.WMMSE and fractional programming are identified as common transformation techniques.
2) Waveguide Division:: Geographically isolated waveguides can block cross-user channels, inherently eliminate inter-user interference, and yield a single-user SISO model.User priorities can then be controlled by adjusting the power allocation factors ν_k.
3) Waveguide Multiplexing:: Waveguide multiplexing sends all users’ signals into every waveguide and applies to both sub-connected and fully-connected architectures.The sub-connected architecture is used for exposition, with received signals containing desired-signal and inter-user-interference terms.
3) Waveguide Multiplexing:: Waveguide multiplexing is more general but significantly more challenging because transmit and pinching beamforming must be jointly optimized across all users.A penalty-based approach is cited for handling highly coupled pinching-beamforming terms.
3) Waveguide Multiplexing:: The paper compares different beamforming protocols for waveguide multiplexing in Table III.The supplied passage identifies the comparison but does not provide the table’s quantitative results.
D. Wideband OFDM Beamforming: PASS wideband OFDM beamforming is examined for frequency-selective fading through available bandwidth, waveguide dispersion, and related system characteristics.The analysis emphasizes distinct in-waveguide signal propagation enabled by PASS.

1) Available Bandwidth: … A. Pilot-Based Channel Estimation

PASS wideband operation is constrained by waveguide modal bandwidth and dispersion, requiring frequency-dependent beamforming and careful cyclic-prefix design. CSI acquisition remains essential, with pilot-based methods addressing rank deficiency through sequential activation, compressed sensing, or parameter sensing, each involving practical tradeoffs.

1) Available Bandwidth:: PASS bandwidth is limited by waveguide material, geometry, structure, and modal transitions between single-mode and multimode operation.Unlike free space, waveguides support discrete electromagnetic modes over specific frequency ranges.
1) Available Bandwidth:: 58 GHz is the approximate maximum single-mode frequency for ro = 2 mm, no = 1.4, and nc = 1.Lower-frequency operation is also constrained by dominant-mode cutoff, material losses, coupling efficiency, and feed limitations.
2) Waveguide Dispersion:: Waveguide dispersion makes signal velocity frequency-dependent, producing differential delays and inter-symbol interference in wideband PASS transmissions.The OFDM cyclic prefix must account for multipath, antenna-array geometry, and in-waveguide dispersion.
3) Frequency-Dependent Pinching Beamforming:: Wideband PASS requires frequency-dependent beamforming because channel gain, radiated power, and effective refractive index vary across subcarriers.PA positions must maximize beamforming gains across all subcarriers rather than target a single narrowband frequency.
E. Discussion and Outlook: Future PASS research should develop practical, analytically tractable wideband signal models and account for activation or mechanical-movement latency.These needs support efficient protocol design while mitigating latency effects in fast-varying or mobile networks.
V. PASS CSI ACQUISITION: Accurate CSI is foundational for PASS optimization, but conventional fixed-position antenna estimation methods cannot directly address PASS requirements.PASS’s spatial flexibility makes CSI availability the prerequisite for implementing optimization algorithms.
A. Pilot-Based Channel Estimation: Pilot-based channel estimation discretizes waveguide positions into candidate grids, while the in-waveguide channel need not be estimated because it is position-determined.Adjacent grid points should be spaced farther than λ/2 to suppress mutual coupling under valid TDD operation.
A. Pilot-Based Channel Estimation: Rank deficiency prevents unique recovery of the full-dimensional channel from conventional pilots, motivating sequential activation, compressed sensing, and parameter sensing.Sequential activation yields full-rank in-waveguide matrices but incurs overhead proportional to M; compressed sensing exploits wavenumber sparsity, while parameter sensing enables continuous estimation.

B. Beam Training

PASS beam training exploits its ability to create LoS or sparse-scatter conditions by selecting antenna positions and beams through codebook-based measurements. The section outlines hierarchical, site-specific, and sensing-aided approaches, each trading training overhead or codebook size against environmental assumptions or additional hardware.

Beam-training framework: Beam training sweeps predefined antenna-position and beam codebooks, reports local measurements, and selects transmission modes through the corresponding indices.The optimization maximizes beam gains for a given free-space channel vector h using selection functions f(·) and g(·).
Motivation and related use: Beam training is widely used in mmWave MIMO because of its simplicity and computational efficiency, and is integrated into the 5G NR beam-management framework.PASS beam training is motivated by its ability to create LoS or sparse-scatter transmission conditions.
Three Stage Hierarchical Beam Training: Three-stage hierarchical training progressively searches PASS serving-area positions along the x-direction, then y-direction, and finally the best grid at fine resolution.The procedure follows coarse-to-fine hierarchical searches across spatial coordinates.
Site-Specific Codebook Design: Site-specific codebook design uses environment information to train codewords and neural-network beam-selection functions, reducing codebook size under stationary channel maps.The approach may lose effectiveness when the network is dynamic or the served-area layout changes.
Sensing Aided Beam Training: Sensing-aided beam training traverses only position-related codebook subsets, greatly reducing training overhead and avoiding repeated training in mobile networks.It requires additional sensing hardware, which increases implementation complexity.

C. Discussion and Outlook … 2) DNN Architectures for Learning the Policies:

The paper identifies practical CSI-acquisition challenges in PASS and motivates machine learning for cost-efficient optimization and autonomous configuration. It then defines optimization policies and surveys GNN- and transformer-based architectures for learning them, emphasizing scalability, permutation properties, and KKT-guided performance.

C. Discussion and Outlook: PASS CSI acquisition faces a performance–complexity tradeoff because practical methods estimate channels only at discrete antenna positions along potentially very long waveguides.Sampling hundreds or thousands of potential pinching-antenna positions can become prohibitive.
C. Discussion and Outlook: NLoS environments require dedicated channel-estimation and beam-training designs that balance direct-link coverage, scattered-link coverage, sweep length, and scalability.Greedy alignment to the strongest LoS direction may not maximize overall channel performance in indoor or other multipath settings.
VI. MACHINE LEARNING FOR PASS: PASS’s reconfigurability increases system complexity, operational overhead, and design intricacy, motivating ML for cost-efficient optimization and CSI acquisition.The paper frames ML as a response to burdens arising during both system optimization and CSI acquisition.
A. Motivation for Exploiting ML in PASS: ML can accelerate nonconvex PASS optimization and CSI acquisition while improving performance, using fixed-layer neural networks and learned mappings beyond initialization-dependent conventional optimizers.The approach can integrate conventional optimization principles into neural networks and learn global mappings from large-scale training samples.
A. Motivation for Exploiting ML in PASS: ML models can enable autonomous PASS configuration by detecting channel or hardware issues and predicting user movements and traffic variations.Such models may be deployed at the edge or in the cloud to interact with dynamic environments.
B. ML-empowered Optimization: Deep learning treats a policy as a mapping from known parameters, such as user positions, to optimization decisions, including pinching beamforming and power allocation.The power-allocation policy applies to wideband systems and maps user positions to optimized pinching-antenna positions and power allocation.
2) DNN Architectures for Learning the Policies:: Beamforming and power-allocation policies can be learned with GNNs, which offer better size generalizability and scalability by exploiting permutation properties in wireless policies.A trained GNN can operate across different problem scales without retraining and can be trained with low complexity at large scales.
2) DNN Architectures for Learning the Policies:: Transformers capture global dependencies through attention, while KKT-guided designs improve joint beamforming learning by approximating KKT points better than black-box ResNet and transformer methods.The KDL-Transformer uses encoder self-attention for inter-user CSI dependencies, decoder cross-attention for PA interactions, and differentiable KKT-derived reconstruction.

3) Training the DNN Architectures: … I. Define policies from optimization problems

The paper compares supervised, unsupervised, and reinforcement-learning strategies for defining PASS policies, favoring label-free methods when nonconvex optimization lacks reliable optimal solutions. It also describes neural approaches for CSI acquisition under limited measurements and varied PA layouts.

3) Training the DNN Architectures:: PASS DNN policies can be trained through supervised, unsupervised, or reinforcement-learning methods.The section introduces these three training manners for resource-allocation policies.
3) Training the DNN Architectures:: Supervised learning uses optimal or suboptimal resource-allocation solutions as labels paired with environmental parameters and learned outputs.For beamforming, each sample contains Φ[i], X⋆[i], and W⋆[i].
3) Training the DNN Architectures:: Because PASS optimization is usually nonconvex, suboptimal labels can degrade supervised-learning performance, making unsupervised learning an attractive alternative.Unsupervised training can minimize the negative objective averaged over training samples, while output activations enforce constraints.
3) Training the DNN Architectures:: Reinforcement learning suits multi-step Markov decision processes, whereas supervised or unsupervised learning better fits PASS beamforming and power allocation decisions confined to one time slot.In RL, actions affect subsequent states; here, current actions do not affect future states.
I. Define policies from optimization problems: For PASS policy architectures, GCNs can exploit permutation-equivariant properties for scalable power allocation, while attention-based transformers or graph transformers can model beamforming interference.GPASS uses a processor that learns attention among users.
1) Machine Learning for CE:: CSI acquisition addresses high-dimensional PASS channels with limited pilot measurements and RF chains by training multiple experts for different PA layouts.A gating network assigns each expert a weight and combines their predicted outputs.
1) Machine Learning for CE:: Transformer experts represent PAs as tokens, learn spatial relationships through self-attention, and support activation of arbitrary numbers of PAs.Their variable-token processing accommodates different PASS deployments.
1) Machine Learning for CE:: CSI probing activates PAs at different positions, while compressed sensing can estimate angle and distance parameters to recover LoS and NLoS multipath components.The passage notes that rank deficiency typically necessitates additional treatment, and diffusion modeling represents the channel as a function of PA positions.

2) Machine Learning for Beam Training: … VIII. CONCLUSIONS

The paper presents ML-assisted beam training for PASS and surveys deployment opportunities, open challenges, and future directions spanning sensing, communications, security, mobility, and 6G networks.

2) Machine Learning for Beam Training:: ML assists PASS beam training through pinching alignment, tracking, and prediction without requiring full and explicit CSI estimation.Alignment requires both distance-domain pathloss minimization and phase alignment; tracking adapts PA positions to mobility and environmental changes.
2) Machine Learning for Beam Training:: Beam selection uses MAB algorithms to choose PA activation patterns, whereas beam adaptation uses neural networks to generate arbitrary PA activation positions.UCB and Thompson Sampling can explore predefined configurations, while codebook adaptation networks successively adapt measurement positions.
D. Discussion and Outlook: PASS ML models face challenges in generalizing across network scales, layouts, mobility patterns, and arbitrary numbers of users, PAs, or waveguides.Further issues include incorporating electromagnetic, geometric, and hardware constraints, while maintaining reliability and scalability under dynamic, uncertain, and resource-constrained conditions.
A. Localization/Sensing for PASS: PASS supports sensing by bypassing blockages to create LoS links and by providing large apertures with sparsely distributed PAs, enhancing near-field effects.These properties motivate localization and sensing applications, including full-dimensional sensing capabilities.
B. PASS for ISAC: PASS is a promising ISAC platform because sensing and communication can share resource blocks, while both PASS sensing and communication advantages have been demonstrated.Existing works have begun investigating PASS for ISAC.
C. Waveguide Division Multiple Access: PASS multi-user communications are challenging because PAs on one waveguide share the same signal source, motivating NOMA and joint baseband and pinching beamforming.These approaches address single-waveguide and multiple-waveguide configurations, respectively.
D. Physical Layer Security: Physical-layer security can safeguard PASS transmissions by exploiting pinching beamforming for simultaneous desired-signal enhancement and interference mitigation.The LoS-dominated, short-range links provided by PASS may facilitate information eavesdropping.
E. PASS-assisted UAVs: PASS can support aerial, space, vehicular, and UAV communications through infrastructure-mounted waveguides, blockage-aware trajectory design, and coordinated distributed waveguides.These deployments aim to maintain robust LoS links and consistent, low-latency connectivity for high-speed UAVs.

APPENDIX A MULTIPORT NETWORK-BASED MODEL … POWER SCALING LAW

The appendices formulate PASS through a multiport scattering and waveguide model, derive the outage expression, and characterize maximum received-power scaling using upper and lower bounds. The power bounds are connected by optimized antenna placement and the squeeze theorem.

APPENDIX A MULTIPORT NETWORK-BASED MODEL: The multiport model represents incident and reflected voltage waves at the PA ports and relates them through a scattering matrix.The formulation identifies the three-port incident and reflected wave vectors as the basis of the PA network model.
APPENDIX B A FULL DERIVATION OF (36): The outage probability is expanded by conditioning on the activation-related variable ε, weighting the conditional outage events by Pr(ε = 0) and Pr(ε = 1).Bayes’ theorem is then applied to the resulting outage-probability expression.
POWER SCALING LAW: Under equal power radiation and continuous activation, the receive power is upper bounded, with the bound maximized by uniformly placing PAs at minimum spacing and centering the aperture at the user projection.The maximizing placement satisfies xm = (m − 1)∆min + x1 for m > 1 and xM + x1 = 2xR.
POWER SCALING LAW: Antenna position refinement tightly approaches the upper bound by aligning free-space and waveguide phase shifts through small perturbations from an initially uniform minimum-spaced placement.The resulting optimized receive power provides a tight approximation to the maximum achievable receive power.
POWER SCALING LAW: A lower bound is obtained when all antennas are phase-aligned using a uniformly spaced array centered at the user location and spacing ∆max on the order of the wavelength.The bound is derived from the largest inter-antenna spacing among optimized positions and its uniform-spacing construction.
POWER SCALING LAW: Both upper and lower bounds on maximum received power scale like O as M →∞, establishing the power scaling law through the squeeze theorem.The appendices therefore rigorously characterize the asymptotic scaling of maximum received power.