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Channel Estimation for Pinching-Antenna Systems (PASS)

Jian Xiao, Ji Wang, Yuanwei Liu

arXiv:2503.13268v4cs.ITeess.SP

TL;DR

PASS channel estimation is difficult because coupled channels must be inferred from low-dimensional pilots under changing PA configurations. The paper proposes PAMoE and PAformer deep-learning estimators, and reports superior accuracy, reduced pilot overhead, zero-shot generalization, and complementary specialization-versus-scalability trade-offs.

  • Problem

    PASS channel estimation is an underdetermined problem because highly coupled waveguide and wireless channels require high-dimensional channel vectors to be inferred from low-dimensional pilot observations.

  • Method

    The paper proposes PAMoE, which combines dynamic padding, feature processing, PA positions, and mixture-of-experts specialization, and PAformer, which uses self-attention for per-antenna prediction.

  • Results

    The proposed deep-learning estimators outperform conventional methods, reduce pilot overhead, generalize zero-shot to dynamic PA configurations, and show complementary accuracy and scalability strengths.

  • Takeaways & Limitations

    PAMoE offers higher accuracy through specialized expert processing, while PAformer natively supports arbitrary PA counts with scalable per-antenna prediction.

Abstract

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Pinching Antennas (PAs) represent a revolutionary flexible antenna technology that leverages dielectric waveguides and electromagnetic coupling to mitigate large-scale path loss. This letter is the first to explore channel estimation for Pinching-Antenna SyStems (PASS), addressing their uniquely ill-conditioned and underdetermined channel characteristics. In particular, two efficient deep learning-based channel estimators are proposed. 1) PAMoE: This estimator incorporates dynamic padding, feature embedding, fusion, and mixture of experts (MoE) modules, which effectively leverage the positional information of PAs and exploit expert diversity. 2) PAformer: This Transformer-style estimator employs the self-attention mechanism to predict channel coefficients in a per-antenna manner, which offers more flexibility to adaptively deal with dynamic numbers of PAs in practical deployment. Numerical results demonstrate that 1) the proposed deep learning-based channel estimators outperform conventional methods and exhibit excellent zero-shot learning capabilities, and 2) PAMoE delivers higher channel estimation accuracy via MoE specialization, while PAformer natively handles an arbitrary number of PAs, trading self-attention complexity for superior scalability.

I. INTRODUCTION

PASS uses flexible pinching antennas and dielectric-waveguide coupling to establish adjustable LoS links and mitigate large-scale path loss, but its coupled, underdetermined channels make estimation difficult. This letter introduces the first PASS channel-estimation study and proposes PAMoE and PAformer deep-learning estimators.

  • System motivation: Pinching antennas transfer electromagnetic waves from dielectric waveguides to nearby dielectric material, enabling flexible positioning and adjustable LoS links.Their movement ranges can span thousands to tens of thousands of wavelengths while supporting many connected antennas on one waveguide.
  • Research gap: Existing PASS optimization strategies depend on precise channel estimation, but PASS channel estimation remains insufficiently investigated because of new channel-coupling challenges.The waveguide channel and wireless propagation channels are highly coupled, complicating estimation.
  • Proposed estimators: The letter proposes PAMoE, a mixture-of-experts estimator that combines PA positions and pilot features to model dynamic PASS channel distributions.The approach extends linear estimators for benchmarking and seeks improved accuracy with reduced pilot overhead.
  • Proposed estimators: PAformer uses self-attention to predict channel coefficients per antenna, supporting dynamic PA counts with greater scalability.The system model includes LoS and NLoS propagation, with spherical wavefronts used for array responses because the PA aperture may exceed the Rayleigh distance.
  • Reported outcomes: The proposed deep-learning estimators achieve higher accuracy, reduced pilot overhead, and zero-shot generalization to dynamic PA configurations without retraining.The paper reports these outcomes relative to conventional channel estimators.
  • Research gap: A fixed waveguide merges multiple PA signals, so even many pilot slots may provide only one linearly independent scalar measurement per slot for estimating a high-dimensional channel vector.This underdetermined structure limits conventional error-criterion-based estimators such as least squares.

III. DEEP LEARNING BASED CHANNEL ESTIMATION

PASS channel estimation must learn highly variable channels from changing PA configurations and time-varying signal dimensions. The proposed architectures are designed to adapt to these spatial, temporal, and dimensional variations.

  • Challenges: PASS channel characteristics vary dramatically as PAs change positions, requiring networks with enough capacity to learn an extended channel state space.The challenge arises from flexible PA placement within designated regions.
  • Challenges: Dynamic activation of candidate PAs creates time-varying channel dimensions and heterogeneous signal distributions.The estimator therefore must adapt to changing input structure rather than a single fixed configuration.
  • Design requirement: The proposed estimator architecture must adapt to spatio-temporal variation while estimating high-dimensional channels from low-dimensional received pilots.This requirement motivates the architectural designs developed in the subsequent estimators.

A. Dataset Construction

The dataset construction collects paired pilot observations, PA positions, and corresponding channel samples, while antenna switching provides LS and LMMSE benchmarks at added practical cost.

  • A. Dataset Construction: Offline training uses paired pilot observations, PA position sets, and corresponding channel samples.The pilot observation is collected at the base station alongside PA positions and the corresponding channel sample.
  • A. Dataset Construction: The network input combines PA positions with pilot observations transformed using the in-waveguide channel.This transformation aligns the network input dimension with the current number of PAs.
  • A. Dataset Construction: The training label represents the real and imaginary parts of the wireless channel for each PA.The channel label is converted into a real-valued tensor for network training.
  • A. Dataset Construction: Antenna switching enables independent pilot measurements for LS and LMMSE benchmark estimators.Switching subsets of PAs across time slots separates their signals for benchmark channel estimation.
  • A. Dataset Construction: Switching introduces hardware overhead, longer measurement time, and potential switch losses that reduce practicality.These costs arise from switching each PA in different time slots.

B. PAMoE: Mixture of Experts-Based Channel Estimation

PAMoE addresses high-dimensional dynamic channel estimation from low-dimensional received pilots by combining dynamic padding, feature embedding, fusion, and position-aware mixture-of-experts modules.

  • B. PAMoE: Mixture of Experts-Based Channel Estimation: PAMoE combines dynamic padding, feature embedding, fusion, and position-aware MoE modules for dynamic channel estimation.The estimator is designed to infer high-dimensional channels from low-dimensional received pilots.

1) Dynamic Padding:

Dynamic padding lets PAMoE accommodate variable PA counts by extending position and pilot tensors to a shared maximum length with learnable padding embeddings.

  • 1) Dynamic Padding:: PAMoE pads variable-length PA inputs to a maximum PA count N_max.Padding is applied along the PA dimension when the current count N is smaller than N_max.
  • 1) Dynamic Padding:: Learnable padding embeddings extend both PA-position and pilot-signal tensors to length N_max.Separate embeddings are used for positions and pilot signals, with N_pad = N_max − N padded entries.

2) Feature Embedding:

PAMoE embeds continuous PA positions with multi-scale Fourier features and maps pilot signals into a compatible hidden representation for subsequent processing.

  • 2) Feature Embedding:: A Fourier positional embedding represents continuous PA spatial information using exponentially increasing frequency bases.The approach is intended to support efficient extrapolation across PA positions.
  • 2) Feature Embedding:: Sinusoidal transformations produce sine and cosine position features that are concatenated.These features form the positional representation before projection into the embedding space.
  • 2) Feature Embedding:: The concatenated positional features are projected into an embedding space, while pilot signals are mapped to the same hidden dimension.A learnable linear projection handles positional features, and an MLP-based module embeds pilot data.

3) Feature Fusion:

Feature fusion combines PA-position information with pilot-signal features through a gating function before expert processing.

  • The gating function generates a gate from PA-position features and applies it to pilot-signal features.
  • PAformer is presented as a channel-estimation model using self-attention-based processing.
  • The gate uses a linear layer with d_hid neurons followed by a Sigmoid activation.
  • Each expert processes the fused representation with an MLP-Mixer block across feature and spatial dimensions.

4) MoE With Gating Network:

The MoE module pools fused features to generate expert weights, combines expert outputs, and ultimately maps fused representations to estimated channels.

  • A gating network pools fused features over the PA dimension and applies softmax to produce expert weights.
  • The gating weights are produced by a linear layer with E neurons and sum to one for each batch sample.
  • The MoE output is formed by broadcasting the gating weights over the PA dimension and computing a weighted sum of expert outputs.
  • PAMoE concatenates positional and MoE features, then maps them to the estimated channel.
  • PAformer uses permutation-equivariant self-attention to accommodate PAs of arbitrary size N and predict coefficients per antenna.
  • Per-antenna prediction allows PAformer to handle new data with more antennas than seen during training.

1) Input Embedding: 

PAformer embeds input features, processes them through stacked pre-norm Transformer self-attention blocks, and produces channel estimates independently for each antenna.

  • The input is mapped into a hidden representation Z(0) using an MLP-based embedding network.
  • Each Transformer block combines multi-head self-attention and a feedforward network with layer normalization and residual connections.
  • Layer normalization is applied before the self-attention module in each pre-norm Transformer block.
  • The self-attention output is added through a residual connection before the feedforward network is applied.
  • A second residual connection completes each Transformer sub-layer, and stacking P blocks yields the final feature representation.
  • The final mapping converts each antenna-wise feature vector into an estimated channel coefficient indexed by PA i.

IV. NUMERICAL RESULTS

The proposed estimators are evaluated against linear and deep-learning benchmarks across SNR, PA counts, complexity, and runtime. PAMoE achieves higher accuracy through positional specialization, while PAformer offers scalable variable-PA processing.

  • Experimental setup: The simulations use fixed 16-PA training data and test dynamic configurations from 8 to 32 PAs.NMSE is the performance metric, with antenna-switching LS and LMMSE as conventional benchmarks.
  • Experimental setup: The evaluation compares the proposed estimators with antenna-switching LS, LMMSE, SA-RN-CE, and DACEN benchmarks.SA-RN-CE and DACEN are attention-based deep-learning comparison models.
  • NMSE performance: The proposed deep-learning estimators outperform existing linear estimators and deep-learning models with reduced pilot overhead.This comparison is reported for NMSE performance in Fig. 4.
  • NMSE performance: PAMoE achieves higher accuracy than PAformer by exploiting pinching-antenna positional information through a more specialized design.PAformer uses a more general mechanism to support variable PA counts.
  • Dynamic PA configurations: Both proposed estimators generalize to dynamic PA configurations without retraining, demonstrating zero-shot learning under distinct test distributions.Fig. 5 evaluates varying PA counts at 0 dB SNR.
  • Complexity and runtime: PAformer FLOPs increase linearly with PA count, whereas PAMoE FLOPs remain constant through uniform padding to Nmax.Both models achieve microsecond-level channel-estimation runtime, supporting real-time deployment feasibility.

V. CONCLUSIONS

The letter investigates channel estimation for PASS and proposes two deep-learning estimators for inferring high-dimensional channels from low-dimensional pilot observations. PAMoE exploits multi-expert diversity and variable configurations, while PAformer uses self-attention to handle arbitrary PA counts; both outperform conventional methods and reduce pilot overhead.

  • V. CONCLUSIONS: The paper proposes two deep-learning estimators that infer high-dimensional channel vectors from inherently low-dimensional pilot observations.The estimators use advanced neural-network architectures for PASS channel estimation.
  • V. CONCLUSIONS: PAMoE accommodates variable PA configurations and exploits multi-expert diversity in an MLP-Mixer for improved channel estimation.
  • V. CONCLUSIONS: PAformer handles an arbitrary number of PAs through its self-attention mechanism.
  • V. CONCLUSIONS: The proposed estimators outperform conventional methods and significantly reduce pilot overhead.
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