User Localization and Channel Estimation for Pinching-Antenna Systems (PASS)

This letter proposes a novel user localization and channel estimation framework for pinching-antenna systems (PASS), where pinching antennas are grouped into subarrays on each waveguide to cooperatively estimate user/scatterer locations, thus reconstructing channels. Both single-waveguide (SW) and multi-waveguide (MW) structures are considered. SW consists of multiple alternatingly activated subarrays, while MW deploys one subarray on each waveguide to enable concurrent subarray measurements. For the 2D scenarios with a fixed user/scatter height, an orthogonal matching pursuit-based geometry-consistent localization (OMP-GCL) algorithm is proposed, which leverages inter-subarray geometric relationships and compressed sensing for precise estimation. Theoretical analysis on Cramér-Rao lower bound (CRLB) demonstrates that: 1) The estimation accuracy can be improved by increasing the geometric diversity through multi-subarray deployment; and 2) SW provides a limited geometric diversity within a $180^\circ$ half space and leads to angle ambiguity, while MW enables full-space observations and reduces overheads. The OMP-GCL algorithm is further extended to 3D scenarios, where user and scatter heights are also estimated. Numerical results validate the theoretical analysis, and verify that MW achieves centimeter- and decimeter-level localization accuracy in 2D and 3D scenarios with only three waveguides.

💡 Research Summary

This paper presents a groundbreaking framework for user localization and channel reconstruction within Pinching-Antenna Systems (PASS), a next-generation wireless architecture where antennas can dynamically move along waveguides. Unlike traditional fixed-MIMO systems, PASS offers unprecedented physical degrees of freedom, which the authors leverage to enhance estimation precision through multi-subarray cooperation.

The study investigates two distinct architectural configurations: Single-Waveguide (SW) and Multi-Waveguide (MW). The SW structure utilizes multiple subarrays on a single waveguide that are activated sequentially. While cost-effective due to lower hardware complexity, the SW approach is limited to a 180-degree half-space observation, inherently leading to angle sign ambiguity. In contrast, the MW structure deploys one subarray per waveguide, enabling simultaneous measurements across a full 360-degree field of view. This simultaneous activation not only resolves the ambiguity problem but also significantly reduces the measurement overhead.

To address the localization challenge, the authors propose the Orthogonal Matching Pursuit-Geometry Consistent Localization (OMP-GCL) algorithm. This algorithm integrates Compressed Sensing (CS) with geometric constraints. In 2D scenarios, the algorithm utilizes an angle-domain dictionary parameterized by distance and angle. It employs OMP to extract the cosine of the angle ($\cos \theta$) and then performs an exhaustive search over all $2^M$ possible sign combinations to ensure geometric consistency between subarrays. By formulating a projection distance minimization problem augmented with a direction consistency penalty, the algorithm achieves highly accurate localization. The framework is further extended to 3D scenarios, where the algorithm simultaneously estimates the user’s 3D coordinates and the height of the scatterer.

A significant theoretical contribution of this work is the derivation of the Cramér-Rao Lower Bound (CRLB), which quantifies the fundamental limits of estimation accuracy. The analysis reveals that increasing geometric diversity—specifically the variance of observation directions among subarrays—is crucial for improving accuracy. A key finding is that the estimation error is heavily dependent on the minimum eigenvalue ($\lambda_{min}$) of the projection matrix $P_m = I - u_m u_m^T$. Consequently, the authors provide a practical design guideline: placing subarrays at the boundaries or corners of the service area maximizes $\lambda_{min}$, thereby drastically reducing the CRLB.

Numerical simulations validate these theoretical insights. The MW structure demonstrates exceptional performance, achieving centimeter-level accuracy in 2D and decimeter-level accuracy in 3D using only three waveguides. Conversely, the SW structure exhibits much higher error rates due to its inability to resolve angle ambiguity. Ultimately, this paper provides both a robust algorithmic solution and essential design principles for implementing high-precision, scalable, and flexible antenna systems in future wireless networks.