⚡ electrical engineering

Uplink Positioning for PASS in Multipath Environments

This paper proposes an uplink multi-carrier positioning framework for Pinching-antenna systems (PASS) in multipath environments, featuring Matrix pencil and low-complexity Rank-1 ranging algorithms combined with a two-stage weighted nonlinear least-squares estimator, and validates their performance through theoretical error bounds and numerical results showing the trade-off between the MP-based algorithm's superior accuracy and the Rank-1 algorithm's lower complexity.

Original authors: Yaoyu Zhang, Xin Sun, Tianwei Hou, Anna Li, Yuanwei Liu

Published 2026-07-23

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CC BY 4.0

Original authors: Yaoyu Zhang, Xin Sun, Tianwei Hou, Anna Li, Yuanwei Liu

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to find a friend in a crowded, echoey room. If you shout "Where are you?" and they shout back, you can guess their distance by how long it takes for the sound to return. But in a real room, the sound bounces off walls, tables, and people, creating a messy mix of echoes that arrive at different times. This makes it incredibly hard to tell the true distance just by listening. This is the same problem facing modern wireless networks. As we try to use radio waves to not only talk to our devices but also to know exactly where they are (a field called "localization"), the signals bounce around, creating confusion.

To fix this, engineers have been inventing new types of antennas. One exciting new idea is called a "Pinching-Antenna System" (PASS). Think of a PASS like a long, invisible garden hose (a waveguide) running along the ceiling of a room. Instead of having one big sprinkler head, you can "pinch" the hose at different spots to make water (or in this case, radio signals) squirt out exactly where you need it. These "pinch points" are the antennas. Because you can move these pinch points around easily and cheaply, they offer a super-flexible way to talk to your phone or tablet. But here's the catch: to make these systems work perfectly, the network needs to know exactly where your phone is. If the network guesses wrong, the signal might miss you entirely. The big question is: how do we find the phone's location accurately when the radio signals are bouncing off everything in the room, creating a chaotic mess of echoes?

This paper tackles that exact problem. The authors, a team of researchers, propose a new way to figure out where a user is in a room filled with these bouncing radio signals, using the flexible PASS system. They didn't just guess; they built a mathematical framework and ran computer simulations to test two different methods for solving the "echo puzzle."

The first method they invented is like a high-powered, super-smart detective. It uses a technique called "Matrix Pencil" (MP). Imagine the messy radio signal as a complex song played by many instruments. This algorithm is so good at listening that it can separate the main melody (the direct path from the phone to the antenna) from all the background noise and echoes bouncing off the walls. By isolating that clean, direct path, it can calculate the distance with incredible precision. The simulations showed that this method is extremely accurate, even when the room is full of echoes, and its performance gets even better if you use more radio frequencies (subcarriers) to listen.

However, being a super-smart detective takes a lot of brainpower (computing power). The authors realized that sometimes, we need a faster, simpler solution. So, they created a second method called the "Rank-1" algorithm. Think of this as a quick-and-dirty estimate. Instead of listening to every single instrument in the orchestra, it just grabs the loudest sound (the strongest signal) and assumes that's the direct path. It ignores the quieter echoes. This makes it much faster and easier to run on simple devices. But there's a trade-off: because it doesn't fully separate the echoes, it sometimes gets stuck with a small, unchangeable error (an "error floor") when the room is quiet. It's like trying to guess the distance in a silent room by only listening to the loudest echo; you might get close, but you'll never be perfectly precise.

The researchers tested both methods in a simulated room that was 6 meters by 10 meters by 3 meters, using 4 movable antennas. They found that the "smart detective" (MP) method was the clear winner for accuracy, consistently finding the user's location within a few centimeters, and its results matched their theoretical predictions perfectly. The "quick estimate" (Rank-1) method was much faster to compute but had a hard limit on how accurate it could get, no matter how quiet the room was, because it couldn't fully ignore the confusing echoes.

In the end, the paper doesn't claim to have solved every problem in the universe, but it offers a clear roadmap for the future. If you need pinpoint accuracy for a high-tech application and have the computing power to spare, the MP method is the way to go. If you need something fast and simple, and can live with a tiny bit of inaccuracy, the Rank-1 method is a solid, lightweight alternative. The authors suggest that as we move forward with these flexible antenna systems, having both options will help engineers build smarter, more reliable networks that can find us anywhere, even in the most echoey rooms.

Technical Summary: Uplink Positioning for PASS in Multipath Environments

Problem Statement
Pinching-antenna systems (PASS) offer a promising alternative to conventional fixed-position antenna arrays and fluid antenna systems by enabling meter-scale antenna reconfigurability through low-cost dielectric waveguides. While PASS has been extensively studied for communication performance optimization (e.g., beamforming, resource allocation), its positioning capabilities remain underexplored. Existing positioning studies for PASS are largely restricted to line-of-sight (LoS) scenarios or rely on high-complexity methods like dictionary-based sparse recovery or iterative Bayesian inference, which suffer from grid mismatch and computational burdens. In practical indoor environments, multipath propagation is inevitable, and non-line-of-sight (NLoS) components introduce significant bias. There is a critical need for low-complexity uplink positioning algorithms that can accurately separate LoS delays from NLoS components in multipath environments to fully exploit the communication gains of PASS.

Methodology
The paper establishes an uplink multi-carrier positioning framework for PASS in multipath environments. The system model involves an access point (AP) connected to four waveguides, each equipped with a movable pinching antenna (PA). The user transmits pilot symbols across $K$ subcarriers. The channel is modeled as a sparse millimeter-wave channel containing $L$ multipath components, where the LoS path is dominant.

The proposed solution consists of two ranging algorithms and a positioning algorithm:

Matrix Pencil (MP)-Based Ranging Algorithm:
- This method constructs Hankel matrices from the coherent averaged channel observations.
- It exploits the shift-invariance property of the Hankel matrix to separate the LoS component from NLoS components.
- By performing Singular Value Decomposition (SVD) and projecting onto the signal subspace, the algorithm extracts signal poles.
- A unit circle filter removes spurious poles caused by noise, and the shortest estimated delay corresponds to the LoS distance.
- Complexity: High ( $O(\kappa^3)$ ), involving full SVD, pseudo-inverse computation, and eigenvalue decomposition.
Low-Complexity Rank-1 Ranging Algorithm:
- Designed to reduce computational cost, this method approximates the Hankel matrix using a truncated SVD to obtain the optimal Rank-1 approximation.
- It assumes the LoS component dominates the signal power, effectively isolating the dominant LoS delay while suppressing NLoS components and noise.
- The LoS signal pole is extracted directly via a Least Squares (LS) criterion on shifted submatrices, avoiding matrix inversions and full eigenvalue decomposition.
- Complexity: Low ( $O(\kappa^2)$ ), scaling linearly with the number of subcarriers and matrix dimensions.
Two-Stage Weighted Nonlinear Least-Squares (WNLS) Positioning:
- Using the estimated LoS distances from either ranging algorithm, a two-stage process estimates the 3D user position.
- Stage 1: An initial linear estimate is obtained by eliminating quadratic terms in the distance equations.
- Stage 2: The initial estimate is refined using a WNLS algorithm, where weights are assigned based on the estimated amplitude of the LoS components to improve robustness.

Key Contributions

Framework: Proposal of a comprehensive uplink multi-carrier positioning framework for PASS specifically designed for practical multipath environments.
Algorithms: Development of two ranging algorithms: a high-accuracy MP-based method that separates LoS/NLoS paths, and a low-complexity Rank-1 method that isolates the dominant LoS path via truncated SVD.
Theoretical Analysis: Derivation of closed-form ranging variances for both algorithms under high-SNR approximations. The paper establishes the Fisher Information Matrix (FIM) and derives the Position Error Bound (PEB) to reveal the error propagation mechanism from ranging errors to 3D positioning errors, highlighting the impacts of subcarrier count, bandwidth, and Geometric Dilution of Precision (GDoP).
Performance Characterization: Demonstration that the MP algorithm achieves higher accuracy and robustness, while the Rank-1 algorithm offers a lightweight alternative with a trade-off in accuracy due to multipath bias.

Results
Numerical simulations conducted in a 6m $\times$ 10m $\times$ 3m room with 4 PAs and 200 random multipath environments yield the following findings:

Accuracy vs. Complexity: The MP-based algorithm achieves higher ranging and positioning accuracy and follows the derived PEB trend. The Rank-1-based algorithm exhibits an error floor in low-noise scenarios due to residual multipath bias but offers significantly lower computational complexity.
Subcarrier Impact: Increasing the number of subcarriers ( $K$ ) improves the positioning accuracy of the MP algorithm by providing denser frequency-domain sampling. In contrast, the Rank-1 algorithm shows negligible improvement with increased $K$ because its performance is limited by deterministic NLoS-induced bias rather than random noise.
Robustness: The MP algorithm demonstrates greater robustness to variations in user height and multipath environments. The Rank-1 algorithm is more sensitive to user height changes, leading to larger error increases as the user moves closer to ceiling-mounted PAs (worsening GDoP).
Error Floor: The Rank-1 algorithm's positioning error remains relatively constant across a range of noise powers once the noise is low enough that deterministic bias dominates, whereas the MP algorithm's error decreases monotonically with noise power.

Significance
The paper claims that accurate uplink positioning is a fundamental prerequisite for optimizing PASS deployment and beamforming. By providing low-complexity algorithms and rigorous error analysis, this work addresses the gap in PASS positioning research for multipath environments. The results suggest that the MP-based algorithm is suitable for high-precision scenarios where computational resources are available, while the Rank-1 algorithm provides a viable, lightweight solution for scenarios where computational constraints are tight or noise levels are high. The derived PEB and error propagation analysis offer theoretical insights into the fundamental limits of PASS-based positioning.

Technical Summary: Uplink Positioning for PASS in Multipath Environments

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