⚡ electrical engineering

Dual-Waveguide Pinching Antennas for PLS: Parallel Placement or Orthogonal Placement?

This paper investigates the application of dual-waveguide pinching antennas for physical-layer security by comparing parallel and orthogonal placement strategies, formulating secure sum rate and energy efficiency maximization problems, and proposing a two-stage FeaPSO-SCA algorithm that demonstrates the superiority of orthogonal placement in enhancing security performance.

Original authors: Yang Lu, Xinke Xie, Yanqing Xu, Bo Ai, Octavia A. Dobre, Arumugam Nallanathan

Published 2026-06-04

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CC BY 4.0

Original authors: Yang Lu, Xinke Xie, Yanqing Xu, Bo Ai, Octavia A. Dobre, Arumugam Nallanathan

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 send a secret message to a group of friends (Legitimate Users) in a large, open room, but there is a eavesdropper (Eve) standing nearby trying to steal the message. In traditional wireless systems, the "signal" travels like a flashlight beam from a fixed tower. If Eve stands between the tower and your friends, she can easily intercept the message, and you can't do much about it because the tower can't move.

This paper introduces a new technology called Pinching Antennas (PAs) to solve this problem. Here is how it works, broken down into simple concepts:

1. The New Tool: The "Slippery Slide" (Waveguides)

Instead of a fixed tower, imagine two long, flexible slides (called waveguides) stretched across the room. Along these slides, you can place small "pinching" devices (the antennas).

The Magic: Unlike a fixed antenna, these pinching devices can slide back and forth along the tracks.
The Benefit: You can move the antennas closer to your friends to make the signal stronger and clearer, or move them away from the eavesdropper to make the signal weak and garbled for her. It's like being able to physically move your megaphone to whisper directly into your friend's ear while shouting at the spy.

2. The Big Question: How to Arrange the Slides?

The researchers asked: "If we have two of these slides, how should we set them up to get the best security?" They tested two main layouts:

Parallel Placement: Imagine two slides running side-by-side, like train tracks.
Orthogonal Placement: Imagine the slides crossing each other to form a giant "T" or "L" shape.

The Finding: While both setups work well on average, the Orthogonal (crossing) layout is a secret weapon. If the eavesdropper happens to stand directly in front of your friends, the crossing layout gives you a better angle to hide the signal from her. It creates a "blind spot" for the spy that the parallel layout can't always achieve.

3. The Two-Step Strategy (The Algorithm)

Finding the perfect spot for every sliding antenna and the perfect way to shout the message is a massive math puzzle. The authors created a two-step "recipe" to solve it:

Step 1: The "Smart Search" (FeaPSO): First, they use a computer method that acts like a swarm of birds searching for food. They fly around the room, testing different positions for the sliding antennas. If a position is impossible (like two antennas crashing into each other), a special "correction module" gently pushes them back into a valid spot.
Step 2: The "Fine-Tuning" (SCA): Once the antennas are in good spots, the computer fine-tunes the "beamforming." Think of this as adjusting the focus of a camera lens or the direction of a flashlight to ensure the message is crystal clear for the friends but fuzzy for the spy. They also add "artificial noise"—like static on a radio—that confuses the spy but doesn't bother the friends.

4. The Results: Why It Matters

The researchers ran thousands of simulations to see how this system performed compared to old, fixed antennas.

Better Security: The sliding antennas significantly increased the "Secure Sum Rate" (how much secret data can be sent) and "Secure Energy Efficiency" (how much data you get per unit of battery power).
The "Attenuation" Factor: They also looked at what happens if the signal gets weaker as it travels inside the slide (like a hose losing water pressure over a long distance). They found that if the slide is very long or the material is "leaky," this loss matters. However, for shorter distances, the signal remains strong.
The Verdict: The system works best when you use the Orthogonal (crossing) layout, especially in tricky situations where the spy is close to the friends.

Summary

This paper proves that by using movable antennas on sliding tracks, we can physically reshape the airwaves to protect secrets. It's like having a security guard who can instantly move to block a thief's view while guiding your friends to safety. The study shows that arranging these tracks in a crossing pattern is often the smartest move, and a clever two-step computer algorithm can figure out the perfect positions in real-time.

Technical Summary: Dual-Waveguide Pinching Antennas for Physical-Layer Security

1. Problem Statement

This paper investigates the application of Pinching Antennas (PAs) to enhance Physical-Layer Security (PLS) in wireless communication systems. While traditional PLS relies on channel diversity between Legitimate Users (LUs) and Eavesdroppers (Eves), it is often constrained by spatial degrees of freedom (DoF), particularly when Eves are positioned close to the base station or directly between the transmitter and LUs.

Existing flexible-antenna technologies (e.g., RIS, movable antennas) often focus on phase shifts or require dense deployment of access points without reconfigurable channel capabilities. The authors address the specific challenge of optimizing a dual-waveguide PA system where multiple PAs are deployed along two waveguides to serve multiple LUs in the presence of an Eve.

The core research questions are:

How do different waveguide placement strategies (Parallel vs. Orthogonal) impact PLS performance?
How do different in-waveguide channel models (considering phase shifts only vs. phase shifts plus attenuation) affect system design?
How can one jointly optimize PA positions, baseband beamforming, and artificial noise (AN) vectors to maximize Secure Sum Rate (SSR) and Secure Energy Efficiency (SEE)?

2. Methodology

System Model

The system consists of a dual-waveguide transmitter (Alice) serving $K$ LUs and facing one Eve. Each waveguide hosts $N$ movable PAs.

Placement Strategies:
- Parallel: Two waveguides deployed parallel to each other at a fixed distance.
- Orthogonal: Two waveguides deployed perpendicularly, intersecting at the origin.
Channel Models:
- Model A: In-waveguide phase shifts only (neglecting attenuation).
- Model B: In-waveguide phase shifts plus attenuation (modeling power loss along the waveguide).
Signal Processing: The system utilizes baseband beamforming vectors ( $w_k$ ) and pinching beamforming (controlled by PA positions $\psi^{Pin}_{l,n}$ ). Artificial noise is generated to degrade the Eve's channel.

Optimization Framework

The authors formulate two non-convex optimization problems:

P1: Maximize SSR.
P2: Maximize SEE.
Both problems involve coupled variables (PA positions and beamforming vectors) and exponential terms arising from the pinching beamforming matrix.

Proposed Algorithm: Two-Stage Approach

To solve these non-convex problems, a two-stage algorithm is proposed:

Stage 1: PA Placement Optimization (FeaPSO)
- Method: Particle Swarm Optimization (PSO) enhanced with a Feasibility Module (FeaPSO).
- Mechanism: Since gradient-based methods fail due to the sine/cosine nature of the rate functions, PSO is used. The feasibility module ensures that generated PA positions satisfy physical constraints (e.g., minimum guard distance $\Delta$ and boundary limits $[-D, D]$ ) by sorting and adjusting coordinates.
- Output: Near-optimal PA positions ( $\psi^{Pin}$ ) and preliminary beamforming vectors.
Stage 2: Beamforming and AN Optimization (SCA)
- Method: Successive Convex Approximation (SCA).
- Mechanism: With fixed PA positions, the problem is reformulated using auxiliary variables and first-order Taylor approximations (Gaussian approximation) to convexify non-convex constraints.
- Output: Refined baseband beamforming vectors and AN vectors to maximize SSR or SEE.

3. Key Contributions

Dual-Waveguide PLS Formulation: The paper is the first to investigate PLS in a dual-waveguide PA scenario, explicitly comparing parallel and orthogonal placement strategies.
Comprehensive Channel Modeling: Unlike prior works that often neglect attenuation, this study incorporates two channel models: one with only phase shifts and another including in-waveguide attenuation, analyzing their impact on SSR and SEE.
Novel Algorithm (FeaPSO-SCA): A two-stage algorithm is proposed that combines a feasibility-adjusted PSO for discrete PA placement with SCA for continuous beamforming optimization. This approach handles the strong coupling between position and transmission parameters.
Analytical Insights on Placement: The authors derive analytical expectations for the squared vertical distances between LUs and waveguides. They demonstrate that while average performance is similar for both strategies, orthogonal placement offers superior channel diversity when the Eve is positioned in front of the LUs (sharing similar X-coordinates), thereby enhancing PLS.

4. Simulation Results

Numerical experiments were conducted with $N=2$ PAs per waveguide and $K=2$ LUs in a $20m \times 20m$ area.

Algorithm Effectiveness: The proposed FeaPSO-SCA algorithm achieves performance very close to an exhaustive search (ES-0.4) but with significantly lower computational time (ES-0.4 takes ~20% more time).
SSR and SEE Performance:
- PA-enabled systems significantly outperform fixed-position antenna systems in both SSR and SEE.
- Orthogonal vs. Parallel: The orthogonal placement strategy slightly outperforms the parallel strategy in both SSR and SEE. The CDF analysis shows that orthogonal placement introduces an additional spatial DoF, diversifying channel conditions between LUs and the Eve, which is particularly beneficial when the Eve is located in front of the LUs.
Impact of Parameters:
- Power Budget: SSR increases monotonically with power budget. SEE initially increases and then slightly decreases as power budget grows, due to the trade-off between rate gains and power consumption.
- Number of PAs ( $N$ ): Increasing $N$ improves SSR and SEE for PA systems by providing more DoFs for beamforming, whereas fixed-antenna systems show no improvement as $N$ increases (since the number of physical antennas remains fixed).
- Attenuation: As the in-waveguide attenuation coefficient ( $\zeta$ ) increases, the performance gap between the "phase-shift-only" model and the "phase-shift-plus-attenuation" model widens. The paper concludes that attenuation cannot be neglected in scenarios with large waveguide lengths or high attenuation coefficients.

5. Significance and Claims

The paper claims that Pinching Antennas offer a new degree of freedom for PLS by enabling large-scale, on-demand adjustments to wireless channels. Specifically:

Movable PAs can mitigate path loss by moving close to LUs and construct links bypassing Eves, even in scenarios where Eves are positioned directly between the transmitter and users.
Orthogonal Placement is explicitly verified as necessary in specific scenarios (Eve in front of LUs) to maximize channel condition diversity, a capability not present in parallel-only deployments.
The proposed two-stage algorithm provides a practical and efficient solution for the complex, non-convex optimization problems inherent in PA-enabled systems, bridging the gap between theoretical PLS gains and implementable designs.

The authors conclude that while existing flexible-antenna technologies have limitations, PAs offer a promising avenue for enhancing both communication quality and security, though future work is needed to address the deep coupling of variables and the integration with other flexible-antenna technologies.