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Rate Maximization for Downlink Pinching-Antenna Systems
Yanqing Xu, Zhiguo Ding, George K. Karagiannidis
TL;DR
The paper asks how to maximize downlink rate when pinching-antenna locations jointly affect path loss and dual phase shifts. It develops a relaxed problem and two-stage low-complexity algorithm, and simulations show higher rates than conventional fixed-position systems with near-optimal algorithmic performance.
Problem
The paper studies downlink rate maximization for multiple pinching antennas serving a single-antenna user when locations affect both path losses and dual phase shifts.
Method
A relaxed optimization problem is solved with a two-stage algorithm that first reduces large-scale path loss and then refines locations for constructive signal combination.
Results
Simulations show higher data rates than conventional fixed-position antenna systems, while the proposed algorithm achieves almost the same performance as the optimal solution.
Takeaways & Limitations
Pinching-antenna systems provide flexible deployment that can reduce path-loss effects and support effective downlink system design.
Abstract
from arXiv · showhide
In this letter, we consider a new type of flexible-antenna system, termed pinching-antenna, where multiple low-cost pinching antennas, realized by activating small dielectric particles on a dielectric waveguide, are jointly used to serve a single-antenna user. Our goal is to maximize the downlink transmission rate by optimizing the locations of the pinching antennas. However, these locations affect both the path losses and the phase shifts of the user's effective channel gain, making the problem challenging to solve. To address this challenge and solve the problem in a low complexity manner, a relaxed optimization problem is developed that minimizes the impact of path loss while ensuring that the received signals at the user are constructive. This approach leads to a two-stage algorithm: in the first stage, the locations of the pinching antennas are optimized to minimize the large-scale path loss; in the second stage, the antenna locations are refined to maximize the received signal strength. Simulation results show that pinching-antenna systems significantly outperform conventional fixed-location antenna systems, and the proposed algorithm achieves nearly the same performance as the highly complex exhaustive search-based benchmark.
I. INTRODUCTION
Pinching antennas extend flexible-antenna systems by enabling location adjustments that can influence large-scale path loss. This paper studies their design challenges and rate-maximization potential for serving a single-antenna user.
- Flexible-antenna systems adjust antenna locations to improve channel conditions, unlike traditional fixed-antenna systems.
- Traditional fluid- and movable-antenna systems are limited to wavelength-scale movement, restricting their influence on large-scale path loss.
- Pinching-antenna systems are studied as flexible, cost-effective systems suited to environments such as industrial IoT and urban deployments.
- The paper optimizes multiple pinching-antenna locations on one waveguide to maximize downlink transmission rate for a single-antenna user.
II. SYSTEM MODEL AND PROBLEM FORMULATION
The system model considers a base station with N antennas serving a randomly deployed single-antenna user within a square region.
- A base station with N antennas serves a single-antenna mobile user randomly deployed within a square area of side length D.
A. Conventional Antenna System
The conventional reference system uses fixed-position base-station antennas arranged above the deployment region, with antenna locations and spacing specified for channel modeling.
- The N conventional antennas are fixed above the square area's centroid at height d.
- The n-th antenna location is represented as ¯ψ_n=[¯x_n,0,d], with neighboring spacing Δ used to avoid antenna coupling.
- The spherical-wave channel model defines the user location and propagation parameters, including the wavelength λ and carrier frequency f_c.
- The additive white Gaussian noise power at the user is denoted by w.
B. Pinching-Antenna Systems
The pinching-antenna system places jointly operated antennas on a waveguide, whose adjustable locations affect path loss and dual phase shifts. Rate maximization is therefore formulated as a constrained, nonconvex optimization problem.
- B. Pinching-Antenna Systems: N pinching antennas mounted on an x-axis-parallel waveguide jointly serve a single-antenna user.
- B. Pinching-Antenna Systems: The n-th pinching antenna location is [˜x_n,0,d], while the feed point and guided wavelength depend on the waveguide geometry and effective refractive index.
- B. Pinching-Antenna Systems: Unlike fixed-position systems, pinching-antenna locations are adjustable beyond wavelength-scale movement, but waveguide propagation adds phase-shift design challenges.
- B. Pinching-Antenna Systems: The received signal combines contributions from the pinching antennas with evenly distributed total transmit power and additive noise.
- B. Pinching-Antenna Systems: The optimization maximizes the pinching-system downlink rate over antenna locations subject to minimum spacing constraints that avoid antenna coupling.
- B. Pinching-Antenna Systems: Maximizing downlink rate is recast as maximizing SNR, but the resulting problem remains difficult because locations affect path-loss terms, denominators, and complex exponents.
III. PROPOSED ALGORITHM TO SOLVE PROBLEM (8)
The proposed solution relaxes the original rate-maximization problem by separately addressing path loss and phase alignment. This yields a low-complexity two-stage procedure for antenna-location optimization.
- Pinching-antenna locations affect both large-scale path loss and phase shifts from propagation inside and outside the waveguide.
- The relaxed problem minimizes path-loss effects while requiring received signals from different pinching antennas to combine constructively.
- The first algorithm stage maximizes the sum of reciprocal antenna-user distances subject to antenna-spacing constraints.
- The second stage refines antenna locations to satisfy the constructive-combination constraint.
A. Maximize the Summation of Reciprocals of Distances
The first stage reduces the path-loss optimization to a one-dimensional problem and exploits its structure to obtain antenna locations in closed form. The resulting distance-based solution still requires phase-based refinement.
- A. Maximize the Summation of Reciprocals of Distances: The first-stage problem maximizes the sum of reciprocal distances from pinching antennas to the user under antenna-spacing constraints.
- A. Maximize the Summation of Reciprocals of Distances: At the optimum, the antenna-spacing constraints hold with equality.
- A. Maximize the Summation of Reciprocals of Distances: The multi-variable optimization reduces to a problem involving only the location of the first pinching antenna.
- A. Maximize the Summation of Reciprocals of Distances: When C ≥ (N − 1)^2∆^2, the reduced objective is unimodal and its maximizing location has a closed-form solution.For N = 8, f = 26 GHz, and ∆ equal to half a wavelength, the stated condition requires C ≥ 0.0306.
- A. Maximize the Summation of Reciprocals of Distances: The distance-based solutions do not necessarily maximize received signal strength because dual propagation phase shifts also affect the effective channel gain.
B. Refine the Pinching Antenna Locations to Satisfy (9c)
The second stage refines the distance-optimized locations so signals from different pinching antennas combine constructively. It sequentially searches short antenna-location segments using phase alignment criteria.
- B. Refine the Pinching Antenna Locations to Satisfy (9c): The remaining optimization refines pinching-antenna locations to satisfy the constructive-combination constraint.
- B. Refine the Pinching Antenna Locations to Satisfy (9c): For odd N, the central pinching antenna is initially placed at [x_m, 0, d] according to Lemma 2.
- B. Refine the Pinching Antenna Locations to Satisfy (9c): The next antenna is refined within a short segment by selecting the first location that minimizes its phase modulo 2π.
- B. Refine the Pinching Antenna Locations to Satisfy (9c): Remaining antennas are obtained successively over short segments by minimizing the phase difference with the previously placed antenna.
- B. Refine the Pinching Antenna Locations to Satisfy (9c): For even N, the same sequential scheme applies after initially fixing the N/2-th antenna using Lemma 2.
IV. SIMULATION RESULTS
Simulations evaluate rate performance across transmission power and deployment-region size, and compare the proposed algorithm with exhaustive search. Pinching antennas outperform conventional fixed-position systems, while the proposed algorithm nearly matches the benchmark.
- IV. SIMULATION RESULTS: The simulations evaluate pinching-antenna and conventional systems using data rates versus transmission power and deployment-region side length.The figures use P = 30 dBm for the side-length comparison and D = 10 meters for the transmission-power comparison.
- IV. SIMULATION RESULTS: Pinching-antenna systems yield higher ergodic achievable data rates than conventional fixed-position antenna systems.
- IV. SIMULATION RESULTS: Both pinching-antenna and conventional systems achieve higher rates as the number of antennas increases.
- IV. SIMULATION RESULTS: As deployment-region side length D increases, both systems’ rates decrease, while the performance gap favoring pinching antennas increases.The passage attributes the rate decrease to larger path losses and describes the growing gap as evidence of path-loss compensation and robustness to diverse deployment.
- IV. SIMULATION RESULTS: For N = 2, the proposed algorithm achieves almost the same performance as the exhaustive-search optimal solution.Exhaustive search uses a step size of λ/50, and its complexity increases quickly with the number of pinching antennas.
V. CONCLUSIONS
The paper formulates downlink rate maximization for a waveguide-based pinching-antenna system and addresses the coupled location effects with a low-complexity two-stage algorithm. Simulations demonstrate system advantages and algorithmic efficiency, while identifying power allocation and multi-user extensions as future directions.
- The study considers N pinching antennas deployed on a waveguide to serve a single-antenna user.
- A relaxed optimization problem enables a low-complexity two-stage solution to the challenging location-optimization problem.The difficulty arises because antenna locations affect both path losses and dual phase shifts of the effective channel gain.
- Simulation results demonstrate the advantages of the considered pinching-antenna system and the efficiency of the proposed algorithm.
- Future work includes more flexible power allocation among pinching antennas and system designs for multi-user scenarios.These directions target higher spectral efficiency and more practical pinching-antenna systems.
A. Proof of Lemma 1
The proof shows that when the relevant constraints are inactive, antenna locations can be moved until those constraints become equalities while increasing the objective function. It handles the two possible orderings symmetrically.
- If ˜x∗ n−1 ≤2xm, moving the (n−1)-th antenna toward the n-th antenna increases the objective function.The movement preserves the other antenna locations and decreases the corresponding squared-distance term.
- When the obtained solution does not make constraints (10b) active, another antenna-location set can satisfy those constraints with equality and a larger objective value.This contradiction completes the proof of Lemma 1.
B. Proof of Lemma 2
The proof establishes that g(˜x1) is unimodal under C ≥(N −1)2∆2, with its unique maximizer at ˜x∗ 1 = xm −N−1 2 ∆. The argument combines derivative analysis across the relevant regions and parity cases.
- The proof analyzes g(˜x1) in three derivative-based steps to establish unimodality.
- The derivative satisfies g′(xm −N−1 2 ∆) = 0 for both even and odd N.The proof derives this using the corresponding behavior of h′ in the two parity cases.
- For C ≥(N −1)2∆2, g′(˜x1) > 0 when ˜x1 < xm −N−1 2 ∆, so g is increasing on that region.
- For C ≥(N−1)2∆2, g′(˜x1) < 0 when ˜x1 >xm−N−1 2 ∆, so g is decreasing on that region.
- Therefore, g(˜x1) is unimodal and has the unique maximizer ˜x∗ 1 = xm −N−1 2 ∆.