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A Low-Complexity Placement Design of Pinching-Antenna Systems
Ximing Xie, Fang Fang, Zhiguo Ding, Xianbin Wang
TL;DR
Sophisticated pinching-antenna placement optimization is computationally demanding for practical implementation. This paper derives low-complexity closed-form placements for selected OMA and NOMA settings, and simulations show higher sum rates than conventional fixed-antenna systems. The multiple-antenna NOMA case remains outside the paper's closed-form scope.
Problem
Sophisticated optimization of pinching-antenna placements has high computational complexity, making practical implementation challenging.
Method
The paper derives closed-form placement solutions from user locations for single-antenna OMA and NOMA, and multiple-antenna OMA scenarios.
Results
Simulations show pinching-antenna systems achieve higher sum rates than conventional fixed-antenna systems across the considered scenarios.
Takeaways & Limitations
Closed-form placement avoids complex optimization in the studied cases while retaining the sum-rate advantage of pinching-antenna systems.
Takeaways & Limitations
Multiple-antenna NOMA placement lacks a closed-form solution and requires sophisticated optimization, left for future work.
Abstract
from arXiv · showhide
Pinching-antenna systems have recently been proposed as a new candidate for flexible-antenna systems, not only inheriting the reconfiguration capability but also offering a unique feature: establishing line-of-sight links to mitigate large-scale path loss. However, sophisticated optimization of the placement of pinching antennas has very high complexity, which is challenging for practical implementation. This paper proposes a low-complexity placement design, providing the closed-form expression of the placement of pinching antennas, to maximize the sum rate of multiple downlink users. Orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) are both investigated when the pinching-antenna system is only equipped with a single antenna and only the OMA case is studied when there are multiple antennas equipped by the pinching-antenna system. Simulation results indicate pinching-antenna systems can outperform conventional fixed-antenna systems and are more suitable for large service areas.
I. INTRODUCTION
Pinching-antenna placement directly affects wireless channels, but sophisticated placement optimization has high computational complexity. The paper therefore derives low-complexity closed-form placements for several access and antenna configurations, with higher simulated sum rate than fixed-antenna systems.
- Placement optimization is crucial because pinching-antenna locations directly affect wireless channels and achievable performance.
- Sophisticated placement optimization has high computational complexity, creating practical implementation challenges.
- The paper derives closed-form antenna placements based on user locations for three sum-rate maximization scenarios.
- The studied scenarios are single-antenna OMA, multiple-antenna OMA, and single-antenna NOMA networks.
- Simulations show higher sum rate than conventional fixed-antenna systems in all considered scenarios.
II. PINCHING ANTENNA ASSISTED OMA NETWORKS
Under TDMA, only one user is served in each time slot, so placement depends on that slot's served user's location.
- TDMA serves only one user during each time slot.
- The pinching-antenna placement in each slot depends on the location of the served user.
- This setting makes placement user-specific across time slots.
A. A Single Pinching Antenna on a Waveguide
The single-antenna TDMA model places a movable antenna on a waveguide serving users distributed in a rectangular area. Maximizing each user's rate leads to full transmit power and a closed-form placement aligned with that user's x-coordinate.
- The model uses one pinching antenna on a waveguide to serve M users in a TDMA downlink network.
- Users are distributed in a rectangular service area in the x-y plane, while the waveguide runs parallel to the x-axis at height d.
- The antenna can move to a specific waveguide location quickly enough that movement time is neglected.
- Each user's rate is optimized by maximizing transmission power and minimizing the distance to the pinching antenna.
- The optimal transmission power is P*_m = Pmax for every user.
- The optimal antenna location is ψ*_Pin,m = (x_m, 0, d) for every user.
B. Multiple Pinching Antennas on a Waveguide
For multiple pinching antennas on one waveguide, the paper formulates sum-rate maximization and derives closed-form placement solutions with low-complexity computation.
- System model: The system models N active pinching antennas on a shared waveguide and derives users’ received signals and data rates under TDMA.The channel uses a spherical-wave model, with phase shifts determined by the waveguide wavelength.
- Optimization formulation: Because each TDMA user is served individually, the placement optimization can be performed separately for each user.The user’s data rate increases as the pinching antenna moves closer, motivating placement near the closest waveguide position.
- Closed-form placement: The optimal placement starts from the closest waveguide position and introduces the smallest offset satisfying the phase-related constraint.The offset is assumed non-negative and is obtained by finding the minimal feasible integer index and solving the resulting equation.
- Closed-form placement: Proposition 1 establishes that the placement equation always has a positive real solution.The proof uses continuity and the intermediate value theorem after constructing a function whose endpoint values have opposite signs.
- Complexity and behavior: The antenna offset is within a few wavelengths, and the resulting placement can be computed efficiently because the governing equation is quadratic.The few-wavelength offset has negligible impact on distance, particularly at very high carrier frequencies.
III. PINCHING ANTENNA ASSISTED NOMA NETWORKS
In NOMA networks, simultaneous service prevents precise user-specific antenna adjustment, so the paper motivates placing the pinching antenna at a preset position for fixed user locations.
- NOMA motivation: Because a waveguide’s pinching antenna transmits the same signal, NOMA is suitable for simultaneous service of multiple users.The users’ signals are superimposed, and antenna placement cannot be adjusted exclusively for one user during the shared transmission period.
A. A Single Pinching Antenna on a Waveguide
For a single pinching antenna in NOMA, the paper formulates coupled placement and power-allocation optimization and proposes a two-phase design to solve it efficiently.
- Signal model: The transmitted NOMA signal superimposes each user’s signal with its allocated power.This construction supports simultaneous service of multiple users.
- Channel and decoding: Each user’s channel gain depends on both the user location and the pinching antenna position.Under power-domain NOMA, stronger-channel users decode weaker users’ signals before decoding their own, while stronger users create interference for weaker-user decoding.
- Optimization formulation: The NOMA sum-rate problem jointly accounts for antenna placement, power allocation, channel-gain ordering, interference sets, power limits, and SIC constraints.Changing the antenna position can change the channel ordering and therefore the interference set.
- Solution strategy: The original problem is non-convex and difficult to solve in polynomial time because its optimization variables are coupled.The proposed remedy separates placement optimization from power allocation in two phases.
1) Placement Optimization for the Pinching Antenna:
The placement problem is reformulated from direct non-convex optimization into minimizing total path loss, which becomes a convex distance-based problem with a closed-form optimal solution.
- Placement reformulation: The method minimizes total path loss as a sub-optimal alternative to directly optimizing the non-convex placement problem.The reformulation uses the given transmission power and user locations.
- Placement reformulation: Minimizing total path loss is equivalent to minimizing the sum of squared distances between the pinching antenna and users.
- Closed-form solution: The resulting problem P7 is convex, so its optimum is obtained from the first-order derivative condition.
- Closed-form solution: Proposition 3 gives the optimal solution of P7 in closed form.
2) Power Allocation for Users:
The power-allocation analysis orders users by channel gain and allocates power first for rate requirements, then to the strongest channel; the section also notes a closed-form limitation for multi-antenna NOMA.
- NOMA decoding: SIC decoding order is determined by sorting users according to their channel gains.
- Power allocation: For sum-rate maximization, each user first receives the minimum power needed for its rate requirement, and remaining power goes to the best channel.
- Power allocation: The sum rate is then expressed using the resulting power-allocation scheme.
- Scope limitation: With multiple pinching antennas in NOMA, user channel gains contain sums of complex numbers, complicating closed-form placement derivation under interference and SIC.The paper identifies sophisticated optimization as a future research direction.
IV. SIMULATION RESULTS
Simulations compare pinching-antenna and conventional fixed-antenna systems across transmit power, access scheme, service area, and antenna count. Pinching antennas achieve higher sum rates, with gains depending on the deployment and access scheme.
- Simulation setup: The simulations use four users and compare against a fixed antenna deployed at (0, 0, d), with fc = 28 GHz, d = 3m, and σ2 = −90 dBm.
- Single-antenna results: For one pinching antenna, sum rate increases with transmit power for all schemes, and pinching antennas outperform fixed antennas under both TDMA and NOMA.
- Single-antenna results: With one pinching antenna, the performance gain is less obvious in NOMA than TDMA because TDMA permits movement toward each served user, whereas NOMA uses one pre-designed position.
- Multiple-antenna results: With multiple antennas under TDMA, pinching antennas retain higher sum rates than fixed antennas, and sum rate increases as antenna count increases.
V. CONCLUSION
The paper proposes low-complexity pinching-antenna placement to maximize downlink sum rate, deriving closed-form placements across single-antenna OMA/NOMA and multiple-antenna OMA scenarios.
- Conclusion: The design targets sum-rate maximization for multiple downlink users while avoiding complex placement optimization.
- Conclusion: Closed-form placement expressions are derived for single-antenna TDMA and NOMA and multiple-antenna TDMA scenarios.
- Conclusion: Simulation results verify higher sum-rate performance than conventional fixed-antenna systems.