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Antenna Activation for NOMA Assisted Pinching-Antenna Systems
Kaidi Wang, Zhiguo Ding, Robert Schober
TL;DR
The paper addresses how many pinching antennas to activate and where to place them among preconfigured waveguide positions in a NOMA downlink. It formulates sum-rate maximization as a one-sided matching problem and develops a low-complexity activation algorithm. Simulations show higher sum rate than conventional fixed-antenna systems and strong performance from the matching-based method.
Problem
The paper asks how to select the locations and number of activated pinching antennas to maximize throughput in a NOMA-assisted downlink system.
Method
The paper formulates antenna activation as sum-rate maximization and recasts it as one-sided matching between antennas and preconfigured positions.
Results
The matching-based algorithm achieves around 99% of the global-optimal performance within 20 iterations.
Takeaways & Limitations
The considered NOMA-assisted pinching-antenna system outperforms conventional fixed-antenna systems in sum rate, while matching-based activation provides a low-complexity near-optimal solution.
Abstract
from arXiv · showhide
In this letter, a non-orthogonal multiple access (NOMA) assisted downlink pinching-antenna system is investigated, where multiple pinching antennas can be activated at pre-configured positions along a dielectric waveguide to serve users via NOMA. In particular, the objective of this letter is to study at what locations and how many pinching antennas should be activated in order to maximize the system throughput. To this end, a sum rate maximization problem with antenna activation is formulated. With the help of matching theory, the formulated problem can be recast as a one-sided one-to-one matching, for which a low-complexity algorithm is developed. Simulation results indicate that the considered NOMA assisted pinching-antenna system can outperform conventional fixed-antenna systems in terms of sum rate, and the proposed matching based antenna activation algorithm yields a significant performance gain over the considered benchmarks.
I. INTRODUCTION
The paper studies practical antenna activation for NOMA-assisted pinching-antenna systems, using preconfigured waveguide positions rather than arbitrary continuous placement. It formulates sum-rate maximization and develops matching-based activation for selecting antenna locations and quantity.
- Motivation: Pinching-antenna systems use low-cost dielectric materials and can reconfigure antenna locations along a waveguide, addressing limitations of wavelength-scale position variation.Existing flexible-antenna systems may have limited movement ranges and high costs, while pinching antennas are proposed as a practical alternative.
- System motivation: Because activated pinching antennas on one waveguide transmit the same signal, the system applies NOMA to serve users simultaneously.The single-radio-frequency-chain architecture requires user signals to be superimposed before transmission.
- Practical design: The proposed implementation installs antennas at preconfigured positions and activates only a subset, converting continuous placement into discrete antenna-selection variables.The system is designed to reduce implementation complexity while selecting useful antenna locations for downlink transmission.
- System model: A waveguide of length D1 contains L uniformly spaced candidate positions, with adjacent spacing D1/(L−1) constrained to be at least half a wavelength.The BS serves N single-antenna users with K activated antennas, where K ≤ L.
- Signal model: The channel model incorporates free-space propagation, waveguide phase shifts, and attenuation for antennas activated at selected positions.The transmitted signal includes antenna-dependent power and phase terms, with λg = λ/neff describing the guided wavelength.
B. Antenna Activation Principle and SIC Decoding Design
The system represents activated antennas as a selected subset of candidate positions and evaluates NOMA rates using effective-channel ordering for successive interference cancellation. Equal antenna power allocation and waveguide attenuation are included in the model.
- Antenna activation: Antenna activation selects a subset S of the L available positions, with |S| constrained by the available antenna count.The activated set determines the received signal and the normalized channel used for rate evaluation.
- Power and propagation: The model assumes equal transmit-power allocation across activated antennas while accounting for dielectric-waveguide attenuation κ.κ = 0 is the special case of a lossless dielectric and perfectly conducting surface.
- SIC decoding: NOMA successive interference cancellation orders users by effective channel gain, from weakest to strongest.User (m) decodes and removes symbols for users with lower ordered indices, then treats higher-index symbols as interference.
- SIC decoding: The strongest-channel user can remove the other users’ symbols before decoding its own signal.Achievable rates use power-allocation coefficients and residual interference or noise according to the decoding order.
C. Antenna Activation Problem Formulation
The paper formulates antenna activation as a sum-rate maximization problem because user rates depend on the selected antenna positions. The formulation restricts activation to preconfigured locations and limits the number of activated antennas.
- Objective: The selected antenna-position set S affects users’ achievable rates, motivating optimization of S for maximum spectral efficiency.The paper denotes the optimal activated-position set by S* and formulates sum-rate maximization around it.
- Constraints: The optimization constrains activated antennas to preconfigured positions.This implements the paper’s practical discrete-position assumption.
- Constraints: The number of activated antennas cannot exceed the number of available antennas.This cardinality constraint limits the feasible activated-position sets.
III. MATCHING BASED ANTENNA ACTIVATION
The antenna-activation integer program is recast as a one-sided matching between antennas and candidate positions, enabling a low-complexity solution for selecting the activated set.
- Matching formulation: Matching theory constructs assignments between antennas K and positions L to obtain the optimal activated-position set S*.The matching formulation addresses the original challenging integer programming problem.
A. Formulation of One-Sided Matching
The antenna activation problem is modeled as a one-sided one-to-one matching between pinching antennas and positions, with unmatched players allowed. Each antenna can occupy at most one position, and each position can be assigned to at most one antenna.
- A. Formulation of One-Sided Matching: The problem is defined as a one-sided one-to-one matching between pinching antennas and antenna positions, with both sides permitted to remain unmatched.Only antennas have preferences over positions, while unmatched states are allowed for antennas and positions.
- A. Formulation of One-Sided Matching: Each pinching antenna is mapped to one position or to the unmatched state ∅.The mapping satisfies Φ(k) ∈ L ∪ {∅} for every antenna k.
- A. Formulation of One-Sided Matching: Each pinching antenna can be assigned to at most one position.This is the cardinality condition |Φ(k)| = {0, 1}.
- A. Formulation of One-Sided Matching: Each antenna position cannot be occupied by more than one pinching antenna.If Φ(k) = l, then no other antenna k′ can be mapped to l.
B. Design of Matching Based Antenna Activation Algorithm
The activation algorithm constructs antenna preferences from sum-rate changes and iteratively adjusts antenna-position assignments or deactivates antennas when these moves improve utility. It starts from a random full matching and stops when no antenna can be adjusted during a complete cycle.
- B. Design of Matching Based Antenna Activation Algorithm: Antenna preferences are constructed from the system sum rate, with each user’s data rate contributing to the utility.The utility is the sum of user data rates, U(Φ) = Σ_n∈N R_n(Φ).
- B. Design of Matching Based Antenna Activation Algorithm: The matching has externalities because changing one antenna alters channel conditions and received signals for all users.Consequently, an antenna’s preference depends on the other antennas’ assignments.
- B. Design of Matching Based Antenna Activation Algorithm: An antenna prefers a new position when the resulting matching strictly increases utility.The comparison evaluates the current assignment against a candidate assignment at another position.
- B. Design of Matching Based Antenna Activation Algorithm: A candidate reassignment is accepted when the antenna prefers it to the current matching; otherwise, the algorithm can accept deactivation when that alternative improves utility.The update rules compare candidate positions and the unmatched state ∅ against the current assignment.
- B. Design of Matching Based Antenna Activation Algorithm: The solution is characterized through the core, where no alternative matching weakly benefits every antenna while strictly benefiting at least one.This is the blocking condition used in the core definition.
- B. Design of Matching Based Antenna Activation Algorithm: The algorithm begins by randomly matching pinching antennas and positions, with all antennas activated in the initial matching.The initial matching is denoted Φ0, after which antennas are examined sequentially across candidate positions.
- B. Design of Matching Based Antenna Activation Algorithm: The algorithm terminates when no antenna can be adjusted during a complete cycle, and the final matching yields the solution ψPin of the activation problem.The solution is obtained through the final matching after the main loop stops.
C. Properties Analysis for the Proposed Algorithm
This subsection analyzes the properties of the proposed matching based antenna activation algorithm.
- C. Properties Analysis for the Proposed Algorithm: The subsection analyzes the properties of the proposed matching based antenna activation algorithm.
1) Complexity:
The algorithm’s worst-case complexity is determined by evaluating every antenna-position pair across a fixed number of cycles.
- 1) Complexity:: O(CKL) is the worst-case computational complexity for K antennas, L positions, and C cycles.Each complete cycle performs KL computations when all antennas attempt activation at all positions.
2) Convergence:
The matching-based algorithm records successive antenna-position assignments that strictly increase utility. Because the matching space is finite, this monotonic process converges to a final matching that cannot be further improved.
- Convergence:: Each successful antenna reassignment or deactivation transforms the current matching into a new matching with strictly higher utility.The algorithm records a new matching whenever an antenna is assigned to a position.
- Convergence:: The utility sequence is strictly increasing from the initial matching through the final matching.U(Φ0) < U(Φ1) < U(Φ2) < ··· < U(Φfinal).
- Convergence:: Because the numbers of antennas and candidate locations are finite, only finitely many matchings are possible.
- Convergence:: The proposed matching-based algorithm is guaranteed to converge to a final matching whose utility cannot be further increased.
3) Stability:
The proposed matching-based activation algorithm is stable, improves sum rate over fixed and benchmark activation schemes, and approaches the global optimum with few iterations. Results also show that antenna count and placement should be jointly optimized for throughput.
- 3) Stability:: The final matching produced by Algorithm 1 is always stable because no antenna reassignment or deactivation can further increase its utility.The stability argument follows from contradiction with the algorithm’s final matching condition.
- Simulation results: The pinching-antenna system outperforms the conventional fixed-antenna system in sum rate, with the gap increasing as the rectangular area length grows.The conventional system suffers worsening channel gains with length, whereas only comparatively insignificant waveguide propagation loss increases for pinching antennas.
- Simulation results: Matching-based activation dynamically adjusts antenna locations according to propagation loss, making performance less sensitive to that loss.Across schemes, nonzero waveguide propagation loss causes only a slight sum-rate reduction, indicating that free-space path loss is dominant.
- Simulation results: The matching-based activation algorithm achieves the best performance among the evaluated activation schemes as transmit power increases.The comparison includes random activation and distance-based activation benchmarks.
- Simulation results: As the number of available positions grows, sum rate increases and more antennas are activated because positions can be adjusted more precisely.Fewer users reduce both the sum rate and required antenna count, while the effect of activated-antenna count is otherwise scenario dependent.
- Simulation results: Around 99% of the global-optimal performance is reached within 20 iterations, supporting the algorithm’s characterization as low-complexity and near-optimal.Exhaustive search also shows that a higher sum rate can be obtained with fewer pinching antennas, highlighting the importance of optimizing activation count.
V. CONCLUSIONS
The letter studies antenna activation in a NOMA-assisted pinching-antenna system and formulates activation over potential positions as a matching problem. A low-complexity matching-based algorithm is proposed, and simulations demonstrate benefits for the system and algorithm.
- A sum rate maximization problem is formulated for antenna activation in a NOMA-assisted pinching-antenna system.
- The formulation is treated as a one-sided matching problem over potential pinching-antenna positions.
- A low-complexity matching-based antenna activation algorithm obtains a near-optimal solution.
- Simulation results reveal benefits from the considered pinching-antenna system and the proposed matching-based algorithm.