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Downlink Beamforming with Pinching-Antenna Assisted MIMO Systems
Ali Bereyhi, Saba Asaad, Chongjun Ouyang, Zhiguo Ding, H. Vincent Poor
TL;DR
This paper studies multiuser downlink beamforming with pinching-antenna systems, addressing joint optimization of digital precoding and pinching-element locations. It develops an iterative fractional-programming and block-coordinate-descent design and reports higher throughput than conventional fixed-location antenna systems.
Problem
The paper investigates the unexplored potential of PAS for general multiuser downlink transmission beyond earlier simple two-user studies.
Method
The proposed hybrid beamforming design jointly optimizes the AP's digital precoder and pinching-element locations using a low-complexity iterative algorithm based on fractional programming and block coordinate descent.
Results
PAS achieves significantly higher throughput than conventional fixed-location antenna systems in numerical experiments.
Takeaways & Limitations
PAS shows potential for improving throughput in next-generation wireless systems while using flexible, low-cost pinching elements.
Abstract
from arXiv · showhide
Pinching antennas have been recently proposed as a promising flexible-antenna technology, which can be implemented by attaching low-cost pinching elements to dielectric waveguides. This work explores the potential of employing pinching antenna systems (PASs) for downlink transmission in a multiuser MIMO setting. We consider the problem of hybrid beamforming, where the digital precoder at the access point and the activated locations of the pinching elements are jointly optimized to maximize the achievable weighted sum-rate. Invoking fractional programming, a novel low-complexity algorithm is developed to iteratively update the precoding matrix and the locations of the pinching antennas. We validate the proposed scheme through extensive numerical experiments. Our investigations demonstrate that using PAS the system throughput can be significantly boosted as compared with the conventional fixed-location antenna systems, enlightening the potential of PAS as an enabling candidate for next-generation wireless networks.
I. INTRODUCTION
Flexible antenna technologies reconfigure wireless channels, while PAS offers a low-cost way to position radiating elements near users. This work addresses multiuser downlink transmission by jointly optimizing pinching-element locations and digital precoding to maximize weighted sum-rate.
- Flexible antenna technologies provide additional degrees of freedom for controlling effective end-to-end channel gains.
- A. Pinching-Antenna Systems: PAS uses low-cost dielectric materials with pinching elements that can be applied along dielectric waveguides for radiation.
- A. Pinching-Antenna Systems: PAS can strengthen line-of-sight links by activating pinching elements close to the serving user.
- B. Contributions: Earlier PAS MIMO work considered a simple two-user scenario, leaving general multiuser downlink transmission unexplored.
- B. Contributions: The proposed hybrid design jointly optimizes pinching-element locations and digital precoding to maximize weighted achievable sum-rate.
- B. Contributions: An iterative algorithm alternately optimizes the transmitter's digital precoder and pinching-element locations, with simulations showing higher sum-rate than fixed-location systems.
II. SYSTEM MODEL AND PROBLEM FORMULATION
The system uses multiple dielectric waveguides with movable pinching elements to serve single-antenna users. Element locations are design variables because they determine the radiating positions along the waveguides.
- Each of M dielectric waveguides carries a pinching element that can move freely along the waveguide.The element location on waveguide m is represented by v_m = [ℓ_m, (m −1)d, a].
- The access point feeds the waveguides to serve K single-antenna users distributed in a known two-dimensional area.
- The pinching element radiates a phase-shifted version of the waveguide signal, with phase determined by its location and the waveguide reflective index.
A. Characterizing End-to-End Channel
The end-to-end channel is modeled under line-of-sight propagation and depends on pinching-element locations. Moving elements changes user-specific phase and attenuation through their distances to users.
- The channel model assumes users are in line of sight of the waveguides and neglects non-line-of-sight paths as typically weaker.
- The end-to-end channel is a function of the vector of pinching-element locations.
- The effective channel coefficient depends on the distance between each pinching element and user, together with propagation and shadowing parameters.
- Unlike IRS-assisted channels, PAS modifies each user's channel through phase shift and attenuation that depend on that user's element distances.
B. Downlink Beamforming
Downlink transmission uses linear digital beamforming across waveguides, while the received signal depends jointly on the digital precoder and pinching-element locations. This creates a hybrid beamforming design problem.
- The AP forms each waveguide's feeding signal as a linear combination of the K user signals.
- The transmitted waveguide signal is represented by a beamforming matrix W subject to the power constraint tr{W W^H} ≤ P.
- The received signal depends on both the digital beamforming matrix and the pinching-element location vector.
III. HYBRID BEAMFORMING DESIGN
The design jointly optimizes the digital precoder and pinching-element locations as a hybrid beamforming problem. Its objective is the weighted sum-rate determined by users’ SINRs and quality-of-service weights.
- The digital precoder W and analog locations l are jointly designed in a hybrid beamforming problem.
- The received signal is formed from users’ digital beamforming vectors and additive noise.
- Each user’s achievable rate is log(1 + SINR), where SINR measures its desired signal relative to interference and noise.
- The objective is a weighted sum-rate with coefficients proportional to users’ expected quality of service.
A. Optimal Beamforming Design
The optimal design maximizes weighted sum-rate under power and physical waveguide constraints. Because the problem is non-convex, the paper establishes full-power operation and reformulates the design for tractable optimization.
- The access point maximizes weighted sum-rate subject to a power budget and physical waveguide limitations.
- The optimization is non-convex, so the global solution is infeasible to compute and is approximated by an efficient suboptimal algorithm.
- Every optimal solution satisfies the transmit-power constraint with equality.
- Scaling any underpowered solution to meet the power budget preserves feasibility and improves the objective, ruling out an optimal solution with unused power.
- For fixed locations, the optimal hybrid beamforming can be obtained through an equivalent reformulated optimization involving the weighted-rate objective.
- The reformulated problem expresses the design in terms of the weighted rates and user SINRs.
B. Variational Solution via Fractional Programming
The weighted-rate problem is transformed into a variational form and approximated using fractional programming. A block coordinate descent procedure then alternates between marginal updates, followed by quadratic transformation for smoother optimization.
- The variational formulation maximizes a sum of log ratios and is approximated using fractional programming.
- The transformed problem has the same optimal objective value as the original variational problem, but remains non-convex.
- Block coordinate descent alternates between optimizing the auxiliary variables for fixed beamforming and location variables and updating those design variables.
- The fixed-design marginal problem is converted into a quadratic form through the quadratic transform.
- A two-tier BCD algorithm is used because non-convexity persists through auxiliary variables, multiplicative expressions, and the channel dependence on locations.
C. Two-tier Iterative Algorithm
The iterative algorithm alternates updates of fractional-programming variables, digital precoding, and antenna locations. Location updates use sequential scalar optimization, with grid search preferred because oscillatory objectives create many stationary points.
- The outer loop alternates updates of auxiliary variables q and the design variables s = (W, l).
- The inner problem is non-convex because the channel and precoder appear multiplicatively, but it is marginally convex in W and G(l).
- With locations fixed, the precoder update reduces to regularized zero-forcing using an effective channel.
- The location update sequentially optimizes each antenna position while treating the other positions as fixed.
- Each scalar location objective is optimized over a fixed interval using grid search.
- Gradient-based methods are unsuitable because cosine oscillations create numerous stationary points in the scalar objective.
- Algorithm 1 repeats auxiliary-variable, precoder, and location updates until the objective increase falls below ϵ, then scales W.
D. Overall Algorithm, Convergence, and Complexity
The FP-BCD algorithm alternates block updates for the beamforming and antenna-location variables. Its objective is nondecreasing and bounded, ensuring convergence, while each update uses either a closed-form solution or a low-complexity one-dimensional search.
- Overall Algorithm, Convergence, and Complexity: FP-BCD updates the optimization variables through block coordinate descent, with each block solved by a closed-form method or low-complexity one-dimensional search.The algorithm is described as computationally efficient because its individual updates avoid high-complexity optimization procedures.
- Overall Algorithm, Convergence, and Complexity: The objective value is nondecreasing across block updates and bounded above by the power constraint, guaranteeing convergence of Algorithm 1.
IV. NUMERICAL INVESTIGATIONS
Numerical experiments compare PAS with conventional fixed-location antennas under specified simulation settings. PAS achieves higher throughput, with gains that increase in larger deployment areas, while the proposed algorithm converges across tested antenna counts.
- Experimental Setting: The experiments use uniformly distributed users in a square region, uniform weighting, free-space path loss, and a 28 GHz carrier frequency.The waveguides are placed at height a = 3 m and span the region.
- Experimental Setting: The experiments average results over 500 random channel realizations and use the conventional fixed-location antenna system as the baseline.The baseline deploys M half-wavelength-spaced antennas along the y-axis within the square region.
- Numerical Results: 6 dB gain is achieved by PAS over the fixed-antenna baseline when FP-BCD is used, increasing to 11 dB against conventional ZF beamforming.The comparison is based on weighted sum-rate versus maximum total transmit power.
- Numerical Results: Sum-rates for both PAS and the baseline decrease monotonically as the number of users K increases, primarily because of increased inter-user interference.
- Numerical Results: PAS performance gains over the baseline grow as the square-region side length D increases.The conventional setting suffers higher path loss as users move farther from the center, whereas PAS can position elements closer to users.
- Numerical Results: The weighted sum-rate gradually increases with iterations and converges to a stable value for all tested numbers of antenna elements M.Figure 3 reports convergence under P = 20 dBm, D = 30 m, and K = 4.
V. CONCLUSION
The paper develops a joint beamforming design for PAS-aided multiuser MIMO and validates it numerically. The results report higher throughput than conventional fixed-location designs and indicate PAS potential for future wireless networks.
- Conclusion: The proposed design jointly optimizes the digital beamformer and pinching-element locations using fractional programming and block coordinate descent.The objective is to maximize achievable sum-rate in a multiuser MIMO downlink.
- Conclusion: Numerical experiments validate the effectiveness of the proposed PAS-aided beamforming design.
- Conclusion: PAS-aided MIMO achieves superior throughput compared with conventional fixed-location designs, highlighting its potential for next-generation wireless networks.