Downlink Beamforming with Pinching-Antenna Assisted MIMO Systems

• Flexible antenna technologies provide additional degrees of freedom for controlling effective end-to-end channel gains.Source: §I · p. 1

A. Pinching-Antenna Systems

• PAS uses low-cost dielectric materials with pinching elements that can be applied along dielectric waveguides for radiation.Source: A. Pinching-Antenna Systems · p. 1
• PAS can strengthen line-of-sight links by activating pinching elements close to the serving user.Source: A. Pinching-Antenna Systems · p. 1

B. Contributions

• Earlier PAS MIMO work considered a simple two-user scenario, leaving general multiuser downlink transmission unexplored.Source: B. Contributions · p. 1
• The proposed hybrid design jointly optimizes pinching-element locations and digital precoding to maximize weighted achievable sum-rate.Source: B. Contributions · pp. 1–2
• An iterative algorithm alternately optimizes the transmitter's digital precoder and pinching-element locations, with simulations showing higher sum-rate than fixed-location systems.Source: B. Contributions · p. 2

• 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].Source: §II · p. 2
• The access point feeds the waveguides to serve K single-antenna users distributed in a known two-dimensional area.Source: §II · p. 2
• The pinching element radiates a phase-shifted version of the waveguide signal, with phase determined by its location and the waveguide reflective index.Source: §II · p. 2

• The channel model assumes users are in line of sight of the waveguides and neglects non-line-of-sight paths as typically weaker.Source: A. Characterizing End-to-End Channel · p. 2
• The end-to-end channel is a function of the vector of pinching-element locations.Source: A. Characterizing End-to-End Channel · p. 2
• The effective channel coefficient depends on the distance between each pinching element and user, together with propagation and shadowing parameters.Source: A. Characterizing End-to-End Channel · p. 2
• Unlike IRS-assisted channels, PAS modifies each user's channel through phase shift and attenuation that depend on that user's element distances.Source: A. Characterizing End-to-End Channel · pp. 2–3

• The AP forms each waveguide's feeding signal as a linear combination of the K user signals.Source: B. Downlink Beamforming · p. 3
• The transmitted waveguide signal is represented by a beamforming matrix W subject to the power constraint tr{W W^H} ≤ P.Source: B. Downlink Beamforming · p. 3
• The received signal depends on both the digital beamforming matrix and the pinching-element location vector.Source: B. Downlink Beamforming · p. 3

• The digital precoder W and analog locations l are jointly designed in a hybrid beamforming problem.Source: §III · p. 3
• The received signal is formed from users’ digital beamforming vectors and additive noise.Source: §III · p. 3
• Each user’s achievable rate is log(1 + SINR), where SINR measures its desired signal relative to interference and noise.Source: §III · p. 3
• The objective is a weighted sum-rate with coefficients proportional to users’ expected quality of service.Source: §III · p. 3

• The access point maximizes weighted sum-rate subject to a power budget and physical waveguide limitations.Source: A. Optimal Beamforming Design · p. 3
• The optimization is non-convex, so the global solution is infeasible to compute and is approximated by an efficient suboptimal algorithm.Source: A. Optimal Beamforming Design · p. 3
• Every optimal solution satisfies the transmit-power constraint with equality.Source: A. Optimal Beamforming Design · p. 3
• Scaling any underpowered solution to meet the power budget preserves feasibility and improves the objective, ruling out an optimal solution with unused power.Source: A. Optimal Beamforming Design · p. 3
• For fixed locations, the optimal hybrid beamforming can be obtained through an equivalent reformulated optimization involving the weighted-rate objective.Source: A. Optimal Beamforming Design · p. 3
• The reformulated problem expresses the design in terms of the weighted rates and user SINRs.Source: A. Optimal Beamforming Design · p. 3

• The variational formulation maximizes a sum of log ratios and is approximated using fractional programming.Source: B. Variational Solution via Fractional… · p. 4
• The transformed problem has the same optimal objective value as the original variational problem, but remains non-convex.Source: B. Variational Solution via Fractional… · p. 4
• Block coordinate descent alternates between optimizing the auxiliary variables for fixed beamforming and location variables and updating those design variables.Source: B. Variational Solution via Fractional… · p. 4
• The fixed-design marginal problem is converted into a quadratic form through the quadratic transform.Source: B. Variational Solution via Fractional… · p. 4
• A two-tier BCD algorithm is used because non-convexity persists through auxiliary variables, multiplicative expressions, and the channel dependence on locations.Source: B. Variational Solution via Fractional… · p. 4

• The outer loop alternates updates of auxiliary variables q and the design variables s = (W, l).Source: C. Two-tier Iterative Algorithm · p. 4
• The inner problem is non-convex because the channel and precoder appear multiplicatively, but it is marginally convex in W and G(l).Source: C. Two-tier Iterative Algorithm · p. 4
• With locations fixed, the precoder update reduces to regularized zero-forcing using an effective channel.Source: C. Two-tier Iterative Algorithm · p. 4
• The location update sequentially optimizes each antenna position while treating the other positions as fixed.Source: C. Two-tier Iterative Algorithm · p. 4
• Each scalar location objective is optimized over a fixed interval using grid search.Source: C. Two-tier Iterative Algorithm · p. 4
• Gradient-based methods are unsuitable because cosine oscillations create numerous stationary points in the scalar objective.Source: C. Two-tier Iterative Algorithm · p. 4
• Algorithm 1 repeats auxiliary-variable, precoder, and location updates until the objective increase falls below ϵ, then scales W.Source: C. Two-tier Iterative Algorithm · p. 5

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.Source: D. Overall Algorithm, Convergence, and… · p. 5
• The objective value is nondecreasing across block updates and bounded above by the power constraint, guaranteeing convergence of Algorithm 1.Source: D. Overall Algorithm, Convergence, and… · p. 5

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.Source: §IV · p. 5
• 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.Source: §IV · p. 5

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.Source: §IV · p. 5
• Sum-rates for both PAS and the baseline decrease monotonically as the number of users K increases, primarily because of increased inter-user interference.Source: §IV · p. 5
• 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.Source: §IV · pp. 5–6
• 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.Source: §IV · p. 6, Figure 3 · p. 6

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.Source: §V · p. 6
• Numerical experiments validate the effectiveness of the proposed PAS-aided beamforming design.Source: §V · p. 6
• PAS-aided MIMO achieves superior throughput compared with conventional fixed-location designs, highlighting its potential for next-generation wireless networks.Source: §V · p. 6