Minimum Data Rate Maximization for Uplink Pinching-Antenna Systems

• Centralized MIMO can mitigate small-scale fading, but its performance still degrades as path loss increases, a concern for uplink connectivity.The introduction connects uplink effectiveness to edge computing and intelligence.Source: §I · p. 1
• PAs activate selected points along a waveguide to control radiation locations, enabling flexible deployment and dynamically established LoS links.The paper presents this as a way to mitigate LoS blockage and path loss.Source: §I · p. 1
• The paper formulates multi-user PA uplink design as maximizing the minimum device data rate to balance system throughput and user fairness.Source: §I · pp. 1–2
• The proposed approach separately optimizes PA positions and resource allocation, reformulating antenna positioning as a convex problem and deriving a closed-form resource-allocation solution.Simulations report superior performance over corresponding counterparts.Source: §I · p. 2

• The uplink system has a BS with N PAs and M single-antenna devices randomly placed in a rectangular area in the x-y plane.Device positions are ψ_m = (x_m, y_m, 0), with x_m and y_m drawn uniformly over the stated area dimensions.Source: §II · p. 2
• The model treats each PA's transmitted signal as a phase-shifted replica of the waveguide feed signal and defines the guided wavelength using the free-space wavelength and effective refractive index.The waveguide is described as parallel to the x-axis and of length D_x.Source: §II · p. 2
• The received-signal model includes additive white Gaussian noise, with the denominator's N accounting for noise and interference at each PA.Source: §II · p. 2
• The BS is assumed to know device positions, and PA operation allows configuration of channel phase shifts and path loss.Source: §II · p. 2
• OMA, including TDMA or FDMA, is used, and PA positions remain unchanged when serving different devices.The model defines each device's allocated resource share as the product of its bandwidth and time portions.Source: §II · p. 2

• A shared set of PA positions couples device rates, since placement that improves one device can potentially degrade others.The formulation therefore targets fairness alongside overall system performance.Source: §III · p. 2
• The optimization maximizes the minimum achievable device rate by choosing PA positions and the resource-allocation vector.Source: §III · p. 3
• The constraints enforce minimum spacing between adjacent PAs to avoid coupling effects and limit the resource blocks allocated among devices.Source: §III · p. 3
• The solution separates PA-position optimization with fixed power allocation from resource allocation with fixed PA positions.Source: §III · p. 3

A. Optimization of PA Positions

• Positioning must align phases and favor path losses for all devices, making the shared-antenna design challenging.The optimization targets close phase alignment for each device while balancing the effects of antenna placement across users.Source: A. Optimization of PA Positions · p. 3
• Weighted squared phase errors are bounded by ε relative to a per-device phase, with weights tied to distances from starting PA positions.For M=N, one PA is initially placed above each device; the weights are defined to support fairness and reduce path loss, and when M≠N, expression (7) must be modified.Source: A. Optimization of PA Positions · p. 3
• Auxiliary variables and second-order cone programming reformulate the fixed-allocation rate objective and constraints, while SCA linearizes the remaining non-convex constraint.The non-convex term is approximated by a first-order Taylor expansion around updated initial points, yielding a convex form.Source: A. Optimization of PA Positions · pp. 3–4

B. Resource Allocation

• The resource-allocation subproblem is convex because its objective and constraints C3 and C4 are linear, and the rate function is concave for nonnegative allocation.The paper gives the second derivative of the rate function with respect to q_m as negative for q_m ≥ 0.Source: B. Resource Allocation · p. 4
• Setting the allocation Lagrangian’s derivative to zero gives each device’s optimal resource allocation in closed form using the Lambert W function.The Lagrange multipliers are nonnegative.Source: B. Resource Allocation · p. 4
• The algorithm searches squared-error bounds with SCA for PA positions, stores the best-rate positions, then computes resource allocation in closed form; it converges with O(N^3) complexity.The stated complexity is driven by the interior-point solution of the positioning subproblem; closed-form allocation has negligible complexity.Source: B. Resource Allocation · p. 4
• PA positions remain fixed across served devices; per-slot TDMA repositioning is possible but costly and complex, while simultaneous FDMA service precludes it.The fixed-position assumption is presented as a practical alternative to instantaneous antenna reconfiguration.Source: B. Resource Allocation · p. 4

IV. NUMERICAL RESULTS

• The proposed framework is compared with optimized PA positions using equal resource allocation and with a conventional system whose BS antennas are fixed at the area edge.The simulations use a 30×10 m² area and parameters including −90 dBm noise power and a 28 GHz carrier frequency.Source: §IV · p. 4
• More than 5 dB gain for M=N=2 and approximately 3 dB gain for M=N=3 are reported for the proposed method over the conventional system.Figs. 2 and 3 show maximum minimum achievable data rate versus transmit power for different device and PA counts at d=3 m and d=4 m.Source: Figure 2 · p. 5, Figure 3 · p. 5, §IV · p. 5
• Rates increase with transmit power, while denser configurations have flatter slopes; at d=4 m, rates are slightly lower because of increased path loss.The improvement over the conventional system remains evident at both heights considered.Source: §IV · p. 5
• For M=N=4, the gain becomes more limited as simultaneous phase alignment across devices becomes harder.The paper also reports that PA positioning affects performance more than resource allocation, which supports prioritizing antenna placement in the design.Source: §IV · p. 5

V. CONCLUSIONS

• The proposed framework maximizes the minimum achievable data rate across devices to promote fairness in PA uplinks.It decouples antenna positioning and resource allocation.Source: §V · p. 5
• Simulations validate the approach and show improvements in addressing line-of-sight blockage and large-scale path loss.Source: §V · p. 5
• The authors describe PA technology as promising for practical and scalable next-generation communication solutions.Source: §V · p. 5