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RIS-Assisted Downlink Pinching-Antenna Systems With NLOS Environments
Yue Geng, Kah Chan Teh, Tee Hiang Cheng
TL;DR
Physically constrained PASS can leave users with obstacle-blocked direct links, while prior RIS-assisted PASS studies mainly considered LOS users. The paper uses ZF-based alternating optimization to jointly optimize RIS reflection coefficients and PA positions, reporting lower transmit power and execution time than element-wise 1-D search.
Problem
Prior RIS-assisted PASS studies mainly considered LOS users, while obstacles can block direct links for users outside the constrained installation range of PASS.
Source: §I · p. 1Method
The paper uses ZF beamforming and alternating optimization to jointly optimize RIS reflection coefficients and PA activation positions for transmit-power minimization.
Source: §V · p. 6Results
1.28 dB average reduction in transmit power versus the “1-D search” scheme; overall, the proposed AO achieves lower transmit power and substantially reduced execution time.
Source: §IV · p. 5, §V · p. 6Takeaways & Limitations
Joint gradient updates reduce execution-time growth as RIS elements, waveguides, or PAs increase, making the method more suitable for practical implementation.
Source: §IV · p. 6
Abstract
from arXiv · showhide
This paper investigates a reconfigurable intelligent surface (RIS)-assisted downlink pinching-antenna system (PASS) in the presence of non-line-of-sight (NLOS) users caused by unavoidable obstacles. An RIS is deployed to extend the coverage of the physically constrained PASS by establishing virtual line-of-sight (LOS) links. To improve system performance, we propose a zero-forcing (ZF) beamforming-based alternating optimization (AO) framework that minimizes the transmit power by jointly optimizing the RIS reflection coefficients and pinching-antenna (PA) activation positions. Specifically, the RIS reflection coefficients are optimized using the Riemannian conjugate gradient (RCG) method, while a novel projected gradient-based method is developed to efficiently optimize the PA activation positions. Simulation results demonstrate that the proposed AO framework outperforms baseline schemes in terms of both transmit power and computational efficiency under different system configurations including the rate requirements and RIS sizes.
I. INTRODUCTION
RIS and PASS offer complementary control of wireless propagation and antenna positions, and their integration has been studied mainly for LOS users. This paper addresses the largely unexplored mixed LOS/NLOS setting, where RIS-reflected virtual LOS links can extend PASS coverage beyond its constrained direct-link region.
I. INTRODUCTION
- RIS controls propagation through adjustable passive phase shifts, while PASS adjusts PA positions along dielectric waveguides to add spatial degrees of freedom.PASS can also jointly position multiple PAs to control signal phases and realize pinching beamforming.Source: §I · p. 1
- Earlier RIS-assisted PASS work added a configurable reflected link to enhance a single user’s capacity or jointly optimized PA positions and RIS phases with a GNN.These studies are described as primarily serving users through LOS links.Source: §I · p. 1
- Obstacles can block direct links for users beyond PASS’s constrained installation range, limiting coverage; RIS can provide virtual LOS paths around them.The corresponding RIS-assisted PASS system optimization for NLOS environments remains largely unexplored.Source: §I · p. 1
- The paper formulates transmit-power minimization and develops an AO framework centered on PA positioning for mixed LOS/NLOS users.PA positions affect both LOS channels and the RIS-assisted NLOS-user channel, a positioning problem not studied in prior mixed-user RIS-assisted PASS systems.Source: §I · p. 1
II. SYSTEM MODEL AND PROBLEM FORMULATION
The system combines a PASS with an RIS to serve LOS and NLOS users around an obstacle. The paper formulates ZF transmit-power minimization over RIS reflection coefficients and PA activation positions, subject to QoS and hardware-related constraints.
II. SYSTEM MODEL AND PROBLEM FORMULATION
- The model places the PASS on an exterior wall and uses a one-dimensional RIS beside the obstacle to assist LOS and NLOS users.The RIS is described as a half-wavelength-spaced uniform linear array; the system considers one single-antenna user in each region.Source: §II · pp. 1–2
- The channel model omits in-waveguide propagation loss because it is treated as negligible relative to free-space path loss.Source: §II · p. 2
- ZF beamforming is adopted to satisfy both users’ rate thresholds when RIS coefficients and PA positions are fixed.The paper assumes the channel matrix has full row rank for the stated ZF beamformer.Source: §II · pp. 2–3
- The optimization minimizes ZF transmit power over RIS reflection coefficients and PA activation positions in the mixed LOS/NLOS system.The formulation’s non-convex objective, constraints, and coupled variables motivate the AO framework.Source: §II · p. 3
- The formulation constrains PA spacing to avoid coupling, keeps PAs on their waveguides, and imposes unit modulus on RIS reflection coefficients.Source: §II · p. 3
III. THE PROPOSED AO-BASED FRAMEWORK
The proposed framework solves the formulated problem by alternating between RIS reflection-coefficient optimization and PA activation-position optimization.
III. THE PROPOSED AO-BASED FRAMEWORK
- The AO framework alternately optimizes RIS reflection coefficients and PA activation positions to solve the formulated problem.Source: §III · p. 3
A. RIS Reflection Coefficients Optimization
With PA positions fixed, the RIS coefficient subproblem is treated as optimization on a complex circle manifold. The paper uses the standard RCG method for this subproblem.
A. RIS Reflection Coefficients Optimization
- With PA positions fixed, the RIS coefficient subproblem lies on the complex circle manifold defined by unit-modulus coefficients.Source: A. RIS Reflection Coefficients… · p. 3
- The authors use standard RCG to solve the smooth, unconstrained Riemannian RIS coefficient problem.Implementation details are omitted, with readers referred to –.Source: A. RIS Reflection Coefficients… · p. 3
B. PA Activation Position Optimization
With the RIS reflection coefficients fixed, this section optimizes PA activation positions using a projected gradient-based method.
B. PA Activation Position Optimization
- With the RIS reflection coefficients fixed, the section formulates an optimization problem for the PA activation positions.Source: B. PA Activation Position Optimization · p. 3
- A projected gradient-based method is developed to solve the PA position problem.Source: B. PA Activation Position Optimization · p. 3
1) Obtain the Gradient and Step Size:
The PA-position objective is differentiable, so its gradient is obtained with respect to the activation positions; a Barzilai–Borwein step size adapts the gradient update.
1) Obtain the Gradient and Step Size:
- The PA-position objective is continuously differentiable, and its gradient is taken with respect to the activation positions using channel vectors from Section II.Source: 1) Obtain the Gradient and Step Size · p. 3
- The Barzilai–Borwein spectral step size uses local curvature from successive iterates to adapt the gradient step at negligible additional computational cost.Source: 1) Obtain the Gradient and Step Size · p. 3
- The step size is safeguarded within a prescribed interval to avoid a negative value.Source: 1) Obtain the Gradient and Step Size · p. 3
2) Projection to the Feasible Set:
The unconstrained PA-position trial point is projected onto the feasible set, whose waveguide-specific constraints reduce to bounded isotonic regression solved efficiently with PAVA.
2) Projection to the Feasible Set:
- The gradient-descent trial point may violate PA feasibility constraints, so it is projected onto the feasible set before updating positions.Source: 2) Projection to the Feasible Set · p. 3
- The projection constraints are separable across waveguides, and each waveguide's bounded isotonic regression can be solved with PAVA.Source: 2) Projection to the Feasible Set · pp. 3–4
- For each waveguide, the PA-spacing and length constraints are converted into a bounded monotonicity constraint for the projection problem.The bound is B = A − (N − 1)d_min.Source: 2) Projection to the Feasible Set · p. 4
- PAVA merges adjacent blocks that violate monotonicity and clips their block values to obtain feasible projected positions.Source: 2) Projection to the Feasible Set · p. 4
3) Update the PA Positions:
After projection, the method uses a feasible descent direction and Armijo backtracking to update PA positions within an alternating optimization loop.
3) Update the PA Positions:
- The projection-based update direction is a descent direction, and updates with step sizes in (0, 1] remain feasible.Source: 3) Update the PA Positions · p. 4
- Armijo backtracking selects the step size by starting at 1 and reducing it until the sufficient-decrease condition holds.Source: 3) Update the PA Positions · p. 4
- The AO loop updates RIS coefficients with RCG for fixed PA positions, then updates PA positions using the projected-gradient procedure until its stopping test is met.Source: 3) Update the PA Positions · p. 4
C. Initialization and Summary of the AO Method
The AO method initializes PA positions with a 1-D search and alternates RIS and PA updates. Its complexity scales with the RIS, waveguide, and PA counts, with an additional initialization search cost.
C. Initialization and Summary of the AO Method
- The initialization places PAs symmetrically around the RIS, optimizes RIS coefficients with RCG, then accepts sampled group centers only when they reduce ZF transmit power.The search samples S centers per waveguide while holding PA spacing and RIS coefficients fixed; the resulting AO objective is monotonically non-increasing and convergent.Source: C. Initialization and Summary of the… · p. 4
- The AO iterations have complexity O(I[Tϕ(1+Bϕ)+Tψ(1+Bψ)]LMN), while initialization adds O(SLM^2N).The RCG and projected-gradient stages each have iteration costs proportional to LMN, including their Armijo line-search steps.Source: C. Initialization and Summary of the… · pp. 4–5
IV. SIMULATION RESULTS
Simulations compare the proposed AO framework with placement baselines and a sequential 1-D search across rate requirements, RIS sizes, and PA configurations. AO achieves lower transmit power and execution-time growth than 1-D search in the reported comparisons.
IV. SIMULATION RESULTS
- Simulation results average 1,024 independent realizations of randomly generated LOS and NLOS user locations; the default PASS has four waveguides, four PAs per waveguide, and 36 RIS reflecting elements.Compared baselines place the PA array near the RIS, near the LOS user, or midway between their y-coordinates.Source: §IV · p. 5
- The proposed AO method reduces transmit power relative to the 1-D search scheme by 0.83 dB at L = 24 and 1.60 dB at L = 48, with its advantage increasing as L grows.The figure uses ΓL = 8 bps/Hz and ΓN = 4 bps/Hz.Source: Figure 3 · p. 5, §IV · p. 6
- For different waveguide counts M and PA counts N per waveguide, increasing M and N adds spatial DoFs and lowers transmit power; proposed AO consistently outperforms the 1-D search scheme.The comparison uses ΓL = 8 bps/Hz and ΓN = 4 bps/Hz.Source: §IV · p. 6, Figure 4 · p. 6
- AO substantially reduces execution-time growth versus “1-D search” as RIS elements, waveguides, or PAs increase.The 1-D search cost rises with repeated element-wise searches; Table I compares average execution time across configurations.Source: §IV · p. 6, Table I · p. 6
V. CONCLUSION
The study uses RIS to extend PASS coverage so LOS and NLOS users can be served together, and proposes joint optimization of RIS reflection coefficients and PA activation positions. Simulations report lower transmit power and execution time than an existing element-wise 1-D search scheme.
V. CONCLUSION
- The RIS extends PASS coverage to enable simultaneous service of LOS and NLOS users.Source: §V · p. 6
- Joint optimization significantly outperforms heuristic PA deployment schemes, while the proposed AO method achieves lower transmit power and execution time than the existing element-wise 1-D search scheme.The system uses ZF beamforming to satisfy communication rate constraints while minimizing transmit power.Source: §V · p. 6
- The AO framework jointly optimizes RIS reflection coefficients and PA activation positions for transmit power minimization under ZF beamforming.Source: §V · p. 6
- Future work will investigate advanced beamforming designs and extend the framework to multiple LOS and NLOS users.Source: §V · p. 6