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6D Movable Antenna Enhanced Multi-Access Point Coordination via Position and Orientation Optimization

Xiangyu Pi, Lipeng Zhu, Haobin Mao, Zhenyu Xiao, Xiang-Gen Xia, Rui Zhang

arXiv:2412.10736v1eess.SP

TL;DR

Crowded spectrum and fixed antennas’ limited spatial degrees of freedom challenge massive WLAN access and interference control. This paper models and jointly optimizes the positions, orientations, and receive combining of 6DMA-equipped coordinated APs. Its offline designs are reported to improve performance over fixed-antenna schemes for uni- and dual-polarized antennas.

  • Problem

    Crowded spectrum and dense UTs challenge massive access, while fixed antennas’ limited spatial degrees of freedom constrain channel quality and spatial multiplexing.

    Source: §I · pp. 1–2

  • Method

    The paper models position- and orientation-dependent channels and jointly optimizes 6DMA positions, orientations, and receive combining for uplink weighted sum rate.

    Source: §I · p. 2

  • Results

    The offline statistical-CSI design achieves considerable performance improvement over fixed antennas with both uni-polarized and dual-polarized antennas.

    Source: §I · p. 3

  • Takeaways & Limitations

    The authors report that flexible antenna movement can decrease channel correlation and enable access for more UTs within limited frequency bandwidth.

    Source: §I · p. 2

Abstract

from arXiv · show

The effective utilization of unlicensed spectrum is regarded as an important direction to enable the massive access and broad coverage for next-generation wireless local area network (WLAN). Due to the crowded spectrum occupancy and dense user terminals (UTs), the conventional fixed antenna (FA)-based access points (APs) face huge challenges in realizing massive access and interference cancellation. To address this issue, in this paper we develop a six-dimensional movable antenna (6DMA) enhanced multi-AP coordination system for coverage enhancement and interference mitigation. First, we model the wireless channels between the APs and UTs to characterize their variation with respect to 6DMA movement, in terms of both the three-dimensional (3D) position and 3D orientation of each distributed AP's antenna. Then, an optimization problem is formulated to maximize the weighted sum rate of multiple UTs for their uplink transmissions by jointly optimizing the antenna position vector (APV), the antenna orientation matrix (AOM), and the receive combining matrix over all coordinated APs, subject to the constraints on local antenna movement regions. To solve this challenging non-convex optimization problem, we first transform it into a more tractable Lagrangian dual problem. Then, an alternating optimization (AO)-based algorithm is developed by iteratively optimizing the APV and AOM, which are designed by applying the successive convex approximation (SCA) technique and Riemannian manifold optimization-based algorithm, respectively. Simulation results show that the proposed 6DMA-enhanced multi-AP coordination system can significantly enhance network capacity, and both of the online and offline 6DMA schemes can attain considerable performance improvement compared to the conventional FA-based schemes.

I. INTRODUCTION

Dense WLAN traffic and fixed antennas’ limited spatial degrees of freedom make massive access and interference control difficult. The paper proposes coordinated APs equipped with 6DMAs, whose positions and orientations can be optimized to improve multiuser communication.

I. INTRODUCTION

  • Crowded unlicensed spectrum and fixed antennas’ limited spatial degrees of freedom challenge massive access, channel quality, and spatial multiplexing.High channel correlation also makes UT signals harder to distinguish, increasing multiuser interference and reducing total data rate.Source: §I · pp. 1–2
  • Earlier movable-antenna work focused on centralized systems, leaving distributed multi-AP coordination as the gap addressed here.The paper positions 6DMA-enhanced coordination as a way to improve coverage and mitigate multiuser interference in Wi-Fi networks.Source: §I · p. 2
  • The proposed system jointly optimizes APV, AOM, and receive combining to maximize uplink UT weighted sum rate under local antenna-movement constraints.Its AO algorithm uses MMSE combining, SCA for positions, and Riemannian manifold optimization for orientations; an offline design uses statistical CSI.Source: §I · p. 2

II. SYSTEM MODEL AND PROBLEM FORMULATION

  • Each distributed 6DMA AP cooperates to serve single-FA UTs, with a central processing unit connecting the APs and coordinating their operation.The system model assumes directional AP antennas and initially considers uni-polarized antennas.Source: §II · p. 3

A. Antenna Movement

  • Each 6DMA has six movement degrees of freedom: a 3D position in a cuboid region and an orientation represented by two orthogonal unit vectors.The vectors encode the antenna-plane normal and an in-plane direction.Source: A. Antenna Movement · p. 3

B. Channel Model

The channel model accounts for antenna position, orientation, propagation environment, and polarization. Under the far-field assumption, position changes path phase while orientation changes path amplitude.

B. Channel Model

  • The proposed 6DMA channel model incorporates antenna polarization, extending earlier field-response channel modeling for movable antennas.The paper notes that prior 6DMA channel models neglected polarization,, and extends models in,.Source: B. Channel Model · p. 3
  • Under the far-field assumption, each path's angle of arrival remains fixed as antennas move; position changes phase, while orientation changes amplitude through antenna gain.The assumption is that signal propagation distance greatly exceeds each AP's antenna movement region.Source: B. Channel Model · p. 4
  • The channel response combines a propagation-environment-dependent path-response vector with an orientation-dependent diagonal matrix of per-path effective antenna gains.The gains vary with orientation because the multipath signals arrive from different angles, changing effective aperture and polarization loss.Source: B. Channel Model · p. 4
  • Antenna orientation controls effective aperture and polarization losses, while position and orientation jointly determine the channel coefficient.The model describes polarization loss as arising from mismatch between receive-antenna polarization and the incident wave's electric field.Source: B. Channel Model · p. 4

C. Signal Model

The signal model combines uplink transmissions from multiple UTs across coordinated APs, with the CPU decoding the forwarded signals. It defines achievable rates and formulates weighted-sum-rate maximization over antenna positions, orientations, and receive combining, subject to movement and orientation constraints.

C. Signal Model

  • The APs forward received signals to a CPU for centralized decoding, with UTs assumed to use the same maximum transmit power.The model represents receiver noise as zero-mean AWGN with power σ^2.Source: C. Signal Model · p. 4
  • The collective channel and combining matrices collect each UT’s channels and combining vectors across APs, supporting the rate and SINR model.The channel and radiation-pattern model can apply to 6DMA systems with arbitrary antenna radiation patterns.Source: C. Signal Model · pp. 4–5
  • The design maximizes multiple UTs’ weighted sum rate by jointly choosing antenna positions, orientations, and receive combining, subject to local movement and orthogonal-orientation constraints.The resulting problem is non-convex with highly coupled variables, so the paper develops an alternating-optimization approach to obtain a suboptimal solution.Source: C. Signal Model · p. 5

III. PROPOSED SOLUTION

The proposed solution reformulates weighted-sum-rate optimization with auxiliary variables, then alternates updates of the receiver and antenna variables. It uses a closed-form MMSE combiner and separately optimizes positions and orientations.

III. PROPOSED SOLUTION

  • The overall method alternates position and orientation optimization with updates to the receive combiner, using SCA for positions and Riemannian manifold optimization for orientations.The approach seeks a suboptimal solution to the original problem.Source: §III · p. 5

A. Problem Transformation

  • The original objective is reformulated using auxiliary variables, enabling alternating updates of those variables and the antenna and receiver design.The transformation applies Lagrangian dual and quadratic transforms inspired by fractional programming.Source: A. Problem Transformation · p. 5

B. Optimization of Receive Combining

  • For a fixed collective channel, the receive combining matrix has a closed-form MMSE solution that yields each UT’s maximum SINR.The combiner is updated as antenna positions and orientations change the collective channel.Source: B. Optimization of Receive Combining · p. 5

C. Optimization of Antenna Position

Each AP’s antenna position is optimized in turn while other positions and design variables are fixed. The method uses successive convex approximation to form a tractable position update within the feasible movement region.

C. Optimization of Antenna Position

  • For each position update, the algorithm fixes the other AP positions and applies a surrogate-based SCA step to the selected antenna.A majorization-minimization bound and local second-order approximation lead to a convex quadratic program; projection keeps the update within the feasible region.Source: C. Optimization of Antenna Position · pp. 5–6
  • The SCA position iterations repeatedly update the antenna position and collective channel until the objective increase falls below a threshold, yielding a suboptimal solution.The update uses the closed-form position rule and the feasible-region constraints.Source: C. Optimization of Antenna Position · p. 6

D. Optimization of Antenna Orientation

The orientation subproblem is optimized on a Stiefel manifold, whose structure enforces the orientation’s orthogonality constraint. A Riemannian conjugate-gradient procedure updates each AP orientation while keeping iterates on the manifold.

D. Optimization of Antenna Orientation

  • Each AP orientation is optimized separately, and its orthogonality constraint is represented by a Stiefel-manifold formulation.The orientation subproblem has a non-concave objective over a non-convex orthogonal-matrix constraint.Source: D. Optimization of Antenna Orientation · pp. 6–7
  • The Riemannian gradient is the projection of the objective Jacobian onto the manifold’s tangent space, providing a feasible direction for orientation optimization.The tangent space consists of tangent matrices at the current manifold point.Source: D. Optimization of Antenna Orientation · p. 7
  • A conjugate-gradient update uses tangent-space transport and a retraction to update the orientation while maintaining manifold feasibility.The retraction uses QR decomposition, and the stated update keeps the objective non-decreasing across iterations.Source: D. Optimization of Antenna Orientation · p. 7
  • The orientation iterations stop when the objective increase falls below a threshold and return a suboptimal solution.The objective is described as monotonically non-decreasing during the iterations.Source: D. Optimization of Antenna Orientation · p. 7

E. Overall Algorithm

Algorithm 3 alternates 6DMA position and orientation updates with receive-combiner and auxiliary-variable updates. Its objective is non-decreasing and upper-bounded, while the paper gives complexity orders for the component updates and overall algorithm.

E. Overall Algorithm

  • Algorithm 3 alternates APV and AOM optimization across APs, refreshing the receive combiner and auxiliary variables as antenna positions and orientations change.It stops when the objective increase falls below a predefined threshold, yielding a local optimum for problem (13).Source: E. Overall Algorithm · pp. 7–8
  • The objective value is non-decreasing across iterations and upper-bounded, guaranteeing convergence of the overall algorithm.The MMSE combiner maximizes each UT’s SINR under the current collective channel matrix; convergence of the position and orientation algorithms supports the successive updates.Source: E. Overall Algorithm · p. 8
  • The overall algorithm’s computational complexity is O(Tmax M(M^3 + Lmax^3.5 + Imax K Lmax + Nmax K Lmax)).The combining-matrix design has complexity O(M^3); position and orientation update costs depend on path count and their maximum iteration counts.Source: E. Overall Algorithm · p. 8

F. Offline Solution Based on Statistical CSI

The offline approach optimizes antenna positions and orientations using statistical CSI, approximating average WSR with Monte Carlo channel realizations. The resulting antenna configuration remains fixed for a long period and is applied online to instantaneous channels.

F. Offline Solution Based on Statistical CSI

  • Statistical-CSI optimization of APV and AOM uses Monte Carlo channel realizations to approximate average WSR, then keeps the optimized antenna configuration fixed for a long period.For each realization, the receive combiner is obtained using the MMSE receiver; the SCA and orientation-gradient calculations are averaged over realizations.Source: F. Offline Solution Based on… · pp. 8–9
  • Offline-designed APV and AOM are applied online over instantaneous channels together with receive combining.The antenna positions and orientations remain constant for a long period, reducing antenna-movement overhead.Source: F. Offline Solution Based on… · pp. 8–9
  • The paper states that deployed 6DMAs can still attain good system performance despite instantaneous channel changes.The claimed performance is to be validated by the simulation results.Source: F. Offline Solution Based on… · p. 9

G. Extension to Dual-polarized Antenna

The system is extended to dual-polarized antennas, with each AP antenna providing two co-located orthogonal polarizations treated as independent antennas. Their orientations can be optimized using the proposed Riemannian-manifold-based approach.

G. Extension to Dual-polarized Antenna

  • Each dual-polarized AP antenna has two co-located orthogonal polarizations, treated as two independent antennas.The extension is motivated by the advantage of dual polarization in avoiding polarization mismatch between transceivers.Source: G. Extension to Dual-polarized Antenna · p. 9
  • The dual-polarized system updates the collective channel matrix to represent both polarization channels.The channel matrix is formed by stacking the two channel components and has dimensions 2M by K.Source: G. Extension to Dual-polarized Antenna · p. 9
  • Dual-polarized antenna orientations remain optimizable by the proposed Riemannian-manifold-based algorithm.The resulting optimization can be solved by a gradient-ascent-based algorithm.Source: G. Extension to Dual-polarized Antenna · p. 9

IV. SIMULATION RESULTS

In the simulated multi-hotspot setting, the proposed 6DMA system’s WSR converges within 100 iterations and rises from 35.3 to 45.6 bps/Hz. The evaluation averages results across 100 random UT-location and channel realizations.

A. Simulation Setup

  • Simulations consider K FA-UTs served by M 6DMA-APs in a 3D multi-hotspot scenario, with most UTs randomly placed in two nonoverlapping hotspots and remaining UTs uniformly distributed elsewhere.Each AP’s 6DMA moving region is a cube of size 2λ × 2λ × 2λ; the simulations adopt a geometry Rician fading channel model with Rician factor χ.Source: A. Simulation Setup · p. 9
  • Each plotted simulation point averages results over 100 random UT-location and channel realizations.The setup uses a 3D multi-hotspot scenario, with most UTs randomly placed in two nonoverlapping hotspots and the remainder distributed across other areas.Source: A. Simulation Setup · p. 9

B. Algorithm Convergence Evaluation

C. Performance Comparison with Benchmark Schemes

Across the tested settings, 6DMA schemes improve weighted sum rate over fixed antennas, while offline 6DMA retains gains with reduced antenna-movement overhead. The comparison also finds a dual-polarized option with performance comparable to uni-polarized operation while requiring half as many APs.

C. Performance Comparison with Benchmark Schemes

  • With more UTs, both proposed 6DMA schemes outperform the benchmarks and approach exhaustive search; offline-6DMA remains significantly above fixed antennas.Antenna movement can target lower-correlation regions and improve desired channel power, helping suppress multiuser interference.Source: Figure 5 · p. 10, C. Performance Comparison with… · pp. 10–11
  • Doubling the number of APs yields nearly proportional rate improvement, and proposed 6DMA achieves performance comparable to exhaustive search with lower complexity and overhead.The proposed schemes remain superior to the other benchmarks except exhaustive search.Source: Figure 6 · p. 10, C. Performance Comparison with… · pp. 10–11
  • As transmit power increases, proposed schemes consistently surpass all benchmarks except exhaustive search, with a widening gap over fixed antennas.The passage attributes the widening gap to reduced user-channel correlation in the high-SNR, interference-limited regime.Source: Figure 7 · p. 11, C. Performance Comparison with… · p. 11
  • Under imperfect instantaneous CSI, both 6DMA schemes degrade, but outperform fixed antennas; the online-to-offline performance gap narrows as PRV error grows.Receive combiners use perfect CSI for both systems, while offline antenna designs based on statistical CSI show robust improvement.Source: Figure 8 · p. 11, C. Performance Comparison with… · p. 11
  • In both polarization modes, antenna position and orientation optimization improves rate; uni-polarized operation performs better, while dual-polarized operation uses half as many APs with comparable performance.The uni-polarized advantage is attributed to greater independent antenna-movement spatial degrees of freedom; the dual-polarized option reduces deployment and movement overhead.Source: Figure 9 · p. 11, C. Performance Comparison with… · pp. 11–12

V. CONCLUSION

  • The conclusion presents joint APV, AOM, and receive-combiner optimization, plus a statistical-CSI offline design that retains gains over fixed antennas with reduced movement overhead.The optimization uses a Lagrangian dual formulation and alternating optimization, with SCA for APV and Riemannian manifold optimization for AOM.Source: §V · p. 12

APPENDIX A DERIVATIONS OF ∇¯F(qm) AND ∇2 ¯F(qm)

The appendix derives the gradient vector and Hessian matrix of F̄(q_m).

APPENDIX A DERIVATIONS OF ∇̄F(q_m) AND ∇² F̄(q_m)

  • The appendix gives the gradient vector and Hessian matrix of F̄(q_m).The supplied derivation passage identifies these derivatives but does not provide enough readable detail to summarize their expressions.Source: Appendix A · p. 12

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