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Movable-Antenna Enhanced Multiuser Communication via Antenna Position Optimization

Lipeng Zhu, Wenyan Ma, Boyu Ning, Rui Zhang

arXiv:2302.06978v2cs.ITeess.SP

TL;DR

The paper addresses uplink multiuser communication with movable antennas, whose positions can exploit spatial channel variation beyond fixed-position arrays. It models the channels using field responses and jointly optimizes antenna positions, transmit powers, and BS combining through ZF- and MMSE-based MDD algorithms. Simulations report lower total transmit power than FPA systems with antenna selection under perfect and imperfect field-response information.

  • Problem

    Fixed-position arrays do not fully exploit continuous spatial channel variation, motivating movable-antenna optimization for multiuser uplink communication.

  • Method

    The paper uses a 3D field-response channel model and jointly optimizes MA positions, user powers, and BS receive combining with ZF- and MMSE-based MDD algorithms.

  • Results

    The proposed MA-ZF and MA-MMSE solutions significantly decrease total user transmit power versus conventional FPA systems employing antenna selection under perfect and imperfect field-response information.

  • Takeaways & Limitations

    Movable antennas provide interference-mitigation and power-saving gains in the studied multiuser access system, with gains depending on channel paths and moving-region size.

Abstract

from arXiv · show

Movable antenna (MA) is a promising technology to improve wireless communication performance by varying the antenna position in a given finite area at the transceivers to create more favorable channel conditions. In this paper, we investigate the MA-enhanced multiple-access channel (MAC) for the uplink transmission from multiple users each equipped with a single MA to a base station (BS) with a fixed-position antenna (FPA) array. A field-response based channel model is used to characterize the multi-path channel between the antenna array of the BS and each user's MA with a flexible position. To evaluate the MAC performance gain provided by MAs, we formulate an optimization problem for minimizing the total transmit power of users, subject to a minimum-achievable-rate requirement for each user, where the positions of MAs and the transmit powers of users, as well as the receive combining matrix of the BS are jointly optimized. To solve this non-convex optimization problem involving intricately coupled variables, we develop two algorithms based on zero-forcing (ZF) and minimum mean square error (MMSE) combining methods, respectively. Specifically, for each algorithm, the combining matrix of the BS and the total transmit power of users are expressed as a function of the MAs' position vectors, which are then optimized by using the proposed multi-directional descent (MDD) framework. It is shown that the proposed ZF-based and MMSE-based MDD algorithms can converge to high-quality suboptimal solutions with low computational complexities. Simulation results demonstrate that the proposed solutions for MA-enhanced multiple access systems can significantly decrease the total transmit power of users as compared to conventional FPA systems employing antenna selection under both perfect and imperfect field-response information.

I. INTRODUCTION

The paper motivates movable antennas as a way to exploit continuous spatial channel variation beyond fixed-position arrays, then studies their use in uplink multiuser communication. It formulates joint antenna-position, power, and receive-combining optimization and develops ZF- and MMSE-based solutions.

  • Fixed-position antennas limit diversity and spatial multiplexing by constraining access to continuous spatial channel variation.
  • Movable antennas can select favorable channel positions to exploit spatial diversity and mitigate interference.The paper describes improved channel gain and reduced interference as motivations for antenna movement.
  • The study extends a field-response channel model to 3D space for multiple single-MA users communicating uplink to a base station with an FPA array.
  • The optimization minimizes users’ total transmit power subject to each user’s minimum achievable rate while jointly optimizing MA positions, transmit powers, and BS receive combining.
  • ZF- and MMSE-based MDD algorithms address the coupled non-convex problem and are designed to converge to high-quality suboptimal solutions with low computational complexity.
  • The system model uses a BS UPA with N = N1 × N2 antennas serving K single-MA users, with each MA position represented in a 3D local region.

A. Channel Model

The channel model represents each user’s movable-antenna channel under a far-field, narrow-band setting, where antenna position changes path phases while path angles and amplitudes remain fixed. Field-response vectors and matrices express how positions modify the resulting channel vectors.

  • The model assumes narrow-band, slow-fading transmission over one quasi-static block and a far-field relationship between users’ moving regions and the BS UPA.
  • Under the plane-wave model, MA movement changes channel-path phases, whereas each path’s AoD, AoA, and complex-coefficient amplitude remain unchanged within its region.
  • The model assumes omnidirectional MAs with fixed orientation, so only antenna position is optimized.
  • The transmit and receive field-response vectors capture phase differences across the user-side and BS-side channel paths caused by antenna positions.
  • The field-response matrix at the BS is constant because its antennas are fixed, while MA positioning changes the field-response vector and thus the channel-vector combination.

B. Problem Formulation

The paper formulates joint MA-position, transmit-power, and BS-combining optimization for minimizing total uplink power under per-user rate requirements. The resulting problem is difficult because MA-dependent channels are highly non-convex and the variables are coupled.

  • Problem objective: The objective is to minimize multiple users’ total transmit power while satisfying each user’s minimum achievable-rate requirement.
  • Optimization variables: The optimization jointly selects each MA’s position, each user’s transmit power, and the BS receive combining matrix.
  • Constraints: The achievable-rate constraint requires log2(1 + γk) ≥ rk for every user k.
  • Constraints: Each MA must remain in its moving region Ck, and every user transmit power must be non-negative.
  • Non-convexity: The problem is difficult because channel vectors and achievable rates are highly non-convex with respect to MA positions, while matrix and vector variables are coupled.
  • Solution challenge: Alternating optimization can become trapped at an undesired local optimum because updated MA positions may not change significantly under a fixed combining matrix.
  • Assumption: The optimization assumes perfect field-response information at the BS, while imperfect information is evaluated through simulations.
  • Proposed solutions: The paper develops ZF- and MMSE-based solutions to obtain suboptimal solutions for the total-power problem.

A. ZF-Based Solution

The ZF-based method expresses combining and minimum required powers as functions of MA positions, then optimizes those positions with multi-directional descent. Backtracking and projection maintain feasible descent, while convergence is to a local or boundary solution rather than the global optimum.

  • ZF reduction: For fixed MA positions, the channel vectors are fixed and the BS ZF combining matrix becomes a function of the MA-position vector.
  • Power optimization: Under ZF combining, each user’s minimum transmit power is selected to satisfy its minimum achievable-rate requirement.
  • Assumption: The ZF formulation assumes a column-full-rank multiuser channel; otherwise, channel correlation can make rate requirements difficult to satisfy.
  • MDD framework: MDD updates MA positions along multiple candidate descent directions generated from weighted combinations of descent-direction components.
  • Feasibility: Projection maps out-of-region position coordinates to feasible boundaries during the iterations.
  • Step selection: Backtracking line search shrinks each candidate step until the Armijo–Goldstein condition is satisfied, after which the candidate with minimum objective value is selected.
  • Convergence: The algorithm terminates at a point where all candidate descent directions vanish or at the boundary of the feasible region, yielding a local optimum.
  • Complexity: The maximum complexity is O(T̄max(K^3NQ̄ + ĪmaxK^2NM̄)).

B. MMSE-Based Solution

The MMSE-based method exploits the optimal MMSE combiner for fixed positions and powers, then alternates power updates with MDD position updates. Its objective is non-increasing and bounded below, guaranteeing convergence, while the method remains computationally demanding.

  • MMSE formulation: For fixed MA positions and user powers, the MMSE receiver is optimal for maximizing the achievable-rate region and minimizing total power under rate requirements.
  • Power update: Minimum-power operation sets every user’s SINR exactly to its minimum requirement and solves the resulting linear power equations.
  • Feasibility: The non-negative power constraint is enforced through a spectral-radius condition on the interference-coupling matrix.
  • Solution challenge: The MMSE problem is more challenging because its position constraint is non-convex and MA positions are coupled with transmit powers.
  • Alternating optimization: The algorithm alternates MDD updates of MA positions with updates of the transmit-power matrix and MMSE combining.
  • Step selection: Candidate steps use backtracking line search subject to the Armijo–Goldstein condition and the spectral-radius constraint.
  • Convergence: Because the total transmit power is non-negative and the objective sequence is non-increasing, Algorithm 2 is guaranteed to converge.
  • Complexity: The maximum complexity is O(T̂max(KN^3Q̂ + ÎmaxN^3M̂)).

C. Alternative Solution for the Single-User Case

For a single MA user, interference disappears, so ZF and MMSE both reduce to MRC. The resulting position optimization maximizes channel gain to minimize the user’s required transmit power.

  • Single-user combining: With one served user, ZF and MMSE combining both reduce to maximum ratio combining because no interference exists.
  • MRC solution: The optimal MRC vector equals the user’s channel vector, wMRC(u) = h(u).
  • Power requirement: The minimum transmit power is determined by the user’s minimum-rate requirement through the corresponding SNR condition.
  • Position optimization: Minimizing transmit power reduces to maximizing the channel-vector gain over the antenna’s moving region.
  • Solution method: The single-user position problem can be solved using the proposed MDD framework.

IV. SIMULATION RESULTS

The simulations evaluate the performance of the proposed MA-enabled multiple-access systems and verify the efficacy of the proposed algorithms.

  • The simulations evaluate the performance of the proposed MA-enabled multiple-access systems.
  • The numerical results are presented after describing the simulation setup and benchmark schemes.

A. Simulation Setup and Benchmark Schemes

The simulations use a field-response channel model with specified user, path, spatial-region, and rate settings, and compare proposed methods with antenna-selection and maximum-channel-power benchmarks.

  • Simulation Setup: Users are uniformly distributed around the BS, with distances randomly generated from 20 to 100 m.
  • Simulation Setup: Each user’s channel uses equal transmit and receive path counts, with path-response coefficients modeled by a diagonal random matrix.
  • Simulation Setup: The spatial region for each movable antenna is a cube, and all users share the same minimum-achievable-rate requirement r in bps/Hz.
  • Simulation Setup: Simulation results average over 10^3 user distributions and use three candidate descent directions for both proposed algorithms.
  • Benchmark Schemes: The proposed methods are compared with fixed-position antenna selection and maximum-channel-power schemes using ZF and MMSE combining.

B. Convergence Evaluation of Proposed Algorithms

Both proposed algorithms converge as iterations proceed, while the MMSE-based method achieves greater total transmit-power savings by balancing interference and noise.

  • Convergence Evaluation: After 40 iterations, both algorithms’ total transmit-power curves reach a steady state.
  • Convergence Evaluation: The ZF-based algorithm reduces total transmit power from 39.8 dBm to 29.7 dBm, yielding about 90% power-saving.
  • Convergence Evaluation: The MMSE-based algorithm reduces total transmit power from 35.8 dBm to 28.4 dBm, yielding about 81% power-saving.
  • Convergence Evaluation: The MMSE-based solution outperforms the ZF-based solution because MMSE balances interference and noise, whereas ZF can amplify noise.
  • Receive-Power Evaluation: During iterations, normalized signal power decreases by 1 dB while normalized interference power decreases by more than 4 dB.

C. Channel Characteristics under Antenna Position Optimization

Movable-antenna position optimization changes channel gains and reduces channel-vector correlation, reflecting a tradeoff between individual channel strength and multiuser interference mitigation.

  • Single-User Channel Characteristics: For a single user, antenna movement within a 2D square can substantially change channel power gain because of small-scale spatial fading.
  • Single-User Channel Characteristics: The initial position has channel power gain −84.5 dB, while the optimized position [−0.8λ, −0.5λ] provides a 6 dB increase.
  • Multiple-User Channel Characteristics: For K = 12 users, average channel power gain decreases during joint position optimization, whereas normalized channel cross-correlation decreases for both algorithms.
  • Multiple-User Channel Characteristics: Joint optimization does not simply maximize each user’s average channel power; it also tends to reduce channel-vector correlation and multiuser interference.
  • Multiple-User Channel Characteristics: Compared with ZF, the MMSE-based solution achieves a better tradeoff between average channel power gain and normalized channel cross-correlation.

D. Performance Comparison with Benchmark Schemes

Across benchmark comparisons, MA positioning reduces total transmit power, with gains becoming more pronounced as user demands, channel complexity, or movable-region size increase. The results attribute this advantage primarily to reduced multiuser channel correlation and interference.

  • Rate requirements: Proposed MA-ZF and MA-MMSE solutions outperform AS and MCP schemes, especially when minimum-achievable-rate requirements are large.For small rate requirements, MA-MMSE can also outperform MA-ZF because ZF noise amplification is more damaging in the low-SNR region.
  • Number of users: Total transmit power increases with the number of users because each user must satisfy its rate requirement while multiuser interference also rises.The higher interference requires users to increase their transmit powers.
  • Channel paths and AoAs: Total transmit power decreases as the number of channel paths increases, although the reduction becomes small beyond L=10.More paths improve spatial diversity and reduce channel-vector correlation, while limited BS-side AoAs constrain further improvement.
  • Channel paths and AoAs: Increasing the total number of AoAs at the BS makes it easier for MA positioning to reduce correlation among users’ channel vectors.When receive field-response matrices have similar columns, local MA movement cannot substantially decorrelate the MAC.
  • Movable-region size: MA systems require much less total transmit power than AS and MCP schemes as the users’ normalized movable-region size increases.Larger regions provide more channel variation for positioning optimization, whereas greedy channel-gain maximization can increase MAC correlation.

E. Impact of Imperfect FRI

The imperfect-FRI study evaluates position optimization using estimated channel information while calculating combining and transmit powers from actual channels. The proposed MA methods remain advantageous under AoD and PRM errors, with quantified performance degradation for large errors.

  • Error models: AoD error is modeled as a bounded difference between estimated and actual departure angles, with maximum error μ and a uniform distribution.The optimization uses estimated FRI, while actual channel vectors determine post-deployment combining and transmit power.
  • Error models: PRM error is modeled as a circularly symmetric complex Gaussian difference between estimated and actual path-response elements, with variance ν.The normalized mean-square error of the estimated PRM is approximately equal to the defined normalized PRM-error variance.
  • AoD error: Total transmit power increases slightly with maximum AoD error, but the MA advantage over AS remains significant.At μ=0.2, the proposed MA-ZF and MA-MMSE solutions incur no more than a 0.6 dB power increment relative to perfect FRI.
  • PRM error: As normalized PRM-error variance ν increases from 0 to 0.2, MA-ZF and MA-MMSE transmit powers increase by 2.8 dB and 1.7 dB, respectively.Despite this degradation, the proposed MA schemes remain significantly better than conventional AS schemes at large ν.

V. CONCLUSION

The paper formulates MA-enhanced uplink MAC power minimization and solves it with ZF- and MMSE-based MDD algorithms. Simulations show lower transmit power than FPA antenna-selection benchmarks and robustness to FRI errors, while broader multi-MA and multi-cell settings remain future work.

  • Problem formulation: The study jointly optimizes user MA positions, transmit powers, and BS receive combining under per-user minimum-achievable-rate constraints.A field-response channel model represents each user’s multipath channel to the BS FPA array.
  • Proposed algorithms: ZF- and MMSE-based algorithms express combining and total transmit power as functions of MA positions, then update positions with the MDD framework.The MDD iterations use multiple candidate descent directions and backtracking line search.
  • Findings: The proposed MA-ZF and MA-MMSE solutions significantly reduce total user transmit power versus conventional FPA systems using antenna selection.The interference-mitigation benefit is stronger with many users or high achievable-rate requirements, and performance remains robust to AoD and PRM errors.
  • Future scope: Extending the framework to multi-MA users and multi-cell systems requires studying joint user precoding, receive combining, and MA-position optimization.The paper also identifies efficient FRI estimation as necessary to balance training overhead and communication performance.
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