Movable-Antenna Enhanced Multiuser Communication via Antenna Position Optimization

• Fixed-position antennas limit diversity and spatial multiplexing by constraining access to continuous spatial channel variation.Source: §I · p. 1
• 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.Source: §I · pp. 1–2
• 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.Source: §I · p. 2
• 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.Source: §I · p. 2
• 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.Source: §I · p. 3
• 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.Source: §II · p. 3

• 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.Source: A. Channel Model · pp. 3–4
• 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.Source: A. Channel Model · p. 4
• The model assumes omnidirectional MAs with fixed orientation, so only antenna position is optimized.Source: A. Channel Model · p. 4
• The transmit and receive field-response vectors capture phase differences across the user-side and BS-side channel paths caused by antenna positions.Source: A. Channel Model · p. 4
• 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.Source: A. Channel Model · p. 4

Problem objective

• The objective is to minimize multiple users’ total transmit power while satisfying each user’s minimum achievable-rate requirement.Source: B. Problem Formulation · p. 5

Optimization variables

• The optimization jointly selects each MA’s position, each user’s transmit power, and the BS receive combining matrix.Source: B. Problem Formulation · p. 5

Constraints

• The achievable-rate constraint requires log2(1 + γk) ≥ rk for every user k.Source: B. Problem Formulation · p. 5
• Each MA must remain in its moving region Ck, and every user transmit power must be non-negative.Source: B. Problem Formulation · p. 5

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.Source: B. Problem Formulation · p. 5

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.Source: §III · p. 5

Assumption

• The optimization assumes perfect field-response information at the BS, while imperfect information is evaluated through simulations.Source: §III · p. 5

Proposed solutions

• The paper develops ZF- and MMSE-based solutions to obtain suboptimal solutions for the total-power problem.Source: §III · p. 5

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.Source: A. ZF-Based Solution · p. 5

Power optimization

• Under ZF combining, each user’s minimum transmit power is selected to satisfy its minimum achievable-rate requirement.Source: A. ZF-Based Solution · p. 5

Assumption

• The ZF formulation assumes a column-full-rank multiuser channel; otherwise, channel correlation can make rate requirements difficult to satisfy.Source: A. ZF-Based Solution · p. 5

MDD framework

• MDD updates MA positions along multiple candidate descent directions generated from weighted combinations of descent-direction components.Source: A. ZF-Based Solution · p. 6

Feasibility

• Projection maps out-of-region position coordinates to feasible boundaries during the iterations.Source: A. ZF-Based Solution · p. 6

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.Source: A. ZF-Based Solution · p. 6

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.Source: A. ZF-Based Solution · p. 7

Complexity

• The maximum complexity is O(T̄max(K^3NQ̄ + ĪmaxK^2NM̄)).Source: A. ZF-Based Solution · p. 7

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.Source: B. MMSE-Based Solution · p. 7

Power update

• Minimum-power operation sets every user’s SINR exactly to its minimum requirement and solves the resulting linear power equations.Source: B. MMSE-Based Solution · p. 7

Feasibility

• The non-negative power constraint is enforced through a spectral-radius condition on the interference-coupling matrix.Source: B. MMSE-Based Solution · p. 7

Solution challenge

• The MMSE problem is more challenging because its position constraint is non-convex and MA positions are coupled with transmit powers.Source: B. MMSE-Based Solution · p. 7

Alternating optimization

• The algorithm alternates MDD updates of MA positions with updates of the transmit-power matrix and MMSE combining.Source: B. MMSE-Based Solution · pp. 7–8

Step selection

• Candidate steps use backtracking line search subject to the Armijo–Goldstein condition and the spectral-radius constraint.Source: B. MMSE-Based Solution · p. 8

Convergence

• Because the total transmit power is non-negative and the objective sequence is non-increasing, Algorithm 2 is guaranteed to converge.Source: B. MMSE-Based Solution · p. 8

Complexity

• The maximum complexity is O(T̂max(KN^3Q̂ + ÎmaxN^3M̂)).Source: B. MMSE-Based Solution · pp. 8–9

Single-user combining

• With one served user, ZF and MMSE combining both reduce to maximum ratio combining because no interference exists.Source: C. Alternative Solution for the… · p. 9

MRC solution

• The optimal MRC vector equals the user’s channel vector, wMRC(u) = h(u).Source: C. Alternative Solution for the… · p. 9

Power requirement

• The minimum transmit power is determined by the user’s minimum-rate requirement through the corresponding SNR condition.Source: C. Alternative Solution for the… · p. 9

Position optimization

• Minimizing transmit power reduces to maximizing the channel-vector gain over the antenna’s moving region.Source: C. Alternative Solution for the… · p. 9

Solution method

• The single-user position problem can be solved using the proposed MDD framework.Source: C. Alternative Solution for the… · p. 9

• The simulations evaluate the performance of the proposed MA-enabled multiple-access systems.Source: §IV · p. 9
• The numerical results are presented after describing the simulation setup and benchmark schemes.Source: §IV · p. 9

Simulation Setup

• Users are uniformly distributed around the BS, with distances randomly generated from 20 to 100 m.Source: A. Simulation Setup and Benchmark… · p. 9
• Each user’s channel uses equal transmit and receive path counts, with path-response coefficients modeled by a diagonal random matrix.Source: A. Simulation Setup and Benchmark… · p. 9
• The spatial region for each movable antenna is a cube, and all users share the same minimum-achievable-rate requirement r in bps/Hz.Source: A. Simulation Setup and Benchmark… · p. 9
• Simulation results average over 10^3 user distributions and use three candidate descent directions for both proposed algorithms.Source: A. Simulation Setup and Benchmark… · p. 9

Benchmark Schemes

• The proposed methods are compared with fixed-position antenna selection and maximum-channel-power schemes using ZF and MMSE combining.Source: A. Simulation Setup and Benchmark… · p. 10

Convergence Evaluation

• After 40 iterations, both algorithms’ total transmit-power curves reach a steady state.Source: B. Convergence Evaluation of Proposed… · p. 10, Figure 3 · p. 10
• The ZF-based algorithm reduces total transmit power from 39.8 dBm to 29.7 dBm, yielding about 90% power-saving.Source: B. Convergence Evaluation of Proposed… · p. 10
• The MMSE-based algorithm reduces total transmit power from 35.8 dBm to 28.4 dBm, yielding about 81% power-saving.Source: B. Convergence Evaluation of Proposed… · p. 10
• The MMSE-based solution outperforms the ZF-based solution because MMSE balances interference and noise, whereas ZF can amplify noise.Source: B. Convergence Evaluation of Proposed… · p. 10

Receive-Power Evaluation

• During iterations, normalized signal power decreases by 1 dB while normalized interference power decreases by more than 4 dB.Source: B. Convergence Evaluation of Proposed… · pp. 10–11, Figure 4 · p. 11

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.Source: C. Channel Characteristics under… · p. 11, Figure 6 · p. 11
• The initial position has channel power gain −84.5 dB, while the optimized position [−0.8λ, −0.5λ] provides a 6 dB increase.Source: Figure 6 · p. 11

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.Source: C. Channel Characteristics under… · p. 11
• Joint optimization does not simply maximize each user’s average channel power; it also tends to reduce channel-vector correlation and multiuser interference.Source: C. Channel Characteristics under… · pp. 11–12
• Compared with ZF, the MMSE-based solution achieves a better tradeoff between average channel power gain and normalized channel cross-correlation.Source: C. Channel Characteristics under… · p. 12

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.Source: D. Performance Comparison with… · p. 12

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.Source: D. Performance Comparison with… · p. 12

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.Source: D. Performance Comparison with… · pp. 12–13
• 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.Source: D. Performance Comparison with… · p. 13, Figure 10 · p. 13

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.Source: D. Performance Comparison with… · p. 13

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.Source: E. Impact of Imperfect FRI · pp. 13–14
• 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.Source: E. Impact of Imperfect FRI · p. 14

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.Source: E. Impact of Imperfect FRI · p. 14

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.Source: E. Impact of Imperfect FRI · p. 14

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.Source: §V · p. 14

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.Source: §V · pp. 14–15

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.Source: §V · p. 15

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.Source: §V · p. 15