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Multiuser Communications with Movable-Antenna Base Station: Joint Antenna Positioning, Receive Combining, and Power Control

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

arXiv:2308.09512v1cs.ITeess.SP

TL;DR

The paper studies how multiple movable antennas at a base station can improve fair multiuser uplink rates, a setting not addressed by prior continuous-position MA work. It jointly optimizes antenna positions, receive combining, and transmit powers with a two-loop PSO–BCD procedure, and reports a 63% improvement in minimum achievable rate over the evaluated iterations.

  • Problem

    Prior work had not addressed continuous-position multiple-MA deployment at the base station for fair multiuser uplink communication.

  • Method

    The paper models the position-dependent uplink channel and uses outer-loop PSO with inner-loop BCD optimization of receive combining and user transmit powers.

  • Results

    The minimum achievable rate increases from 1.44 bps/Hz to 2.36 bps/Hz, yielding about 63% performance improvement.

  • Takeaways & Limitations

    Deploying and optimizing multiple MAs at the base station improves multiuser uplink rate performance relative to conventional fixed-position-antenna operation.

Abstract

from arXiv · show

Movable antenna (MA) is an emerging technology which enables a local movement of the antenna in the transmitter/receiver region for improving the channel condition and communication performance. In this paper, we study the deployment of multiple MAs at the base station (BS) for enhancing the multiuser communication performance. First, we model the multiuser channel in the uplink to characterize the wireless channel variation due to MAs' movements at the BS. Then, an optimization problem is formulated to maximize the minimum achievable rate among multiple users for MA-aided uplink multiuser communications by jointly optimizing the MAs' positions, their receive combining at the BS, and the transmit power of users, under the constraints of finite moving region for MAs, minimum inter-MA distance, and maximum transmit power of each user. To solve this challenging non-convex optimization problem, a two-loop iterative algorithm is proposed by leveraging the particle swarm optimization (PSO) method. Specifically, the outer-loop updates the positions of a set of particles, where each particle's position represents one realization of the antenna position vector (APV) of all MAs. The inner-loop implements the fitness evaluation for each particle in terms of the max-min achievable rate of multiple users with its corresponding APV, where the receive combining matrix of the BS and the transmit power of each user are optimized by applying the block coordinate descent (BCD) technique. Simulation results show that the antenna position optimization for MAs-aided BSs can significantly improve the rate performance as compared to conventional BSs with fixed-position antennas (FPAs).

I. INTRODUCTION

The paper addresses the previously unstudied use of multiple movable antennas at a base station for fair multiuser uplink communication. It models position-dependent channels and jointly optimizes antenna positions, receive combining, and user transmit powers.

  • Motivation: Conventional fixed-position antennas cannot fully exploit continuous spatial-domain degrees of freedom for spatial diversity and multiplexing.Movable antennas use flexible-cable connections and adjustable positions within a spatial region to seek more favorable channels.
  • Research gap: Existing work had not investigated continuous-position movable antennas at the base station for multiuser uplink communication.The paper identifies multiple-MA deployment at the base station as an unaddressed problem.
  • Contributions: The paper jointly optimizes MA positions, base-station receive combining, and user transmit powers to maximize the minimum achievable rate.Constraints include finite moving regions, minimum inter-MA distance, and maximum user transmit power.
  • Contributions: A two-loop PSO-based algorithm obtains a suboptimal solution to the highly coupled non-convex optimization problem.The inner loop applies BCD to receive combining and transmit powers for a given antenna position vector.
  • System model: The system serves K single-FPA users with M base-station MAs using uplink SDMA, with K ≤ M.Each MA moves within a local two-dimensional region, while the receive signal is digitally combined at the base station.

A. Channel Model

The channel model represents each user's base-station channel as a position-dependent multipath response. Antenna movement changes path phases and therefore affects rates, receive combining, and transmit-power optimization.

  • Channel assumptions: Under the far-field assumption, channel-path AoAs and amplitudes remain fixed as MAs move, while only their phases vary.This models channel variation across the base-station receive region through antenna positions.
  • Channel model: The field-response channel is formed by superposing the coefficients of multiple paths between each user and the base-station MAs.The field-response matrix captures position-dependent responses, while the path-response vector contains multipath coefficients.
  • Channel variation: Small MA movements can significantly change every user’s channel through multipath phase variations.Because all MAs share the base-station receive region, moving one MA generally changes channels from all users.
  • Problem formulation: Each user’s achievable rate depends on the antenna position vector, which determines the channel matrix and influences receive combining and transmit powers.The optimization therefore treats antenna positions, combining, and power control as coupled variables.
  • Problem formulation: The max-min objective is constrained by the finite moving region, minimum inter-MA distance, and nonnegative user powers bounded by maximum values.The formulation assumes angular-domain field-response information is known.
  • Problem formulation: The resulting optimization is highly non-convex, with three high-dimensional variable types coupled through the objective.The paper consequently develops a PSO-based two-loop method rather than relying directly on existing polynomial-complexity tools.

III. PROPOSED SOLUTION

The proposed solver separates antenna-position search from receive-combining and power optimization. PSO explores antenna position vectors, while BCD and bisection evaluate each position through its max-min achievable rate.

  • APV optimization: A PSO outer loop searches antenna position vectors, using each vector’s inner-loop max-min rate as its fitness value.This avoids relying on conventional alternating optimization across all highly coupled variables.
  • Transmit power: The transmit-power update uses bisection to find the largest feasible minimum SINR under nonnegative and maximum-power constraints.Each midpoint is tested by checking the resulting powers against their bounds.
  • Inner-loop optimization: For a fixed antenna position vector, the inner loop alternates receive-combining and transmit-power optimization using BCD.The resulting objective is the max-min achievable rate associated with that position vector.
  • Receive combining: The receive-combining update uses a closed-form MMSE solution for fixed antenna positions and transmit powers.The power matrix is held fixed while the receive combiner is updated.
  • Convergence: BCD repeats the power and receive-combining updates until the objective’s relative increase falls below a convergence threshold.The final matrices correspond to the max-min achievable rate for the given antenna position vector.

B. APV Optimization

The APV optimization uses an outer PSO loop to search antenna positions and an inner evaluation to optimize receive combining and transmit power for each candidate. Feasibility is enforced through boundary projection and adaptive penalties for inter-MA spacing.

  • PSO-based APV search: The original problem is transformed into optimizing the max-min achievable rate as a function R(˜r) of the APV.For each APV, the inner loop calculates the optimal receive combining matrix and transmit power matrix before the outer-loop fitness evaluation.
  • PSO-based APV search: PSO is introduced because R(˜r) is highly non-convex and the 2M-dimensional APV search space can make direct optimization computationally prohibitive.Each particle represents a possible APV solution.
  • PSO-based APV search: Each particle updates its velocity and position using its local-best and global-best positions, random learning factors, and a decreasing inertia weight.The inertia weight is decreased during iterations to balance search speed and accuracy.
  • Feasibility handling: Boundary projection keeps every APV component within the finite moving region throughout the iterations.The projection function ensures that the APV remains in the feasible region.
  • Feasibility handling: An adaptive penalty reduces the fitness of particles violating the minimum inter-MA distance, driving the search toward APVs satisfying the spacing constraint.The violation set contains MA pairs whose Euclidean distance is smaller than D.
  • Algorithm output: After convergence, the best particle provides a generally suboptimal APV, whose corresponding receive combining and transmit power matrices are then calculated.The complete PSO-based algorithm initializes particles, evaluates fitness, updates positions, and returns ˜r, W, and P.

C. Convergence and Complexity Analysis

The two-loop method has non-decreasing inner and outer objectives, while boundedness guarantees convergence of the overall algorithm. Its complexity depends on user count, inner iterations, swarm size, and outer iterations.

  • Algorithm procedure: Algorithm 3 initializes particles, evaluates them with Algorithm 2, updates velocities and positions, and returns the best APV with its combining and power matrices.The outer loop runs for at most T iterations with swarm size N.
  • Convergence: The BCD inner loop has guaranteed convergence because alternating optimization of MMSE combining and transmit power makes the objective value non-decreasing.The receive combiner is optimized for the current power matrix, while transmit power is searched by bisection under the current combiner.
  • Convergence: The PSO outer loop has a non-decreasing global-best fitness, and boundedness of problem (7) guarantees convergence of the overall two-loop algorithm.Overall convergence depends on the convergence of both the BCD and PSO components.
  • Complexity: Algorithm 1 has complexity O(K^3 log^2 ϵ^-1), while the overall complexity increases with the inner-loop iteration limit J, swarm size N, and outer-loop limit T.The paper gives the complexity expressions in terms of these accuracy and iteration parameters.

IV. SIMULATION RESULTS

The simulation section evaluates the proposed MA-aided multiuser communication system and its algorithms, focusing on maximizing the minimum achievable rate among users.

  • Simulation objective: Numerical simulations evaluate the performance of the proposed MA-aided multiuser communication system and the effectiveness of its optimization algorithms.The evaluation targets maximization of the minimum achievable rate among users.
  • Simulation objective: The simulations assess the proposed algorithms for maximizing the minimum achievable rate among multiple users.This objective matches the system optimization target.
  • Reported outcomes: The supplied simulation passage states the evaluation objective but does not report numerical performance comparisons or convergence values.

A. Simulation Setup

The simulations consider K FPA users served by a BS with M MAs under randomized user distances, a square MA moving region, and a common number of receive paths.

  • Scenario: User distances are modeled as independent uniform variables over [20, 100] meters, with K FPA users served by a BS equipped with M MAs.The distance of user k is denoted d_k.
  • Scenario: The MA moving region is a square defined by [−A/2, A/2] × [−A/2, A/2].This region bounds the antenna-position search.
  • Channel model: The geometry channel model uses the same number of receive paths L for every user.The setup imposes L_k = L for 1 ≤ k ≤ K.
  • Channel model: Each user's elevation and azimuth angles of arrival are independently and uniformly distributed over [−π/2, π/2].The angles are denoted θ_k,l and ϕ_k,l.

B. Convergence Performance of Proposed Algorithms

The proposed algorithm converges quickly while improving the minimum achievable rate and satisfying the minimum inter-MA distance constraint. Its rate gains arise from increasing normalized target-signal power and reducing normalized interference power.

  • The minimum achievable rate increases from 1.44 bps/Hz to 2.36 bps/Hz, yielding about 63% performance improvement.The rate remains nearly unchanged after 250 iterations.
  • The penalty value remains zero after 50 iterations, indicating that the minimum inter-MA distance constraint is satisfied.
  • Normalized target-signal power increases from 4 dB to 6.7 dB during the iterations.APV optimization leverages spatial DoFs to obtain higher channel power gain.
  • Normalized interference power decreases from −4 dB to −8.1 dB, validating interference mitigation through reduced channel-vector correlation.The proposed algorithm enhances rate performance through channel-gain improvement and multiuser-interference suppression.

C. Channel Characteristics under APV Optimization

APV optimization changes the MAs’ positions to improve channel gains for both users while reducing their channel cross-correlation. The resulting positions support approximately equal user gains and lower multiuser interference.

  • APV optimization trades off the users’ distinct channel-gain maps and selects positions favorable to both users.The optimized gains are approximately equal, supporting max-min fairness.
  • User 1 and user 2 channel power gains increase from −70.1 dB and −73.1 dB to −67.2 dB and −67.2 dB, respectively.The MAs move from initial positions with low channel power gains to optimized positions with high channel power gains.
  • Normalized channel cross-correlation between user 1 and user 2 decreases from 0.1461 to 0.0518.The reduced correlation suppresses multiuser interference.

D. Performance Comparison with Benchmark Schemes

The proposed MA scheme is compared with fixed-position and discrete-position benchmarks across antenna, user, region-size, transmit-power, and channel-path settings. It consistently achieves the strongest minimum-rate performance by jointly exploiting continuous spatial degrees of freedom and MMSE-based interference mitigation.

  • Number of antennas: The MA scheme outperforms FPA, APS, and MPZF as the number of antennas increases.Joint continuous optimization of all MA positions leverages spatial degrees of freedom and can reduce the antennas required for a given rate.
  • Number of users: The MA scheme remains best as the number of users increases, while all schemes’ minimum rates decrease because mutual interference becomes more severe.For K = 16, MPZF becomes worse than APS, indicating the benefit of MMSE combining and corresponding power control.
  • Moving-region size: Increasing the normalized moving-region size raises the MA scheme’s minimum achievable rate, but with diminishing improvement.A larger region exposes more spatial degrees of freedom for antenna placement.
  • Transmit power: The minimum achievable rate increases with maximum transmit power for every scheme, and MA remains the best-performing scheme.The MA advantage over MPZF is pronounced at pmax = 0 dBm but nearly disappears at pmax = 30 dBm because ZF noise amplification matters less at high SNR.
  • Number of channel paths: With more channel paths, all schemes improve, while MA’s minimum rate increases faster than FPA’s through reduced channel correlation and greater spatial diversity.The rate becomes nearly unchanged around 14 or 16 paths when the moving region is insufficient to fully exploit additional channel variation.

E. Impact of Imperfect FRI

The imperfect-FRI study evaluates AoA and PRV errors by optimizing APV with estimated channel information and evaluating combining and power control with actual information. Errors degrade performance, but the MA scheme generally retains an advantage over the benchmarks.

  • Error model: The baseline optimization and simulations assume perfect FRI, including AoAs and PRVs, although such errors are generally inevitable in practice.The study therefore evaluates their effect on optimized APV performance.
  • AoA errors: AoA errors are modeled as i.i.d. uniform deviations from the actual angles, with maximum error µ.The estimated AoAs are used for APV optimization, while actual AoAs are used for subsequent combining and power-control evaluation.
  • AoA errors: The MA scheme’s minimum achievable rate decreases as AoA error increases but still significantly exceeds FPA performance at µ = 0.2.Larger AoA errors can place MAs where multiuser interference is higher, harming ZF-based MPZF performance.
  • PRV errors: The MA scheme remains better than the benchmarks under high PRV error, although its improvement diminishes as normalized PRV-error variance increases.PRV errors make APV optimization less accurate and also degrade MPZF through multiuser interference.

V. CONCLUSION

The paper develops a multiple-MA base-station architecture and jointly optimizes antenna positions, receive combining, and user transmit powers for max-min uplink rate. A PSO-based two-loop algorithm yields significant rate gains over FPA systems while also examining imperfect FRI.

  • Conclusion: The paper models the multiuser channel as a function of the antenna position vector and formulates a constrained joint optimization for max-min achievable rate.The design covers MA positioning, BS receive combining, and each user’s transmit power under moving-region, inter-MA-distance, and power constraints.
  • Conclusion: A PSO-based two-loop iterative algorithm efficiently addresses the resulting non-convex optimization problem.The paper also evaluates how imperfect FRI affects the optimized APV solution.
  • Conclusion: Simulation results show significant rate-performance improvements over FPA-based systems through antenna-position optimization.The improvement exploits the additional spatial design degree of freedom provided by movable antennas.
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