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Movable Antenna Enabled Integrated Sensing and Communication

Wanting Lyu, Songjie Yang, Yue Xiu, Zhongpei Zhang, Chadi Assi, Chau Yuen

arXiv:2410.19763v2eess.SP

TL;DR

This paper addresses how to improve communication and sensing together when fixed antenna positions limit channel adjustment in ISAC. It jointly optimizes beamforming coefficients and movable-antenna positions using a fractional-programming and alternating-optimization method with a three-stage SPGA search. Simulations report that four MAs with SPGA outperform eight fixed antennas in a large feasible moving region.

Abstract

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In this paper, we investigate a novel integrated sensing and communication (ISAC) system aided by movable antennas (MAs). A bistatic radar system, in which the base station (BS) is configured with MAs, is integrated into a multi-user multiple-input-single-output (MU-MISO) system. Flexible beamforming is studied by jointly optimizing the antenna coefficients and the antenna positions. Compared to conventional fixed-position antennas (FPAs), MAs provide a new degree of freedom (DoF) in beamforming to reconfigure the field response, and further improve the received signal quality for both wireless communication and sensing. We propose a communication rate and sensing mutual information (MI) maximization problem by flexible beamforming optimization. The complex fractional objective function with logarithms are first transformed with the fractional programming (FP) framework. Then, we propose an efficient algorithm to address the non-convex problem with coupled variables by alternatively solving four sub-problems. We derive the closed-form expression to update the antenna coefficients by Karush-Kuhn-Tucker (KKT) conditions. To improve the direct gradient ascent (DGA) scheme in updating the positions of the antennas, a 3-stage search-based projected GA (SPGA) method is proposed. Simulation results show that MAs significantly enhance the overall performance of the ISAC system, achieving 59.8\% performance gain compared to conventional ISAC system enabled by FPAs. Meanwhile, the proposed SPGA-based method has remarkable performance improvement compared the DGA method in antenna position optimization.

I. INTRODUCTION

Prior ISAC work combines communication and sensing objectives, but fixed-position antennas limit spatial channel adjustment. This paper studies movable-antenna ISAC, jointly optimizing beamforming coefficients and antenna positions to improve both functions.

I. INTRODUCTION

  • Continuous antenna positioning can reconfigure wireless channels, unlike discrete antenna selection, while earlier array synthesis emphasizes radiation patterns over physical communication channels.The paper frames movable antennas as an additional beamforming degree of freedom for exploiting spatial diversity.Source: §I · p. 1

A. Related Works

  • Prior ISAC studies use varied sensing metrics and objective priorities, while the cited weighted-objective approaches and comparisons remain based on fixed-position antennas.The reviewed sensing metrics include beampattern gain, CRB, SCNR, and sensing MI.Source: A. Related Works · p. 2
  • Earlier movable-antenna work studied communication capacity and optimization, while sensing work considered antenna-position design for angle-of-arrival accuracy.The communication examples include MA-enabled MU-MISO and flexible precoding; the sensing example minimizes AoA CRB.Source: A. Related Works · p. 2

B. Motivation and Contributions

  • The paper formulates a cluttered bistatic MA-ISAC system that jointly optimizes transmit coefficients and positions to maximize weighted communication rate and sensing MI.The weighting factor controls the priority assigned to the two functions.Source: B. Motivation and Contributions · p. 3
  • A fractional-programming and alternating-optimization approach solves four subproblems, with a three-stage SPGA position search replacing DGA; simulations also examine beampatterns and CRB.The paper reports that the SPGA-based algorithm improves both sensing and communication performance.Source: B. Motivation and Contributions · p. 3

C. Organizations and Notations

The system uses a bistatic transmitter and sensing receiver, with movable transmit antennas serving multiple users and sensing a target amid clutter. The signal model links antenna positions to communication channels and sensing echoes.

II. SYSTEM MODEL AND PROBLEM FORMULATION

  • The bistatic system separates the DFRC base station transmitter from the sensing receiver, which helps avoid full-duplex self-interference, and includes C sensing clutters.The BS has a linear array of N movable antennas; each user and the sensing receiver has one fixed-position antenna.Source: §II · p. 3

A. Channel Model

  • Under the far-field assumption, array response across transmit antennas depends on phase differences, and the one-dimensional movable-antenna positions form the vector x.Communication channels use a multipath model; the sensing model assumes detectable line-of-sight paths to the target and clutters.Source: A. Channel Model · pp. 3–4

B. Communication and Sensing Signal Model

  • The model transmits K user streams and one sensing stream, assumes known CSI and waveform knowledge at the sensing receiver, and derives communication rates from position-dependent user channels.The sensing receiver uses the transmitted communication and sensing streams to process target and clutter echoes.Source: B. Communication and Sensing Signal… · p. 4
  • Sensing mutual information measures the information between the received echo and target parameter, using the sensing receiver's prior knowledge of the transmitted waveform.The paper employs sensing MI to align sensing evaluation with the logarithmic form of communication rate.Source: B. Communication and Sensing Signal… · p. 4

C. Problem Formulation

The formulation maximizes weighted communication rate and sensing mutual information by choosing beamforming and movable-antenna positions. Antenna positions must remain within the movable region and satisfy a minimum separation constraint.

C. Problem Formulation

  • The antenna-position design is constrained to a predetermined feasible region and requires sufficient separation between antenna elements to mitigate coupling.The paper also allows element ordering to change during optimization and rearranges indices afterward.Source: C. Problem Formulation · p. 5
  • The objective maximizes the weighted sum of communication rate and sensing MI, with the weights controlling the priority of the two functions.The weights sum to one.Source: C. Problem Formulation · p. 5
  • The problem is non-convex because its fractional logarithmic objective depends on antenna positions through complex array responses, alongside coupled variables and non-convex constraints.The study focuses on a single target for simplicity and states that the approach can be adapted to multiple targets by treating other target echoes as radar interference.Source: C. Problem Formulation · p. 5

III. PROPOSED SPGA-FP BASED APPROACH FOR FLEXIBLE BEAMFORMING

The approach transforms the rate-and-sensing-MI objective using fractional programming, then alternates updates across four subproblems to address coupled variables. Its framework updates beamforming, antenna positions, and auxiliary variables in turn.

III. PROPOSED SPGA-FP BASED APPROACH FOR FLEXIBLE BEAMFORMING

  • Fractional programming transforms the multi-ratio logarithmic objective using Lagrangian dual and quadratic transforms, introducing auxiliary variables.The transformed problem is then optimized iteratively because its variables are mutually coupled.Source: §III · p. 5
  • Alternating optimization decomposes the transformed problem into updates for the beamforming matrix, antenna positions, and auxiliary variables.Each variable is updated while holding the others at their preceding-iteration values.Source: §III · p. 5

A. Updating Transmit Beamforming.

The transmit-beamforming subproblem is convex and can be solved with a low-complexity closed-form update derived using Lagrangian dual decomposition and KKT conditions. A bisection search can select the power-constraint multiplier when needed.

A. Updating Transmit Beamforming.

  • The beamforming subproblem is convex, and a closed-form solution based on Lagrangian dual decomposition reduces the complexity of solving it with standard solvers such as CVX.The KKT conditions are used to solve the dual problem.Source: A. Updating Transmit Beamforming · p. 6
  • The multiplier λ corresponds to the transmit-power constraint, and the optimal beamformer is obtained from the solution to the KKT conditions.If the primal feasibility condition holds at λ = 0, the optimal beamforming is f_k(0).Source: A. Updating Transmit Beamforming · p. 6
  • Because h(λ) decreases monotonically with λ, bisection can be used to find the multiplier.Source: A. Updating Transmit Beamforming · p. 6

B. Updating Antenna Positions.

The antenna-position objective is differentiable but non-convex, so direct gradient ascent can reach a nearby stationary point or stop at a constraint boundary. The proposed SPGA combines an initial search, unconstrained gradient ascent, and feasibility projection.

B. Updating Antenna Positions.

  • DGA can stop at a constraint boundary or converge to a nearby stationary point, resulting in suboptimal performance for the non-convex position problem.The objective is differentiable across the feasible region, but antenna moves can violate position and minimum-distance constraints.Source: B. Updating Antenna Positions · p. 6
  • SPGA addresses this by combining a preliminary search, gradient ascent that initially ignores constraints, and projection of violating positions into the feasible region.The three stages are initial point search, gradient ascent updating, and feasibility region projection.Source: B. Updating Antenna Positions · p. 7

1) Initial point search:

The position update begins by selecting antenna starting points from a uniform set covering the feasible region, then alternates gradient-ascent updates until the objective reaches a stationary point.

1) Initial point search:

  • Uniform discrete points covering the feasible region A are searched to choose each antenna's initial position that maximizes the objective.Source: 1) Initial point search · p. 7

2) Gradient ascent updating:

  • With other antennas fixed, positions are updated in an inner loop by gradient ascent with step size κt until the objective converges to a stationary point.Source: 2) Gradient ascent updating · p. 7

3) Feasible region projection:

After position optimization, the antenna locations are projected into the feasible region while restoring their sequential order and minimum spacing. The auxiliary variable μ is updated using the derivative of the transformed objective.

3) Feasible region projection:

  • Projection enforces the movable-region and distance constraints, reorders antenna indices if needed, and maintains at least D0 spacing between adjacent elements.The projection assigns feasible positions in sequence while respecting the array bounds and minimum-distance requirement.Source: 3) Feasible region projection · p. 7

C. Updating Auxiliary Variable for Lagrangian Dual Transform.

D. Updating Auxiliary Variable for Quadratic Transform

The auxiliary-variable update exploits concavity in the quadratic-transform variables. The overall algorithm alternates updates across four sub-problems until the objective converges, with complexity dominated by gradient ascent.

D. Updating Auxiliary Variable for Quadratic Transform

E. Overall Algorithm and Complexity Analysis

  • The algorithm's total complexity is dominated by gradient ascent and is O(IaIgN^2K^2L^2p).Ia is the number of alternating-optimization iterations and Ig is the number of gradient-update iterations.Source: E. Overall Algorithm and Complexity… · p. 8
  • Algorithm 2 alternates updates to F, antenna positions x, and auxiliary variables, projecting x into the feasible region and stopping when the objective converges.The position step searches for initial points before iterating; the algorithm outputs F⋆ and x⋆.Source: E. Overall Algorithm and Complexity… · p. 8

IV. NUMERICAL RESULTS

The simulations evaluate flexible beamforming with movable antennas across SNR, moving-region size, and sensing–communication weighting. The results report performance gains for SPGA-based position optimization and show that outcomes vary with the weighting and operating mode.

IV. NUMERICAL RESULTS

  • The simulations use K = 4 users, C = 3 clutters, N = 4 or 8 transmit MAs, and 200 Monte Carlo simulations.The feasible moving-region lower bound is Xmin = 0, while Xmax varies.Source: §IV · pp. 8–9

A. Overall Utility versus number of iterations.

B. Sum rate and MI versus SNR and maximum moving region.

  • With 8 transmit MAs, SPGA-FP achieves 18.5% and 37.5% performance gains compared to DGA and FPAs, respectively.The objective function grows with SNR and antenna count, and SPGA's advantage over DGA and FPAs is especially apparent at high SNR.Source: Figure 4 · p. 9, B. Sum rate and MI versus SNR and… · p. 9
  • With an extended moving region, SPGA-FP improves ISAC performance; 4 SPGA MAs outperform 8 FPAs particularly at large Xmax.DGA shows only modest gains over FPAs and slight improvement as Xmax grows; it tends to converge near its initial value without a search stage.Source: Figure 5 · p. 9, B. Sum rate and MI versus SNR and… · p. 10

C. Trade-off between sensing and communication.

  • When ϖc = 1, sensing MI remains weak; when ϖs = 1, communication is likewise weak, while more MAs maintain better overall performance at higher hardware expense.The results indicate that weighting factors and configuration parameters need consideration in practical engineering.Source: Figure 6 · p. 10, C. Trade-off between sensing and… · p. 10

D. Sensing and communication performance versus SNR.

  • SPGA-FP achieves 32.8% and 97.6% performance gains in sensing MI compared to SPGA-optimized-MA random beamforming and the basic FPA array, respectively.The sensing-focused evaluation sets ϖs = 0.8; sensing MI rises substantially as SNR increases from -20 dB to 10 dB.Source: Figure 7 · p. 10, D. Sensing and communication… · p. 10
  • In communication-focused ISAC with ϖc = 0.8, communication-rate performance improvement is more significant than sensing-MI improvement.The figure compares communication rate versus SNR.Source: Figure 8 · p. 10, D. Sensing and communication… · p. 10

E. Pure sensing/communication versus maximum moving region

The moving-region experiments show different sensing and communication responses, while the beampattern and CRB analyses examine sensing benefits from antenna-position optimization. The conclusion reports gains over fixed-position antennas and DGA-based position optimization.

E. Pure sensing/communication versus maximum moving region

  • Sensing MI remained nearly constant as Xmax increased, and MA gains over an optimized FPA array were marginal; antenna-coefficient optimization had greater sensing potential than position optimization.Source: E. Pure sensing/communication versus… · p. 11
  • Both antenna-coefficient and position design significantly increased user rate, with coefficient optimization performing better and SPGA gains increasing for larger moving regions.Source: E. Pure sensing/communication versus… · p. 11

F. Beampattern versus angle.

G. CRB versus angle.

V. CONCLUSION

  • 4 MAs outperformed 8 FPAs, while SPGA gained over DGA in large moving regions and high-SNR settings; MAs performed better in multipath communication than single-path sensing.Source: §V · p. 12

APPENDIX A DERIVATION OF CRB

The appendix derives a Cramér–Rao bound for target-parameter estimation from the sensing echo model. Its analysis focuses on target angle and models clutter and noise as effective noise.

APPENDIX A DERIVATION OF CRB

  • The echo model treats the target signal as deterministic and clutter echo as zero-mean Gaussian noise.The derivation begins from the sensing receiver's echo signal over T time indices.Source: Appendix A · p. 12
  • Noise is independently and identically distributed across time indices, and clutter plus noise is represented as effective Gaussian noise.Source: Appendix A · p. 12
  • The estimated parameter vector contains target angle and the real and imaginary parts of its complex amplitude, from which the Fisher information matrix is formed.Source: Appendix A · p. 12
  • The appendix computes the CRB only for the target angle because that is the parameter of interest.Source: Appendix A · p. 12
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