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Movable Antenna Enhanced Downlink Multi-User Integrated Sensing and Communication System

Yanze Han, Min Li, Xingyu Zhao, Ming-Min Zhao, Min-Jian Zhao

TL;DR

The paper addresses joint optimization of movable antenna geometry and downlink multi-user ISAC beamforming to maximize sensing beampattern gain while satisfying per-user SINR constraints. It introduces an augmented Lagrangian formulation with auxiliary variables and a double-loop penalty-dual decomposition algorithm (PDD-JAPB), employing SDR and projected gradient updates for the inner loop and gradient-based dual updates in the outer loop. Theoretical guarantees include convergence to stationary solutions and a rank-one recovery result for the SDR subproblems, along with demonstrated sensing-beampattern gains over fixed-array and alternative MA designs, particularly for sparse, large-aperture configurations. The work highlights the practical potential of movable antennas to enhance sensing resolution and beam control in ISAC systems, with avenues for multi-target extension and alternative sensing metrics such as the CRB.

Abstract

This work investigates the potential of exploiting movable antennas (MAs) to enhance the performance of a multi-user downlink integrated sensing and communication (ISAC) system. Specifically, we formulate an optimization problem to maximize the transmit beampattern gain for sensing while simultaneously meeting each user's communication requirement by jointly optimizing antenna positions and beamforming design. The problem formulated is highly non-convex and involves multivariate-coupled constraints. To address these challenges, we introduce a series of auxiliary random variables and transform the original problem into an augmented Lagrangian problem. A double-loop algorithm based on a penalty dual decomposition framework is then developed to solve the problem. Numerical results validate the effectiveness of the proposed design, demonstrating its superiority over MA designs based on successive convex approximation optimization and other baseline approaches in ISAC systems. The results also highlight the advantages of MAs in achieving better sensing performance and improved beam control, especially for sparse arrays with large apertures.

Movable Antenna Enhanced Downlink Multi-User Integrated Sensing and Communication System

TL;DR

The paper addresses joint optimization of movable antenna geometry and downlink multi-user ISAC beamforming to maximize sensing beampattern gain while satisfying per-user SINR constraints. It introduces an augmented Lagrangian formulation with auxiliary variables and a double-loop penalty-dual decomposition algorithm (PDD-JAPB), employing SDR and projected gradient updates for the inner loop and gradient-based dual updates in the outer loop. Theoretical guarantees include convergence to stationary solutions and a rank-one recovery result for the SDR subproblems, along with demonstrated sensing-beampattern gains over fixed-array and alternative MA designs, particularly for sparse, large-aperture configurations. The work highlights the practical potential of movable antennas to enhance sensing resolution and beam control in ISAC systems, with avenues for multi-target extension and alternative sensing metrics such as the CRB.

Abstract

This work investigates the potential of exploiting movable antennas (MAs) to enhance the performance of a multi-user downlink integrated sensing and communication (ISAC) system. Specifically, we formulate an optimization problem to maximize the transmit beampattern gain for sensing while simultaneously meeting each user's communication requirement by jointly optimizing antenna positions and beamforming design. The problem formulated is highly non-convex and involves multivariate-coupled constraints. To address these challenges, we introduce a series of auxiliary random variables and transform the original problem into an augmented Lagrangian problem. A double-loop algorithm based on a penalty dual decomposition framework is then developed to solve the problem. Numerical results validate the effectiveness of the proposed design, demonstrating its superiority over MA designs based on successive convex approximation optimization and other baseline approaches in ISAC systems. The results also highlight the advantages of MAs in achieving better sensing performance and improved beam control, especially for sparse arrays with large apertures.

Paper Structure

This paper contains 14 sections, 1 theorem, 24 equations, 6 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Signal Model and Performance Metrics
  4. Signal Model
  5. Performance Metrics
  6. Problem Formulation
  7. Proposed Algorithm
  8. Problem Reformulation
  9. Subproblem With Respect to
  10. Subproblem With Respect to
  11. Update of Dual Variables and Penalty Factor
  12. Convergence and Computational Complexity Analysis
  13. Numerical Results
  14. Conclusion

Key Result

Theorem 1

If the relaxed version of (P3.a) without constraint rank is feasible, the optimal solution $\mathbf{W}^{*}_k$ of relaxed (P3.a) always satisfies rank($\mathbf{W}_k^{*}$)=1, $\forall k \in \{1: K\}$.

Figures (6)

  • Figure 1: An illustration of the system model considered.
  • Figure 2: Convergence behavior with $\Gamma_k=10$dB.
  • Figure 3: Transmit beampattern gain versus SINR $\Gamma_k$.
  • Figure 4: Transmit beampattern gain versus $N_\text{t}$.
  • Figure 5: CRB performance evaluation and comparison.
  • ...and 1 more figures

Theorems & Definitions (1)

  • Theorem 1