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Grey-Box Bayesian Optimization for ISAC in Fluid-Antenna Assisted Air-Ground Network

Gangyong Zhu, Jia Yan, Miaowen Wen, Shijian Gao

Abstract

Fluid antenna systems (FAS) provide extra position agile spatial diversity for integrated sensing and communication (ISAC), by jointly optimizing the port selection and precoding. However, this optimization is challenging in air ground networks due to the intricate dual objective Pareto frontier, complex self-interference, and prohibitive channel state information overhead. To overcome these bottlenecks, this work proposes a novel grey box multi objective Bayesian optimization framework to address the joint design of discrete port selection and ISAC precoding. Unlike black box methods, this architecture explicitly leverages known physical system models to learn unknown channel constituents, dramatically reducing sample complexity. To navigate high dimensional combinatorial spaces, an adaptive trust region mechanism powered by expected hypervolume improvement (EHI) acquisition is implemented. Furthermore, the framework incorporates a spatio-temporal tracking strategy to handle the continuous mobility of users and targets, robustly capturing the drifting optimum in time varying environments. Simulations demonstrate that this framework achieves significantly faster convergence and discovers superior Pareto optimal configurations, validating its efficiency for dynamic real time FAS-ISAC deployments.

Grey-Box Bayesian Optimization for ISAC in Fluid-Antenna Assisted Air-Ground Network

Abstract

Fluid antenna systems (FAS) provide extra position agile spatial diversity for integrated sensing and communication (ISAC), by jointly optimizing the port selection and precoding. However, this optimization is challenging in air ground networks due to the intricate dual objective Pareto frontier, complex self-interference, and prohibitive channel state information overhead. To overcome these bottlenecks, this work proposes a novel grey box multi objective Bayesian optimization framework to address the joint design of discrete port selection and ISAC precoding. Unlike black box methods, this architecture explicitly leverages known physical system models to learn unknown channel constituents, dramatically reducing sample complexity. To navigate high dimensional combinatorial spaces, an adaptive trust region mechanism powered by expected hypervolume improvement (EHI) acquisition is implemented. Furthermore, the framework incorporates a spatio-temporal tracking strategy to handle the continuous mobility of users and targets, robustly capturing the drifting optimum in time varying environments. Simulations demonstrate that this framework achieves significantly faster convergence and discovers superior Pareto optimal configurations, validating its efficiency for dynamic real time FAS-ISAC deployments.

Paper Structure

This paper contains 25 sections, 3 theorems, 42 equations, 6 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model
  3. FAS-enabled ISAC Networks
  4. Communication and Sensing Model
  5. Mobility and Time-Varying Channel Model
  6. Kinematic Evolution of Users and Targets
  7. Time-Varying ISAC Channel Evolution
  8. Grey box BO Method for FAS-ISAC Precoding
  9. Problem Formulation
  10. Surrogate Modeling and Acquisition
  11. Gaussian Process Surrogate
  12. Random Forest Surrogate for Grey box Modeling
  13. EHI Acquisition Function
  14. Constrained Local Search via Trust Region Adaptation
  15. Pareto Frontier Tracking via Adaptive Trust Region Resizing
  16. ...and 10 more sections

Key Result

Proposition 1

With probability at least $1-\delta$, the cumulative hypervolume regret is globally bounded by: where $\gamma_N(\mathcal{Z})$ is the maximum information gain for the chosen GP kernel over the domain $\mathcal{Z}$, and $C>0$ is a constant dependent on the noise level and confidence scaling. The exact growth rate of $\gamma_N(\mathcal{Z})$ depends fundamentally on the kernel (e.g., $\mathcal{O}(

Figures (6)

  • Figure 1: System of the proposed FAS-ISAC setup.
  • Figure 2: Illustration of the surrogate modeling approaches. (a) The predictive mean landscape of a Gaussian Process. (b) The ensemble structure of the Random Forest surrogate.
  • Figure 3: Performance evaluation: (a) Impact of transmit power budget on Scalarized objective ($\alpha = 0.5$), (b) Hypervolume convergence over evaluations, and (c) The trade-off between communication (Sum-Rate) and sensing (MI).
  • Figure 4: Internal ablation study comparing the hypervolume convergence of Grey-Box and Black-Box modeling across RF and GP surrogates.
  • Figure 5: Performance evaluation for different port spacing.
  • ...and 1 more figures

Theorems & Definitions (6)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3: Sample Efficiency of Grey-Box Modeling
  • proof