A Dual Belief-Driven Bayesian-Stackelberg Framework for Low-Complexity and Secure Near-Field ISAC Systems

Ensuring robust security in near-field Integrated Sensing and Communication (ISAC) systems remains a critical challenge due to dynamic channel conditions, multi-eavesdropper threats, and the high computational burden of real-time optimization at mmWave and THz frequencies. To address these challenges, this paper introduces a novel Bayesian-Stackelberg framework that jointly optimizes sensing, beamforming, and communication. The dual-algorithm design integrates (i) Adaptive Hybrid Node Role Switching between secure transmission and cooperative jamming (ii) Belief-Driven Sensing and Beamforming for confidence based resource allocation. The proposed unified framework significantly improves robustness against attacks while preserving linear computational complexity. Simulation results across carrier frequencies ranging from 28 to 410 GHz demonstrate that the method achieves up to a 35% increase in secrecy rates and a success rate exceeding 98%, outperforming conventional communication systems with minimal runtime overhead. These findings underscore the scalability of belief-driven ISAC security solutions for low-complexity deployment in next generation communications.

💡 Research Summary

This paper tackles the pressing problem of physical‑layer security in near‑field Integrated Sensing and Communication (ISAC) systems that operate at millimeter‑wave (mmWave) and terahertz (THz) frequencies. In such bands, severe path loss, beam leakage, and the broadcast nature of wireless signals dramatically increase the vulnerability to passive eavesdropping and active jamming, especially when the system must simultaneously perform high‑resolution sensing and high‑rate data transmission. Existing solutions either assume static channel conditions, focus on a single objective (e.g., beamforming), or rely on computationally intensive optimization that cannot keep up with the rapid dynamics of mmWave/THz links.

To address these gaps, the authors propose a unified, low‑complexity framework that merges Bayesian inference with a Stackelberg game. The ISAC base station (IBS) acts as the Stackelberg leader, while a set of hybrid nodes (HNs) serve as followers. Each HN can switch between two roles on a per‑time‑slot basis: (i) secure data reception (normal mode) or (ii) cooperative friendly jamming (FJ mode). The role decision is driven by a predicted secrecy rate compared against a target secrecy threshold.

Key components of the framework:

1. Bayesian Belief Prediction:
   At the beginning of each slot, the leader maintains a discrete probability distribution over possible eavesdropper directions. The belief is propagated using a Gaussian‑like transition kernel that models smooth angular drift, and it is updated with pseudo‑likelihoods derived from tapered sensing beams steered toward the current maximum‑a‑posteriori (MAP) direction. The Shannon entropy of the belief quantifies uncertainty; a high entropy triggers a larger sensing weight (γ), allocating more power to wide‑field sensing, whereas low entropy focuses the beam for high‑gain narrow‑field sensing.

2. Stackelberg Leader Optimization:
   Using the updated belief, the leader predicts each HN’s expected secrecy rate and broadcasts a compact control policy θ = {γ, protected angle set B, leakage cap ρ_leak}. This policy anticipates the followers’ best‑response actions and defines the Stackelberg equilibrium for the slot.

3. Follower Best‑Response (Role Switching):
   Each HN compares its predicted secrecy rate to the threshold. If the prediction falls short, the node switches to FJ mode (Jam_u = 1) and transmits a jamming beam aligned with the belief distribution while placing notches at protected angles B. Otherwise, it remains in secure transmission mode. The binary decision incurs negligible computational load.

4. Dual Updates and Meta‑Adaptation:
   After the slot, the leader evaluates key performance indicators: average secrecy rate, secrecy‑outage probability, and belief entropy. Two Lagrange multipliers—λ_O for secrecy outage and λ_H for entropy deviation—are updated via subgradient steps. The kernel width σ is adaptively widened when secrecy is poor (encouraging exploration) and narrowed when secrecy is satisfactory (favoring exploitation).

5. Low‑Complexity Utility Function:
   The leader maximizes
   U = ω_R·min_u R_s(u) – ω_J·P_FJ – λ_H·