Accelerating High-Dimensional Waveform Optimization for Cognitive Radar via Decoupled Imitation-Reinforcement Learning

Waveform optimization is pivotal for enhancing the performance of cognitive radar, yet it confronts a fundamental dilemma: the pursuit of higher performance necessitates expanding the optimization space, which inevitably leads to the curse of dimensionality, preventing strategy convergence in real-time systems and forcing existing methods to compromise between performance and efficiency. Therefore, this paper proposes an effective high-dimensional waveform optimization framework (HWOF). The core innovation of this work is the establishment and proof of a principle of hierarchical decomposability, which mathematically demonstrates that the high-dimensional joint optimization problem under main-lobe suppression jamming can be decomposed into two sub-problems with a dominant-subordinate relationship. This theory provides a solid foundation for our design of a decoupled optimization method, enabling the application of specialized acceleration algorithms to sub-problems with distinct characteristics, such as data-driven multi-target tracking (MTT) and sample-sparse anti-jamming. Specifically, the MTT optimization module leverages a value decomposition network (VDN) and historical data to efficiently and cooperatively optimize four-dimensional waveform parameters. Concurrently, the anti-jamming module incorporates imitation learning (IL) to address the challenge of sparse interaction samples with non-cooperative jammers by constructing a virtual environment, thereby significantly accelerating strategy convergence. Simulation results under two typical jamming scenarios demonstrate that our theory-driven framework achieves rapid convergence within limited interactions and outperforms baseline strategies, including traditional End-to-End optimization, with an average tracking accuracy improvement of over 20$\%$.