基于Stackelberg模型的弹载雷达和干扰波形设计

现代电子战中，弹载雷达与干扰机间存在着二元零和动态博弈。针对博弈条件下弹载雷达和干扰机性能降低问题，分别以雷达和干扰为博弈主导者，建立Stackelberg博弈模型，基于信干噪比准则提出了二次注水的波形设计方法。在雷达主导的博弈模型中，干扰通过min策略最小化雷达接收端信干噪比，雷达通过二次注水的maxmin策略分配信号频域功率，降低干扰影响；在干扰主导的博弈中，雷达通过max策略最大化自身信干噪比，干扰机利用minmax策略提高干扰效能。实验仿真表明，maxmin策略中雷达检测性能较min策略最高提升9.17%，而minmax策略中目标被探测概率较max策略最多降低11.42%；为博弈条件下雷达信号和干扰信号的优化分别提供了解决方案。 

Waveform Design of Missile-borne Radar and Jammer Based on Stackelberg Model

A novel two-step water-filling waveform design method based on Signal-to-Interference-plus-Noise Ratio (SINR) criterion is proposed to improve game performance of radar and jammer in this paper. There is a two-person zero-sum dynamic game between missile-borne radar and jammer in modern electronic warfare. Based on game theory, Stackelberg leadership models are established in clutter and noise. When radar is the game leader, the jammer uses water-filling method to minimize the output SINR. In order to reduce the impact of jamming, radar allocates signal power in frequency domain through two-step water-filling method. In the jammer-dominated game, radar makes use of max strategy to maximize SINR. The jammer improves jamming performance according to minmax strategy. Simulation results reveal that compared with min strategy, radar detection performance in maxmin strategy can be improved by 9.17%. In minmax strategy, target detection probability could decrease by up to 11.42% compared to max strategy. This demonstrates that two-step water-filling method provides a solution for waveform design in games.