博弈條件下雷達(dá)波形設(shè)計(jì)策略研究
doi: 10.11999/JEIT190114
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空軍工程大學(xué)信息與導(dǎo)航學(xué)院 西安 710077
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信息感知技術(shù)協(xié)同創(chuàng)新中心 西安 710077
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中國人民解放軍95019部隊(duì) 襄陽 441800
基金項(xiàng)目: 國家自然科學(xué)基金(61571456)，航空科學(xué)基金(20160196001)
Research on Radar Waveform Design Strategy under Game Condition
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Information and Navigation College, Aire Force Engineering University, Xi’an 710077, China
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Collaborative Innovation Center of Information Sensing and Understading, Xi’an 710077, China
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95019 troop of the PLA, Xiangyang 441800, China
Funds: The National Natural Science Foundation of China (61571456), The Aeronautical Science Foundation of China (20160196001)
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摘要: 為提高電子戰(zhàn)中彈載雷達(dá)檢測性能，該文提出基于納什均衡的雷達(dá)波形設(shè)計(jì)方法。首先建立電子戰(zhàn)條件下雷達(dá)與干擾信號博弈模型，基于最大化信干噪比(SINR)準(zhǔn)則，分別設(shè)計(jì)了雷達(dá)和干擾的波形策略；然后通過數(shù)學(xué)推導(dǎo)論證了博弈納什均衡解的存在性，設(shè)計(jì)了一種重復(fù)剔除嚴(yán)格劣勢的多次迭代注水方法來實(shí)現(xiàn)納什均衡；通過二步注水法推導(dǎo)了非均衡的maxmin優(yōu)化方案；最后通過仿真實(shí)驗(yàn)測試不同策略下雷達(dá)檢測性能。仿真結(jié)果證明，基于納什均衡的雷達(dá)信號設(shè)計(jì)有助于提升博弈條件下雷達(dá)檢測性能，對比未博弈時(shí)，雷達(dá)檢測概率最高可提升12.02%，較maxmin策略最高可提升3.82%，證明所設(shè)計(jì)的納什均衡策略更接近帕累托最優(yōu)。
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關(guān)鍵詞:
- 雷達(dá)波形設(shè)計(jì) /
- 納什均衡 /
- 信干噪比 /
- 迭代注水法 /
- maxmin方法
Abstract: In order to improve missile-borne radar detection performance in modern electronic warfare, a radar waveform design method based on Nash equilibrium is proposed. Firstly, the radar and jammer game signal models are established in electronic warfare. Based on maximum Signal-to-Interference-plus-Noise Ratio (SINR), waveform strategies of radar and jammer are designed respectively. Secondly, the existence of Nash equilibrium solution is demonstrated by mathematical derivation and verified in experimental simulation. A multiple iterative water-filling method which repeatedly eliminates strict disadvantages is designed to achieve Nash equilibrium. The maxmin scheme of disequilibrium game is deduced by two-step water-filling method. Finally, the radar detection performance of optimization strategies is tested by simulation experiments. Simulation results reveal that the radar waveform design based on Nash equilibrium is beneficial to improve the radar detection performance under game conditions. Compared with no-game and maxmin strategies, the radar detection probability of Nash equilibrium strategy can be increased by 12.02% and 3.82%, respectively. It is proved that the Nash equilibrium strategy of this paper is closer to the Pareto optimality. -
表 1 迭代注水算法
(1) 初始化雙方策略) $\left| {S({f_k})} \right| = {\left| {S({f_k})} \right|_0}$, $J({f_k}) = J{({f_k})_0}$ (2) 最大化雷達(dá)效益$\mathop {\max }\limits_{{\rm{SINR}}} \left( {{{\left| {S({f_k})} \right|}^*},\lambda } \right)$ (3) 更新雷達(dá)策略$\left| {S({f_k})} \right| = {\left| {S({f_k})} \right|^ * }$ (4) 最大化干擾效益$\mathop {\min }\limits_{{\rm{SINR}}} \left( {J{{({f_k})}^*},\gamma } \right)$ (5) 更新干擾策略$J({f_k}) = J{({f_k})^ * }$ (6) 重復(fù)步驟(2)—步驟(5)直到${\left| {S({f_k})} \right|^ * }$與$J{({f_k})^ * }$保持不變 
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表 2 各頻帶功率分配策略及性能
策略 子帶1(W) 子帶2(W) 子帶3(W) 子帶4(W) 子帶5(W) SINR(dB) 檢測概率(%) 運(yùn)算時(shí)間(s) 納什均衡 雷達(dá) 7.0313 7.5312 18.2321 39.5216 27.6882 9.761 52.72 1.537 干擾 6.3916 6.5261 18.0624 40.6172 28.4126 maxmin 雷達(dá) 6.0337 4.3443 12.8720 40.5470 36.2027 9.554 49.31 0.485 干擾 6.2589 7.7107 18.3573 39.6503 28.0359
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