WO2021258734A1 - 博弈条件下基于低截获性能的组网雷达最优波形设计方法 - Google Patents

博弈条件下基于低截获性能的组网雷达最优波形设计方法 Download PDF

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WO2021258734A1
WO2021258734A1 PCT/CN2021/074624 CN2021074624W WO2021258734A1 WO 2021258734 A1 WO2021258734 A1 WO 2021258734A1 CN 2021074624 W CN2021074624 W CN 2021074624W WO 2021258734 A1 WO2021258734 A1 WO 2021258734A1
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radar
waveform
frequency
target
networked
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PCT/CN2021/074624
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French (fr)
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时晨光
丁琳涛
王奕杰
周建江
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南京航空航天大学
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/38—Jamming means, e.g. producing false echoes
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
    • Y02T10/40—Engine management systems

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  • the invention relates to radar signal processing technology, in particular to a method for designing an optimal waveform of a netted radar based on low interception performance under game conditions.
  • the networked radar system has the characteristics of discrete spatial distribution. It can extract target feature information from multiple dimensions and multiple perspectives, and use the inter-radar data link to transmit the data to the system fusion center for information fusion processing, so as to realize the sharing of information and intelligence resources.
  • the networked radar also has many excellent features. For example, the coverage of each radar in the system overlaps with each other, and a better target track can be obtained, so the tracking performance is better. In addition, through reasonable tactical configuration, it can interfere with and deceive the enemy's detection equipment. In summary, the detection advantages and battlefield survivability of the netted radar system are unmatched by a single radar.
  • the existing research results involve the design of optimal waveforms for networked radars based on low intercept performance, under the condition of meeting the preset target cooperative detection performance or parameter estimation performance, the transmission waveforms of each radar are adaptively optimized.
  • the design reduces the total radiated energy of the networked radar system and improves the low intercept performance of the networked radar system.
  • the existing research results have not considered the optimal waveform design based on low interception performance under the binary zero-sum game conditions of networked radar and interference, which has certain limitations, and there is no group based on low interception performance under game conditions.
  • the optimal waveform design method of net radar has been published in public reports.
  • the objective of the present invention is to provide an optimal waveform design method for netted radar based on low interception performance under game conditions.
  • the optimal waveform design method of netted radar based on low interception performance under game conditions of the present invention includes the following steps:
  • step (1) it is assumed that the intelligent jamming system is carried by the enemy's target.
  • the networked radar system composed of M radar nodes conducts a binary zero-sum game with the enemy's jamming, according to the prior information of the battlefield, Obtain the frequency response H i (f) of the target relative to radar i at frequency point f, the environmental clutter power spectral density S cc,i (f) corresponding to radar i at frequency point f, and the environmental noise corresponding to radar i at frequency point f
  • step (2) it is assumed that the networked radar transmission waveform bandwidth is W, the upper limit of the total interference energy of the intelligent interference system is E J , and the preset target parameter estimation performance mutual information threshold is ⁇ .
  • step (3) mutual information is used to characterize the target parameter estimation performance, and it is assumed that radar i has obtained the interference waveform J i (f) of the intelligent jamming system at frequency point f through the prior information; Under the condition of a predetermined mutual information threshold ⁇ , the optimal waveform design model of netted radar based on low interception performance under game conditions is established as follows:
  • S i (f) represents the emission waveform of radar i at frequency f
  • 2 represents the modulus square of the emission waveform of radar i at frequency f
  • W represents the bandwidth of the networked radar emission waveform
  • Ty represents the duration of the target echo signal
  • 2 represents the modulus square of the frequency response of the target relative to radar i at frequency point f
  • E J represents the upper limit of the total interference energy
  • M represents the number of radars
  • H i (f) Represents the frequency response of the target at frequency f relative to radar i
  • S cc,i (f) represents the environmental clutter power spectral density corresponding to radar i at frequency f
  • S nn,i (f) represents radar i at frequency f Corresponding environmental noise power spectral density.
  • the Lagrangian multiplier ⁇ 0 is introduced in step (4), and the Lagrangian objective function is constructed as follows:
  • ⁇ (
  • M is the number of radar
  • W denotes the bandwidth of the transmitted waveform radar netting
  • S i (f) i represents the radar frequency of f Transmission waveform
  • Ty represents the duration of the target echo signal
  • H i (f) represents the frequency response of the target relative to radar i at frequency f
  • S cc,i (f) represents the environmental clutter corresponding to radar i at frequency f
  • Power spectral density S nn,i (f) represents the environmental noise power spectral density corresponding to radar i at frequency point f
  • ⁇ is the target parameter estimation performance mutual information threshold
  • 2 , ⁇ ) is to find the first-order partial derivatives of
  • R i (f), B i (f), Di (f), A are intermediate variables, and the calculation formula is:
  • step (5) in order to minimize the amount of target information obtained by the networked radar, thereby reducing the performance of the networked radar system, the intelligent jamming system needs to optimize the design of the interference waveform according to the intercepted radar waveform parameters; assume the radar waveform Distribute uniformly in the bandwidth W, and establish the optimal design model for the interference waveform of the networked radar system under the condition of a binary zero-sum game:
  • M represents the number of radars
  • W represents the bandwidth of the networked radar transmission waveform
  • Ty represents the duration of the target echo signal
  • S i (f) represents the transmission waveform of radar i at frequency f
  • H i (f) represents frequency
  • 2 represents the modulus square of the frequency response of the target on frequency f relative to radar i
  • E J represents the upper limit of the total interference energy
  • S cc,i (f) represents The environmental clutter power spectral density corresponding to radar i at frequency f
  • S nn,i (f) represents the environmental noise power spectral density corresponding to radar i at frequency f
  • J i (f) is the prior information that radar i has passed Obtain the jamming waveform of the intelligent jamming system at frequency f for radar i.
  • the Lagrangian multiplier ⁇ 0 is introduced in step (6), and the Lagrangian objective function is constructed as follows:
  • M represents the number of radars
  • W represents the bandwidth of the networked radar transmission waveform
  • Ty represents the duration of the target echo signal
  • S i (f) represents the transmission waveform of radar i at frequency f
  • H i (f) represents frequency The frequency response of the target on f relative to radar i
  • 2 represents the modulus square of the frequency response of the target on frequency f relative to radar i
  • E J represents the upper limit of the total interference energy
  • S cc,i (f) represents The environmental clutter power spectral density corresponding to radar i at frequency f
  • S nn,i (f) represents the environmental noise power spectral density corresponding to radar i at frequency f
  • J i (f) is the prior information that radar i has passed Obtain the interference waveform of the intelligent jamming system against radar i at frequency point f;
  • the present invention considers the binary zero-sum game between the networked radar and the intelligent jamming system carried by the enemy target, and first obtains the target relative to each radar in the networked radar system according to the battlefield prior information. Node frequency response, environmental clutter power spectral density, interference waveform and environmental noise power spectral density. On this basis, the optimization goal is to minimize the total radiation energy of the networked radar system under the game condition to meet the preset target parameter estimation performance mutual information threshold as the constraint condition, and establish a group based on low interception performance under the game condition. Net radar optimal waveform design model, adaptively optimize the design of the transmit waveform of each radar node.
  • the optimization model is solved iteratively by using the Carlo Need-Kuhn-Tucker necessary conditions, and the radar emission waveforms under the pre-set target parameter estimation performance conditions are obtained as the optimal solution, so as to meet the pre-set target Under the constraint of parameter estimation performance, it can effectively improve the low interception performance of the netted radar system under the condition of binary zero-sum game.
  • the present invention has the following advantages:
  • the present invention is designed to adaptively optimize the transmission waveform of each radar node in the networked radar system under the condition of binary zero-sum game, which not only meets the preset mutual information threshold of target parameter estimation performance, but also effectively reduces The total radiation energy of the networked radar system is improved, thereby improving the low interception performance of the networked radar system under the condition of binary zero-sum game.
  • the reason for this advantage is that the present invention considers the binary zero-sum game between the networked radar and the intelligent jamming system carried by the enemy target, and first obtains the target relative to each radar in the networked radar system according to the battlefield prior information. Node frequency response, environmental clutter power spectral density, interference waveform and environmental noise power spectral density.
  • the optimization goal is to minimize the total radiation energy of the networked radar system under the game condition to meet the preset target parameter estimation performance mutual information threshold as the constraint condition, and establish a group based on low interception performance under the game condition.
  • Net radar optimal waveform design model adaptively optimize the design of the transmit waveform of each radar node.
  • the optimization model is solved iteratively by using the Carlo Need-Kuhn-Tucker necessary conditions, and the radar emission waveforms under the pre-set target parameter estimation performance conditions are obtained as the optimal solution, so as to meet the pre-set target Under the constraint of parameter estimation performance, it can effectively improve the low interception performance of the netted radar system under the condition of binary zero-sum game.
  • the method of the present invention not only satisfies the preset target parameter estimation performance mutual information threshold, but also realizes the adaptive optimization design of the transmission waveform of the networked radar system under the condition of binary zero-sum game between the radar and the interference, thereby minimizing The total radiation energy of the netted radar effectively improves the low intercept performance of the netted radar system under the condition of binary zero-sum game.
  • the optimal waveform design method of netted radar based on low interception performance under game conditions of the present invention includes the following steps:
  • the intelligent jamming system is carried by an enemy target.
  • a netted radar system composed of M radar nodes conducts a binary zero-sum game with the enemy’s interference, according to the battlefield prior information, the frequency response H i (f), The environmental clutter power spectral density S cc,i (f) corresponding to radar i at frequency f and the environmental noise power spectral density S nn,i (f) corresponding to radar i at frequency f.
  • the networked radar transmit waveform bandwidth is W
  • the upper limit of the total interference energy of the intelligent jamming system is E J
  • the preset target parameter estimation performance mutual information threshold is ⁇ .
  • S i (f) represents the transmission waveform of radar i at frequency f
  • 2 represents the modulus square of the radar i transmission waveform at frequency f
  • W represents the bandwidth of the networked radar transmission waveform
  • T y represents the duration of the target echo signal
  • 2 represents the modulus square of the frequency response of the target relative to the radar i at frequency f
  • E J represents the upper limit of the total interference energy.
  • the Lagrangian objective function is constructed as follows:
  • 2 , ⁇ ) respectively calculates the first-order partial derivatives of
  • R i (f), B i (f), Di (f), A are intermediate variables, and the calculation formula is:
  • the intelligent jamming system needs to optimize the design of the jamming waveform according to the intercepted radar transmission waveform parameters. Assuming that the radar waveform is evenly distributed in the bandwidth W, the optimal design model for the interference waveform of the networked radar system under the condition of a binary zero-sum game is established as:
  • the present invention considers that under the condition that the networked radar and the intelligent jamming system carried by the enemy target perform a binary zero-sum game, according to the battlefield prior information, the frequency response and environmental clutter of the target relative to each radar node in the networked radar system are obtained.
  • the power spectrum density, the interference waveform, and the environmental noise power spectrum density are used to calculate the mutual information value of the target parameter estimation performance obtained by the networked radar system; and the present invention takes minimizing the total radiated energy of the networked radar system under the gaming condition as the optimization objective, and takes Meet the pre-set target parameter estimation performance mutual information threshold as the constraint condition, establish the optimal waveform design model of the networked radar based on the low interception performance under the game condition, and adaptively optimize the design of the transmission waveform of each radar node.
  • the optimization model is solved iteratively by using the Carlo Need-Kuhn-Tucker necessary conditions, and the radar emission waveforms under the pre-set target parameter estimation performance conditions are obtained as the optimal solution, so as to meet the pre-set target Under the constraint of parameter estimation performance, it can effectively improve the low interception performance of the netted radar system under the condition of binary zero-sum game.

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  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Radar Systems Or Details Thereof (AREA)

Abstract

本发明公开了一种博弈条件下基于低截获性能的组网雷达最优波形设计方法，首先获取目标相对组网雷达系统中各雷达节点的频率响应、环境杂波功率谱密度、干扰波形以及环境噪声功率谱密度；然后以最小化博弈条件下组网雷达系统的总辐射能量为优化目标，以满足预先设定的目标参数估计性能互信息阈值为约束条件，建立博弈条件下基于低截获性能的组网雷达最优波形设计模型，自适应优化设计各雷达节点的发射波形；通过利用卡罗需-库恩-塔克必要条件迭代求解该优化模型，得到在满足预先设定的目标参数估计性能条件下的各雷达发射波形作为最优解，从而在满足预先设定的目标参数估计性能约束下，有效提升二元零和博弈条件下组网雷达系统的低截获性能。

Description

博弈条件下基于低截获性能的组网雷达最优波形设计方法 技术领域
本发明涉及雷达信号处理技术，具体涉及博弈条件下基于低截获性能的组网雷达最优波形设计方法。
背景技术
在现代战场上，电子情报系统(Electronic Intelligence,ELINT)、电子支援措施(Electronic Support Measures,ESM)、雷达告警接收机(Radar Warning Receiver,RWR)、反辐射导弹(Anti-Radiation Missile,ARM)等先进无源探测器被广泛使用，通过接收雷达辐射的电磁波来获取作战平台的位置和属性等信息，并且自身无需辐射电磁波，具有作用距离远、隐蔽性强的特点，这严重威胁了雷达系统的战场生存能力。因此，低截获技术的研究必须得到重视并加以实际运用。
组网雷达系统具有空间分布离散的特性，可以从多维度、多视角提取目标特征信息，并且借助雷达间数据链将数据传送至系统融合中心进行信息融合处理，从而实现信息情报资源的共享。除此以外，组网雷达还拥有许多优异的特点。例如，系统中各部雷达的覆盖范围相互有重叠，可以获得更好的目标航迹，因此跟踪性能更为优越。另外，通过合理的战术配置，能够起到干扰和欺骗敌方探测设备的效果。综上所述，组网雷达系统的探测优势以及战场生存能力是单部雷达所无法比拟的。在信息战逐渐走向网络化的时代，组网雷达系统的发展与应用也成为了先进作战雷达系统发展的必然趋势。因此，研究基于低截获性能的组网雷达发射波形优化技术具有重大的应用价值和战略意义。
然而，已有的研究成果虽然涉及基于低截获性能的组网雷达最优波形设计问题，在满足预先设定的目标协同探测性能或参数估计性能条件下，通过对各雷达发射波形进行自适应优化设计，降低组网雷达系统的总辐射能量，提升了组网雷达系统的低截获性能。然而，已有研究成果均未考虑组网雷达与干扰二元零和博弈条件下基于低截获性能的最优波形设计，具有一定的局限性，而且目前尚未有博弈条件下基于低截获性能的组网雷达最优波形设计方法见诸公开报道。
发明内容
发明目的：本发明的目的是提供一种博弈条件下基于低截获性能的组网雷达最优波形设计方法。
技术方案：本发明的博弈条件下基于低截获性能的组网雷达最优波形设计方法，包括以下步骤：
(1)获取目标与环境先验信息；
(2)确定组网雷达系统与智能干扰系统的辐射参数以及目标参数估计性能互信息阈值χ；
(3)构建博弈条件下基于低截获性能的组网雷达最优波形设计模型；
(4)构建拉格朗日目标函数Υ(|S i(f)| 2，η)，并采用卡罗需-库恩-塔克必要条件进行求解；
(5)构建二元零和博弈条件下针对组网雷达系统的干扰波形优化设计模型；
(6)构建拉格朗日目标函数Ω(J i(f)，κ)，并采用卡罗需-库恩-塔克必要条件进行求解；
(7)重复步骤(3)至步骤(6)，直至|S i(f)| 2与J i(f)均不再发生变化。此时，所得|S i(f)| 2即为博弈条件下基于低截获性能的雷达i最优发射波形的模平方。
进一步的，步骤(1)中假设智能干扰系统由敌方目标搭载，在由M部雷达节点组成的组网雷达系统与敌方干扰进行二元零和博弈的条件下，根据战场先验信息，获取频点f上目标相对雷达i的频率响应H i(f)、频点f上雷达i对应的环境杂波功率谱密度S cc,i(f)以及频点f上雷达i对应的环境噪声功率谱密度S nn,i(f)。
进一步的，步骤(2)中设组网雷达发射波形带宽为W，智能干扰系统总干扰能量的上限为E J，预先设定的目标参数估计性能互信息阈值为χ。
进一步的，步骤(3)中采用互信息表征目标参数估计性能，并假设雷达i已通过先验信息获得频点f上智能干扰系统针对雷达i的干扰波形J i(f)；在满足预先设定的互信息阈值χ条件下，建立博弈条件下基于低截获性能的组网雷达最优波形设计模型如下：
Figure PCTCN2021074624-appb-000001
其中，S i(f)表示频点f上雷达i的发射波形，|S i(f)| 2表示频点f上雷达i发射波形的模平方，W表示组网雷达发射波形带宽，T y表示目标回波信号持续时间，|H i(f)| 2表示频点f上目标相对雷达i频率响应的模平方，E J表示总干扰能量的上限，M表示雷达数目，H i(f)表示频点f上目标相对雷达i的频率响应，S cc,i(f)表示频点f上雷达i对应的环境杂波功率谱密度，S nn,i(f)表示频点f上雷达i对应的环境噪声功率谱密度。
进一步的，步骤(4)中引入拉格朗日乘子η<0，构建拉格朗日目标函数如下：
Figure PCTCN2021074624-appb-000002
其中，Υ(|S i(f)| 2，η)为拉格朗日目标函数，M表示雷达数目，W表示组网雷达发射波形带宽，S i(f)表示频点f上雷达i的发射波形，T y表示目标回波信号持续时间，H i(f)表示频点f上目标相对雷达i的频率响应，S cc,i(f)表示频点f上雷达i对应的环境杂波功率谱密度，S nn,i(f)表示频点f上雷达i对应的环境噪声功率谱密度，χ为目标参数估计性能互信息阈值；
然后，拉格朗日目标函数Υ(|S i(f)| 2，η)分别对|S i(f)| 2与η求一阶偏导数；令：
Figure PCTCN2021074624-appb-000003
另外，由于|S i(f)| 2≥0，采用非线性最优化求解的卡罗需-库恩-塔克必要条件，得到博弈条件下基于低截获性能的雷达i最优波形的模平方表达式为：
Figure PCTCN2021074624-appb-000004
其中，R i(f)、B i(f)、D i(f)、A是中间变量，计算公式为：
Figure PCTCN2021074624-appb-000005
进一步的，步骤(5)中为了尽量减少组网雷达所获得的目标信息量，从而降低组网雷达系统性能，智能干扰系统需根据截获到的各雷达发射波形参数优化设计干扰波形；假设雷达波形在带宽W内均匀分布，建立二元零和博弈条件下针对组网雷达系统的干扰波形优化设计模型为：
Figure PCTCN2021074624-appb-000006
其中，M表示雷达数目，W表示组网雷达发射波形带宽，T y表示目标回波信号持续时间，S i(f)表示频点f上雷达i的发射波形，H i(f)表示频点f上目标相对雷达i的频率响应，|H i(f)| 2表示频点f上目标相对雷达i频率响应的模平方，E J表示总干扰能量的上限，S cc,i(f)表示频点f上雷达i对应的环境杂波功率谱密度，S nn,i(f)表示频点f上雷达i对应的环境噪声功率谱密度，J i(f)为雷达i已通过先验信息获得频点f上智能干扰系统针对雷达i的干扰波形。
进一步的，步骤(6)中引入拉格朗日乘子κ<0，构建拉格朗日目标函数如下：
Figure PCTCN2021074624-appb-000007
其中，M表示雷达数目，W表示组网雷达发射波形带宽，T y表示目标回波信号持续时间，S i(f)表示频点f上雷达i的发射波形，H i(f)表示频点f上目标相对雷达i的频率响应，|H i(f)| 2表示频点f上目标相对雷达i频率响应的模平方，E J表示总干扰能量的上限，S cc,i(f)表示频点f上雷达i对应的环境杂波功率谱密度，S nn,i(f)表示频点f上雷达i对应的环境噪声功率谱密度，J i(f)为雷达i已通过先验信息获得频点f上智能干扰系统针对雷达i的干扰波形；
然后，拉格朗日目标函数Ω(J i(f)，κ)分别对J i(f)与κ求一阶偏导数；令：
Figure PCTCN2021074624-appb-000008
另外，由于J i(f)≥0，采用非线性最优化求解的卡罗需-库恩-塔克必要条件，得到二元零和博弈条件下针对组网雷达系统的最优干扰波形表达式为：
Figure PCTCN2021074624-appb-000009
其中，
Figure PCTCN2021074624-appb-000010
是中间变量，计算公式为：
Figure PCTCN2021074624-appb-000011
工作原理及工作过程：
本发明从实际工程应用需求出发，在考虑组网雷达与敌方目标搭载的智能干扰系统进行二元零和博弈的条件下，根据战场先验信息，首先获取目标相对组网雷达系统中各雷达节点的频率响应、环境杂波功率谱密度、干扰波形以及环境噪声功率谱密度。在此基础上，以最小化博弈条件下组网雷达系统的总辐射能量为优化目标，以满足预先设定的目标参数估计性能互信息阈值为约束条件，建立博弈条件下基于低截获性能的组网雷达最优波形设计模型，自适应优化设计各雷达节点的发射波形。通过利用卡罗需-库恩-塔克必要条件迭代求解该优化模型，得到在满足预先设定的目标参数估计性能条件下的各雷达发射波形作为最优解，从而在满足预先设定的目标参数估计性能约束下，有效提升二元零和博弈条件下组网雷达系统的低截获性能。
有益效果：与现有技术相比，本发明具有以下优点：
(1)本发明是通过对二元零和博弈条件下组网雷达系统中各雷达节点的发射波形进行自适应优化设计，既满足了预先设定的目标参数估计性能互信息阈值，而且有效降低了组网雷达系统的总辐射能量，从而提升了二元零和博弈条件下组网雷达系统的低截获性能。产生该优点的原因是本发明在考虑在组网雷达与敌方目标搭载的智能干扰系统进行二元零和博弈的条件下，根据战场先验信息，首先获取目标相对组网雷达系统中各雷达节点的频率响应、环境杂波功率谱密度、干扰波形以及环境噪声功率谱密度。在此基础上，以最小化博弈条件下组网雷达系统的总辐射能量为优化目标，以满足预先设定的目标参数估计性能互信息阈值为约束条件，建立博弈条件下基于低截获性能的组网雷达最优波形设计模型，自适应优化设计各雷达节点的发射波形。通过利用卡罗需-库恩-塔克必要条件迭代求解该优化模型，得到在满足预先设定的目标参数估计性能条件下的 各雷达发射波形作为最优解，从而在满足预先设定的目标参数估计性能约束下，有效提升二元零和博弈条件下组网雷达系统的低截获性能。
(2)本发明方法不仅满足了预先设定的目标参数估计性能互信息阈值，而且实现了雷达与干扰进行二元零和博弈条件下组网雷达系统发射波形的自适应优化设计，从而最小化组网雷达的总辐射能量，有效提升了二元零和博弈条件下组网雷达系统的低截获性能。
具体实施方式
下面结合具体实施例对本发明进行详细说明。
本发明的一种博弈条件下基于低截获性能的组网雷达最优波形设计方法，包括以下步骤：
1、获取目标与环境先验信息；
假设智能干扰系统由敌方目标搭载。在由M部雷达节点组成的组网雷达系统与敌方干扰进行二元零和博弈的条件下，根据战场先验信息，获取频点f上目标相对雷达i的频率响应H i(f)、频点f上雷达i对应的环境杂波功率谱密度S cc,i(f)以及频点f上雷达i对应的环境噪声功率谱密度S nn,i(f)。
2、确定组网雷达系统与智能干扰系统的辐射参数以及目标参数估计性能互信息阈值χ；
设组网雷达发射波形带宽为W，智能干扰系统总干扰能量的上限为E J，预先设定的目标参数估计性能互信息阈值为χ。
3、构建博弈条件下基于低截获性能的组网雷达最优波形设计模型；
采用互信息表征目标参数估计性能，并假设雷达i已通过先验信息获得频点f上智能干扰系统针对雷达i的干扰波形J i(f)。在满足预先设定的互信息阈值χ条件下，建立博弈条件下基于低截获性能的组网雷达最优波形设计模型如下：
Figure PCTCN2021074624-appb-000012
式中，S i(f)表示频点f上雷达i的发射波形，|S i(f)| 2表示频点f上雷达i发射波形的模平方，W表示组网雷达发射波形带宽，T y表示目标回波信号持续时间，|H i(f)| 2表示频点f上目标相对雷达i频率响应的模平方，E J表示总干扰能量的上限。
4、构建拉格朗日目标函数Υ(|S i(f)| 2，η)，并采用卡罗需-库恩-塔克必要条件进行求解；
引入拉格朗日乘子η<0，构建拉格朗日目标函数如下：
Figure PCTCN2021074624-appb-000013
然后，拉格朗日目标函数Υ(|S i(f)| 2，η)分别对|S i(f)| 2与η求一阶偏导数。令：
Figure PCTCN2021074624-appb-000014
另外，由于|S i(f)| 2≥0，采用非线性最优化求解的卡罗需-库恩-塔克必要条件，可以得到博弈条件下基于低截获性能的雷达i最优波形的模平方表达式为：
Figure PCTCN2021074624-appb-000015
其中，R i(f)、B i(f)、D i(f)、A是中间变量，计算公式为：
Figure PCTCN2021074624-appb-000016
5、构建二元零和博弈条件下针对组网雷达系统的干扰波形优化设计模型；
为了尽量减少组网雷达所获得的目标信息量，从而降低组网雷达系统性能，智能干扰系统需根据截获到的各雷达发射波形参数优化设计干扰波形。假设雷达波形在带宽W内均匀分布，建立二元零和博弈条件下针对组网雷达系统的干扰波形优化设计模型为：
Figure PCTCN2021074624-appb-000017
6、构建拉格朗日目标函数Ω(J i(f)，κ)，并采用卡罗需-库恩-塔克必要条件进行求解；
引入拉格朗日乘子κ<0，构建拉格朗日目标函数如下：
Figure PCTCN2021074624-appb-000018
然后，拉格朗日目标函数Ω(J i(f)，κ)分别对J i(f)与κ求一阶偏导数。令：
Figure PCTCN2021074624-appb-000019
另外，由于J i(f)≥0，采用非线性最优化求解的卡罗需-库恩-塔克必要条件，可以得到二元零和博弈条件下针对组网雷达系统的最优干扰波形表达式为：
Figure PCTCN2021074624-appb-000020
其中，
Figure PCTCN2021074624-appb-000021
是中间变量，计算公式为：
Figure PCTCN2021074624-appb-000022
7、重复步骤3至步骤6，直至|S i(f)| 2与J i(f)均不再发生变化。此时，所得|S i(f)| 2即为博弈条件下基于低截获性能的雷达i最优发射波形的模平方。
本发明考虑在组网雷达与敌方目标搭载的智能干扰系统进行二元零和博弈的条件下，根据战场先验信息，获取目标相对组网雷达系统中各雷达节点的频率响应、环境杂波功率谱密度、干扰波形以及环境噪声功率谱密度，计算组网雷达系统获得的目标参数估计性能互信息值；且本发明以最小化博弈条件下组网雷达系统的总辐射能量为优化目标，以满足预先设定的目标参数估计性能互信息阈值为约束条件，建立博弈条件下基于低截获性能的组网雷达最优波形设计模型，自适应优化设计各雷达节点的发射波形。通过利用卡罗需-库恩-塔克必要条件迭代求解该优化模型，得到在满足预先设定的目标参数估计性能条件下的各雷达发射波形作为最优解，从而在满足预先设定的目标参数估计性能约束下，有效提升二元零和博弈条件下组网雷达系统的低截获性能。

Claims (7)

  1. 一种博弈条件下基于低截获性能的组网雷达最优波形设计方法，其特征在于，包括以下步骤：
    (1)获取目标与环境先验信息；
    (2)确定组网雷达系统与智能干扰系统的辐射参数以及目标参数估计性能互信息阈值χ；
    (3)构建博弈条件下基于低截获性能的组网雷达最优波形设计模型；
    (4)构建拉格朗日目标函数Υ(|S i(f)| 2，η)，并采用卡罗需-库恩-塔克必要条件进行求解；
    (5)构建二元零和博弈条件下针对组网雷达系统的干扰波形优化设计模型；
    (6)构建拉格朗日目标函数Ω(J i(f)，κ)，并采用卡罗需-库恩-塔克必要条件进行求解；
    (7)重复步骤(3)至步骤(6)，直至|S i(f)| 2与J i(f)均不再发生变化。此时，所得|S i(f)| 2即为博弈条件下基于低截获性能的雷达i最优发射波形的模平方。
  2. 根据权利要求1所述的博弈条件下基于低截获性能的组网雷达最优波形设计方法，其特征在于，步骤(1)中假设智能干扰系统由敌方目标搭载，在由M部雷达节点组成的组网雷达系统与敌方干扰进行二元零和博弈的条件下，根据战场先验信息，获取频点f上目标相对雷达i的频率响应H i(f)、频点f上雷达i对应的环境杂波功率谱密度S cc,i(f)以及频点f上雷达i对应的环境噪声功率谱密度S nn,i(f)。
  3. 根据权利要求1所述的博弈条件下基于低截获性能的组网雷达最优波形设计方法，其特征在于，步骤(2)中设组网雷达发射波形带宽为W，智能干扰系统总干扰能量的上限为E J，预先设定的目标参数估计性能互信息阈值为χ。
  4. 根据权利要求1所述的博弈条件下基于低截获性能的组网雷达最优波形设计方法，其特征在于，步骤(3)中采用互信息表征目标参数估计性能，并假设雷达i已通过先验信息获得频点f上智能干扰系统针对雷达i的干扰波形J i(f)；在满足预先设定的互信息阈值χ条件下，建立博弈条件下基于低截获性能的组网雷达最优波形设计模型如 下：
    Figure PCTCN2021074624-appb-100001
    其中，S i(f)表示频点f上雷达i的发射波形，|S i(f)| 2表示频点f上雷达i发射波形的模平方，W表示组网雷达发射波形带宽，T y表示目标回波信号持续时间，|H i(f)| 2表示频点f上目标相对雷达i频率响应的模平方，E J表示总干扰能量的上限，M表示雷达数目，H i(f)表示频点f上目标相对雷达i的频率响应，S cc,i(f)表示频点f上雷达i对应的环境杂波功率谱密度，S nn,i(f)表示频点f上雷达i对应的环境噪声功率谱密度。
  5. 根据权利要求1所述的博弈条件下基于低截获性能的组网雷达最优波形设计方法，其特征在于，步骤(4)中引入拉格朗日乘子η<0，构建拉格朗日目标函数如下：
    Figure PCTCN2021074624-appb-100002
    其中，Υ(|S i(f)| 2，η)为拉格朗日目标函数，M表示雷达数目，W表示组网雷达发射波形带宽，S i(f)表示频点f上雷达i的发射波形，T y表示目标回波信号持续时间，H i(f)表示频点f上目标相对雷达i的频率响应，S cc,i(f)表示频点f上雷达i对应的环境杂波功率谱密度，S nn,i(f)表示频点f上雷达i对应的环境噪声功率谱密度，χ为目标参数估计性能互信息阈值；
    然后，拉格朗日目标函数Υ(|S i(f)| 2，η)分别对|S i(f)| 2与η求一阶偏导数；令：
    Figure PCTCN2021074624-appb-100003
    另外，由于|S i(f)| 2≥0，采用非线性最优化求解的卡罗需-库恩-塔克必要条件，得到博弈条件下基于低截获性能的雷达i最优波形的模平方表达式为：
    Figure PCTCN2021074624-appb-100004
    其中，R i(f)、B i(f)、D i(f)、A都是中间变量，计算公式如下：
    Figure PCTCN2021074624-appb-100005
  6. 根据权利要求1所述的博弈条件下基于低截获性能的组网雷达最优波形设计方法，其特征在于，步骤(5)中为了尽量减少组网雷达所获得的目标信息量，从而降低组网雷达系统性能，智能干扰系统需根据截获到的各雷达发射波形参数优化设计干扰波形；假设雷达波形在带宽W内均匀分布，建立二元零和博弈条件下针对组网雷达系统的干扰波形优化设计模型为：
    Figure PCTCN2021074624-appb-100006
    其中，M表示雷达数目，W表示组网雷达发射波形带宽，T y表示目标回波信号持续时间，S i(f)表示频点f上雷达i的发射波形，H i(f)表示频点f上目标相对雷达i的频率响应，|H i(f)| 2表示频点f上目标相对雷达i频率响应的模平方，E J表示总干扰能量的上限，S cc,i(f)表示频点f上雷达i对应的环境杂波功率谱密度，S nn,i(f)表示频点f上雷达i对应的环境噪声功率谱密度，J i(f)为雷达i已通过先验信息获得频点f上智能干扰系统针对雷达i的干扰波形。
  7. 根据权利要求1所述的博弈条件下基于低截获性能的组网雷达最优波形设计方法，其特征在于，步骤(6)中引入拉格朗日乘子κ<0，构建拉格朗日目标函数如下：
    Figure PCTCN2021074624-appb-100007
    其中，M表示雷达数目，W表示组网雷达发射波形带宽，T y表示目标回波信号持续时间，S i(f)表示频点f上雷达i的发射波形，H i(f)表示频点f上目标相对雷达i的频率响应，|H i(f)| 2表示频点f上目标相对雷达i频率响应的模平方，E J表示总干扰能量的上限，S cc,i(f)表示频点f上雷达i对应的环境杂波功率谱密度，S nn,i(f)表示频点f上雷达i对应的环境噪声功率谱密度，J i(f)为雷达i已通过先验信息获得频点f上智能干扰系统针对雷达i的干扰波形；
    然后，拉格朗日目标函数Ω(J i(f)，κ)分别对J i(f)与κ求一阶偏导数；令：
    Figure PCTCN2021074624-appb-100008
    另外，由于J i(f)≥0，采用非线性最优化求解的卡罗需-库恩-塔克必要条件，得到二元零和博弈条件下针对组网雷达系统的最优干扰波形表达式为：
    Figure PCTCN2021074624-appb-100009
    其中，
    Figure PCTCN2021074624-appb-100010
    是中间变量，计算公式为：
    Figure PCTCN2021074624-appb-100011
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