WO2021244030A1 - 针对子孔径-频控阵雷达的射频隐身发射功率优化方法 - Google Patents

针对子孔径-频控阵雷达的射频隐身发射功率优化方法 Download PDF

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WO2021244030A1
WO2021244030A1 PCT/CN2021/070302 CN2021070302W WO2021244030A1 WO 2021244030 A1 WO2021244030 A1 WO 2021244030A1 CN 2021070302 W CN2021070302 W CN 2021070302W WO 2021244030 A1 WO2021244030 A1 WO 2021244030A1
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frequency
aperture
array radar
transmission power
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时晨光
丁琳涛
王奕杰
周建江
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Nanjing University of Aeronautics and Astronautics
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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
    • G01S7/40—Means for monitoring or calibrating
    • G01S7/4004—Means for monitoring or calibrating of parts of a radar system
    • G01S7/4008—Means for monitoring or calibrating of parts of a radar system of transmitters
    • 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
    • G01S7/40—Means for monitoring or calibrating
    • G01S7/4004—Means for monitoring or calibrating of parts of a radar system
    • G01S7/4008—Means for monitoring or calibrating of parts of a radar system of transmitters
    • G01S7/4013—Means for monitoring or calibrating of parts of a radar system of transmitters involving adjustment of the transmitted power

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  • the invention relates to radar signal processing technology, in particular to a method for optimizing radio frequency stealth transmission power for sub-aperture-frequency-controlled array radar.
  • the frequency-controlled array radar performs joint estimation of the azimuth and range of the target
  • the Cramer-Raw lower bound of the frequency-controlled array radar's azimuth and range estimation will become very large. This is due to the coupling of the frequency-controlled array radar in the azimuth and range. Therefore, the traditional frequency-controlled array radar is not suitable for direct joint estimation of the target's azimuth and range parameters, while the sub-aperture-frequency-controlled array radar can better overcome this problem.
  • Radar radio frequency stealth technology means that by controlling the radio frequency radiation characteristics of one's own radar signals, the effective range of the enemy's passive detection system on the radar is shortened, and the survivability of the radar platform is improved. Radar radio frequency stealth research runs through the entire process of the enemy passive detection system's discovery, sorting, identification and positioning of radar signals. Therefore, radar radio frequency stealth technology has important military significance and practical needs.
  • the present invention proposes a radio frequency stealth transmission power optimization method for sub-aperture-frequency-controlled array radar, which effectively reduces the transmission power of the sub-aperture-frequency-controlled array radar system and achieves an improved system The purpose of radio frequency stealth performance.
  • the method for optimizing radio frequency stealth transmission power for sub-aperture-frequency-controlled array radar includes the following steps:
  • the step (1) neutron aperture - frequency phased array radar system comprising N T array elements, the system will be uniform linear array radar is divided into two subarrays average, the number of array elements is contained in each sub-array N S, And the element spacing of each sub-array is D; the two sub-arrays adopt different frequency increments, among which, the transmit frequency increment of the first sub-array element is ⁇ F 1 , and the second sub-array element’s transmit frequency increment is ⁇ F 2 , the wavelength of the transmitted signal of the sub-aperture-frequency-controlled array radar is ⁇ ;
  • the distance between the acquired target and the sub-aperture-frequency control array radar is R
  • the azimuth angle of the target relative to the sub-aperture-frequency control array radar is ⁇ .
  • step (2) is specifically as follows:
  • ⁇ F 1 is the increase in the transmission frequency of the first sub-array element
  • ⁇ F 2 is the increase in the transmission frequency of the second sub-array element
  • N T is the number of elements in the sub-aperture-frequency control array radar system
  • N S is the number of elements contained in each sub-array
  • SNR represents the output signal-to-noise ratio of the sub-aperture-frequency-controlled array radar receiver, expressed as:
  • P rad is the transmit power of the sub-aperture-frequency-controlled array radar, Is the scattering coefficient of the target relative to the sub-aperture-frequency array radar, Is the noise power of the sub-aperture-frequency-controlled array radar receiver;
  • ⁇ is the wavelength of the sub-aperture-frequency-controlled array radar transmitting signal
  • D is the element spacing of each sub-array
  • ⁇ is the azimuth angle of the target relative to the sub-aperture-frequency-controlled array radar.
  • step (3) according to the given target distance parameter estimate the Cramer-Rao lower threshold ⁇ R and the target azimuth parameter estimate the Cramer-Rao lower threshold ⁇ ⁇ , establish the radio frequency for the sub-aperture-frequency control array radar Stealth transmit power optimization model:
  • P rad is the transmission power of the sub-aperture-frequency-controlled array radar
  • CRB R is the Cramer-Raw lower bound of the sub-aperture-frequency-controlled array radar system to estimate the target distance parameter
  • CRB ⁇ is the sub-aperture-frequency control array radar system Cramer-Raw lower bound for the estimation of target azimuth parameters
  • It is the upper limit of the transmission power of the sub-aperture-frequency-controlled array radar.
  • step (4) the specific solution for the radio frequency stealth transmission power optimization model for the sub-aperture-frequency-controlled array radar is as follows:
  • c is the speed of light
  • ⁇ F 2 is the second sub-membered transmit bursts of frequency increment
  • N T is the subaperture - Frequency array element in the phased array radar system Number
  • N S is the number of elements contained in each sub-array
  • ⁇ is the wavelength of the sub-aperture-frequency-controlled array radar emission signal
  • D is the element spacing of each sub-array
  • ⁇ is the target relative to the sub-aperture-frequency-controlled array The azimuth of the radar
  • the present invention has the following advantages:
  • the present invention proposes a radio frequency stealth transmission power optimization method for sub-aperture-frequency-controlled array radars.
  • the main task completed by this method is to estimate the parameters of traditional frequency-controlled array radars in the range and azimuth direction.
  • the uniform linear radar array is divided into two sub-arrays, and each sub-array uses a different frequency increment; on this basis, the target is obtained according to the prior information of the battlefield.
  • the Kramer-Raw lower bound expressions are used to characterize the estimation performance of the sub-aperture-frequency array radar system on the target range parameter and azimuth angle parameter.
  • the given target distance parameter estimation Cramer-Rao lower threshold and target azimuth parameter estimation Cramer-Rao lower threshold as the constraint conditions, and to minimize the transmission power of the sub-aperture-frequency-controlled array radar as the optimization goal.
  • a radio frequency stealth transmission power optimization model for sub-aperture-frequency control array radar is established to effectively reduce the transmission power of sub-aperture-frequency control array radar to achieve the purpose of improving the system's radio frequency stealth performance.
  • the advantage of the invention is that it not only meets the requirements of the Cramer-Rao lower threshold of the given target distance parameter estimation and the Cramer-Rao lower threshold of the target azimuth parameter estimation, but also effectively reduces the transmission power of the sub-aperture-frequency-controlled array radar system. , Thereby improving the radio frequency stealth performance of the system.
  • the present invention adopts a radio frequency stealth transmission power optimization method for sub-aperture-frequency-controlled array radar, which satisfies a given target distance parameter estimation Cramer-Rao lower bound threshold and target azimuth parameter estimation carat
  • the lower threshold of the United States-Romania is a constraint condition, and the optimization goal is to minimize the transmission power of the sub-aperture-frequency-controlled array radar, and a radio frequency stealth transmission power optimization model for the sub-aperture-frequency control array radar is established.
  • the transmission power of the sub-aperture-frequency array radar system is minimized under the conditions of satisfying the given target distance parameter estimation Cramer-Rao lower threshold and target azimuth parameter estimation Cramer-Rao lower threshold.
  • the transmit power value is taken as the optimal solution, thereby effectively improving the radio frequency stealth performance of the sub-aperture-frequency-controlled array radar system.
  • the radio frequency stealth transmission power optimization method for sub-aperture-frequency-controlled array radar proposed in the present invention not only satisfies the given target distance parameter estimation Cramer-Rao lower bound threshold and target azimuth angle
  • the parameter estimates the Cramer-Raw lower threshold threshold, and effectively reduces the transmission power of the sub-aperture-frequency-controlled array radar system, thereby improving the system's radio frequency stealth performance.
  • Figure 1 is a flow chart of the method of the present invention.
  • the present invention firstly aims at the situation that there is coupling in the range and azimuth direction when the traditional frequency-controlled array radar estimates the parameters of the target, considers a sub-aperture-frequency-controlled array radar system, and averages the uniform linear radar array Divided into two sub-arrays, each sub-array uses a different frequency increment; on this basis, according to the battlefield prior information, the distance between the target and the sub-aperture-frequency-controlled array radar and the target relative to the sub-aperture-frequency control The azimuth of the array radar. Then, the Kramer-Raw lower bound expressions are used to characterize the estimation performance of the sub-aperture-frequency array radar system for the target range parameter and azimuth angle parameter.
  • a radio frequency stealth transmission power optimization model for sub-aperture-frequency-controlled array radar is established, so as to effectively reduce the transmission power of sub-aperture-frequency control array radar, so as to achieve the purpose of improving the system's radio frequency stealth performance.
  • the RF stealth transmission power optimization method for sub-aperture-frequency control array radar includes the following steps:
  • a sub-aperture-frequency-controlled array radar system consisting of NT array elements is considered.
  • the system divides the uniform linear radar array into two sub-arrays equally.
  • the number of elements in each sub-array is N S
  • the distance between each sub-array is D.
  • the two sub-arrays adopt different frequency increments. Among them, the first sub-array element's transmit frequency increment is ⁇ F 1 , and the second sub-array element's transmit frequency increment is ⁇ F 2 .
  • the wavelength of the sub-aperture-frequency-controlled array radar emission signal is ⁇ .
  • the distance between the acquired target and the sub-aperture-frequency control array radar is R
  • the azimuth angle of the target relative to the sub-aperture-frequency control array radar is ⁇ .
  • the Cramer-Raw lower bound expressions are used to characterize the estimation performance of the sub-aperture-frequency array radar system for the target range parameter and azimuth angle parameter, as shown below:
  • SNR represents the output signal-to-noise ratio of the sub-aperture-frequency-controlled array radar receiver, which can be expressed as:
  • P rad is the transmit power of the sub-aperture-frequency-controlled array radar
  • the superscript * represents the optimal solution, namely Represents the optimal solution of the sub-aperture-frequency control array radar transmitting power P rad , min ⁇ x,y ⁇ represents the minimum value of x and y, max ⁇ k,j ⁇ represents the maximum value of k and j value.
  • the present invention firstly considers a sub-aperture-frequency-controlled array radar system in view of the situation that the traditional frequency-controlled array radar performs parameter estimation on the target when there is coupling in the range and azimuth directions.
  • the uniform linear radar array is equally divided into two sub-arrays. Each sub-array adopts different frequency increments; on this basis, the distance between the target and the sub-aperture-frequency-controlled array radar and the azimuth angle of the target relative to the sub-aperture-frequency-controlled array radar are obtained according to the prior information of the battlefield.
  • the Kramer-Raw lower bound expressions are used to characterize the estimation performance of the sub-aperture-frequency array radar system for the target range parameter and azimuth angle parameter.

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  • Radar, Positioning & Navigation (AREA)
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Abstract

一种针对子孔径-频控阵雷达的射频隐身发射功率优化方法，包括：确定子孔径-频控阵雷达系统组成及目标先验信息；分别采用克拉美-罗下界表达式表征子孔径-频控阵雷达系统对目标距离参数和方位角参数的估计性能；建立针对子孔径-频控阵雷达的射频隐身发射功率优化模型；求解针对子孔径-频控阵雷达的射频隐身发射功率优化模型。不仅满足了给定的目标距离参数估计克拉美-罗下界阈值和目标方位角参数估计克拉美-罗下界阈值要求，而且有效降低了子孔径-频控阵雷达系统的发射功率，从而提高了系统的射频隐身性能。

Description

针对子孔径-频控阵雷达的射频隐身发射功率优化方法 技术领域
本发明涉及雷达信号处理技术，具体涉及针对子孔径-频控阵雷达的射频隐身发射功率优化方法。
背景技术
2006年，美国学者Antonik和Wicks在每年一度的IEEE雷达年会上首次提出了频控阵雷达的概念，随后便引起了巨大的反响。频控阵雷达阵列的相邻阵元之间存在一个很小的频率增量，且远小于载频。由此一来，频控阵雷达的波束指向便同时具有角度依赖性和距离依赖性。
然而，当频控阵雷达对目标进行方位角与距离的联合估计时，频控阵雷达方位角与距离估计的克拉美-罗下界将会变得很大。这是由于频控阵雷达在方位角向和距离向存在耦合。因此，传统频控阵雷达并不适用于直接对目标的方位角和距离参数进行联合估计，而子孔径-频控阵雷达可以较好地克服这一难题。
雷达射频隐身技术是指通过控制己方雷达信号的射频辐射特征，缩短敌方无源探测系统对雷达的有效作用距离，提高雷达平台的生存能力。雷达射频隐身研究贯穿于敌方无源探测系统对雷达信号的发现、分选识别和定位的全过程。因此，雷达射频隐身技术具有重要的军事意义和现实需求。
然而，现有技术中尚未有针对子孔径-频控阵雷达的射频隐身发射功率优化方法。
发明内容
发明目的：为解决现有技术的不足，本发明提出了针对子孔径-频控阵雷达的射频隐身发射功率优化方法，有效降低了子孔径-频控阵雷达系统的发射功率，达到了提高系统射频隐身性能的目的。
技术方案：为实现上述发明目的，本发明采用以下技术方案：
针对子孔径-频控阵雷达的射频隐身发射功率优化方法，包括以下步骤：
(1)确定子孔径-频控阵雷达系统组成及目标距离和方位先验信息；
(2)分别采用克拉美-罗下界表达式表征子孔径-频控阵雷达系统对目标距离参数和方位角参数的估计性能；
(3)建立针对子孔径-频控阵雷达的射频隐身发射功率优化模型；
(4)求解针对子孔径-频控阵雷达的射频隐身发射功率优化模型。
进一步的，步骤(1)中子孔径-频控阵雷达系统包括N T个阵元，该系统将均匀线性雷达阵列平均分为两个子阵，每个子阵所含的阵元数目为N S，且每个子阵的阵元间距均为D；两个子阵采用不同的频率增量，其中，第一个子阵阵元发射频率增量为ΔF 1，第二个子阵阵元发射频率增量为ΔF 2，子孔径-频控阵雷达发射信号波长为λ；
另外，根据战场先验信息，获取目标与子孔径-频控阵雷达之间的距离为R，目标相对于子孔径-频控阵雷达的方位角为θ。
进一步的，步骤(2)具体为：
子孔径-频控阵雷达系统对目标距离参数估计的克拉美-罗下界表达式为：
Figure PCTCN2021070302-appb-000001
其中，c为光速，
Figure PCTCN2021070302-appb-000002
Figure PCTCN2021070302-appb-000003
其中，ΔF 1为第一个子阵阵元发射频率增量，ΔF 2为第二个子阵阵元发射频率增量，N T为子孔径-频控阵雷达系统中的阵元个数，N S为每个子阵所含的阵元数目；
SNR表示子孔径-频控阵雷达接收机的输出信噪比，表示为：
Figure PCTCN2021070302-appb-000004
其中，P rad为子孔径-频控阵雷达的发射功率，
Figure PCTCN2021070302-appb-000005
为目标相对于子孔径-频控阵雷达的散射系数，
Figure PCTCN2021070302-appb-000006
为子孔径-频控阵雷达接收机的噪声功率；
子孔径-频控阵雷达系统对目标方位角参数估计的克拉美-罗下界表达式为：
Figure PCTCN2021070302-appb-000007
其中，λ为子孔径-频控阵雷达发射信号波长，D为每个子阵的阵元间距，θ为目标相对于子孔径-频控阵雷达的方位角。
进一步的，步骤(3)中根据给定的目标距离参数估计克拉美-罗下界阈值ξ R和目标方位角参数估计克拉美-罗下界阈值ξ θ，建立针对子孔径-频控阵雷达的射频隐身发射功率优化模型：
Figure PCTCN2021070302-appb-000008
其中，P rad为子孔径-频控阵雷达的发射功率，CRB R为子孔径-频控阵雷达系统对目标距离参数估计的克拉美-罗下界，CRB θ为子孔径-频控阵雷达系统对目标方位角参数估计的克拉美-罗下界，
Figure PCTCN2021070302-appb-000009
为子孔径-频控阵雷达发射功率的上限。
进一步的，步骤(4)中求解针对子孔径-频控阵雷达的射频隐身发射功率优化模型具体为：
令
Figure PCTCN2021070302-appb-000010
Figure PCTCN2021070302-appb-000011
其中，c为光速，ΔF 1为第一个子阵阵元发射频率增量，ΔF 2为第二个子阵阵元发射频率增量，N T为子孔径-频控阵雷达系统中的阵元个数，N S为每个子阵所含的阵元数目，λ为子孔径-频控阵雷达发射信号波长，D为每个子阵的阵元间距，θ为目标相对于 子孔径-频控阵雷达的方位角，
Figure PCTCN2021070302-appb-000012
Figure PCTCN2021070302-appb-000013
将式(7)和式(8)代入步骤(3)中的子孔径-频控阵雷达的射频隐身发射功率优化模型中，即得到在满足给定的目标距离参数估计克拉美-罗下界阈值和目标方位角参数估计克拉美-罗下界阈值条件下，使得子孔径-频控阵雷达系统发射功率最小的发射功率值为：
Figure PCTCN2021070302-appb-000014
其中，
Figure PCTCN2021070302-appb-000015
表示子孔径-频控阵雷达的发射功率P rad的最优解，min{x,y}表示求取x与y中的最小值，max{k,j}表示求取k与j中的最大值，
Figure PCTCN2021070302-appb-000016
为子孔径-频控阵雷达接收机的噪声功率；ξ R为目标距离参数估计克拉美-罗下界阈值，ξ θ为目标方位角参数估计克拉美-罗下界阈值，
Figure PCTCN2021070302-appb-000017
为目标相对于子孔径-频控阵雷达的散射系数，
Figure PCTCN2021070302-appb-000018
为子孔径-频控阵雷达发射功率的上限。
有益效果：与现有技术相比，本发明具有以下优点：
(1)本发明提出了针对子孔径-频控阵雷达的射频隐身发射功率优化方法，该方法所完成的主要任务是针对传统频控阵雷达对目标进行参数估计时在距离向和方位向存在耦合的情况，考虑一种子孔径-频控阵雷达系统，将均匀线性雷达阵列平均分为两个子阵，每个子阵采用不同的频率增量；在此基础上，根据战场先验信息，获取目标与子孔径-频控阵雷达之间的距离以及目标相对于子孔径-频控阵雷达的方位角。然后，分别采用克拉美-罗下界表达式表征子孔径-频控阵雷达系统对目标距离参数和方位角参数的估计性能。其次，以满足给定的目标距离参数估计克拉美-罗下界阈值和目标方位角参数估计克拉美-罗下界阈值为约束条件，以最小化子孔径-频控阵雷达的发射功率为优化目标，建立针对子孔径-频控阵雷达的射频隐身发射功率优化模型，从而有效降低子孔径-频控阵雷达的发射功率，以达到提高系统射频隐身性能的目的。
该发明的优点是不仅满足了给定的目标距离参数估计克拉美-罗下界阈值和目标方 位角参数估计克拉美-罗下界阈值要求，而且有效降低了子孔径-频控阵雷达系统的发射功率，从而提高了系统的射频隐身性能。产生该优点的原因是本发明采用了针对子孔径-频控阵雷达的射频隐身发射功率优化方法，该方法以满足给定的目标距离参数估计克拉美-罗下界阈值和目标方位角参数估计克拉美-罗下界阈值为约束条件，以最小化子孔径-频控阵雷达的发射功率为优化目标，建立针对子孔径-频控阵雷达的射频隐身发射功率优化模型。通过求解该优化模型，得到在满足给定的目标距离参数估计克拉美-罗下界阈值和目标方位角参数估计克拉美-罗下界阈值条件下，使得子孔径-频控阵雷达系统发射功率最小的发射功率值作为最优解，从而有效提高了子孔径-频控阵雷达系统的射频隐身性能。
(2)与现有技术相比，本发明提出的针对子孔径-频控阵雷达的射频隐身发射功率优化方法，不仅满足了给定的目标距离参数估计克拉美-罗下界阈值和目标方位角参数估计克拉美-罗下界阈值要求，而且有效降低了子孔径-频控阵雷达系统的发射功率，从而提高了系统的射频隐身性能。
附图说明
图1是本发明方法的流程图。
具体实施方式
下面结合附图和具体实施例对本发明的技术方案进行详细说明。
本发明从实际工程应用需求出发，首先针对传统频控阵雷达对目标进行参数估计时在距离向和方位向存在耦合的情况，考虑一种子孔径-频控阵雷达系统，将均匀线性雷达阵列平均分为两个子阵，每个子阵采用不同的频率增量；在此基础上，根据战场先验信息，获取目标与子孔径-频控阵雷达之间的距离以及目标相对于子孔径-频控阵雷达的方位角。然后，分别采用克拉美-罗下界表达式表征子孔径-频控阵雷达系统对目标距离参数和方位角参数的估计性能。其次，以满足给定的目标距离参数估计克拉美-罗下界阈值和目标方位角参数估计克拉美-罗下界阈值为约束条件，以最小化子孔径-频控阵雷达的发射功率为优化目标，建立针对子孔径-频控阵雷达的射频隐身发射功率优化模型，从而有效降低子孔径-频控阵雷达的发射功率，以达到提升系统射频隐身性能的目的。
如图1所示，针对子孔径-频控阵雷达的射频隐身发射功率优化方法，包括以下步骤：
1、确定子孔径-频控阵雷达系统组成及目标距离和方位先验信息：
针对传统频控阵雷达对目标进行参数估计时在距离向和方位向存在耦合的情况，考虑一部共由N T个阵元组成的子孔径-频控阵雷达系统。该系统将均匀线性雷达阵列平均分为两个子阵，每个子阵所含的阵元数目为N S，且每个子阵的阵元间距均为D。两个子阵采用不同的频率增量，其中，第一个子阵阵元发射频率增量为ΔF 1，第二个子阵阵元发射频率增量为ΔF 2。子孔径-频控阵雷达发射信号波长为λ。
另外，根据战场先验信息，获取目标与子孔径-频控阵雷达之间的距离为R，目标相对于子孔径-频控阵雷达的方位角为θ。
2、分别采用克拉美-罗下界表达式表征子孔径-频控阵雷达系统对目标距离参数和方位角参数的估计性能，如下所示：
子孔径-频控阵雷达系统对目标距离参数估计的克拉美-罗下界表达式为：
Figure PCTCN2021070302-appb-000019
其中，c为光速；
Figure PCTCN2021070302-appb-000020
Figure PCTCN2021070302-appb-000021
SNR表示子孔径-频控阵雷达接收机的输出信噪比，可以表示为：
Figure PCTCN2021070302-appb-000022
其中，P rad为子孔径-频控阵雷达的发射功率，
Figure PCTCN2021070302-appb-000023
为目标相对于子孔径-频控阵雷达的散射系数，
Figure PCTCN2021070302-appb-000024
为子孔径-频控阵雷达接收机的噪声功率。
子孔径-频控阵雷达系统对目标方位角参数估计的克拉美-罗下界表达式为：
Figure PCTCN2021070302-appb-000025
3、建立针对子孔径-频控阵雷达的射频隐身发射功率优化模型：
根据给定的目标距离参数估计克拉美-罗下界阈值ξ R和目标方位角参数估计克拉美-罗下界阈值ξ θ，建立针对子孔径-频控阵雷达的射频隐身发射功率优化模型：
Figure PCTCN2021070302-appb-000026
其中，
Figure PCTCN2021070302-appb-000027
为子孔径-频控阵雷达发射功率的上限。
4、对优化模型公式(6)进行求解：
令
Figure PCTCN2021070302-appb-000028
Figure PCTCN2021070302-appb-000029
将式(7)和式(8)代入优化模型公式(6)中，即可得到在满足给定的目标距离参数估计克拉美-罗下界阈值和目标方位角参数估计克拉美-罗下界阈值条件下，使得子孔径-频控阵雷达系统发射功率最小的发射功率值为：
Figure PCTCN2021070302-appb-000030
其中，上标*表示最优解，即
Figure PCTCN2021070302-appb-000031
表示子孔径-频控阵雷达的发射功率P rad的最优解，min{x,y}表示求取x与y中的最小值，max{k,j}表示求取k与j中的最大值。
描述本发明创造的工作原理及工作过程：
本发明首先针对传统频控阵雷达对目标进行参数估计时在距离向和方位向存在耦合的情况，考虑一种子孔径-频控阵雷达系统，将均匀线性雷达阵列平均分为两个子阵，每个子阵采用不同的频率增量；在此基础上，根据战场先验信息，获取目标与子孔径-频控阵雷达之间的距离以及目标相对于子孔径-频控阵雷达的方位角。然后，分别采用克拉美-罗下界表达式表征子孔径-频控阵雷达系统对目标距离参数和方位角参数的 估计性能。其次，以满足给定的目标距离参数估计克拉美-罗下界阈值和目标方位角参数估计克拉美-罗下界阈值为约束条件，以最小化子孔径-频控阵雷达的发射功率为优化目标，建立针对子孔径-频控阵雷达的射频隐身发射功率优化模型。最后，对所建立的优化模型进行求解。通过求解该优化模型，得到在满足给定的目标距离参数估计克拉美-罗下界阈值和目标方位角参数估计克拉美-罗下界阈值条件下，使得子孔径-频控阵雷达系统发射功率最小的发射功率值
Figure PCTCN2021070302-appb-000032
作为最优解，即可得到符合约束条件的子孔径-频控阵雷达系统射频隐身发射功率。

Claims (5)

  1. 针对子孔径-频控阵雷达的射频隐身发射功率优化方法，其特征在于，包括以下步骤：
    (1)确定子孔径-频控阵雷达系统组成及目标距离和方位先验信息；
    (2)分别采用克拉美-罗下界表达式表征子孔径-频控阵雷达系统对目标距离参数和方位角参数的估计性能；
    (3)建立针对子孔径-频控阵雷达的射频隐身发射功率优化模型；
    (4)求解针对子孔径-频控阵雷达的射频隐身发射功率优化模型。
  2. 根据权利要求1所述的针对子孔径-频控阵雷达的射频隐身发射功率优化方法，其特征在于，步骤(1)中子孔径-频控阵雷达系统包括N T个阵元，该系统将均匀线性雷达阵列平均分为两个子阵，每个子阵所含的阵元数目为N S，且每个子阵的阵元间距均为D；两个子阵采用不同的频率增量，其中，第一个子阵阵元发射频率增量为△F 1，第二个子阵阵元发射频率增量为△F 2，子孔径-频控阵雷达发射信号波长为λ；
    另外，根据战场先验信息，获取目标与子孔径-频控阵雷达之间的距离为R，目标相对于子孔径-频控阵雷达的方位角为θ。
  3. 根据权利要求1所述的针对子孔径-频控阵雷达的射频隐身发射功率优化方法，其特征在于，步骤(2)具体为：
    子孔径-频控阵雷达系统对目标距离参数估计的克拉美-罗下界表达式为：
    Figure PCTCN2021070302-appb-100001
    其中，c为光速，
    Figure PCTCN2021070302-appb-100002
    Figure PCTCN2021070302-appb-100003
    其中，△F 1为第一个子阵阵元发射频率增量，△F 2为第二个子阵阵元发射频率增量，N T为子孔径-频控阵雷达系统中的阵元个数，N S为每个子阵所含的阵元数目；
    SNR表示子孔径-频控阵雷达接收机的输出信噪比，表示为：
    Figure PCTCN2021070302-appb-100004
    其中，P rad为子孔径-频控阵雷达的发射功率，
    Figure PCTCN2021070302-appb-100005
    为目标相对于子孔径-频控阵雷达的散射系数，
    Figure PCTCN2021070302-appb-100006
    为子孔径-频控阵雷达接收机的噪声功率；
    子孔径-频控阵雷达系统对目标方位角参数估计的克拉美-罗下界表达式为：
    Figure PCTCN2021070302-appb-100007
    其中，λ为子孔径-频控阵雷达发射信号波长，D为每个子阵的阵元间距，θ为目标相对于子孔径-频控阵雷达的方位角。
  4. 根据权利要求1所述的针对子孔径-频控阵雷达的射频隐身发射功率优化方法，其特征在于，步骤(3)中根据给定的目标距离参数估计克拉美-罗下界阈值ξ R和目标方位角参数估计克拉美-罗下界阈值ξ θ，建立针对子孔径-频控阵雷达的射频隐身发射功率优化模型：
    Figure PCTCN2021070302-appb-100008
    其中，P rad为子孔径-频控阵雷达的发射功率，CRB R为子孔径-频控阵雷达系统对目标距离参数估计的克拉美-罗下界，CRB θ为子孔径-频控阵雷达系统对目标方位角参数估计的克拉美-罗下界，
    Figure PCTCN2021070302-appb-100009
    为子孔径-频控阵雷达发射功率的上限。
  5. 根据权利要求1所述的针对子孔径-频控阵雷达的射频隐身发射功率优化方法，其特征在于，步骤(4)中求解针对子孔径-频控阵雷达的射频隐身发射功率优化模型具体为：
    令
    Figure PCTCN2021070302-appb-100010
    Figure PCTCN2021070302-appb-100011
    其中，c为光速，△F 1为第一个子阵阵元发射频率增量，△F 2为第二个子阵阵元发射频率增量，N T为子孔径-频控阵雷达系统中的阵元个数，N S为每个子阵所含的阵元数目，λ为子孔径-频控阵雷达发射信号波长，D为每个子阵的阵元间距，θ为目标相对于子孔径-频控阵雷达的方位角，
    Figure PCTCN2021070302-appb-100012
    Figure PCTCN2021070302-appb-100013
    将式(7)和式(8)代入步骤(3)中的子孔径-频控阵雷达的射频隐身发射功率优化模型中，即得到在满足给定的目标距离参数估计克拉美-罗下界阈值和目标方位角参数估计克拉美-罗下界阈值条件下，使得子孔径-频控阵雷达系统发射功率最小的发射功率值为：
    Figure PCTCN2021070302-appb-100014
    其中，
    Figure PCTCN2021070302-appb-100015
    表示子孔径-频控阵雷达的发射功率P rad的最优解，min{x,y}表示求取x与y中的最小值，max{k,j}表示求取k与j中的最大值，
    Figure PCTCN2021070302-appb-100016
    为子孔径-频控阵雷达接收机的噪声功率；ξ R为目标距离参数估计克拉美-罗下界阈值，ξ θ为目标方位角参数估计克拉美-罗下界阈值，
    Figure PCTCN2021070302-appb-100017
    为目标相对于子孔径-频控阵雷达的散射系数，
    Figure PCTCN2021070302-appb-100018
    为子孔径-频控阵雷达发射功率的上限。
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CN114285707A (zh) * 2021-12-23 2022-04-05 电子科技大学 基于混沌指数调制的频控阵安全通信方法
CN114285707B (zh) * 2021-12-23 2023-05-16 电子科技大学 基于混沌指数调制的频控阵安全通信方法
CN116106831A (zh) * 2023-01-30 2023-05-12 淮北师范大学 一种提升相控阵雷达系统的射频隐身性能的方法

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