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CN111025276B - Optimal RF Stealth Power Allocation Method for Bistatic Radar in Spectrum Coexistence Environment - Google Patents

Optimal RF Stealth Power Allocation Method for Bistatic Radar in Spectrum Coexistence Environment Download PDF

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CN111025276B
CN111025276B CN201911146383.2A CN201911146383A CN111025276B CN 111025276 B CN111025276 B CN 111025276B CN 201911146383 A CN201911146383 A CN 201911146383A CN 111025276 B CN111025276 B CN 111025276B
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CN111025276A (en
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时晨光
王奕杰
汪飞
李海林
周建江
夏伟杰
孔莹莹
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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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/003—Bistatic radar systems; Multistatic radar systems
    • 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
    • G01S7/36—Means for anti-jamming, e.g. ECCM, i.e. electronic counter-counter measures
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
    • H04W16/14—Spectrum sharing arrangements between different networks

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Abstract

本发明公开了一种频谱共存环境下双基地雷达最优射频隐身功率分配方法，包括确定双基地雷达系统模型及环境先验知识；分别推导表征雷达目标时延估计精度的克拉美‑罗下界表达式和表征通信基站服务质量的信道容量表达式；根据预先设定的雷达目标时延估计精度阈值δCRLB和信道容量阈值Cset，建立频谱共存环境下双基地雷达最优射频隐身功率分配模型；采用线性规划方法对频谱共存环境下双基地雷达最优射频隐身功率分配模型进行求解。本发明方法不仅保证了雷达目标探测性能和通信基站服务质量的要求，而且有效提升了该系统的射频隐身性能。

Figure 201911146383

The invention discloses an optimal radio frequency stealth power allocation method for a bistatic radar in a spectrum coexistence environment, including determining a bistatic radar system model and environmental prior knowledge; and the channel capacity expression characterizing the quality of service of the communication base station; according to the preset radar target delay estimation accuracy threshold δ CRLB and the channel capacity threshold C set , the optimal radio frequency stealth power allocation model for bistatic radar in the spectrum coexistence environment is established; A linear programming method is used to solve the optimal RF stealth power allocation model for bistatic radar in a spectrum coexistence environment. The method of the invention not only ensures the requirements of radar target detection performance and communication base station service quality, but also effectively improves the radio frequency stealth performance of the system.

Figure 201911146383

Description

Bistatic radar optimal radio frequency stealth power distribution method under frequency spectrum coexistence environment
Technical Field
The invention belongs to the technical field of radar power distribution, and particularly provides a bistatic radar optimal radio frequency stealth power distribution method in a frequency spectrum coexistence environment.
Background
In recent years, with the rapid development of wireless communication systems, the shortage of spectrum resources has attracted much attention. Spectrum sharing techniques between radar and communication systems are a promising approach to mitigate competition for radio frequency bandwidth. Under the coexistence environment of the radar communication frequency spectrum, information exchange is realized through coexistence technologies such as waveform optimization and dynamic frequency spectrum sensing, and mutual benefits and win-win can be realized. Meanwhile, the transmitter and the receiver of the bistatic radar system are deployed at different positions in space, and the receiver in the system receives the target echo signal and then performs information fusion, so that the target parameter estimation performance of the bistatic radar system can be effectively improved.
However, most of the current research on radar transmission power distribution under the coexisting spectrum environment focuses on the improvement of the performance of the radar system, and neglects the optimal power distribution of the radar based on radio frequency stealth. Although the existing research results relate to the design problem of the optimal waveform of the bistatic radar system based on radio frequency stealth, the radio frequency stealth performance of the system is improved to a certain extent by optimizing the integrated orthogonal frequency division multiplexing transmission waveform under the condition of meeting the given target parameter estimation performance and communication performance. However, the influence of the bistatic radar optimal radio frequency stealth power distribution problem on the radio frequency stealth performance of the system in the spectrum coexistence environment is not considered in the existing research results, and the method has certain limitations.
Disclosure of Invention
The purpose of the invention is as follows: the optimal radio frequency stealth power distribution method for the bistatic radar in the frequency spectrum coexistence environment is provided, the total transmitting power of a bistatic radar system can be effectively reduced, and the radio frequency stealth performance of the bistatic radar system is effectively improved.
The method considers a bistatic radar system consisting of a monostatic radar and a communication base station, the communication base station transmits communication signals which can be received by a radar receiver through target scattering, namely when the radar receiver works, the receiver simultaneously receives a scattered echo of a radar detection target and a target echo of omnidirectional radiation of the communication base station. In a bistatic radar system, the communication base station can be regarded as a radar transmitter. Acquiring a radar-target-communication base station path response, a radar-target-radar path response and a communication base station-target-radar path response according to the prior knowledge; on the basis, the estimation precision of the specified radar target time delay and the service quality of the communication base station are met as constraint conditions, the minimum bistatic radar total transmitting power is used as an optimization target, an optimal radio frequency stealth power distribution model of the bistatic radar in a spectrum coexistence environment is established, and sub-carrier distribution is optimized in a self-adaptive and overall mode, so that the minimum bistatic radar total transmitting power is achieved, and the purpose of improving the radio frequency stealth performance of the system is achieved.
The technical scheme is as follows: in order to realize the purpose, the invention adopts the following technical scheme:
the invention aims at a bistatic radar system formed by a monostatic radar and a communication base station, and the communication base station can be regarded as a radar transmitter. And according to the priori knowledge, acquiring path response, and respectively constructing a Claramen-Rou lower bound representing the estimation precision of the bistatic radar target time delay and a channel capacity expression of the service quality of the communication base station. Meanwhile, an optimal radio frequency stealth power distribution model of the bistatic radar under the spectrum coexistence environment is established by taking the time delay estimation precision meeting the specified radar target and the service quality of the communication base station as constraint conditions and taking the total emission power of the minimum bistatic radar as an optimization target. The radar subcarrier power distribution scheme obtained by solving the optimization model can adaptively optimize the radar transmitting power distribution on each subcarrier under the condition of meeting a certain radar target time delay estimation precision threshold and a communication base station channel capacity threshold, and the solution obtained by adopting standard linear programming is the radar transmitting power on each subcarrier. The method specifically comprises the following steps:
the bistatic radar optimal radio frequency stealth power distribution method under the spectrum coexistence environment comprises the following steps:
(1) determining a bistatic radar system model and environment prior knowledge;
(2) respectively deducing a Claimei-Rou lower bound expression for representing the radar target time delay estimation precision and a channel capacity expression for representing the service quality of a communication base station;
(3) estimating the precision threshold delta according to the preset radar target time delayCRLBAnd channel capacity threshold CsetEstablishing an optimal radio frequency stealth power distribution model of the bistatic radar in a spectrum coexistence environment;
(4) and (4) solving the bistatic radar optimal radio frequency stealth power distribution model in the spectrum coexistence environment in the step (3) by adopting a linear programming method.
Further, in the step (1), a bistatic radar system formed by a monostatic radar and a communication base station is considered, the communication base station transmits communication signals to be received by a radar receiver through target scattering, namely when the radar receiver works, the receiver simultaneously receives a scattered echo of a radar detection target and a target echo radiated by the communication base station in an omnidirectional manner; in a bistatic radar system, a communication base station is regarded as a radar transmitter; according to the prior knowledge of the environment, the response h of the radar-target-radar path A on the nth subcarrier is obtainedA,nResponse h of communication base station-target-radar path BB,nAnd response h of radar-target-communication base station path CC,n。
Further, in the step (2), a Clarmet-Luo lower bound is adopted to represent the target time delay estimation precision of the bistatic radar system, and the expression is as follows:
CRLBJS(τ)＝FIJS(τ)-1 (1)；
in the formula, τ is the target time delay, and since the fisher information is the inverse of the lower cramer-lo bound, the expression of the lower cramer-lo bound of the target time delay estimation accuracy of the bistatic radar system is as follows:
Figure BDA0002282317540000031
in the formula, n is an orthogonal frequency division multiplexing radar emission waveform subcarrier index; n is the number of sub-carriers of the OFDM radar transmission signal;
Figure BDA0002282317540000032
is the background noise power; Δ f is the subcarrier frequency spacing; | αr,n|2Representing the radar transmission power on the nth subcarrier; | αc,n|2Representing the communication base station transmission power on the nth subcarrier; mu.sA,nRepresenting the gaussian mean on the nth subcarrier of path a; mu.sB,nRepresenting the gaussian mean on the nth subcarrier of path B;
Figure BDA0002282317540000035
representing the operation of the real part; (.)*Represents a conjugate operation; h isA,nRepresents the response of the radar-target-radar path A on the nth sub-carrier, hB,nRepresents the response of the communication base station-target-radar path B;
the channel capacity of the communication base station is adopted to represent the service quality of the communication base station in the bistatic radar system, and the expression is as follows:
Figure BDA0002282317540000033
in the formula, Pr,n＝|αr,n|2Representing the radar transmission power on the nth subcarrier; pc,n＝|αc,n|2Representing the communication base station transmission power on the nth subcarrier; h isC,nIndicating the response of the radar-target-communication base station path C.
Further, in the step (3), the optimal radio frequency stealth power distribution model of the bistatic radar in the spectrum coexistence environment is as follows:
Figure BDA0002282317540000034
wherein, Pr,n＝|αr,n|2Representing the radar transmission power on the nth subcarrier; n is the number of sub-carriers of the OFDM radar transmission signal; deltaCRLBRepresenting a time delay estimation precision threshold of a radar target; csetRepresents a channel capacity threshold; CRLBJS(τ) represents a Cramer-Row lower bound on target delay estimation accuracy for the bistatic radar system; cnIndicating the channel capacity of the communication base station;
the first constraint condition indicates that the target time delay estimation accuracy Clarame-Row lower bound of the bistatic radar system cannot be larger than a given Clarame-Row lower bound threshold value so as to meet the preset target time delay estimation accuracy requirement; the second constraint condition indicates that the channel capacity of the communication base station should not be less than the set channel capacity threshold value to ensure the service of the communication base stationQuality; the third constraint condition represents that the upper limit of the transmitting power of each radar subcarrier is PmaxThe lower limit is 0.
Further, in the step (4), the bistatic radar optimal radio frequency stealth power distribution model established in the step (3) under the spectrum coexistence environment is simplified, that is, the following steps are performed:
Figure BDA0002282317540000041
wherein h isC,nIndicating the response, P, of the radar-target-communication base station path Cc,n＝|αc,n|2Represents the communication base station transmission power on the nth subcarrier,
Figure BDA0002282317540000042
as background noise power, CsetRepresents a channel capacity threshold;
meanwhile, the inverse of the lower bound of Cramer-Rao, namely the Fisher information, is used for representing the estimation precision of the target time delay, so that the optimal radio frequency stealth power distribution model of the bistatic radar in the spectrum coexistence environment equivalently converts into:
Figure BDA0002282317540000043
wherein, Pr,n＝|αr,n|2Representing the radar transmission power on the nth subcarrier; n is the number of sub-carriers of the OFDM radar transmission signal; Δ f is the subcarrier frequency spacing; n is the subcarrier index of the emission waveform of the orthogonal frequency division multiplexing radar; h isA,nRepresents the response of the radar-target-radar path A on the nth sub-carrier, hB,nRepresents the response of the communication base station-target-radar path B; deltaCRLBRepresenting a time delay estimation precision threshold of a radar target; pmaxRepresenting the upper limit of the radar subcarrier transmitting power;
since the formula (6) is a non-convex problem, a standard linear programming method is adopted to solve, and the obtained solution is the radar transmitting power on each subcarrier.
Has the advantages that: compared with the prior art, the invention has the following beneficial effects:
(1) the invention provides a bistatic radar optimal radio frequency stealth power distribution method under a frequency spectrum coexistence environment, which is mainly used for acquiring the response of a radar-target-radar path A, the response of a communication base station-target-radar path B and the response of a radar-target-communication base station path C on a subcarrier in a bistatic radar system according to prior knowledge; on the basis, the estimation precision of the time delay of the specified radar target and the service quality of the communication base station are met as constraint conditions, the minimum total emission power of the bistatic radar is used as an optimization target, an optimal radio frequency stealth power distribution model of the bistatic radar in the spectrum coexistence environment is established, and the radar emission power distribution on each subcarrier is adaptively optimized, so that the total emission power of the bistatic radar is minimized, and the purpose of effectively improving the radio frequency stealth performance of the system is achieved.
The method has the advantages that the requirements of the time delay estimation precision of the given radar target and the service quality of the communication base station are met, the total transmitting power of the bistatic radar is effectively reduced, and the radio frequency stealth performance of the system is improved. The reason for the advantage is that the optimal radio frequency stealth power distribution method of the bistatic radar in the frequency spectrum coexistence environment is adopted, the time delay estimation precision of the specified radar target and the service quality of the communication base station are met as constraint conditions, the total emission power of the minimum bistatic radar is used as an optimization target, and the optimal radio frequency stealth power distribution model of the bistatic radar in the frequency spectrum coexistence environment is established. By solving the power distribution scheme of the radar subcarriers obtained by the optimization model, the radar transmitting power distribution on each subcarrier can be adaptively optimized under the condition of meeting a certain radar target time delay estimation precision threshold and a certain communication base station channel capacity threshold, so that the total transmitting power of the bistatic radar is minimized, and the aim of improving the radio frequency stealth performance of the system is fulfilled.
(2) Compared with the prior art, the optimal radio frequency stealth power distribution method for the bistatic radar in the frequency spectrum coexistence environment not only guarantees the radar target detection performance and the service quality requirement of the communication base station, but also effectively improves the radio frequency stealth performance of the system.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a diagram of a dual ground-based radar system model;
FIG. 3 is a communication base station transmit power;
FIG. 4 is a response of radar-target-radar path A;
fig. 5 is a response of communication base station-target-radar path B;
FIG. 6 is a response of radar-target-communication base station path C;
FIG. 7 shows the optimal RF stealth power distribution results for a bistatic radar system;
FIG. 8 shows the optimal radio frequency stealth power distribution result of the single-base radar system;
fig. 9 shows a comparison of the total radar transmitted power for different power allocation algorithms.
Detailed Description
The technical solution of the present invention is further explained with reference to the accompanying drawings and specific embodiments.
As shown in fig. 1, the method for allocating optimal radio-frequency stealth power of bistatic radar in spectrum coexistence environment of the present invention includes the following steps:
1. determining a bistatic radar system model and environment prior knowledge:
considering a bistatic radar system composed of a monostatic radar and a communication base station, the model diagram of the system is shown in fig. 2, the communication base station transmits communication signals which can be received by a radar receiver through target scattering, namely when the radar receiver works, the receiver simultaneously receives a scattered echo of a radar detection target and a target echo radiated by the communication base station in an omnidirectional manner. In a bistatic radar system, the communication base station can be regarded as a radar transmitter. According to the prior knowledge of the environment, the response h of the radar-target-radar path A on the nth subcarrier is obtainedA,nResponse h of communication base station-target-radar path BB,nAnd response h of radar-target-communication base station path CC,n。
2. Respectively deducing a Clarmet-Rou lower bound expression for representing the radar target time delay estimation precision and a channel capacity expression for representing the service quality of a communication base station, as follows:
the time delay estimation precision of the radar target is represented by a Clarame-Luo lower bound, and the expression is as follows:
CRLBJS(τ)＝FIJS(τ)-1(1)；
in the formula, FIJS(τ)-1Denotes the CrLB lower Cramer-Lou boundaryJSAnd (tau) represents the estimation precision of the radar target time delay, and tau is the target time delay. Since the fischer information is the inverse of the lower cramer-lo bound, the lower cramer-lo bound expression that characterizes the accuracy of the radar target time delay estimation is:
Figure BDA0002282317540000061
in the formula, n is an orthogonal frequency division multiplexing radar emission waveform subcarrier index; n is the number of sub-carriers of the OFDM radar transmission signal;
Figure BDA0002282317540000062
is the background noise power; Δ f is the subcarrier frequency spacing; | αr,n|2Representing the radar transmission power on the nth subcarrier; | αc,n|2Representing the communication base station transmission power on the nth subcarrier; mu.sA,nRepresenting the gaussian mean on the nth subcarrier of path a; mu.sB,nRepresenting the gaussian mean on the nth subcarrier of path B;
Figure BDA0002282317540000064
representing the operation of the real part; (.)*Representing a conjugate operation.
The channel capacity is adopted to represent the service quality of a communication base station in the bistatic radar system, and the expression is as follows:
Figure BDA0002282317540000063
in the formula, Pr,n＝|αr,n|2Representing the radar transmission power on the nth subcarrier; pc,n＝|αc,n|2Representing the communication base station transmit power on the nth subcarrier.
3. Estimating the precision threshold delta according to the preset radar target time delayCRLBAnd channel capacity threshold CsetEstablishing an optimal radio frequency stealth power distribution model of the bistatic radar in a spectrum coexistence environment, which is as follows:
Figure BDA0002282317540000071
the first constraint condition represents that the Clarmet-Row lower bound representing the radar target time delay estimation precision cannot be larger than a given Clarmet-Row lower bound threshold value so as to meet the preset radar target time delay estimation precision requirement; the second constraint condition indicates that the channel capacity of the communication base station should not be less than the set channel capacity threshold value so as to ensure the service quality of the communication base station; the third constraint represents that the upper limit of the radar transmission power on the nth subcarrier is PmaxThe lower limit is 0.
4. And (3) solving the bistatic radar optimal radio frequency stealth power distribution model (4) in the spectrum coexistence environment established in the step (3) by adopting a linear programming method.
Simplifying the bistatic radar optimal radio frequency stealth power distribution model (4) in the spectrum coexistence environment, namely:
Figure BDA0002282317540000072
meanwhile, the inverse of the lower bound of the Cramer-Rao, namely the Fisher information is used for representing the estimation precision of the target time delay, so that the optimal radio frequency stealth power distribution model (4) of the bistatic radar in the spectrum coexistence environment can be equivalently converted into the following steps:
Figure BDA0002282317540000073
because the optimization model formula (6) is a non-convex problem, a standard linear programming method can be adopted for solving, and the obtained solution is the radar transmitting power on each subcarrier.
5. Simulation result
Assume that the parameters in step 2 are as shown in table 1.
Table 1 simulation parameter settings
Figure BDA0002282317540000081
The communication base station transmitting power is shown in fig. 3, the response of the radar-target-radar path a is shown in fig. 4, the response of the communication base station-target-radar path B is shown in fig. 5, the response of the radar-target-communication base station path C is shown in fig. 6, the optimal radio frequency stealth power distribution result of the bistatic radar system is shown in fig. 7, and the most effective radio frequency stealth power distribution result of the monostatic radar system is shown in fig. 8. As can be seen from fig. 7 to 8, the total radar transmission power of the bistatic radar system is significantly reduced by the optimal radio frequency stealth power allocation method, compared with the most available radio frequency stealth power allocation method of the monostatic radar system. With the help of the communication base station, the radio frequency stealth performance of the bistatic radar system is obviously improved. The total radar transmit power ratio for the different power allocation algorithms is shown in fig. 9. Under the condition that external conditions are not changed, the minimum radar transmitting power can be obtained by the bistatic radar optimal radio frequency stealth power distribution method under the spectrum coexistence environment, and therefore the best radio frequency stealth performance is obtained. The communication base station in the bistatic radar system contributes to the estimation accuracy of the radar target, and the optimal radio-frequency stealth power distribution method of the bistatic radar under the spectrum coexistence environment comprehensively considers prior information such as path response. The average power distribution method only distributes the radar transmitting power evenly on the transmittable subcarriers, and does not consider the path response quality of the subcarriers.
According to the simulation result, the optimal radio-frequency stealth power distribution method of the bistatic radar under the frequency spectrum coexistence environment can adaptively optimize the radar transmission power distribution on each subcarrier by taking the total transmission power of the bistatic radar as an optimization target when certain radar target time delay estimation precision and the service quality of a communication base station are met as constraint conditions, so that the total transmission power of the bistatic radar is minimized, and the purpose of effectively improving the radio-frequency stealth performance of the system is achieved.
The working principle and the working process of the invention are as follows:
the invention firstly considers a bistatic radar system formed by a monostatic radar and a communication base station, the communication base station transmits communication signals which can be received by a radar receiver through target scattering, namely, when the radar receiver works, the receiver simultaneously receives the scattered echo of a radar detection target and the target echo of the omnidirectional radiation of the communication base station. In a bistatic radar system, the communication base station can be regarded as a radar transmitter. Then according to prior knowledge, obtaining path response, and respectively constructing a Clarmet-Rou lower bound representing the radar target time delay estimation precision and a channel capacity expression of the communication base station service quality; on the basis, the bistatic radar optimal radio frequency stealth power distribution method under the spectrum coexistence environment takes the time delay estimation precision and the service quality of a communication base station which meet the requirements of a specified radar target as constraint conditions, takes the total emission power of the minimum bistatic radar as an optimization target, and establishes a bistatic radar optimal radio frequency stealth power distribution model under the spectrum coexistence environment. By solving the radar subcarrier power distribution scheme obtained by the optimization model, the radar transmitting power distribution of each subcarrier can be adaptively optimized under the condition of meeting a certain radar target time delay estimation precision threshold and a certain communication base station channel capacity threshold. And finally, solving by adopting a standard linear programming method, wherein the obtained solution is the radar transmitting power on each subcarrier.

Claims (3)

1.频谱共存环境下双基地雷达最优射频隐身功率分配方法，其特征在于，包括以下步骤：1. The optimal radio frequency stealth power allocation method for bistatic radar in a spectrum coexistence environment is characterized in that, comprising the following steps: (1)确定双基地雷达系统模型及环境先验知识；(1) Determine the bistatic radar system model and environmental prior knowledge; (2)分别推导表征雷达目标时延估计精度的克拉美-罗下界表达式和表征通信基站服务质量的信道容量表达式；(2) Deriving respectively the Cramer-Road lower bound expression that characterizes the accuracy of radar target delay estimation and the channel capacity expression that characterizes the quality of service of the communication base station; 采用克拉美-罗下界表征双基地雷达系统的目标时延估计精度，其表达式为：The Kramer-Roman lower bound is used to characterize the target delay estimation accuracy of the bistatic radar system, and its expression is: CRLBJS(τ)＝FIJS(τ)-1 (1)；CRLB JS (τ) = FI JS (τ) -1 (1); 式中，τ为目标时延，由于费舍尔信息是克拉美-罗下界的逆，则双基地雷达系统的目标时延估计精度克拉美-罗下界的表达式为：In the formula, τ is the target time delay. Since the Fisher information is the inverse of the Cramer-Road lower bound, the Kramer-Rohs lower bound of the target delay estimation accuracy of the bistatic radar system can be expressed as:
Figure FDA0003346381580000011
Figure FDA0003346381580000011
 式中，n为正交频分复用雷达发射波形子载波索引；N为正交频分复用雷达发射信号子载波数目；
Figure FDA0003346381580000012
为背景噪声功率；△f为子载波频率间隔；|αr,n|2表示第n个子载波上的雷达发射功率；|αc,n|2表示第n个子载波上的通信基站发射功率；μA,n表示路径A第n个子载波上的高斯均值；μB,n表示路径B第n个子载波上的高斯均值；
Figure FDA0003346381580000013
表示取实部运算；(·)*表示共轭运算；hA,n表示第n个子载波上雷达-目标-雷达路径A的响应，hB,n表示通信基站-目标-雷达路径B的响应；In the formula, n is the sub-carrier index of the OFDM radar transmit waveform; N is the number of sub-carriers of the OFDM radar transmit signal;
Figure FDA0003346381580000012
is the background noise power; △f is the subcarrier frequency spacing; |α r,n | 2 represents the radar transmit power on the nth subcarrier; |αc ,n | 2 represents the communication base station transmit power on the nth subcarrier; μ A,n represents the Gaussian mean value on the nth sub-carrier of path A; μ B,n represents the Gaussian mean value on the nth sub-carrier of path B;
Figure FDA0003346381580000013
Represents the real part operation; (·) * represents the conjugate operation; h A,n represents the response of the radar-target-radar path A on the nth subcarrier, h B,n represents the response of the communication base station-target-radar path B ; 采用通信基站的信道容量表征双基地雷达系统中通信基站的服务质量，其表达式为：The channel capacity of the communication base station is used to characterize the service quality of the communication base station in the bistatic radar system, and its expression is:
Figure FDA0003346381580000014
Figure FDA0003346381580000014
 式中，Pr,n＝|αr,n|2表示第n个子载波上的雷达发射功率；Pc,n＝|αc,n|2表示第n个子载波上的通信基站发射功率；hC,n表示雷达-目标-通信基站路径C的响应；In the formula, P r,n =|α r,n | 2 represents the radar transmit power on the nth subcarrier; P c,n =|α c,n | 2 represents the communication base station transmit power on the nth subcarrier; h C,n represents the response of radar-target-communication base station path C; (3)根据预先设定的雷达目标时延估计精度阈值δCRLB和信道容量阈值Cset，建立频谱共存环境下双基地雷达最优射频隐身功率分配模型；(3) According to the preset radar target delay estimation accuracy threshold δ CRLB and channel capacity threshold C set , establish an optimal radio frequency stealth power allocation model for bistatic radar in a spectrum coexistence environment; 频谱共存环境下双基地雷达最优射频隐身功率分配模型，如下所示：The optimal RF stealth power allocation model for bistatic radar in the spectrum coexistence environment is as follows:
Figure FDA0003346381580000021
Figure FDA0003346381580000021
 其中，Pr,n＝|αr,n|2表示第n个子载波上的雷达发射功率；N为正交频分复用雷达发射信号子载波数目；δCRLB表示雷达目标时延估计精度阈值；Cset表示信道容量阈值；CRLBJS(τ)表示双基地雷达系统的目标时延估计精度克拉美-罗下界；Cn表示通信基站的信道容量；Pmax表示雷达子载波发射功率的上限；Among them, P r,n =|α r,n | 2 represents the radar transmit power on the nth sub-carrier; N is the number of OFDM radar transmit signal sub-carriers; δ CRLB represents the radar target delay estimation accuracy threshold ; C set is the channel capacity threshold; CRLB JS (τ) is the Cramer-Roman lower bound of the target delay estimation accuracy of the bistatic radar system; C n is the channel capacity of the communication base station; P max is the upper limit of the radar sub-carrier transmit power; (4)采用线性规划方法对步骤(3)中的频谱共存环境下双基地雷达最优射频隐身功率分配模型进行求解。(4) The linear programming method is used to solve the optimal radio frequency stealth power allocation model of the bistatic radar in the spectrum coexistence environment in step (3). 2.根据权利要求1所述的频谱共存环境下双基地雷达最优射频隐身功率分配方法，其特征在于，步骤(1)中考虑由一部单基地雷达和一部通信基站构成的双基地雷达系统，通信基站发射通信信号通过目标散射被雷达接收机接收，即当雷达接收机工作时，接收机同时收到雷达探测目标的散射回波以及通信基站全向辐射的目标回波；在双基地雷达系统中，通信基站看作一台雷达发射机；根据环境先验知识，获取第n个子载波上雷达-目标-雷达路径A的响应hA,n，通信基站-目标-雷达路径B的响应hB,n和雷达-目标-通信基站路径C的响应hC,n。2. bistatic radar optimal radio frequency stealth power allocation method under the spectrum coexistence environment according to claim 1 is characterized in that, in step (1), consider the bistatic radar that is formed by a monostatic radar and a communication base station In the system, the communication signal transmitted by the communication base station is received by the radar receiver through target scattering, that is, when the radar receiver is working, the receiver simultaneously receives the scattered echo of the radar detection target and the target echo of the omnidirectional radiation of the communication base station; In the radar system, the communication base station is regarded as a radar transmitter; according to the prior knowledge of the environment, the response h A,n of the radar-target-radar path A on the nth subcarrier is obtained, and the response of the communication base station-target-radar path B is obtained. h B,n and the response h C,n of the radar-target-communication base station path C. 3.根据权利要求1所述的频谱共存环境下双基地雷达最优射频隐身功率分配方法，其特征在于，步骤(4)中对步骤(3)中建立的频谱共存环境下双基地雷达最优射频隐身功率分配模型进行化简，即令：3. bistatic radar optimal radio frequency stealth power allocation method under the spectrum coexistence environment according to claim 1 is characterized in that, in step (4), bistatic radar is optimal under the spectrum coexistence environment established in step (3) The RF stealth power allocation model is simplified, that is:
Figure FDA0003346381580000022
Figure FDA0003346381580000022
 其中，hC,n表示雷达-目标-通信基站路径C的响应，Pc,n＝|αc,n|2表示第n个子载波上的通信基站发射功率，
Figure FDA0003346381580000023
为背景噪声功率，Cset表示信道容量阈值；Among them, h C,n represents the response of the radar-target-communication base station path C, P c,n =|α c,n | 2 represents the communication base station transmit power on the nth subcarrier,
Figure FDA0003346381580000023
is the background noise power, and Cset represents the channel capacity threshold; 同时，用克拉美-罗下界的逆，即费舍尔信息表示目标时延估计精度，则频谱共存环境下双基地雷达最优射频隐身功率分配模型等价转化为：At the same time, using the inverse of the Cramer-Road lower bound, that is, Fisher information to represent the target delay estimation accuracy, the optimal RF stealth power allocation model for bistatic radar in the spectrum coexistence environment is equivalently transformed into:
Figure FDA0003346381580000031
Figure FDA0003346381580000031
 其中，Pr,n＝|αr,n|2表示第n个子载波上的雷达发射功率；N为正交频分复用雷达发射信号子载波数目；△f为子载波频率间隔；n为正交频分复用雷达发射波形子载波索引；hA,n表示第n个子载波上雷达-目标-雷达路径A的响应，hB,n表示通信基站-目标-雷达路径B的响应；δCRLB表示雷达目标时延估计精度阈值；Pmax表示雷达子载波发射功率的上限；Among them, P r,n =|α r,n | 2 represents the radar transmit power on the nth sub-carrier; N is the number of sub-carriers of the OFDM radar transmit signal; Δf is the sub-carrier frequency interval; n is the OFDM radar transmit waveform sub-carrier index; h A,n represents the response of radar-target-radar path A on the nth sub-carrier, h B,n represents the response of communication base station-target-radar path B; δ CRLB represents the accuracy threshold of radar target delay estimation; Pmax represents the upper limit of radar subcarrier transmit power; 由于公式(6)是一个非凸问题，则采用标准线性规划方法进行求解，得到的解即为每个子载波上的雷达发射功率。Since formula (6) is a non-convex problem, the standard linear programming method is used to solve it, and the obtained solution is the radar transmit power on each subcarrier.
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