CN108037487B - Distributed MIMO radar transmitting signal optimization design method based on radio frequency stealth - Google Patents

Distributed MIMO radar transmitting signal optimization design method based on radio frequency stealth Download PDF

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CN108037487B
CN108037487B CN201711155625.5A CN201711155625A CN108037487B CN 108037487 B CN108037487 B CN 108037487B CN 201711155625 A CN201711155625 A CN 201711155625A CN 108037487 B CN108037487 B CN 108037487B
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distributed mimo
radar
mimo radar
matrix
radio frequency
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CN108037487A (en
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时晨光
汪飞
李海林
周建江
夏伟杰
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Nanjing University of Aeronautics and Astronautics
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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
    • G01S7/28—Details of pulse systems
    • G01S7/282—Transmitters

Abstract

The invention discloses a distributed MIMO radar emission signal optimization design method based on radio frequency stealth, which comprises the steps of obtaining a reflection matrix H of a target relative to a radar system, a reflection matrix C of an environment clutter relative to the radar system, and a colored noise matrix N at a radar receiver; establishing a distributed MIMO radar signal optimization design model based on radio frequency stealth; determining an optimal Lagrangian multiplier
Figure DDA0001474167540000011
Will be provided with
Figure DDA0001474167540000012
Obtaining optimal transmitting signal of distributed MIMO radar by substituting KKT necessary condition
Figure DDA0001474167540000013
And obtaining the distributed MIMO radar transmitting signal with radio frequency stealth performance. According to the distributed MIMO radar transmitting signal optimization design method based on the radio frequency stealth, from the practical application, the total transmitting power of the distributed MIMO radar system is reduced, and the radio frequency stealth performance of the distributed MIMO radar system is improved.

Description

Distributed MIMO radar transmitting signal optimization design method based on radio frequency stealth
Technical Field
The invention relates to a radar signal optimization design technology, in particular to a distributed Multiple-Input Multiple-Output (MIMO) radar emission signal optimization design method based on radio frequency stealth.
Background
The distributed MIMO radar system is a new active detection technology, and has attracted great interest of numerous students and scientific research institutions at home and abroad in recent years. The distributed MIMO Radar system has the advantages that the space between the array elements is large, the target can be observed from different angles, large space diversity gain is obtained, the influence of the flicker of the Radar Cross Section (RCS) of the target on the detection performance, the tracking performance and the like of the system can be effectively reduced, and the distributed MIMO Radar system has the advantages of higher spatial resolution, better target detection performance, more flexible resource management design and the like.
Generally, under the influence of the working environment of the radar, clutter, noise and other various interference signals are contained in a radar return signal, and the corresponding clutter, noise and interference signals are randomly distributed. Therefore, the focus of the research on the design of the signal transmitted by the distributed MIMO radar system is how to process the signal, clutter and noise (interference), so as to optimize the performance of the radar system.
In fact, the design of the transmission signal of the distributed MIMO radar is not only constrained by the system conditions, but also needs to be performed under the signal design rule. The system constraints are limited by modern signal processing technology and hardware conditions, such as energy limitation, bandwidth limitation, time-width limitation, constant modulus limitation and the like; the design criterion of the transmitted Signal is closely related to a plurality of factors such as a task and a working environment of the radar, and for target detection, Signal to Interference plus Noise Ratio (SINR), detection probability, detection time, correlation between the Signal and clutter, and the like are generally taken as the design criteria; for target tracking, the tracking error and Mutual Information (MI) between radar received echoes and a target are mostly taken as design criteria; for target identification, a distance measure between target classes, MI between target and echo, and estimation error of target impulse response are generally used as design criteria. Therefore, the distributed MIMO radar transmission signal design process is as follows: establishing a design criterion of a transmitting signal, generating an optimal waveform under the criterion, and simultaneously considering the calculated amount in the design process to ensure the real-time requirement of the system.
However, with the continuous innovation of passive detection technology, the detection and positioning capabilities of passive detection systems are continuously enhanced, and the distributed MIMO radar in modern battlefields also needs to have radio frequency stealth capability. The radio frequency stealth technology can obviously reduce the probability that the active radiation system is intercepted, found, sorted and identified by an enemy passive detection system and attacked by an anti-radiation missile by controlling the radiation energy, waveform parameters and the like of the active radiation system, thereby improving the battlefield viability and the penetration capability of the active radiation system and a carrying platform thereof. Although the ideas of the optimization design of the radar transmitting signals under the conditions of clutter, noise and interference are provided in the methods, the methods mainly use the maximized radar target detection performance and tracking performance as targets, and the optimization design of the transmitting signals based on radio frequency stealth under a distributed MIMO radar system is not considered. Therefore, the problem of optimizing and designing the transmission signal of the distributed MIMO radar based on radio frequency stealth needs to be researched.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the situation that environmental clutter and colored noise exist simultaneously in practical application, the distributed MIMO radar transmitting signal optimization design method based on the radio frequency stealth, which reduces the total transmitting power of a distributed MIMO radar system and improves the radio frequency stealth performance of the distributed MIMO radar system, is provided.
The technical scheme is as follows: a distributed MIMO radar emission signal optimization design method based on radio frequency stealth comprises the following steps:
(1) acquiring a reflection matrix H of a target relative to a radar system, a reflection matrix C of an environment clutter relative to the radar system and a colored noise matrix N at a radar receiver;
(2) establishing a distributed MIMO radar signal optimization design model based on radio frequency stealth;
(3) determining an optimal Lagrangian multiplier
Figure BDA0001474167520000021
Will be provided with
Figure BDA0001474167520000022
Obtaining optimal transmitting signal of distributed MIMO radar by substituting KKT necessary condition
Figure BDA0001474167520000023
(4) And obtaining the distributed MIMO radar transmitting signal with radio frequency stealth performance.
Further, in the step (1), the distributed MIMO radar is provided with M transmitting antennas and N receiving antennas, and the matrix of the transmitting signals of the distributed MIMO radar is
Figure BDA0001474167520000024
Wherein the transmission signal s of the i-th antennaiIs a K multiplied by 1 dimensional vector, K is the length of a radar transmitting signal and satisfies that K is more than or equal to M and K is more than or equal to N, and a target is relative to a reflection matrix of a radar system
Figure BDA0001474167520000025
Obey zero mean complex Gaussian random distribution and satisfy
Figure BDA0001474167520000026
Wherein R isHIs a target reflection covariance matrix; reflection matrix of ambient clutter relative to radar system
Figure BDA0001474167520000027
Obey zero mean complex Gaussian random vector distribution and satisfy
Figure BDA0001474167520000028
Wherein R isCAn environment clutter covariance matrix; colored noise at radar receiver
Figure BDA0001474167520000029
Obey zero mean complex Gaussian random distribution and satisfy
Figure BDA00014741675200000210
Wherein R isNIs a colored noise covariance matrix; due to each radar in the distributed MIMO radar systemThe distance between the receiving antennas is larger, H, C and each column of the N matrix are independent, and S, N is independent of H, C.
Further, the step (2) comprises:
(21) determining radiation parameters and target tracking performance MI threshold gamma of distributed MIMO radar systemMIParameter(s)
According to the requirement of radio frequency stealth performance, the length of a radar signal is assumed to be K, K is more than or equal to M and K is more than or equal to N, and the colored noise power at the radar receiver is sigman,iCalculating to obtain target tracking performance threshold gamma according to given MIMI；
(22) MI threshold gamma according to target tracking performanceMIEstablishing a distributed MIMO radar optimal transmitting signal optimal design mathematical model based on radio frequency stealth, wherein the mathematical model is shown as a formula (1):
Figure BDA0001474167520000031
in the formula (DEG)HRepresents a conjugate transpose of the matrix;
according to the property of determinant, the above formula can be further simplified as follows:
Figure BDA0001474167520000032
in the formula IKIs a unit diagonal matrix;
(23) converting the mathematical model in step (22)
Using eigenvalue decomposition, covariance matrix RH、RC、RNCan be decomposed respectively as follows:
Figure BDA0001474167520000033
in the formula of UH、UCAnd UNRespectively unitary matrix and diagonal matrix LambdaH＝diag[σh,1,…,σh,M]， ΛC＝diag[σc,1,…,σc,M]，ΛN＝diag[σn,1,…,σn,M]Wherein σ ish,i、σc,iAnd σn,iRespectively are characteristic values of corresponding diagonal matrixes;
the mathematical model in step (22) can be converted into:
Figure BDA0001474167520000041
in the formula (I), the compound is shown in the specification,
Figure BDA0001474167520000042
is the eigenvalue of the radar transmit signal matrix S.
Further, the step (3) comprises:
(31) constructing lagrange multipliers
Figure BDA0001474167520000043
Introducing lagrange multipliers
Figure BDA0001474167520000044
Constructing a Lagrange multiplier as shown in formula (5):
Figure BDA0001474167520000045
(32) designing KKT condition for solving Lagrangian multiplier optimization
For determining optimal transmission signal of distributed MIMO system
Figure BDA0001474167520000046
In the formula (5)
Figure BDA0001474167520000047
Respectively to sigmas,iAnd
Figure BDA0001474167520000048
the first partial derivative is calculated and let:
Figure BDA0001474167520000049
satisfy sigma simultaneouslys,iThe KKT requirement for a non-linear optimization solution of ≧ 0 is as follows:
Figure BDA00014741675200000410
wherein, all variables with the mark represent the optimal solution of each parameter respectively;
(33) determining an optimal Lagrangian multiplier via iterative computation
Figure BDA00014741675200000411
And optimal transmission signal of distributed MIMO radar system
Figure BDA00014741675200000412
Furthermore, in the step (33), by solving the equation (7), an optimal lagrangian multiplier is obtained
Figure BDA0001474167520000051
And will be
Figure BDA0001474167520000052
Obtaining optimal transmitting signal of distributed MIMO radar system by substituting KKT necessary condition
Figure BDA0001474167520000053
Comprises the following steps:
Figure BDA0001474167520000054
in the formula (I), the compound is shown in the specification,
Figure BDA0001474167520000055
P*is a constant whose magnitude depends on the MI threshold gammaMI：
Figure BDA0001474167520000056
Through iterative calculation, P satisfying the formula (10)*Substituting the value into formula (8) to obtain a group of transmission signals for minimizing the total transmission power of the distributed MIMO radar system
Figure BDA0001474167520000057
And finally determining the total power of the transmitted signals of the MIMO radar system.
Has the advantages that: the invention provides a distributed MIMO radar transmitted signal optimization design method based on radio frequency stealth, which is mainly used for carrying out adaptive optimization design on a transmitted signal of a distributed MIMO radar system under the condition of meeting certain target tracking performance by taking the total power of the transmitted signal of the distributed MIMO radar system as a target on the basis of acquiring a target, an environment clutter reflection matrix and a colored noise matrix characteristic value according to priori knowledge aiming at the condition that environment clutter and colored noise exist simultaneously in practical application.
Compared with the prior art, the optimal design method for the distributed MIMO radar transmitting signals is adopted, the method takes the total power of the transmitting signals of the minimum distributed MIMO radar system as a target on the basis of obtaining the characteristic values of a target, an environment clutter reflection matrix and a colored noise matrix, and a distributed MIMO radar transmitting signal optimal design model based on radio frequency stealth is established under the condition of meeting certain target tracking performance. The target tracking performance of the distributed MIMO radar system is guaranteed, and the radio frequency stealth performance of the radar system is effectively improved. The distributed MIMO radar system has the optimal radio frequency stealth performance.
Drawings
FIG. 1 is a flow chart of a distributed MIMO radar signal optimization design method;
FIG. 2 is a distributed MIMO radar system model;
FIG. 3 illustrates characteristic values of a target, clutter and colored noise of a distributed MIMO radar;
FIG. 4 shows a result of power distribution of a transmitted signal of a distributed MIMO radar;
fig. 5 is a comparison of total power transmitted by the radar under different signal optimization design methods.
Detailed Description
The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and examples.
The invention provides a distributed MIMO radar transmitted signal optimization design method based on radio frequency stealth, which is mainly used for carrying out adaptive optimization design on transmitted signals of a distributed MIMO radar system under the condition of meeting certain target tracking performance by taking the total power of the transmitted signals of the distributed MIMO radar system as a target on the basis of acquiring a target, an environment clutter reflection matrix and a colored noise matrix characteristic value according to priori knowledge aiming at the condition that environment clutter and colored noise exist simultaneously in practical application.
As shown in fig. 1, the distributed MIMO radar transmission signal optimization design method based on radio frequency stealth of the present invention includes the following steps:
(1) determining a reflection matrix of a target, an environmental clutter relative to a radar system and a colored noise matrix at a radar receiver
The invention provides a distributed MIMO radar transmitted signal optimization design method based on radio frequency stealth. The method utilizes prior knowledge of target reflection characteristics, environment clutter, receiver colored noise and the like, so that a reflection matrix H of a target relative to a distributed MIMO radar system, a reflection matrix C of the environment clutter relative to the distributed MIMO radar system and a colored noise matrix N at a radar receiver are determined firstly.
Assuming that the distributed MIMO radar system model is as shown in fig. 2, let distributed MIMO radar have M transmit antennas and N receive antennas. It should be noted that the distributed MIMO radar transmits the signal matrix of
Figure BDA0001474167520000061
Wherein the transmission signal s of the i-th antennaiThe vector is a K multiplied by 1 dimensional vector, K is the length of a radar transmitting signal and satisfies that K is more than or equal to M and K is more than or equal to N. Reflection matrix of target relative to radar system
Figure BDA0001474167520000062
Obey zero mean complex Gaussian random distribution and satisfy
Figure BDA0001474167520000063
Wherein R isHIs the target reflection covariance matrix. Ambient clutter reflection matrix
Figure BDA0001474167520000064
Obey zero mean complex Gaussian random vector distribution and meet
Figure BDA0001474167520000065
Wherein R isCIs an ambient clutter covariance matrix. Colored noise at radar receiver
Figure BDA0001474167520000066
Obey zero mean complex Gaussian random distribution and satisfy
Figure BDA0001474167520000067
Wherein R isNIs a colored noise covariance matrix. Because the distance between the radar receiving antennas in the distributed MIMO radar system is large, H, C and each column of the N matrix are independent, and S, N is irrelevant to H, C.
(2) Establishing distributed MIMO radar signal optimization design model based on radio frequency stealth
(21) Determining radiation parameters and target tracking performance MI threshold gamma of distributed MIMO radar systemMIEqual parameter
According to the requirement of radio frequency stealth performance, the length of a radar signal is assumed to be K, K is more than or equal to M and K is more than or equal to N, and the colored noise power at the radar receiver is sigman,iCalculating to obtain target tracking performance threshold gamma according to given MIMI。
(22) According to the requirement of a distributed MIMO radar system on target tracking performance, a distributed MIMO radar optimal transmitting signal optimal design mathematical model based on radio frequency stealth is established, and the formula (1) is as follows:
Figure BDA0001474167520000071
in the formula (DEG)HRepresents a conjugate transpose of the matrix;
according to the property of determinant, the above formula can be further simplified as follows:
Figure BDA0001474167520000072
in the formula IKIs a unit diagonal matrix;
(23) converting the mathematical model in step (22)
Using eigenvalue decomposition, covariance matrix RH、RC、RNCan be decomposed respectively as follows:
Figure BDA0001474167520000073
in the formula of UH、UCAnd UNRespectively unitary matrix and diagonal matrix LambdaH＝diag[σh,1,…,σh,M]， ΛC＝diag[σc,1,…,σc,M]，ΛN＝diag[σn,1,…,σn,M]Wherein σ ish,i、σc,iAnd σn,iRespectively are characteristic values of corresponding diagonal matrixes;
the mathematical model in step (22) can be converted into:
Figure BDA0001474167520000081
in the formula (I), the compound is shown in the specification,
Figure BDA0001474167520000082
is the eigenvalue of the radar transmit signal matrix S.
(3) Determining an optimal Lagrangian multiplier
Figure BDA0001474167520000083
(31) Constructing lagrange multipliers
Figure BDA0001474167520000084
Introducing lagrange multipliers
Figure BDA0001474167520000085
Constructing a Lagrange multiplier as shown in formula (5):
Figure BDA0001474167520000086
(32) designing solvable nonlinear equations
Figure BDA0001474167520000087
Optimized KKT condition
For determining optimal transmission signal of distributed MIMO system
Figure BDA0001474167520000088
In the formula (5)
Figure BDA0001474167520000089
Respectively to sigmas,iAnd
Figure BDA00014741675200000810
the first partial derivative is calculated and let:
Figure BDA00014741675200000811
satisfy sigma simultaneouslys,iCarlo-Cohn-Tack condition for solving nonlinear optimization of not less than 0 (Karush-Kuhn)-Tucker, KKT) requirements, as follows:
Figure BDA00014741675200000812
wherein, all variables marked with the mark represent the optimal solution of each parameter respectively.
(33) Determining lagrangian multipliers via iterative calculations
Figure BDA00014741675200000813
And optimal transmission signal of distributed MIMO radar system
Figure BDA0001474167520000091
Implementing a non-linear equation
Figure BDA0001474167520000092
The optimization solution of (1);
by solving equation (7), the optimal Lagrange multiplier is obtained
Figure BDA0001474167520000093
And will be
Figure BDA0001474167520000094
Obtaining optimal transmitting signal of distributed MIMO radar system by substituting KKT necessary condition
Figure BDA0001474167520000095
Comprises the following steps:
Figure BDA0001474167520000096
in the formula (I), the compound is shown in the specification,
Figure BDA0001474167520000097
P*is a constant whose magnitude depends on a given MI threshold:
Figure BDA0001474167520000098
through iterative calculation, P satisfying the formula (10)*Substituting the value into formula (8) to obtain a group of transmission signals for minimizing the total transmission power of the distributed MIMO radar system
Figure BDA0001474167520000099
As an optimal solution, transmitting the optimal transmission signal
Figure BDA00014741675200000910
The minimum transmitting signal total power of the MIMO radar system which meets the constraint condition can be obtained by substituting in the formula (1).
(4) And obtaining the distributed MIMO radar transmitting signal with radio frequency stealth performance.
The working principle is as follows:
the method comprises the steps of firstly, aiming at the situation that environmental clutter and colored noise exist simultaneously in practical application, obtaining characteristic values of a target, an environmental clutter reflection matrix and a colored noise matrix according to priori knowledge; and then, with the total power of the transmitting signals of the distributed MIMO radar as a target, establishing a distributed MIMO radar transmitting signal optimization design model based on radio frequency stealth under the condition of meeting certain target tracking performance, and solving the model by a Lagrange multiplier method. Through iterative calculation, a signal which enables the distributed MIMO radar to transmit the minimum total power under the condition of meeting certain target tracking performance is selected
Figure BDA00014741675200000911
As an optimal solution, transmitting the optimal transmission signal
Figure BDA00014741675200000912
The minimum transmitting signal total power which meets the constraint condition can be obtained by substituting the formula (1).
Aiming at the situation that the environmental clutter and the colored noise exist simultaneously in practical application, the characteristic values of the target, the environmental clutter reflection matrix and the colored noise matrix are obtained according to the priori knowledge, and the MI value obtained by the distributed MIMO radar is obtained through theoretical derivation calculation.
The method comprises the steps of taking the total power of the transmitting signals of the minimum distributed MIMO radar as a target, establishing a distributed MIMO radar transmitting signal optimization design model based on radio frequency stealth under the condition of meeting certain target tracking performance, taking the formula (1) as a target function, solving the problem by adopting a Lagrange multiplier method, and determining the optimal transmitting signal of each transmitting antenna of the distributed MIMO radar through iterative calculation
Figure BDA0001474167520000101
And (3) simulation results:
assume that the parameters in step (2) are as shown in table 1.
Table 1 simulation parameter settings
Figure BDA0001474167520000102
The target, clutter response and colored noise characteristic values of the distributed MIMO radar are shown in fig. 3, and the power distribution result of the transmitted signal of the distributed MIMO radar is shown in fig. 4. The distributed MIMO radar transmitting signal optimization design method based on radio frequency stealth is an optimal transmitting signal obtained through calculation according to target relative to distributed MIMO radar characteristic response, environment clutter characteristic response and colored noise power at a radar receiver. As can be seen from fig. 4, the power distribution result of each transmitting antenna of the distributed MIMO radar system is mainly determined by the reflection matrix eigenvalue, clutter reflection matrix eigenvalue, and colored noise matrix eigenvalue of the target relative to the MIMO radar, and the radar transmitting signal power is mainly distributed to the antenna having the maximum ratio of the target to the clutter response eigenvalue and the minimum colored noise eigenvalue. In order to minimize the total power of the transmitted signals of the distributed MIMO system on the premise of ensuring certain target tracking performance, the distributed MIMO radar transmitted signal optimization design method based on radio frequency stealth performs power distribution according to the water injection principle, namely, the most power is distributed at the antenna with the maximum target-clutter response characteristic value ratio and the minimum colored noise characteristic value.
Fig. 5 shows the comparison of the total power of the radar transmission under different signal optimization design methods. As can be seen from fig. 5, as the requirement for target tracking performance increases, the total transmission power of the distributed MIMO radar system increases continuously. In addition, the total radar transmission power obtained by the optimal radar transmission signal optimization design method is obviously smaller than that obtained by the uniform power distribution signal design method, so that the radio frequency stealth performance of the optimal radar transmission signal is superior to that of the uniform power distribution signal, because the uniform power distribution transmission signal uniformly distributes the total radar signal power to each transmitting antenna under the condition of no prior knowledge about target characteristic response, clutter characteristic response, colored noise power of a radar receiver and the like, the uniform power distribution transmission signal has poorer radio frequency stealth performance.
According to the simulation result, on the basis of acquiring the characteristic response of a target relative to the distributed MIMO radar, the characteristic response of the environmental clutter and the colored noise power of a radar receiver according to the priori knowledge, the optimal design method for the distributed MIMO radar transmitting signal based on the radio frequency stealth takes the total power of the transmitting signal of the distributed MIMO radar system as a target, and performs adaptive optimal design on the transmitting signal of the distributed MIMO radar system, so that the radio frequency stealth performance of the distributed MIMO radar system is effectively improved under the condition of meeting certain target tracking performance.

Claims (4)

1. A distributed MIMO radar emission signal optimization design method based on radio frequency stealth is characterized by comprising the following steps:
(1) acquiring a reflection matrix H of a target relative to a radar system, a reflection matrix C of an environment clutter relative to the radar system and a colored noise matrix N at a radar receiver;
(2) establishing a distributed MIMO radar signal optimization design model based on radio frequency stealth; the method specifically comprises the following steps:
(21) determining radiation parameters and target tracking performance MI threshold gamma of distributed MIMO radarMI；
According to the requirement of radio frequency stealth performance, the length of a radar signal is assumed to be K and K is satisfiedMore than or equal to M, K is more than or equal to N, wherein M is the number of transmitting antennas, N is the number of receiving antennas, and the colored noise power at the radar receiver is sigman,iCalculating to obtain the MI threshold gamma of the target tracking performance according to the given MIMI；
(22) MI threshold gamma according to target tracking performanceMIEstablishing a distributed MIMO radar optimal transmission signal optimization design mathematical model based on radio frequency stealth, wherein the mathematical model is shown as a formula (1):
Figure FDA0002897308600000011
in the formula (DEG)HRepresents the conjugate transpose of the matrix and,
Figure FDA0002897308600000012
for distributed MIMO radar signal matrix, i part of antennaiIs a K x 1 dimensional vector, RHIs a target reflection covariance matrix, RCIs an ambient clutter covariance matrix, RNIs a colored noise covariance matrix;
according to the property of determinant, the above formula can be further simplified as follows:
Figure FDA0002897308600000013
in the formula IKIs a unit diagonal matrix;
(23) converting the mathematical model in step (22)
Using eigenvalue decomposition, covariance matrix RH、RC、RNThe decomposition is as follows:
Figure FDA0002897308600000021
in the formula of UH、UCAnd UNRespectively unitary matrix and diagonal matrix LambdaH＝diag[σh,1,…,σh,M]，ΛC＝diag[σc,1,…,σc,M]，ΛN＝diag[σn,1,…,σn,M]Wherein σ ish,i、σc,iAnd colored noise power σ at the radar receivern,iRespectively are eigenvalues of corresponding diagonal matrixes;
the mathematical model in step (22) can be converted into:
Figure FDA0002897308600000022
in the formula (I), the compound is shown in the specification,
Figure FDA0002897308600000023
characteristic values of a radar emission signal matrix S are obtained;
(3) determining an optimal Lagrangian multiplier
Figure FDA0002897308600000024
Will be provided with
Figure FDA0002897308600000025
Obtaining optimal transmitting signal of distributed MIMO radar by substituting KKT necessary condition
Figure FDA0002897308600000026
Wherein the KKT requirement refers to a Carorovan-Kuen-Take requirement;
(4) and obtaining the distributed MIMO radar transmitting signal with radio frequency stealth performance.
2. The distributed MIMO radar transmitted signal optimization design method based on radio frequency stealth according to claim 1, characterized in that: the distributed MIMO radar is arranged in the step (1) and is provided with M transmitting antennas and N receiving antennas, and the matrix of the transmitting signals of the distributed MIMO radar is
Figure FDA0002897308600000027
WhereinTransmitting signal s of the i-th antennaiIs a K multiplied by 1 dimensional vector, K is the length of a radar transmitting signal and satisfies that K is more than or equal to M and K is more than or equal to N, and a target is relative to a reflection matrix of a radar system
Figure FDA0002897308600000028
Obey zero mean complex Gaussian random distribution and satisfy
Figure FDA0002897308600000029
Wherein R isHIs a target reflection covariance matrix; reflection matrix of ambient clutter relative to radar system
Figure FDA00028973086000000210
Obey zero mean complex Gaussian random vector distribution and meet
Figure FDA00028973086000000211
Wherein R isCAn environment clutter covariance matrix; colored noise at radar receiver
Figure FDA00028973086000000212
Obey zero mean complex Gaussian random distribution and satisfy
Figure FDA00028973086000000213
Wherein R isNIs a colored noise covariance matrix; because the distance between the receiving antennas of each radar in the distributed MIMO radar is large, H, C and each column of the N matrix are independent, and S, N is independent of H, C.
3. The method for optimally designing the transmission signals of the distributed MIMO radar based on the radio frequency stealth as claimed in claim 1, wherein the step (3) comprises:
(31) constructing lagrange multipliers
Figure FDA0002897308600000031
Introducing lagrange multipliers
Figure FDA0002897308600000032
Constructing a Lagrange multiplier as shown in formula (5):
Figure FDA0002897308600000033
(32) designing KKT necessary condition capable of solving Lagrangian multiplier optimization
For determining optimal transmitting signal of distributed MIMO radar
Figure FDA0002897308600000034
In the formula (5)
Figure FDA0002897308600000035
Respectively to sigmas,iAnd
Figure FDA0002897308600000036
taking a first partial derivative, where σs,iThe ith eigenvalue of the radar emission signal matrix S; and order:
Figure FDA0002897308600000037
satisfy sigma simultaneouslys,iThe KKT requirement for a non-linear optimization solution of ≧ 0 is as follows:
Figure FDA0002897308600000038
wherein, all variables with the mark represent the optimal solution of each parameter respectively;
(33) determining an optimal Lagrangian multiplier via iterative computation
Figure FDA0002897308600000039
And the optimal transmitting signal of the ith transmitting antenna of the distributed MIMO radar
Figure FDA00028973086000000310
4. The method as claimed in claim 3, wherein the optimal Lagrangian multiplier is obtained by solving equation (7) in step (33)
Figure FDA00028973086000000311
And will be
Figure FDA00028973086000000312
Obtaining the optimal transmitting signal of the ith transmitting antenna of the distributed MIMO radar by substituting the KKT necessary condition
Figure FDA00028973086000000313
Comprises the following steps:
Figure FDA0002897308600000041
in the formula (I), the compound is shown in the specification,
Figure FDA0002897308600000042
P*is a constant whose magnitude depends on the target tracking performance MI threshold gammaMI：
Figure FDA0002897308600000043
Through iterative calculation, P satisfying the formula (10)*Substituting the value into formula (8) to obtain a group of transmission signals for minimizing the total transmission power of the distributed MIMO radar
Figure FDA0002897308600000044
And finally determining the total power of the transmitting signals of the MIMO radar system.
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