CN108226878B - MIMO radar transmitting waveform synthesis method based on coordinate descent algorithm - Google Patents

MIMO radar transmitting waveform synthesis method based on coordinate descent algorithm Download PDF

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CN108226878B
CN108226878B CN201711291266.6A CN201711291266A CN108226878B CN 108226878 B CN108226878 B CN 108226878B CN 201711291266 A CN201711291266 A CN 201711291266A CN 108226878 B CN108226878 B CN 108226878B
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waveform
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CN108226878A (en
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纠博
郑浩
刘宏伟
周生华
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Xian University of Electronic Science and Technology
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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
    • G01S7/36—Means for anti-jamming, e.g. ECCM, i.e. electronic counter-counter measures
    • 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
    • G01S7/42—Diversity systems specially adapted for radar

Abstract

The invention discloses a method for synthesizing a multi-input multi-output MIMO radar transmitting waveform based on a coordinate descent algorithm, which mainly solves the problem that the transmitting waveform synthesized by the prior art does not have an anti-interference function and constant modulus characteristics. The method comprises the following specific steps: 1. constructing an interference airspace guide vector; 2. constructing a transmit signal covariance matrix; 3. synthesizing a multi-input multi-output constant modulus transmitting waveform matrix; 4. correcting elements in a multi-input multi-output constant modulus transmitting waveform matrix by adopting a coordinate descent algorithm of the following formula; 5. and taking each row element in the multi-input multi-output constant modulus transmitting waveform matrix as the transmitting waveform of each array element of the radar. The invention can synthesize the MIMO radar transmitting waveform with anti-interference function and constant modulus characteristic.

Description

MIMO radar transmitting waveform synthesis method based on coordinate descent algorithm
Technical Field
The invention belongs to the technical field of radars, and further relates to a method for synthesizing a multi-Input multi-output (MIMO) radar emission waveform based on a coordinate descent algorithm in the technical field of cognitive radars. The MIMO radar transmitting waveform matrix with the anti-interference function can be quickly synthesized according to the position information of the interference source of the other party and the position information of the radar detection target.
Background
The general application of digital components in a radar system generates an MIMO radar, which is different from the traditional phased array radar, and each array element of the MIMO radar can transmit different signals. The MIMO radar may be classified into a distributed MIMO radar and a centralized MIMO radar according to the size of the spacing between the transmitting and receiving antennas. For the distributed MIMO radar, the observation angles of the antennas to the target are different, and the echoes are independent. Therefore, in a statistical sense, the distributed MIMO radar can overcome the flickering effect of the target. Compared with a phased array radar, the degree of freedom of the centralized MIMO radar is remarkably improved, and therefore the centralized MIMO radar has the capability of designing a self-adaptive emission directional diagram. In the actual operating environment of a radar, there are often disturbances that affect the ability of the radar to detect targets. Therefore, it is necessary for the radar to reduce interference power in the echo signal by designing the transmission waveform at the transmitting end. The MIMO radar can obtain a specific directional diagram through the design of a transmitting waveform matrix, so that the aim of resisting interference is fulfilled.
S Imani et al, in its published paper, "Transmit Signal Design in colored MIMO random Without Covariance Matrix Optimization" ([ J ]. IEEE Transactions on Aerospace & Electronic Systems, 2017, PP (99):1-1), propose a method for synthesizing MIMO radar Transmit waveforms based on semi-positive Relaxation (SDR). The method comprises the following basic steps: firstly, obtaining an expected emission directional diagram according to prior information, then constructing an SDR model according to the expected emission directional diagram, and solving the model to obtain an MIMO radar emission waveform matrix. The method has the following defects: the SDR model only approaches an expected transmitting directional diagram by a least square criterion, and an anti-interference condition is ignored, so that an anti-interference function cannot be realized by using a transmitting waveform synthesized by the SDR model.
A MIMO radar emission pattern and waveform design method is disclosed in a patent technology 'an MIMO radar emission pattern and waveform design method' (application number: 201510299652.4 grant publication number: CN 105158736B) owned by the twenty-eighth research institute of China electronics science and technology group company. The patent technology comprises the following specific steps: firstly, modeling an expected emission directional diagram according to prior information, then constructing an emission signal into weighted summation of a group of orthogonal sequences, designing an optimization problem about the number and weight of the orthogonal sequences by using and improving a DPS sequence generation principle, and simultaneously obtaining an optimized waveform and an optimized emission directional diagram by solving the optimization problem. The method has the following defects: in actual radar operation, in order to ensure the maximum working efficiency of each array element transmitting power amplifier, a transmitting waveform is required to have constant modulus characteristics, and the method cannot generate the constant modulus transmitting waveform.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a multi-input multi-output MIMO radar transmitting waveform synthesis method based on a coordinate descent algorithm. The method can generate a constant-modulus transmitting waveform, thereby ensuring the maximum working efficiency of each array element transmitting power amplifier of the radar antenna. In addition, the method can sequentially correct each row of elements in the multi-input multi-output constant modulus transmitting waveform matrix so as to ensure that the transmitting waveform has an anti-interference function.
In order to achieve the above object, the method comprises the following steps:
(1) constructing an interference space domain guide vector:
substituting the azimuth angle of the interference source of the other party into an interference guide vector formula to obtain an interference airspace guide vector;
(2) constructing an interference subspace matrix:
substituting the interference airspace guide vector into an interference subspace formula to obtain an interference subspace matrix;
(3) constructing a target airspace guide vector
Substituting the azimuth angle of a target to be detected of the radar into a target guide vector formula to obtain a target airspace guide vector;
(4) constructing a transmit signal covariance matrix:
substituting the target airspace guide vector into a transmitted signal covariance matrix formula to obtain a transmitted signal covariance matrix;
(5) synthesizing a multi-input multi-output constant modulus transmitting waveform matrix:
(5a) randomly generating a multi-input multi-output constant modulus transmitting waveform matrix with all elements in the matrix having equal amplitudes, and taking the matrix as an initial matrix;
(5b) substituting the covariance matrix of the transmitted signals and the initial multi-input multi-output constant modulus transmission waveform matrix into a multi-input multi-output constant modulus transmission waveform matrix formula to obtain a current multi-input multi-output constant modulus transmission waveform matrix;
(5c) substituting the covariance matrix of the transmitted signals and the current multi-input multi-output constant modulus transmission waveform matrix into a constant modulus transmission waveform matrix formula to obtain a new multi-input multi-output constant modulus transmission waveform matrix;
(5d) judging whether the difference between the current multi-input multi-output constant modulus transmitting waveform matrix and the new multi-input multi-output constant modulus transmitting waveform matrix meets a stop condition, if so, executing the step (6), otherwise, executing the step (5c) after taking the new multi-input multi-output constant modulus transmitting waveform matrix as the current multi-input multi-output constant modulus transmitting waveform matrix;
(6) sequentially correcting each row of elements in the multi-input multi-output constant modulus transmitting waveform matrix by adopting a coordinate descent algorithm as follows:
Figure BDA0001499432780000031
wherein the content of the first and second substances,
Figure BDA0001499432780000032
element of line I, x representing modified MIMO constant modulus transmit waveform matrixmRepresenting the m-th row element of the MIMO constant modulus transmit waveform matrix before correction, ⊙ representing the Hadamard multiplication operation between vectors, | | | | | | | survival2Denotes 2 norm operation, vcThe c row elements of the interference subspace matrix are expressed, the values of l, m and c are correspondingly the same, and the value range is [1, N]N represents the total number of the array elements of the radar antenna, V represents an interference subspace matrix, H represents conjugate transpose operation, and x represents conjugate operation;
(7) judging whether the corrected multi-input multi-output constant modulus transmitting waveform matrix meets the anti-interference condition, if so, executing the step (8), otherwise, executing the step (6);
(8) and taking each row element in the multi-input multi-output constant modulus transmitting waveform matrix as the transmitting waveform of each array element of the radar.
Compared with the prior art, the invention has the following advantages:
firstly, on the basis of constructing a transmit signal covariance matrix, a multi-input multi-output constant modulus transmit waveform matrix is synthesized, and each row element of the matrix is used as a transmit waveform of each array element of a radar, so that the radar transmit waveform has constant modulus characteristics, and the defect that the transmit waveform synthesized by the prior art does not have the constant modulus characteristics is overcome. In the actual operation of the radar, in order to ensure the maximum working efficiency of each array element transmitting power amplifier, the transmitting waveform is required to have constant modulus characteristics, so that the radar transmitting waveform generated by the invention can ensure the maximum working efficiency of each array element transmitting power amplifier.
Secondly, on the basis of the synthesized multi-input multi-output constant modulus transmitting waveform matrix, a coordinate descent algorithm is adopted, and each row of elements in the multi-input multi-output constant modulus transmitting waveform matrix are corrected in sequence to meet the anti-interference condition, so that the defect that the anti-interference condition is ignored in the transmitting waveform synthesized in the prior art is overcome, and the radar transmitting waveform generated by the invention has the anti-interference function.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a transmission pattern of a simulated synthesized radar transmission waveform of the present invention;
FIG. 3 is an amplitude diagram of the radar array element transmitting waveform obtained by simulation in the invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The specific steps of the present invention are described below with reference to fig. 1:
step 1, constructing an interference airspace guide vector.
And substituting the azimuth angle of the interference source of the other party into an interference guide vector formula to obtain an interference airspace guide vector.
The interference steering vector formula is as follows:
Figure BDA0001499432780000041
wherein, a (theta)k) Represents the k th interference source azimuth angle theta of the other partykThe value range of K is [1, K ] as the interference space domain steering vector]K represents the total number of interference sources, exp represents exponential operation with natural constant as base, j represents an imaginary unit symbol, pi represents a circumferential rate, and is a multiplication operation, d represents the interval between radar antenna array elements, N represents the serial number of the radar antenna array elements, and the value range of N is [0, N-1 ]]N denotes the total number of elements of the radar antenna, sin denotes sine value operation, lambda denotes the wavelength of the radar emission signal, thetakRepresenting the k-th interferer azimuth.
And 2, constructing an interference subspace matrix.
And substituting the interference airspace guide vector into an interference subspace formula to obtain an interference subspace matrix.
The interference subspace formula is as follows:
V＝[a(θk)]
wherein V represents an interference subspace matrix, [ alpha ], [ alpha]Representing a matrixing operation, a (θ)k) Represents the kth interference source azimuth angle thetakThe value range of K is [1, K ] as the interference space domain steering vector]And K represents the total number of the other interference sources.
And 3, constructing a target airspace guide vector.
And substituting the azimuth angle of the target to be detected of the radar into a target guiding vector formula to obtain a target airspace guiding vector.
The target steering vector formula is as follows:
wherein, a (theta)i) Indicating the azimuth angle theta of the ith target to be detected of the radariThe value range of I is [1, I]Where I represents the total number of targets, exp represents the exponential operation with natural constant as the base, j represents the unit symbol of imaginary number, pi represents the circumferential rate,. represents the multiplication operation, d represents the spacing between radar antenna elements, and n represents the radarThe serial number of the antenna array element and the value range of N are [0, N-1 ]]N denotes the total number of radar antenna elements, sin denotes the operation of taking the sine value, lambda denotes the wavelength of the radar emission signal, thetaiAnd indicating the azimuth angle of the target to be detected of the ith radar of the opposite party.
And 4, constructing a covariance matrix of the transmitting signals.
And substituting the target airspace guide vector into a transmitted signal covariance matrix formula to obtain a transmitted signal covariance matrix.
The transmit signal covariance matrix formula is as follows:
R＝[a(θi)]
wherein R represents a transmit signal covariance matrix]Representing a matrixing operation, a (θ)i) Indicating the azimuth angle theta of the ith radar target to be detectediThe value range of I is [1, I]And I represents the total number of targets to be detected by the radar.
And 5, synthesizing a multi-input multi-output constant modulus transmitting waveform matrix.
Firstly, a multi-input multi-output constant modulus transmitting waveform matrix with all elements in the matrix equal in amplitude is randomly generated and is used as an initial matrix.
And step two, substituting the covariance matrix of the transmitted signals and the initial multi-input multi-output constant modulus transmission waveform matrix into a multi-input multi-output constant modulus transmission waveform matrix formula to obtain a current multi-input multi-output constant modulus transmission waveform matrix.
The multiple-input multiple-output constant modulus emission waveform matrix formula is as follows:
Figure BDA0001499432780000061
wherein, X1Representing the current MIMO constant modulus transmit waveform matrix, exp representing the exponential operation with the natural constant as the base, j representing the imaginary unit sign, and representing the multiplication operation, angle representing the operation of taking the phase value of each element in the matrix, svd representing the singular value decomposition operation on the matrix, X0Representing initial multiple-input multiple-output constant modulus transmit waveform momentsThe matrix, R, represents the transmit signal covariance matrix,
Figure BDA0001499432780000062
denotes the square root operation of taking the matrix, and H denotes the conjugate transpose operation of the matrix.
And thirdly, substituting the covariance matrix of the transmitting signals and the current multi-input multi-output constant modulus transmitting waveform matrix into a constant modulus transmitting waveform matrix formula to obtain a new multi-input multi-output constant modulus transmitting waveform matrix.
And fourthly, judging whether the difference between the current multi-input multi-output constant modulus transmitting waveform matrix and the new multi-input multi-output constant modulus transmitting waveform matrix meets the stop condition, if so, executing the step 6, otherwise, executing the third step after taking the new multi-input multi-output constant modulus transmitting waveform matrix as the current multi-input multi-output constant modulus transmitting waveform matrix.
The stop conditions are as follows:
Figure BDA0001499432780000063
wherein | | | purple hair2The 2-norm operation is shown as being performed,
Figure BDA0001499432780000064
representing the difference between the current mimo constant modulus transmit waveform matrix and the new mimo constant modulus transmit waveform matrix.
And 6, sequentially correcting each row of elements in the multi-input multi-output constant modulus transmitting waveform matrix by adopting a coordinate descent algorithm as follows:
Figure BDA0001499432780000065
wherein the content of the first and second substances,
Figure BDA0001499432780000066
element of line I, x representing modified MIMO constant modulus transmit waveform matrixmRepresenting multiple-input multiple-output constant modulus transmit waveform moments before correctionRow m elements of the array, ⊙, represent hadamard multiplication operations between vectors, | | | | | tory2Denotes 2 norm operation, vcThe c row elements of the interference subspace matrix are expressed, the values of l, m and c are correspondingly the same, and the value range is [1, N]N denotes the total number of elements of the radar antenna array, V denotes the interference subspace matrix, H denotes the conjugate transpose operation, and x denotes the conjugate operation.
And 7, judging whether the corrected multi-input multi-output constant modulus transmitting waveform matrix meets the anti-interference condition, if so, executing a step 8, and otherwise, executing a step 6.
The anti-interference conditions are as follows:
tr[VHXHXV]≤10-4
wherein tr represents the trace operation of the matrix, V represents the interference subspace matrix, X represents the corrected multi-input multi-output constant modulus transmission waveform matrix, and H represents the conjugate transpose operation.
And 8, taking each row element in the multi-input multi-output constant modulus transmitting waveform matrix as the transmitting waveform of each array element of the radar.
The effect of the present invention will be further described with reference to the simulation data.
1. Simulation conditions are as follows:
the simulation running system is an Intel (R) core (TM) i7-2600CPU 650@3.40GHz 32-bit Windows operating system, and simulation software adopts MATLAB (R2012 b).
2. Simulation data and result analysis:
the parameters of the simulation experiment of the invention are that the total number of radar array elements is 16, the spacing between the radar antenna array elements is 0.5 mm, the wavelength of radar emission signals is 1 mm, the total number of interference sources is 2, the azimuth angles of the interference sources are respectively-60 degrees and 20 degrees, the total number of targets is 3, and the azimuth angles of the targets are respectively-35 degrees, 0 degrees and 45 degrees.
Fig. 2 is a transmission pattern of a radar transmission waveform synthesized by a simulation experiment of the present invention. The abscissa in fig. 2 represents the airspace azimuth angle, the range of the azimuth angle is [ -90 degrees, 90 degrees ], and the ordinate represents the power gain of the radar transmission waveform synthesized by the simulation experiment at each airspace azimuth angle, and the unit is dB. And drawing the power gain of the radar transmitting waveform synthesized by the simulation experiment at each airspace azimuth to obtain the transmitting directional diagram of the radar transmitting waveform synthesized by the simulation experiment.
The power gain of the radar transmitting waveform synthesized by the simulation experiment at each airspace azimuth is obtained by the following formula:
P(θ)＝a(θ)HXXHa(θ)
p (theta) represents the power gain of a radar transmitting waveform synthesized in a simulation experiment at an airspace azimuth angle theta, a (theta) represents an airspace guide vector at the airspace azimuth angle theta, H represents a conjugate transpose operation, and X is a multi-input multi-output constant-modulus transmitting waveform matrix synthesized in the simulation experiment.
As can be seen from FIG. 2, the radar has stronger power gain of 20dB at the target azimuth angles of-35 degrees, 0 degrees and 45 degrees and only weak power gain of-50 dB at the interference source azimuth angles of-60 degrees and 20 degrees, so that the radar transmitting waveform synthesized by the method has an anti-interference function.
Fig. 3 is an amplitude diagram of the radar array element transmitting waveform obtained by simulation of the invention. And taking the amplitude values of each row of elements in the multi-input multi-output constant modulus transmission waveform matrix synthesized by the simulation experiment as the amplitude values of the transmission waveforms of each array element of the radar, and drawing the corresponding amplitude of each array element of the radar to obtain an amplitude chart of the transmission waveforms of each array element of the radar.
In fig. 3, the abscissa represents the number of radar array elements, the value range is [1,16], and the ordinate represents the amplitude value of the waveform transmitted by the corresponding array element. As can be seen from fig. 3, the transmitting waveforms of the array elements of the radar are equal in amplitude and are all 1. Therefore, the synthesized transmitting waveform has constant modulus characteristic, and the maximum working efficiency of each array element transmitting power amplifier can be ensured.
In conclusion, the MIMO radar transmitting waveform synthesized by the method has the anti-interference function and the constant modulus characteristic.

Claims (7)

1. A multi-input multi-output MIMO radar transmitting waveform synthesis method based on a coordinate descent algorithm is characterized by comprising the following steps:
(1) constructing an interference space domain guide vector:
substituting the azimuth angle of the interference source of the other party into an interference guide vector formula to obtain an interference airspace guide vector;
(2) constructing an interference subspace matrix:
substituting the interference airspace guide vector into an interference subspace formula to obtain an interference subspace matrix;
(3) constructing a target airspace guide vector
Substituting the azimuth angle of a target to be detected of the radar into a target guide vector formula to obtain a target airspace guide vector;
(4) constructing a transmit signal covariance matrix:
substituting the target airspace guide vector into a transmitted signal covariance matrix formula to obtain a transmitted signal covariance matrix;
(5) synthesizing a multi-input multi-output constant modulus transmitting waveform matrix:
(5a) randomly generating a multi-input multi-output constant modulus transmitting waveform matrix with all elements in the matrix having equal amplitudes, and taking the matrix as an initial matrix;
(5b) substituting the covariance matrix of the transmitted signals and the initial multi-input multi-output constant modulus transmission waveform matrix into the following multi-input multi-output constant modulus transmission waveform matrix formula to obtain a current multi-input multi-output constant modulus transmission waveform matrix;
Figure FDA0002206743670000011
wherein, X1Representing the current MIMO constant modulus transmit waveform matrix, exp representing the exponential operation with the natural constant as the base, j representing the imaginary unit sign, and representing the multiplication operation, angle representing the operation of taking the phase value of each element in the matrix, svd representing the singular value decomposition operation on the matrix, X0Representing an initial multiple-input multiple-output constant modulus transmit waveform matrix, R representing a transmit signal covariance matrix,
Figure FDA0002206743670000012
the square root operation of the matrix is taken, and H represents the conjugate transpose operation of the matrix;
(5c) substituting the transmit signal covariance matrix and the current multiple-input multiple-output constant modulus transmit waveform matrix into the multiple-input multiple-output constant modulus transmit waveform matrix formula in the step (5b) to obtain a new multiple-input multiple-output constant modulus transmit waveform matrix;
(5d) judging whether the difference between the current multi-input multi-output constant modulus transmitting waveform matrix and the new multi-input multi-output constant modulus transmitting waveform matrix meets a stop condition, if so, executing the step (6), otherwise, executing the step (5c) after taking the new multi-input multi-output constant modulus transmitting waveform matrix as the current multi-input multi-output constant modulus transmitting waveform matrix;
(6) sequentially correcting each row of elements in the multi-input multi-output constant modulus transmitting waveform matrix by adopting a coordinate descent algorithm as follows:
Figure FDA0002206743670000021
wherein the content of the first and second substances,
Figure FDA0002206743670000022
element of line I, x representing modified MIMO constant modulus transmit waveform matrixmRepresenting the m-th row element of the MIMO constant modulus transmit waveform matrix before correction, ⊙ representing the Hadamard multiplication operation between vectors, | | | | | | | survival2Denotes 2 norm operation, vcThe c row elements of the interference subspace matrix are expressed, the values of l, m and c are correspondingly the same, and the value range is [1, N]N represents the total number of the array elements of the radar antenna, V represents an interference subspace matrix, H represents conjugate transpose operation, and x represents conjugate operation;
(7) judging whether the corrected multi-input multi-output constant modulus transmitting waveform matrix meets the anti-interference condition, if so, executing the step (8), otherwise, executing the step (6);
(8) and taking each row element in the multi-input multi-output constant modulus transmitting waveform matrix as the transmitting waveform of each array element of the radar.
2. The method for synthesizing MIMO radar transmit waveforms based on coordinate descent algorithm of claim 1, wherein the interference steering vector formula in step (1) is as follows:
Figure FDA0002206743670000023
wherein, a (theta)k) Represents the k th interference source azimuth angle theta of the other partykThe value range of K is [1, K ] as the interference space domain steering vector]K represents the total number of interference sources, exp represents exponential operation with natural constant as base, j represents an imaginary unit symbol, pi represents a circumferential rate, and is a multiplication operation, d represents the interval between radar antenna array elements, N represents the serial number of the radar antenna array elements, and the value range of N is [0, N-1 ]]N denotes the total number of elements of the radar antenna, sin denotes sine value operation, lambda denotes the wavelength of the radar emission signal, thetakRepresenting the k-th interferer azimuth.
3. The method of claim 1, wherein the interference subspace formula in step (2) is as follows:
V＝[a(θk)]
wherein V represents an interference subspace matrix, [ alpha ], [ alpha]Representing a matrixing operation, a (θ)k) Represents the kth interference source azimuth angle thetakThe value range of K is [1, K ] as the interference space domain steering vector]And K represents the total number of the other interference sources.
4. The method for synthesizing multiple-input multiple-output MIMO radar transmission waveforms based on the coordinate descent algorithm of claim 1, wherein the target steering vector formula in the step (3) is as follows:
Figure FDA0002206743670000031
wherein，a(θi) Indicating the azimuth angle theta of the ith target to be detected of the radariThe value range of I is [1, I]I represents the total number of targets, exp represents exponential operation with natural constant as base, j represents an imaginary unit symbol, pi represents a circumferential rate, and is a multiplication operation, d represents the interval between radar antenna array elements, N represents the serial number of the radar antenna array elements, and the value range of N is [0, N-1 ]]N denotes the total number of radar antenna elements, sin denotes the operation of taking the sine value, lambda denotes the wavelength of the radar emission signal, thetaiAnd indicating the azimuth angle of the target to be detected of the ith radar of the opposite party.
5. The method for synthesizing MIMO radar transmit waveforms based on coordinate descent algorithm of claim 1, wherein the transmit signal covariance matrix formula in step (4) is as follows:
R＝[a(θi)]
wherein R represents a transmit signal covariance matrix]Representing a matrixing operation, a (θ)i) Indicating the azimuth angle theta of the ith radar target to be detectediThe value range of I is [1, I]And I represents the total number of targets to be detected by the radar.
6. The coordinate-descent-algorithm-based MIMO radar transmission waveform synthesis method of claim 1, wherein the stop condition in step (5d) is as follows:
Figure FDA0002206743670000041
wherein | | | purple hair2The 2-norm operation is shown as being performed,representing the difference between the current mimo constant modulus transmit waveform matrix and the new mimo constant modulus transmit waveform matrix.
7. The method for synthesizing MIMO radar transmit waveforms based on coordinate descent algorithm according to claim 1, wherein the interference rejection conditions in step (7) are as follows:
tr[VHXHXV]≤10-4
wherein tr represents the trace operation of the matrix, V represents the interference subspace matrix, X represents the corrected multi-input multi-output constant modulus transmission waveform matrix, and H represents the conjugate transpose operation.
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