CN108226878A - MIMO radar transmitted waveform synthetic method based on coordinate descent algorithm - Google Patents
MIMO radar transmitted waveform synthetic method based on coordinate descent algorithm Download PDFInfo
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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
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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
- G01S7/42—Diversity systems specially adapted for radar
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Abstract
The invention discloses a kind of multiple-input and multiple-output MIMO radar transmitted waveform synthetic methods based on coordinate descent algorithm, mainly solve the problems, such as that the transmitted waveform of prior art synthesis does not have anti-interference function and constant modulus property.The present invention the specific steps are：1st, structure interference spatial domain steering vector；2nd, structure transmitting signal covariance matrix；3rd, multiple-input and multiple-output perseverance mould transmitted waveform matrix is synthesized；4th, using the coordinate descent algorithm of following formula, the element in multiple-input and multiple-output perseverance mould transmitted waveform matrix is corrected；5th, using each row element in multiple-input and multiple-output perseverance mould transmitted waveform matrix as the transmitted waveform of each array element of radar.The present invention can synthesize the multiple-input and multiple-output MIMO radar transmitted waveform with anti-interference function and constant modulus property.
Description
Technical field
The invention belongs to Radar Technology field, the one kind further related in cognition Radar Technology field is based under coordinate
Multiple-input and multiple-output MIMO (Multiple Input Multiple Output) radar emission waveform synthetic method of algorithm drops.
The present invention can have according to the location information of other side's interference source and the location information of radar detection target, rapidly synthesis
The MIMO radar transmitted waveform matrix of anti-interference function.
Background technology
Commonly used in radar system of digital component produces MIMO radar, is different from traditional phased-array radar,
Each array element of MIMO radar can emit different signals, and exactly this waveform diversity ability makes MIMO radar and traditional phased array thunder
Up to compared to more advantages.MIMO radar can be divided into according to the spacing size of dual-mode antenna distributed MIMO radar and
Centralized MIMO radar.For distributed MIMO radar, because each antenna is different to the observation angle of target and echo has
Independence.Therefore, under statistical significance, distributed MIMO radar can overcome the scintillation effect of target.Centralized MIMO radar tool
There is the ability for freely designing each array element transmitted waveform, compared to phased-array radar, degree of freedom significantly increases, therefore has
Adaptive transmitting pattern designed capacity.In the actual working environment of radar, usually there is interference, these interference effect thunders
Up to the ability of detection target.Therefore, it is necessary to reduce doing in echo-signal by designing transmitted waveform in transmitting terminal for radar
Disturb power.MIMO radar can obtain specific directional diagram by the design to transmitted waveform matrix, so as to fulfill anti-interference
Purpose.
Paper " the Transmit Signal Design in Colocated MIMO that S Imani et al. are delivered at it
Radar Without Covariance Matrix Optimization”([J].《IEEE Transactions on
Aerospace&Electronic Systems》,2017,PP(99):It is proposed in 1-1) a kind of based on positive semidefinite relaxation (SDR：
Semidefinite Relaxation) MIMO radar transmitted waveform synthetic method.The basic step of this method is：Root first
It obtains it is expected transmitting pattern according to prior information, then according to transmitting pattern structure SDR models it is expected, solves this model
Obtain MIMO radar transmitted waveform matrix.Shortcoming is existing for this method：SDR models only approach the phase with criterion of least squares
It hopes transmitting pattern, has ignored anti-interference condition, so can not realize anti-interference work(using the transmitted waveform that SDR models synthesize
Energy.
Patented technology " a kind of MIMO radar direction of the launch that China Electronics Technology Group Co., Ltd. Second Research Institute 18 possesses
Figure and waveform design method " (application number：201510299652.4 Authorization Notice No.：CN 105158736B) in disclose one kind
MIMO thunder method transmitting patterns and waveform design method.The patented technology comprises the concrete steps that：First according to prior information to the phase
It hopes transmitting pattern modeling, then transmitting signal is configured to the weighted sum of one group of orthogonal sequence, by using for reference and improving DPS
Sequence generating principle is designed about the number of orthogonal sequence and the optimization problem of weights, is obtained simultaneously by solving the optimization problem
Waveform and optimization transmitting pattern must be optimized.Shortcoming is existing for this method：It is every in order to ensure in radar real work
The maximum efficiency of a array element emission power amplifier, it is desirable that transmitted waveform must have constant modulus property, and this method cannot
Generate the transmitted waveform of permanent mould.
Invention content
The purpose of the present invention in view of the above shortcomings of the prior art, proposes that a kind of multi input based on coordinate descent algorithm is more
Export MIMO radar transmitted waveform synthetic method.Method can generate the transmitted waveform of permanent mould, so as to ensure that radar antenna is each
The maximum efficiency of array element emission power amplifier.In addition, method can correct multiple-input and multiple-output perseverance mould transmitted wave successively
Each row element in shape matrix is so as to ensure that transmitted waveform has anti-interference function.
To achieve these goals, specific steps of the invention include as follows：
(1) structure interference spatial domain steering vector：
Source azimuth angle is interfered to substitute into interference steering vector formula other side, obtain interference spatial domain steering vector；
(2) interference space matrix is built：
Interference spatial domain steering vector is substituted into interference space formula, obtains interference space matrix；
(3) structure target spatial domain steering vector
Radar azimuth of target to be detected is substituted into goal orientation vector formulas, obtains target spatial domain steering vector；
(4) structure transmitting signal covariance matrix：
Target spatial domain steering vector is substituted into transmitting signal covariance matrix formula, obtains transmitting signal covariance matrix；
(5) multiple-input and multiple-output perseverance mould transmitted waveform matrix is synthesized：
(5a) randomly generates the multiple-input and multiple-output perseverance mould transmitted waveform square that all elements amplitude in a matrix is equal
Battle array, using it as initial matrix；
(5b) will emit signal covariance matrix and initial multiple-input and multiple-output perseverance mould transmitted waveform matrix, substitute into multi input
In multi output perseverance mould transmitted waveform Matrix Formula, a current multiple-input and multiple-output perseverance mould transmitted waveform battle array is obtained；
(5c) will emit signal covariance matrix and current multiple-input and multiple-output perseverance mould transmitted waveform matrix, substitute into permanent mould hair
In ejected wave shape Matrix Formula, a new multiple-input and multiple-output perseverance mould transmitted waveform matrix is obtained；
(5d) judges current multiple-input and multiple-output perseverance mould transmitted waveform matrix and new multiple-input and multiple-output perseverance mould transmitted wave
Whether the difference of shape matrix meets stop condition, if so, performing step (6), otherwise, new multiple-input and multiple-output perseverance mould is emitted
Waveform matrix is as execution step (5c) after current multiple-input and multiple-output perseverance mould transmitted waveform matrix；
(6) it using the coordinate descent algorithm of following formula, corrects successively every in multiple-input and multiple-output perseverance mould transmitted waveform matrix
One row element：
Wherein,Represent the l row elements of revised multiple-input and multiple-output perseverance mould transmitted waveform matrix, xmIt represents to correct
The m row elements of preceding multiple-input and multiple-output perseverance mould transmitted waveform matrix, ⊙ represent the Hadamard multiplication operations between vector, | | |
|2Represent that 2 norms operate, vcRepresent the c row elements of interference space matrix, the value of l, m, c corresponds to identical, and value range is
[1, N], N represent the sum of radar antenna array element, and V represents interference space matrix, and H represents conjugate transposition operation, and * represents conjugation
Operation；
(7) judge whether revised multiple-input and multiple-output perseverance mould transmitted waveform matrix meets anti-interference condition, if so,
Step (8) is performed, otherwise, performs step (6)；
(8) using each row element in multiple-input and multiple-output perseverance mould transmitted waveform matrix as the transmitted wave of each array element of radar
Shape.
Compared with the prior art, the present invention has the following advantages：
First, the present invention synthesizes a multiple-input and multiple-output perseverance mould on the basis of structure emits signal covariance matrix
Transmitted waveform matrix, using its each row element as the transmitted waveform of each array element of radar so that radar emission waveform has permanent model
Property, it overcomes the transmitted waveform synthesized by the prior art and does not have the shortcomings that constant modulus property.In radar real work, in order to protect
Demonstrate,prove the maximum efficiency of each array element emission power amplifier, it is desirable that transmitted waveform must have constant modulus property, therefore this hair
Open-birth into radar emission waveform can ensure the maximum efficiency of each array element emission power amplifier.
Second, the present invention is declined on the basis of the multiple-input and multiple-output perseverance mould transmitted waveform matrix of synthesis using coordinate
Algorithm, each row element corrected successively in multiple-input and multiple-output perseverance mould transmitted waveform matrix are allowed to meet anti-interference condition, gram
The transmitted waveform for having taken prior art synthesis has ignored the deficiency of anti-interference condition so that the radar emission waveform that the present invention generates
With anti-interference function.
Description of the drawings
Fig. 1 is the flow chart of the present invention；
Fig. 2 is the transmitting pattern of the radar emission waveform of present invention emulation synthesis；
Fig. 3 obtains the map of magnitudes of each array element transmitted waveform of radar for present invention emulation.
Specific embodiment
The present invention is described further below in conjunction with the accompanying drawings.
With reference to attached drawing 1, the specific steps of the present invention are described as follows：
Step 1, structure interference spatial domain steering vector.
Source azimuth angle is interfered to substitute into interference steering vector formula other side, obtain interference spatial domain steering vector.
The interference steering vector formula is as follows：
Wherein, a (θk) represent k-th of interference source azimuth angle theta of other sidekThe interference spatial domain steering vector at place, the value range of k
For [1, K], K represents the sum of interference source, and exp represents that using natural constant as the index operation at bottom j represents imaginary unit's symbol, π
It represents pi, represents multiplication operations, d represents the spacing between radar antenna array element, and n represents the serial number of radar antenna array element, n
Value range for [0, N-1], N represents the sum of radar antenna array element, and sin represents sinusoidal Value Operations, and λ represents radar emission letter
Number wavelength, θkRepresent k-th of interference source azimuth angle of other side.
Step 2, interference space matrix is built.
Interference spatial domain steering vector is substituted into interference space formula, obtains interference space matrix.
The interference space formula is as follows：
V=[a (θk)]
Wherein, V represents interference space matrix, the operation of [] representing matrixization, a (θk) represent k-th of interference source azimuth angle
θkThe interference spatial domain steering vector at place, the value range of k is [1, K], and K represents the sum of other side's interference source.
Step 3, structure target spatial domain steering vector.
Radar azimuth of target to be detected is substituted into goal orientation vector formulas, obtains target spatial domain steering vector.
The goal orientation vector formulas is as follows：
Wherein, a (θi) represent i-th of azimuth of target θ to be detected of radariThe target spatial domain steering vector at place, the value of i
Ranging from [1, I], I represent the sum of target, and exp is represented using natural constant as the index operation at bottom, and j represents imaginary unit's symbol
Number, π represents pi, represents multiplication operations, and d represents the spacing between radar antenna array element, and n represents the sequence of radar antenna array element
Number, the value range of n is [0, N-1], and N represents the sum of radar antenna array element, and sin expressions take sinusoidal Value Operations, and λ represents radar
Emit the wavelength of signal, θiRepresent i-th of radar of other side azimuth of target to be detected.
Step 4, structure transmitting signal covariance matrix.
Target spatial domain steering vector is substituted into transmitting signal covariance matrix formula, obtains transmitting signal covariance matrix.
The transmitting signal covariance matrix formula is as follows：
R=[a (θi)]
Wherein, R represents transmitting signal covariance matrix, the operation of [] representing matrixization, a (θi) represent that i-th of radar is waited to visit
Survey azimuth of target θiThe target spatial domain steering vector at place, the value range of i is [1, I], and I represents the total of radar target to be detected
Number.
Step 5, multiple-input and multiple-output perseverance mould transmitted waveform matrix is synthesized.
The first step randomly generates the multiple-input and multiple-output perseverance mould transmitted waveform that all elements amplitude in a matrix is equal
Matrix, using it as initial matrix.
Second step by transmitting signal covariance matrix and initial multiple-input and multiple-output perseverance mould transmitted waveform matrix, substitutes into more
It inputs in multi output perseverance mould transmitted waveform Matrix Formula, obtains a current multiple-input and multiple-output perseverance mould transmitted waveform battle array.
The multiple-input and multiple-output perseverance mould transmitted waveform Matrix Formula is as follows：
Wherein, X1Represent current multiple-input and multiple-output perseverance mould transmitted waveform matrix, exp is represented using natural constant the bottom of as
Index operation, j are imaginary unit's symbol, represent multiplication operations, and angle expressions take each element phase Value Operations, svd in matrix
It represents to carry out singular value decomposition operation, X to matrix0Represent initial multiple-input and multiple-output perseverance mould transmitted waveform matrix, R represents transmitting
Signal covariance matrix,Expression takes the square root functions of matrix, and H represents to carry out conjugate transposition operation to matrix.
Third walks, and transmitting signal covariance matrix and current multiple-input and multiple-output perseverance mould transmitted waveform matrix substitute into permanent
In mould transmitted waveform Matrix Formula, a new multiple-input and multiple-output perseverance mould transmitted waveform matrix is obtained.
4th step judges that current multiple-input and multiple-output perseverance mould transmitted waveform matrix emits with new multiple-input and multiple-output perseverance mould
Whether the difference of waveform matrix meets stop condition, if so, performing step 6, otherwise, new multiple-input and multiple-output perseverance mould is emitted
Waveform matrix is as execution third step after current multiple-input and multiple-output perseverance mould transmitted waveform matrix.
The stop condition is as follows：
Wherein, | | | |2Represent that 2 norms operate,Represent current multiple-input and multiple-output perseverance mould transmitted waveform matrix with it is new
The difference of multiple-input and multiple-output perseverance mould transmitted waveform matrix.
Step 6, it using the coordinate descent algorithm of following formula, corrects in multiple-input and multiple-output perseverance mould transmitted waveform matrix successively
Each row element：
Wherein,Represent the l row elements of revised multiple-input and multiple-output perseverance mould transmitted waveform matrix, xmIt represents to correct
The m row elements of preceding multiple-input and multiple-output perseverance mould transmitted waveform matrix, ⊙ represent the Hadamard multiplication operations between vector, | | |
|2Represent that 2 norms operate, vcRepresent the c row elements of interference space matrix, the value of l, m, c corresponds to identical, and value range is
[1, N], N represent the sum of radar antenna array element, and V represents interference space matrix, and H represents conjugate transposition operation, and * represents conjugation
Operation.
Step 7, judge whether revised multiple-input and multiple-output perseverance mould transmitted waveform matrix meets anti-interference condition, if
It is then to perform step 8, otherwise, performs step 6.
The anti-interference condition is as follows：
tr[VHXHXV]≤10-4
Wherein, tr expressions take the mark of matrix to operate, and V represents interference space matrix, and X represents that how defeated revised multi input is
Go out permanent mould transmitted waveform matrix, H represents conjugate transposition operation.
Step 8, using each row element in multiple-input and multiple-output perseverance mould transmitted waveform matrix as the transmitting of each array element of radar
Waveform.
The effect of the present invention is further described with reference to emulation data.
1st, simulated conditions：
The simulated running system of the present invention is 650@3.40GHz of Intel (R) Core (TM) i7-2600CPU, 32
Windows operating system, simulation software use MATLAB (R 2012b).
2nd, data and interpretation of result are emulated：
It is 16 that the parameter of emulation experiment of the present invention, which is set as radar array element sum, and the spacing between radar antenna array element is 0.5
Millimeter, the wavelength of radar emission signal is 1 millimeter, and the sum of interference source is 2, and interference source azimuth angle is respectively -60 and 20 °, mesh
Mark sum is 3, and azimuth of target is respectively -35 °, 0 °, 45 °.
Fig. 2 is the transmitting pattern of the radar emission waveform of the emulation experiment synthesis of the present invention.Abscissa in Fig. 2 represents
Spatial domain azimuth, value range are [- 90 °, 90 °], and ordinate represents the radar emission waveform of emulation experiment synthesis each
Power gain at the azimuth of spatial domain, unit dB.The radar emission waveform of emulation experiment synthesis is drawn in each spatial domain orientation
Power gain at angle is the transmitting pattern for the radar emission waveform that can obtain emulation experiment synthesis.
Power gain of the radar emission waveform of emulation experiment synthesis at each spatial domain azimuth is obtained by the following formula：
P (θ)=a (θ)HXXHa(θ)
Wherein, P (θ) represents the power gain of the radar emission waveform that emulation experiment synthesizes at the azimuth angle theta of spatial domain, a (θ)
Represent the spatial domain steering vector at the azimuth angle theta of spatial domain, H represents conjugate transposition operation, and X is that the multi input of emulation experiment synthesis is more
The permanent mould transmitted waveform matrix of output.
Figure it is seen that radar has stronger power gain for 20dB at -35 °, 0 °, 45 ° of azimuth of target,
It is -50dB to interfere -60 ° of source azimuth angle, 20 ° of places only very weak power gain, it can be seen that the radar of the invention synthesized
Transmitted waveform has anti-interference function.
Fig. 3 is the map of magnitudes of each array element transmitted waveform of radar that present invention emulation obtains.By the how defeated of emulation experiment synthesis
Enter range value of the range value of each row element in multi output perseverance mould transmitted waveform matrix as each array element transmitted waveform of radar, draw
The corresponding amplitude of each array element of radar is that can obtain the map of magnitudes of each array element transmitted waveform of radar.
Abscissa represents radar element number of array in Fig. 3, and value range is [1,16], and ordinate represents that corresponding array element is sent out
The range value of ejected wave shape.From figure 3, it can be seen that each array element transmitted waveform amplitude of radar is equal and is 1.It is therefore, it is considered that of the invention
The transmitted waveform of synthesis has constant modulus property, it is ensured that the maximum efficiency of each array element emission power amplifier.
In conclusion the multiple-input and multiple-output MIMO radar transmitted waveform of this method synthesis has anti-interference function and permanent mould
Characteristic.
Claims (8)
1. a kind of multiple-input and multiple-output MIMO radar transmitted waveform synthetic method based on coordinate descent algorithm, which is characterized in that
Include the following steps：
(1) structure interference spatial domain steering vector：
Source azimuth angle is interfered to substitute into interference steering vector formula other side, obtain interference spatial domain steering vector；
(2) interference space matrix is built：
Interference spatial domain steering vector is substituted into interference space formula, obtains interference space matrix；
(3) structure target spatial domain steering vector
Radar azimuth of target to be detected is substituted into goal orientation vector formulas, obtains target spatial domain steering vector；
(4) structure transmitting signal covariance matrix：
Target spatial domain steering vector is substituted into transmitting signal covariance matrix formula, obtains transmitting signal covariance matrix；
(5) multiple-input and multiple-output perseverance mould transmitted waveform matrix is synthesized：
(5a) randomly generates the multiple-input and multiple-output perseverance mould transmitted waveform matrix that all elements amplitude in a matrix is equal, will
Be used as initial matrix；
(5b) will emit signal covariance matrix and initial multiple-input and multiple-output perseverance mould transmitted waveform matrix, how defeated substitute into multi input
Go out in permanent mould transmitted waveform Matrix Formula, obtain a current multiple-input and multiple-output perseverance mould transmitted waveform battle array；
(5c) will emit signal covariance matrix and current multiple-input and multiple-output perseverance mould transmitted waveform matrix, substitute into permanent mould transmitted wave
In shape Matrix Formula, a new multiple-input and multiple-output perseverance mould transmitted waveform matrix is obtained；
(5d) judges current multiple-input and multiple-output perseverance mould transmitted waveform matrix and new multiple-input and multiple-output perseverance mould transmitted waveform square
Whether the difference of battle array meets stop condition, if so, step (6) is performed, otherwise, by new multiple-input and multiple-output perseverance mould transmitted waveform
Matrix is as execution step (5c) after current multiple-input and multiple-output perseverance mould transmitted waveform matrix；
(6) using the coordinate descent algorithm of following formula, every a line in multiple-input and multiple-output perseverance mould transmitted waveform matrix is corrected successively
Element：
Wherein,Represent the l row elements of revised multiple-input and multiple-output perseverance mould transmitted waveform matrix, xmIt represents before correcting
The m row elements of multiple-input and multiple-output perseverance mould transmitted waveform matrix, ⊙ represent the Hadamard multiplication operations between vector, | | | |2Table
Show that 2 norms operate, vcRepresent the c row elements of interference space matrix, the value of l, m, c corresponds to it is identical, value range be [1,
N], N represents the sum of radar antenna array element, and V represents interference space matrix, and H represents conjugate transposition operation, and * represents conjugation behaviour
Make；
(7) judge whether revised multiple-input and multiple-output perseverance mould transmitted waveform matrix meets anti-interference condition, if so, performing
Step (8) otherwise, performs step (6)；
(8) using each row element in multiple-input and multiple-output perseverance mould transmitted waveform matrix as the transmitted waveform of each array element of radar.
2. the multiple-input and multiple-output MIMO radar transmitted waveform synthesis side according to claim 1 based on coordinate descent algorithm
Method, which is characterized in that the interference steering vector formula described in step (1) is as follows：
Wherein, a (θk) represent k-th of interference source azimuth angle theta of other sidekThe interference spatial domain steering vector at place, the value range of k for [1,
K], K represents the sum of interference source, and exp is represented using natural constant as the index operation at bottom, and j represents imaginary unit's symbol, and π is represented
Pi represents multiplication operations, and d represents the spacing between radar antenna array element, and n represents the serial number of radar antenna array element, and n's takes
Ranging from [0, N-1], N represents the sum of radar antenna array element to value, and sin represents sinusoidal Value Operations, and λ represents radar emission signal
Wavelength, θkRepresent k-th of interference source azimuth angle of other side.
3. the multiple-input and multiple-output MIMO radar transmitted waveform synthesis side according to claim 1 based on coordinate descent algorithm
Method, which is characterized in that interference space formula is as follows described in step (2)：
V=[a (θk)]
Wherein, V represents interference space matrix, the operation of [] representing matrixization, a (θk) represent k-th of interference source azimuth angle thetakPlace
Spatial domain steering vector is interfered, the value range of k is [1, K], and K represents the sum of other side's interference source.
4. the multiple-input and multiple-output MIMO radar transmitted waveform synthesis side according to claim 1 based on coordinate descent algorithm
Method, which is characterized in that the goal orientation vector formulas described in step (3) is as follows：
Wherein, a (θi) represent i-th of azimuth of target θ to be detected of radariThe target spatial domain steering vector at place, the value range of i
For [1, I], I represents the sum of target, and exp represents that using natural constant as the index operation at bottom j represents imaginary unit's symbol, π tables
Show pi, represent multiplication operations, d represents the spacing between radar antenna array element, and n represents the serial number of radar antenna array element, n's
Value range is [0, N-1], and N represents the sum of radar antenna array element, and sin expressions take sinusoidal Value Operations, and λ represents radar emission letter
Number wavelength, θiRepresent i-th of radar of other side azimuth of target to be detected.
5. the multiple-input and multiple-output MIMO radar transmitted waveform synthesis side according to claim 1 based on coordinate descent algorithm
Method, which is characterized in that the transmitting signal covariance matrix formula described in step (4) is as follows：
R=[a (θi)]
Wherein, R represents transmitting signal covariance matrix, the operation of [] representing matrixization, a (θi) represent i-th of radar mesh to be detected
Mark azimuth angle thetaiThe target spatial domain steering vector at place, the value range of i is [1, I], and I represents the sum of radar target to be detected.
6. the multiple-input and multiple-output MIMO radar transmitted waveform synthesis side according to claim 1 based on coordinate descent algorithm
Method, which is characterized in that the multiple-input and multiple-output perseverance mould transmitted waveform Matrix Formula described in step (5b) is as follows：
Wherein, X1Represent current multiple-input and multiple-output perseverance mould transmitted waveform matrix, exp is represented using natural constant as the index at bottom
Operation, j are imaginary unit's symbol, represent multiplication operations, and angle expressions take each element phase Value Operations in matrix, and svd is represented
Singular value decomposition operation, X are carried out to matrix0Represent initial multiple-input and multiple-output perseverance mould transmitted waveform matrix, R represents transmitting signal
Covariance matrix,Expression takes the square root functions of matrix, and H represents to carry out conjugate transposition operation to matrix.
7. the multiple-input and multiple-output MIMO radar transmitted waveform synthesis side according to claim 1 based on coordinate descent algorithm
Method, which is characterized in that the stop condition described in step (5d) is as follows：
Wherein, | | | |2Represent that 2 norms operate,Represent current multiple-input and multiple-output perseverance mould transmitted waveform matrix and newly how defeated
Enter the difference of multi output perseverance mould transmitted waveform matrix.
8. the multiple-input and multiple-output MIMO radar transmitted waveform synthesis side according to claim 1 based on coordinate descent algorithm
Method, which is characterized in that the anti-interference condition described in step (7) is as follows：
tr[VHXHXV]≤10-4
Wherein, tr expressions take the mark of matrix to operate, and V represents interference space matrix, and X represents that revised multiple-input and multiple-output is permanent
Mould transmitted waveform matrix, H represent conjugate transposition operation.
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Cited By (3)
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| CN109061578A (en) * | 2018-07-12 | 2018-12-21 | 西安电子科技大学 | Recess directional diagram waveform synthesis design method based on MIMO radar |
| CN111142080A (en) * | 2019-12-28 | 2020-05-12 | 西安电子科技大学 | Rapid constant modulus MIMO radar tracking waveform synthesis method aiming at interference suppression |
| CN114675238A (en) * | 2022-02-24 | 2022-06-28 | 中国人民解放军国防科技大学 | Radar communication integrated waveform direct optimization method and system |
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