CN104865556B - Based on real domain weight minimization l1The MIMO radar system DOA estimation method of Norm Method - Google Patents
Based on real domain weight minimization l1The MIMO radar system DOA estimation method of Norm Method Download PDFInfo
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Abstract
The present invention relates to MIMO radar system technical field, more particularly to the application of MIMO radar system DOA estimations is specifically a kind of to be based on real domain weight minimization l1The MIMO radar system DOA estimation method of Norm Method.The present invention includes：Using dimensionality reduction matrix dimension-reduction treatment is carried out to receiving data；It carries out singular value decomposition and obtains the corresponding model under framework of sparse representation；Using the orthogonality of real domain steering vector noise subspace corresponding with it, design one diagonal entry weight matrix corresponding with real domain MUSIC spectrums is to solve the problems, such as MMV；Realize the estimation to target DOA in MIMO radar system.The present invention converts SNR gain by dimensionality reduction and is strengthened, while designed weighting l1Norm has had better access to l0Norm and sparse solution is enhanced, compares l1SVD and RV l1Svd algorithm has higher resolution ratio.
Description
Technical field
The present invention relates to the applications that MIMO radar system technical field, more particularly to MIMO radar system DOA are estimated, specifically
Say it is that one kind being based on real domain weight minimization l1The MIMO radar system DOA estimation method of Norm Method.
Background technology
In recent years, due to multiple-input and multiple-output (multiple-input multiple-output, MIMO) array
Radar system (IEEE Signal Processing Magazine, 2007,24 (5)：106-114) compared to traditional phased array
The potential advantage of radar system and greatly paid close attention to.In MIMO radar system, angle estimation is a critical problem.
For this problem, some methods based on subspace, such as MUSIC algorithms (IEEE Trans.Antennas and
Propagation, 1986,34 (3)：276-280) and ESPRIT algorithms (IEEE Trans.Signal Process., 1989,
37(7)：984-995), it is applied in the angle estimation of MIMO radar system.On the other hand, MIMO radar is utilized
RD-ESPRIT (Electronics Letters have been proposed in DOA estimations in the special construction of system：2011,47 (4)：
283-284) and conjugation ESPRIT (C-ESPRIT) (Signal Process., 2013,93：2070-2075) algorithm.Based on biography
Send array beam dimensional energy concentration techniques (IEEE Transations on Signal Processing, 2011,59 (6)：
2669-2682) proposition of algorithm improves angle estimation performance.However, the performance of these methods is in low SNR, limited number of snapshots
Or typically it cannot reach requirement in the case of object space tight distribution.
In recent years, the appearance in rarefaction representation field provided new viewpoint to the DOA estimations in array signal processing, in phase
Some sparse representation methods have been proposed in the field of pass.A kind of l proposed for DOA estimations1Svd algorithm (IEEE
Trans.Signal Process., 2005,53 (8)：3010-3022), l is utilized1Norm is punished close to l0Norm is punished, concern
Immediate data.l1- SRACV algorithms (IEEE Trans.Signal Process., 2011,59 (2)：629-638) calculated with CMSR
Method (IEEE Trans.Aerosp.Electron.Syst., 2013,49 (3)) is not using immediate data but is assisted based on array
The sparsity of variance vectors.On the other hand, real domain l1-SVD(RV l1- SVD) algorithm (IEEE Antennas Wireless
Propag.Lett., 2013,12：376-379), compared to l1Svd algorithm has lower computation complexity, better angle
Estimate performance.Method mentioned above is all based on l1Norm is punished, l1Norm punishment cannot have better access to l0At norm
It penalizes.In (Journal of fourier analysis and applications, 2008,14 (5)：It is proposed in 887-905)
A kind of iterative algorithm, weight minimization l1Norm Method has had better access to l0Norm is punished.But this faces two large problems：
1) it is only applicable to single vector that measures and restores problem.However, restoring to the vectors that measure involved in the DOA estimations of MIMO array system more
Problem；2) the complete dictionary of two dimension is needed to restore thinned array in MIMO radar system, perhaps this lose when restoring sparse matrix
Effect.
Invention content
It is an object of the invention to overcome the defect of the above method, propose a kind of new based on real domain weight minimization l1Model
Several MIMO radar system DOA estimation methods.
The object of the present invention is achieved like this：
Include the following steps：
(1) emission array emits mutually orthogonal phase-coded signal, and receiving terminal is connect after carrying out matched filtering processing
Data are received, and dimension-reduction treatment is carried out to receiving data using dimensionality reduction matrix；
(2) unitary transformation matrix is utilized, the augmented sample matrix that data are received after dimensionality reduction is become into real domain, carries out singular value point
It solves and obtains the corresponding model under framework of sparse representation；
(3) orthogonality for utilizing real domain steering vector noise subspace corresponding with it, designs a diagonal entry and reality
Domain MUSIC composes corresponding weight matrix to solve the problems, such as MMV；
(4) design real domain weight minimization l1Norm frame is obtained using programming software packet SOC second order cone computational methods
Restore matrix, find the non-zero row restored in matrix, realizes the estimation to target DOA in MIMO radar system.
In the step (1) dimension-reduction treatment is carried out to receiving data as follows：
(1.1) according to single base MIMO radar system the structure of steering vector is received-emitted it is found that MIMO radar system
Transmitting-reception steering vector meet：
A in formulat(θ) and ar(θ) is respectively to emit steering vector and reception steering vector,
Q=M+N -1, is transition matrix and one-dimensional steering vector respectively,
Wherein,
Jm=[0N×m,IN,0N×(M-m-1)], m=0,1 ..., M-1,
By using matrix GHCorresponding Q different elements, two-dimensional guide vector can be converted to one-dimensional steering vector i.e.
Carry out dimension-reduction treatment；
(1.2) according to transition matrix, dimensionality reduction matrix is W=F-1/2GH, wherein
(1.3) it utilizes W to obtain dimensionality reduction and receives dataThen have
In formulaMeet B=[b (θ1),b(θ2),…,b(θp)],
Unitary transformation matrix is utilized in the step (2) as follows, the augmented sample matrix of data will be received after dimensionality reduction
Become real domain, carry out singular value decomposition and obtains the corresponding model under framework of sparse representation：
(2.1) consider augmented sample matrixWherein ΓQBe have anti-diagonal element be 1, other
Q × Q switching matrixs that element is 0, ()*Indicate that conjugate operation, Y are center Hermite Matrixes and can be converted to a reality
Domain matrix,
Wherein, unitary transformation matrix is
Wherein SΥ=[Φ*S ΦS*ΓJ]U2JIt is real domain signal matrix,It is that real domain is made an uproar
Sound matrix；
(2.2) to YΥUsing singular value decomposition SVD technique, have
WhereinVSIt is the Y by corresponding to P maximum singular valueΥReal domain it is right it is unusual to
Amount is constituted；
(2.3) apply framework of sparse representation, the one-dimensional complete dictionary of real domain that can be expressed as：
The orthogonality of real domain steering vector noise subspace corresponding with it is utilized in the step (3) as follows, if
Count diagonal entry weight matrix corresponding with real domain MUSIC spectrums：
(3.1) the complete dictionary of real domain is divided into two parts：Then have
In formulaIt is the real domain steering vector by corresponding to possible target
P=1,2 ..., P are formed,It is by dictionaryRemaining real domain steering vector composition, VnIt is real domain noise
Subspace, by YΥCarrying out singular value decomposition can obtain；
(3.2) according to the orthogonality of real domain steering vector and corresponding noise subspace, as J → ∞, W1,i→ 0, W2,i＞
0, define weight matrix
Due to W1,i/max(W2) ＜ W2,i/max(W2)。
Real domain weight minimization l is designed as follows in the step (4)1Norm frame utilizes programming software packet SOC
Second order cone computational methods obtain and restore matrix, the non-zero row restored in matrix are found, to the target DOA in MIMO radar system
Estimated：
Real domain weight minimization l1Norm is
In formulaIt is regularization parameter, is calculated using programming software packet SOC second order cones, pass through mapping
The beneficial effects of the present invention are：
The present invention converts SNR gain by dimensionality reduction and is strengthened, while designed weighting l1Norm has had better access to l0
Norm and sparse solution is enhanced, compares l1- SVD and RV l1Svd algorithm has higher resolution ratio；The present invention is converted due to real domain
The application of technology is better than l in low SNR regional perspectives estimation performance1- SVD and RV l1- SVD, and due to above-mentioned hair
Bright advantage it close to CRB；The present invention is due to including front and back Search Space Smoothing and weighting l1Norm technology, for phase relation
Several variations has robustness, and compares l1- SVD and RV l1- SVD has better angle estimation performance.The present invention solves
Based on weighting l1There are the shortcomings of not being suitable for more measurement vectors recoveries in the Wave arrival direction estimating method of norm, and can
It is perfectly suitable for lower number of snapshots.
Description of the drawings
Fig. 1 is the general frame figure of the present invention；
Fig. 2 algorithms of different differentiates two uncorrelated targets the relationship of the probability of success and angle interval；
Relationship of Fig. 3 algorithms of different for the root-mean-square error and signal-to-noise ratio of three uncorrelated target angle estimations；
Fig. 4 algorithms of different estimates two target angles the relationship of root-mean-square error and related coefficient；
Relationship of Fig. 5 algorithms of different for the root-mean-square error and number of snapshots of three uncorrelated target angle estimations.
Specific embodiment
The present invention is described in more detail with reference to the frame diagram of Mutual coupling
The present invention provides a kind of based on real domain weight minimization l1Multiple-input and multiple-output (the multiple-input of norm
Multiple-output, MIMO) the estimation side radar system target direction of arrival (Direction of arrival, abbreviation DOA)
Method, primarily to solve in current MIMO radar system based on the Wave arrival direction estimating method of rarefaction representation there are dictionary complexity
The shortcomings of degree is high and estimated accuracy is undesirable.First according to MIMO radar system the characteristics of, utilizes dimensionality reduction conversion and unitary transformation skill
Art, make reception data be transformed into low-dimensional and be real domain.Then it is composed according to real domain MUSIC, to obtain weight minimization
l1One weight matrix of norm Frame Design, and then DOA is estimated by finding the non-zero row in recovery matrix.Its process
For：The receipt signal model of single base MIMO radar system is established, construction dimensionality reduction matrix carries out dimension-reduction treatment；Then the tenth of the twelve Earthly Branches is utilized to become
Change matrix becomes real domain by the augmented sample matrix for receiving data after dimensionality reduction, carries out singular value decomposition and obtains rarefaction representation frame
Corresponding model under frame；According to the orthogonality of real domain steering vector noise subspace corresponding with it, a diagonal entry is designed
Weight matrix corresponding with real domain MUSIC spectrums, and then design weight minimization l1Norm frame, make its sparse solution closer to
l0Norm is to greatly reinforce sparsity；Recovery matrix is finally obtained, and finds the non-zero row restored in matrix, realization pair
The estimation of target DOA in MIMO radar system.With the existing DOA estimation method l based on rarefaction representation1- SVD and real domain l1-
Svd algorithm is compared, and the present invention has higher resolution ratio, in low SNR and for uncorrelated target and related objective
Better angle estimation performance is all had, and lower number of snapshots can be perfectly suitable for.
The characteristics of present invention is according to MIMO radar system makes reception data change using dimensionality reduction conversion and unitary transformation technology
As low-dimensional and be real domain；Then according to the orthogonality of real domain steering vector noise subspace corresponding with it, design one
A diagonal entry weight matrix corresponding with real domain MUSIC spectrums, and then design weight minimization l1Norm frame keeps its dilute
It discongests closer to l0Norm is to greatly reinforce sparsity；Recovery matrix is finally obtained, and is restored in matrix by finding
Non- zero row DOA is estimated.With the existing DOA estimation method l based on rarefaction representation1- SVD and real domain l1- SVD is calculated
Method is compared, and the present invention has higher resolution ratio, is all had in low SNR and for uncorrelated target and related objective
Better angle estimation performance, and lower number of snapshots can be perfectly suitable for.DOA estimation method of the present invention includes mainly
The following aspects：
1, the receipt signal model of single base MIMO radar is established, and designs dimensionality reduction matrix and is carried out at dimensionality reduction to receiving data
Reason.
Assuming that a narrowband list base MIMO radar system with M transmitting antenna and N number of reception antenna, they are battle arrays
Distance is the space uniform linear array (ULA) of half wavelength between member.In MIMO radar system, emit M using M transmitting antenna
Quadrature wave with same band and centre frequency.Assuming that there is the same range that P target is located at array far field.θpIndicate pth
The direction of arrival (DOA) of a target.After matched filter, the output of receiving array can be expressed as
X (t)=As (t)+n (t) (1)
WhereinIt is to receive data vector,It is signal data arrow
Amount,Middle βp(t) and fpIt is reflectance factor and Doppler frequency respectively.
X=AS+N (2)
Wherein X=[x (t1),…,x(tJ)], S=[s (t1),…,s(tJ)], N=[n (t1),…,n(tJ)]。
According to reception-transmitting steering vectorStructure it is found that transmitting-reception steering vector meets
WhereinWithIt is transition matrix and one-dimensional steering vector, table respectively
It is shown as
Wherein Jm=[0N×m,IN,0N×(M-m-1)], m=0,1 ..., M-1.According to formula (4), we define matrix F=
GHG, as follows
According to formula (3) and formula (6), by using matrix GHCorresponding Q different elements, two-dimensional guide vector can be with
One-dimensional steering vector is converted to, however, utilizing GHColoured noise will be increased.In order to avoid adding coloured noise, dimensionality reduction matrix can be determined
Justice is W=F-1/2GH, meet WWH=IQ.Therefore, dimensionality reduction can be obtained using W and receive dataAs follows
WhereinMeet B=[b (θ1),b(θ2),…,b(θp)],
2, using unitary transformation matrix, the augmented sample matrix that data are received after dimensionality reduction is become into real domain, carries out singular value point
It solves and obtains the corresponding model under framework of sparse representation.
The augmented sample matrix of reception data after dimensionality reduction is become into real domain, as follows
According to formula (7), dimensionality reduction receives data and corresponds to containing weight matrix F1/2Linear array.Therefore it is contemplated that
One augmented sample matrixWherein ΓQBe have anti-diagonal element be 1, other elements be 0 Q × Q
Switching matrix, ()*Indicate conjugate operation.Y is center Hermite Matrix and can be converted to a real domain matrix
Wherein, unitary transformation matrix is defined as
By omitting U2K+1Central row and central series be readily available U2K.It is from formula (8) as can be seen that front and back flat due to merging
Mean value, sample size increase one times from J to 2J.On the other hand, the guiding matrix in formula (7)Meet
WhereinDiag [] indicates diagonalization operation.The result shows that formula (7)
In about receive data linear array dimensionality reduction conversion after be central symmetry array.After unitary transformation, real domain is oriented to matrix can
To be expressed asTherefore, by simple algebraic operation, formula (8) can be written as form
Wherein SΥ=[Φ*S ΦS*ΓJ]U2JIt is real domain signal matrix,It is that real domain is made an uproar
Sound matrix.
It carries out singular value decomposition and obtains the corresponding model under framework of sparse representation, as follows
To YΥUsing singular value decomposition (SVD) technology, have
WhereinVSIt is the Y by corresponding to P maximum singular valueΥReal domain it is right it is unusual to
Amount is constituted.
Based on the sparsity corresponding to entire extraterrestrial target, the signal model in formula (2) can be transformed into one it is dilute
It dredges and indicates model.A series of possible positions are indicated with Ω,(L>>P the grid of covering Ω) is indicated.Therefore, emitted
Standby dictionary and the complete dictionary of reception are expressed asIt constructs complete
Dictionary isUnder framework of sparse representation, the signal model in formula (2) can be write as
WhereinIt is supported with S rows having the same, i.e. matrixIt is sparse.In order to estimateIt is dilute in formula (12)
It dredges and indicates that model is considered as to minimize l1Norm problem, is expressed as
Wherein | | | |1With | | | |2L is indicated respectively1Norm and l2Norm.
WhereinWithThere is identical row to support, it means that matrixIt is sparse.
3, using real domain steering vector (Each row) and its corresponding noise subspace orthogonality, design one it is diagonal
Line element weight matrix corresponding with real domain MUSIC spectrums is to solve the problems, such as MMV.
The complete dictionary of real domain can be divided into two parts：WhereinIt is by corresponding to
The real domain steering vector of possible targetComposition,It is
By dictionaryRemaining real domain steering vector composition.Therefore, have
Wherein, VnIt is real domain noise subspace, by YΥCarrying out singular value decomposition can obtain.As J → ∞, W1,i
→ 0, W2,i＞ 0.Therefore, we define weight matrix
Due to W1,i/max(W2) ＜ W2,i/max(W2), for MMV problems, weight matrix W can realize authority well
Value is used for punishing and being more likely in sparse matrix be those of zero item, and small weights are used for storing the item of bigger, this and for SMV
The iteration weight minimization l of problem1The research method of norm is consistent.
4, design real domain weight minimization l1Norm frame is obtained using programming software packet SOC (second order cone) computational methods
Restore matrix, find the non-zero row restored in matrix, realizes the estimation to target DOA in MIMO radar system.
Real domain weight minimization l1Norm problem becomes
WhereinIt is regularization parameter, formula (17) can utilize programming software packet SOC (second order cone) to calculate, such as
SeDuMi.Pass through mappingDOA estimations can be obtained during solution formula (17).
In formula (17), regularization parameterIt step-up error amount and is played in last DOA estimations performance important
Effect.Regularization parameterSelection rely on beDue to W and Uk(k=Q, 2J) is all orthogonal matrix, is made an uproar
Sound matrix NΥAlso meet real domain Gaussian Profile.Therefore, noise matrixApproximate real domain Gaussian Profile, this is because VSOnly NΥ
A function.Therefore pass through varianceStandardization,Similar to the χ that one degree of freedom is (M+N-1) P2Distribution.Pass through tool
There is 99% confidence intervalUpper limit value selection the present invention regularization parameter
Step 1: establishing the receipt signal model of single base MIMO radar.
Assuming that a narrowband list base MIMO radar system with M transmitting antenna and N number of reception antenna, they are battle arrays
Distance is the space uniform linear array (ULA) of half wavelength between member.In MIMO radar system, emit M using M transmitting antenna
Quadrature wave with same band and centre frequency.Assuming that there is the same range that P target is located at array far field.θpIndicate pth
The direction of arrival (DOA) of a target.After matched filter, the output of receiving array can be expressed as
X (t)=As (t)+n (t) (18)
WhereinIt is to receive data vector,It is signal data arrow
Amount,Middle βp(t) and fpIt is reflectance factor and Doppler frequency respectively.
It is transmitting-reception guiding matrix, whereinIndicate Kronecker
Product operation,It is transmitting steering vector,
It is to receive steering vector.Being one, to have zero-mean and covariance matrix be σ2IMNComplexity it is random complicated high
This white noise vector.By collecting J snap, the reception data in formula (18) become
X=AS+N (19)
Wherein X=[x (t1),…,x(tJ)], S=[s (t1),…,s(tJ)], N=[n (t1) ..., n (tJ)]。
Step 2: design dimensionality reduction matrix carries out dimension-reduction treatment to receiving data.
According to reception-transmitting steering vectorStructure it is found that transmitting-reception steering vector meets
WhereinWith(Q=M+N-1) it is transition matrix and one-dimensional steering vector respectively, is expressed as
Wherein Jm=[0N×m,IN,0N×(M-m-1)], m=0,1 ..., M-1.According to formula (21), we define matrix F=
GHG, as follows
According to formula (20) and formula (23), by using matrix GHCorresponding Q different elements, two-dimensional guide vector can
To be converted to one-dimensional steering vector, however, utilizing GHColoured noise will be increased.In order to avoid adding coloured noise, dimensionality reduction matrix can be with
It is defined as W=F-1/2GH, meet WWH=IQ.Therefore, dimensionality reduction can be obtained using W and receive dataAs follows
WhereinMeet B=[b (θ1),b(θ2),…,b(θp)],
Step 3: using unitary transformation matrix, the augmented sample matrix that data are received after dimensionality reduction is become into real domain.
According to formula (24), dimensionality reduction receives data and corresponds to containing weight matrix F1/2Linear array.Therefore it is contemplated that
One augmented sample matrixWherein ΓQBe have anti-diagonal element be 1, other elements be 0 Q × Q
Switching matrix, ()*Indicate conjugate operation.Y is center Hermite Matrix and can be converted to a real domain matrix
Wherein, unitary transformation matrix is defined as
By omitting U2K+1Central row and central series be readily available U2K.From formula (25) as can be seen that due to merging
Forward backward averaging value, sample size increase one times from J to 2J.On the other hand, the guiding matrix in formula (24)MeetWhereinDiag [] indicates diagonalization operation.Knot
Fruit shows that the linear array in formula (24) about reception data is central symmetry array after dimensionality reduction conversion.After unitary transformation,
Real domain is oriented to matrix and can be expressed asTherefore, by simple algebraic operation, formula (25) can be written as
Form
Wherein SΥ=[Φ*S ΦS*ΓJ]U2JIt is real domain signal matrix,It is that real domain is made an uproar
Sound matrix.
Step 4: carrying out singular value decomposition to real domain augmented sample matrix and obtaining the respective mode under framework of sparse representation
Type.
To YΥUsing singular value decomposition (SVD) technology, have
WhereinVSIt is by corresponding P maximum singular value, YΥReal domain right singular vector structure
At.
Based on the sparsity corresponding to entire extraterrestrial target, the signal model in formula (19) can be transformed into one it is dilute
It dredges and indicates model.A series of possible positions are indicated with Ω,(L>>P the grid of covering Ω) is indicated.Therefore, emit complete
Dictionary and the complete dictionary of reception are expressed asConstruct complete word
Allusion quotation isUnder framework of sparse representation, the signal model in formula (19) can be write as
WhereinIt is supported with S rows having the same, i.e. matrixIt is sparse.In order to estimateIt is dilute in formula (29)
It dredges and indicates that model is considered as to minimize l1Norm problem, is expressed as
Wherein | | | |1With | | | |2L is indicated respectively1Norm and l2Norm.
WhereinWithThere is identical row to support, it means that matrixIt is sparse.
Step 5: being directed to MMV problems, the orthogonality of real domain steering vector noise subspace corresponding with it, design power are utilized
Value matrix.
The complete dictionary of real domain can be divided into two parts：WhereinIt is by corresponding to
The real domain steering vector of possible targetComposition,
It is by dictionaryRemaining real domain steering vector composition.Therefore, have
Wherein, VnIt is real domain noise subspace, by YΥCarrying out singular value decomposition can obtain.As J → ∞, W1,i
→ 0, W2,i＞ 0.Therefore, we define weight matrix
Due to W1,i/max(W2) ＜ W2,i/max(W2), for MMV problems, weight matrix W can realize big weights well
Be more likely in sparse matrix be those of zero item for punishing, and small weights are used for storing the item of bigger, this and SMV is asked
The iteration weight minimization l of topic1The research method of norm is consistent.
Step 6: design real domain weight minimization l1Norm frame obtains and restores matrix, finds the non-zero restored in matrix
Row realizes the estimation to target DOA in MIMO radar system.
Real domain weight minimization l1Norm problem becomes
WhereinIt is regularization parameter, formula (34) can utilize programming software packet SOC (second order cone) to calculate, such as
SeDuMi.Pass through mappingDOA estimations can be obtained during solution formula (34).
In formula (34), regularization parameterIt step-up error amount and is played in last DOA estimations performance important
Effect.Regularization parameterSelection rely on beDue to W and Uk(k=Q, 2J) is all orthogonal matrix, noise
Matrix NΥAlso meet real domain Gaussian Profile.Therefore, noise matrixApproximate real domain Gaussian Profile, this is because VSOnly NΥOne
A function.Therefore pass through varianceStandardization,Similar to the χ that one degree of freedom is (M+N-1) P2Distribution.By having
99% confidence intervalUpper limit value selection the present invention regularization parameter
The effect of the present invention can pass through following emulation explanation：
(1) simulated conditions and content：
By the present invention and l1- SVD, RV l1- SVD and CRB are compared.Assuming that a single base MIMO radar system
System, M=N=5, emission array and receiving array are all the space uniform linear arrays that distance is half wavelength between array element.For emulation
In all methods, assume that target numbers are known.In all methods, space lattice be all be unified for 0.1 ° from -90 ° to
90 ° of ranges, and it is 99% to select the confidence interval of regularization parameter.
(2) simulation result
1, algorithms of different differentiates two uncorrelated targets the relationship of the probability of success and angle interval
Fig. 2 illustrates the relationship for two uncorrelated target resolutions and the angle of departure.Wherein number of snapshots J=50, SNR=
5dB and assume that uncorrelated target comes from θ1=0 °, θ2=0 °+Δ θ, Δ θ ° variation from 1 ° to 10.If occurred in spatial spectrum
At least two spikes, and meetWhereinIt is θiEstimation, then this
Two targets can be regarded as being solved.As shown in Fig. 2, RV l1Svd algorithm is better than l1Svd algorithm.In addition, the present invention is logical
It crosses dimensionality reduction conversion SNR gain to be strengthened, while designed weighting l1Norm has had better access to l0It norm and enhances dilute
It discongests.Therefore, present invention ratio l1- SVD and RV l1Svd algorithm has higher resolution ratio.
2, relationship of the algorithms of different for the root-mean-square error and signal-to-noise ratio of three uncorrelated target angle estimations
Fig. 3 illustrates the SNR of relationship root-mean-square error (RMSE) and to(for) three uncorrelated target angle estimations, wherein
Number of snapshots J=50, and assume that three uncorrelated targets come from θ1=-20 °, θ2=-10 °, θ3=10 °.It can from Fig. 3
Go out, due to real domain switch technology, in the low regions SNR RV l1- SVD compares l1Svd algorithm has better angle estimation.In addition, this hair
Bright angle estimation performance is better than l1- SVD and RV l1- SVD, and due to above-mentioned advantages of the present invention it close to CRB.
3, algorithms of different estimates two target angles the relationship of root-mean-square error and related coefficient
Fig. 4 illustrates the relationship that two target angles are estimated with RMSE and related coefficient.Wherein number of snapshots J=50, SNR
=5dB.Assuming that two targets come from θ1=-20 °, θ2The variation range of=- 10 ° and related coefficient is 0 to 1.Such as Fig. 4 institutes
Show, the present invention has robustness for the variation of related coefficient, and compares l1- SVD and RV l1There is-SVD better angle to estimate
Count performance.This is because the present invention includes front and back Search Space Smoothing and weighting l1Norm technology.
4, relationship of the algorithms of different for the root-mean-square error and number of snapshots of three uncorrelated target angle estimations
Fig. 5 illustrates the number of snapshots of the relationship RMSE and to(for) three uncorrelated target angle estimations.Assuming that SNR=5dB,
Three uncorrelated targets come from θ1=-20 °, θ2=-10 °, θ3=10 °.As shown in figure 5, the angle estimation performance ratio of the present invention
l1- SVD and RV l1Svd algorithm is all good, close to CRB within the scope of all snaps, it means that the present invention can be applicable in well
In lower number of snapshots.
Claims (1)
1. being based on real domain weight minimization l1The MIMO radar system DOA estimation method of Norm Method, which is characterized in that including such as
Lower step：
(1) emission array emits mutually orthogonal phase-coded signal, and receiving terminal obtains reception number after carrying out matched filtering processing
According to, and using dimensionality reduction matrix dimension-reduction treatment is carried out to receiving data；
(2) unitary transformation matrix is utilized, the augmented sample matrix that data are received after dimensionality reduction is become into real domain, carries out singular value decomposition simultaneously
Obtain the corresponding model under framework of sparse representation；
(3) orthogonality for utilizing real domain steering vector noise subspace corresponding with it, designs a diagonal entry and real domain
MUSIC composes corresponding weight matrix to solve the problems, such as MMV；
(4) design real domain weight minimization l1Norm frame obtains using programming software packet SOC second order cone computational methods and restores square
Battle array finds the non-zero row restored in matrix, realizes the estimation to target DOA in MIMO radar system；
In the step (1) dimension-reduction treatment is carried out to receiving data as follows：
(1.1) according to single base MIMO radar system emit-receive steering vector structure it is found that MIMO radar system hair
Penetrate-receive steering vector satisfaction：
A in formulat(θ) and ar(θ) is respectively to emit steering vector and reception steering vector,Q=M
+ N -1, is transition matrix and one-dimensional steering vector respectively,
Wherein,
Jm=[0N×m,IN,0N×(M-m-1)], m=0,1 ..., M-1；
Utilize matrix GHTwo-dimensional guide vector median filters are that one-dimensional steering vector carries out at dimensionality reduction by middle corresponding Q different elements
Reason；
(1.2) according to transition matrix, dimensionality reduction matrix is W=F-1/2GH, wherein
(1.3) it utilizes W to obtain dimensionality reduction and receives dataThen have
In formulaMeet B=[b (θ1),b(θ2),...,b(θp)],S=[s (t1),...,s(tJ)], N=
[n(t1),...,n(tJ)]；S (t)=[s1(t),s2(t),...,sp(t)]T,Middle βp(t) and fpRespectively
It is reflectance factor and Doppler frequency, n (t) is one, and to have zero-mean and covariance matrix be σ2IMNThe multiple height of additional random
This white noise vector, M is transmitting antenna number, N is reception antenna number, θpIndicate the direction of arrival of p-th of target, p=1,2 ..., P；
Unitary transformation matrix is utilized in the step (2) as follows, the augmented sample matrix that data are received after dimensionality reduction is become into real domain,
It carries out singular value decomposition and obtains the corresponding model under framework of sparse representation：
(2.1) consider augmented sample matrixWherein ΓQIt is that have anti-diagonal element be 1, other elements are 0
Q × Q switching matrixs, ()*Indicate that conjugate operation, Y are center Hermite Matrixes and can be converted to a real domain matrix,
Wherein, unitary transformation matrix is
It is oriented to matrixMeetDiag () is indicated
Diagonalization operates, wherein the linear array about reception data is centrosymmetric after dimensionality reduction conversion,
After unitary transformation, real domain is oriented to matrix and is expressed asBy algebraic operation,
It is written as form
Wherein SΥ=[Φ*S ΦS*ΓJ]U2JIt is real domain signal matrix,It is real domain noise square
Battle array；
(2.2) it carries out singular value decomposition and obtains the corresponding model under framework of sparse representation, as follows
To YΥUsing singularity value decomposition, have
WhereinVSIt is by corresponding to P maximum
The Y of singular valueΥReal domain right singular vector constitute；
(2.3) based on the sparsity corresponding to entire extraterrestrial target, the signal model in X=AS+N is transformed into a rarefaction representation mould
Type；A series of possible positions are indicated with Ω,Indicate the grid of covering Ω, P<<L emits complete dictionary and receives complete word
Allusion quotation is expressed asConstructing complete dictionary is
Under framework of sparse representation, the signal model of X=AS+N write as
WhereinIt is supported with S rows having the same, i.e. matrixIt is sparse；
It is transmitting-reception guiding matrix, whereinIndicate Kronecker
Product operation,It is transmitting steering vector,
Using framework of sparse representation, the one-dimensional complete dictionary of real domain is expressed as：
In formulaIn rarefaction representation
Under frame,
The orthogonality of real domain steering vector noise subspace corresponding with it, design pair are utilized in the step (3) as follows
Diagonal element weight matrix corresponding with real domain MUSIC spectrums：
(3.1) the one-dimensional complete dictionary of real domain is divided into two parts：Then have
In formulaIt is the real domain steering vector by corresponding to possible targetP=1,2 ..., P are formed,It is by dictionaryRemaining real domain steering vector composition, VnIt is real domain noise subspace, by YΥCarry out singular value decomposition
It can obtain；
(3.2) according to the orthogonality of real domain steering vector and corresponding noise subspace, as J → ∞, W1,i→ 0, W2,i＞ 0, it is fixed
Adopted weight matrix
Due to W1,i/max(W2) ＜ W2,i/max(W2),
Real domain weight minimization l is designed as follows in the step (4)1Norm frame utilizes programming software packet SOC second orders
Computational methods are bored, obtains and restores matrix, find the non-zero row restored in matrix, the target DOA in MIMO radar system is carried out
Estimation：
Real domain weight minimization l1Norm is
In formulaIt is regularization parameter, is calculated using programming software packet SOC second order cones, completes mapping
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