CN104865556B - Based on real domain weight minimization l1The MIMO radar system DOA estimation method of Norm Method - Google Patents

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

Minimization l based on real domain weighting1Norm method DOA estimation method of MIMO radar system

Technical Field

The invention relates to the technical field of MIMO radar systems, in particular to application of DOA estimation of an MIMO radar system, and specifically relates to a method for minimizing l based on real-domain weighting₁A norm method is used for estimating DOA of the MIMO radar system.

Background

In recent years, much attention has been paid to the potential advantages of a multiple-input multiple-output (MIMO) array radar system (IEEE Signal Processing megazine, 2007, 24 (5): 106-. In MIMO radar systems, angle estimation is a critical issue. For this problem, subspace-based methods, such as the MUSIC algorithm (IEEE Trans. antennas and prediction, 1986, 34 (3): 276-. On the other hand, with the special structure of the MIMO radar system, RD-ESPRIT (Electronics Letters: 2011, 47 (4): 283-. The angle estimation performance is improved based on the proposal of an algorithm of transmission array beam space energy concentration (IEEE transmission on Signal Processing, 2011, 59 (6): 2669-. However, the performance of these methods is often not satisfactory in cases of low SNR, limited fast beat count or close spatial distribution of targets.

In recent years, the emergence of sparse representation fields provides a new viewpoint for DOA estimation in array signal processing, and some sparse representation methods have been proposed in the related art. L proposed for DOA estimation₁SVD algorithm (IEEETranss. Signal Process, 2005, 53 (8): 3010-₁Norm penalty close to l₀Norm penalty, direct data attention. l₁SRACV algorithm (IEEE Trans. Signal Process., 2011, 59 (2): 629-) Sparsity based on array covariance vectors rather than direct data. On the other hand, real field l₁-SVD(RV l₁SVD) algorithm (IEEE Antennas wirelessprop. lett., 2013, 12: 376-₁The SVD algorithm has lower computational complexity and better angle estimation performance. The above-mentioned methods are all based on₁Norm penalty,/₁Norm penalty not being better approximated by l₀And (5) carrying out norm penalty. An iterative algorithm proposed in (Journal of customer analysis and applications, 2008, 14 (5): 887-₁Norm method better approaches l₀And (5) carrying out norm penalty. However, this faces two major problems: 1) only for single measurement vector recovery problems. However, the multiple measurement vector recovery problem is involved in the DOA estimation of the MIMO array system; 2) a two-dimensional complete dictionary is required in a MIMO radar system to recover the sparse array, which may fail in recovering the sparse matrix.

Disclosure of Invention

The invention aims to overcome the defects of the method and provides a novel real-domain-based weighted minimization method₁A norm MIMO radar system DOA estimation method.

The purpose of the invention is realized as follows:

the method comprises the following steps:

(1) the transmitting array transmits mutually orthogonal phase coding signals, the receiving end performs matched filtering processing to obtain received data, and dimension reduction processing is performed on the received data by using a dimension reduction matrix;

(2) changing an augmented sample matrix of the received data after dimensionality reduction into a real domain by using a unitary transformation matrix, performing singular value decomposition and obtaining a corresponding model under a sparse representation frame;

(3) designing a weight matrix of which diagonal elements correspond to a real-domain MUSIC spectrum by utilizing the orthogonality of a real-domain steering vector and a corresponding noise subspace thereof so as to solve the MMV problem;

(4) design real-field weighted minimization₁And a norm framework obtains a recovery matrix by using a programming software package SOC second-order cone calculation method, searches non-zero rows in the recovery matrix and realizes the estimation of the target DOA in the MIMO radar system.

In the step (1), the received data is subjected to dimensionality reduction according to the following steps:

(1.1) according to the structure of the receiving-transmitting guide vector of the monostatic MIMO radar system, the transmitting-receiving guide vector of the MIMO radar system satisfies the following conditions:

in the formula a_t(theta) and a_r(theta) are the transmit steering vector and the receive steering vector respectively,q is M + N-1, which is a transformation matrix and a one-dimensional steering vector respectively,

wherein,

J_m＝[0_N×m,I_N,0_N×(M-m-1)]，m＝0,1,…,M-1，

by using the matrix G^HCorresponding to Q different elements, the two-dimensional guide vector can be converted into a one-dimensional guide vector, namely, dimension reduction processing is carried out;

(1.2) according to the transformation matrix, the dimensionality reduction matrix is W ═ F^-1/2G^HWherein

(1.3) obtaining dimension-reduced received data by using WThen there is

In the formulaSatisfies the condition that B is ═ B (theta)₁),b(θ₂),…,b(θ_p)]，

In the step (2), a unitary transformation matrix is utilized according to the following steps, an augmented sample matrix of the received data after dimensionality reduction is changed into a real domain, singular value decomposition is carried out, and a corresponding model under a sparse representation frame is obtained:

(2.1) consider an augmented sample matrixWherein gamma is_QIs a Q-switched matrix with 1 as the anti-diagonal element and 0 as the other element, (. DEG)^*Representing a conjugate operation, Y is the central hermitian matrix and can be converted to a real domain matrix,

wherein the unitary transformation matrix is

Wherein S_Υ＝[Φ^*S ΦS^*Γ_J]U_2JIs a matrix of the real-domain signals,is a real-domain noise matrix;

(2.2) for Y_ΥUsing singular value decomposition SVD techniques, there are

WhereinV_SIs formed by Y corresponding to P maximum singular values_ΥThe real domain right singular vector of (1);

(2.3) applying the sparse representation framework, the real-domain one-dimensional complete dictionary can be represented as:

in the step (3), a weight matrix of a diagonal element corresponding to the real-domain MUSIC spectrum is designed by utilizing the orthogonality of the real-domain guide vector and the corresponding noise subspace thereof according to the following steps:

(3.1) dividing the real domain complete dictionary into two parts:then there is

In the formulaIs guided by real-field steering vectors corresponding to possible targetsP is 1, 2, …, P,is composed of a dictionaryThe remaining real field steering vector component, V_nIs the real-domain noise subspace, by pair Y_ΥSingular value decomposition is carried out to obtain the product;

(3.2) according to the orthogonality of the real-domain steering vectors and the corresponding noise subspace, when J → ∞ W_1,i→0，W_2,i> 0, defining weight matrix

Due to W_1,i/max(W₂)＜W_2,i/max(W₂)。

In the step (4), the real-domain weighted minimization l is designed according to the following steps₁And (3) obtaining a recovery matrix by using a programming software package SOC second-order cone calculation method through a norm framework, searching non-zero rows in the recovery matrix, and estimating a target DOA in the MIMO radar system:

real-domain weighted minimization l₁Norm of

In the formulaIs a regularization parameter, is calculated by using a programming software package SOC second-order cone, and is mapped

The invention has the beneficial effects that:

the invention enhances SNR gain through dimension reduction conversion, and designs the weight l₁Norm is better close to l₀Norm and enhanced sparse solution, ratio l₁SVD and RV l₁The SVD algorithm has a higher resolution; due to the application of the real-domain conversion technology, the angle estimation performance of the method is superior to l in the low SNR area₁SVD and RV l₁SVD and it is close to CRB due to the advantages of the invention mentioned above; the invention includes a front-back space smoothing technique and a weighting l₁Norm technique, robust to variation of correlation coefficient, and ratio l₁SVD and RV l₁SVD has better angle estimation performance. The invention solves the problem of l based on weighting₁The norm direction-of-arrival estimation method has the defects of being not suitable for multi-measurement vector recovery and the like, and can be well suitable for lower fast beat numbers.

Drawings

FIG. 1 is an overall frame diagram of the present invention;

FIG. 2 shows the relationship between success probability and angle interval for different algorithms for two unrelated targets;

FIG. 3 shows the root mean square error versus signal-to-noise ratio for different algorithms for three uncorrelated target angle estimates;

FIG. 4 is a graph of the root mean square error and correlation coefficient estimated by different algorithms for two target angles;

FIG. 5 shows the root mean square error versus fast beat number for different algorithms for three uncorrelated target angle estimates.

Detailed description of the preferred embodiments

The invention is described in more detail below in connection with a block diagram of direction of arrival estimation

The invention provides a minimization method based on real-domain weighting₁A norm multiple-input multiple-output (MIMO) radar system target Direction of arrival (DOA) estimation method mainly aims to solve the defects that a sparse representation-based Direction of arrival estimation method in an existing MIMO radar system is high in dictionary complexity and unsatisfactory in estimation accuracy. Firstly, according to the characteristics of the MIMO radar system, the received data is converted into low-dimensional and real-domain data by using dimension reduction conversion and unitary transformation technology. Then, based on the real-domain MUSIC spectrum, to obtain a weighted minimization l₁The norm framework designs a weight matrix, and then estimates the DOA by finding the non-zero rows in the recovery matrix. The process is as follows: establishing a receiving signal model of a single-base MIMO radar system, and constructing a dimensionality reduction matrix for dimensionality reduction; then, changing an augmented sample matrix of the received data after dimensionality reduction into a real domain by using a unitary transformation matrix, carrying out singular value decomposition and obtaining a corresponding model under a sparse representation frame; based on the orthogonality of the real-field steering vectors and their corresponding noise subspaces, letA weight matrix corresponding to diagonal elements and the real-domain MUSIC spectrum is calculated, and then a weighted minimization l is designed₁Norm frame to make its sparse solution closer to l₀The norm thereby greatly enhances sparsity; and finally, obtaining a recovery matrix, and searching for a non-zero row in the recovery matrix to realize the estimation of the target DOA in the MIMO radar system. Compared with the existing DOA estimation method l based on sparse representation₁SVD and real Domain l₁Compared with the SVD algorithm, the present invention has higher resolution, better angle estimation performance in low SNR case and for both uncorrelated and correlated targets, and can be well adapted to lower fast beat number.

According to the characteristics of the MIMO radar system, the method utilizes the dimension reduction conversion and unitary transformation technology to convert the received data into low-dimensional and real-domain data; then, according to the orthogonality of the real-domain steering vector and its corresponding noise subspace, designing a weight matrix with diagonal elements corresponding to the real-domain MUSIC spectrum, and further designing weighted minimization l₁Norm frame to make its sparse solution closer to l₀The norm thereby greatly enhances sparsity; and finally, obtaining a recovery matrix, and estimating the DOA by finding out non-zero rows in the recovery matrix. Compared with the existing DOA estimation method l based on sparse representation₁SVD and real Domain l₁Compared with the SVD algorithm, the present invention has higher resolution, better angle estimation performance in low SNR case and for both uncorrelated and correlated targets, and can be well adapted to lower fast beat number. The DOA estimation method mainly comprises the following aspects:

1. and establishing a receiving signal model of the single-base MIMO radar, and designing a dimensionality reduction matrix to perform dimensionality reduction on the received data.

Assume a narrow-band monostatic MIMO radar system with M transmit antennas and N receive antennas, which are spatially Uniform Linear Arrays (ULA) with half a wavelength distance between elements. In a MIMO radar system, M orthogonal waves having the same bandwidth and center frequency are transmitted using M transmit antennas. Suppose that P targets are located far from the arrayThe same extent of the field. Theta_pIndicating the angle of arrival (DOA) of the pth target. After using a matched filter, the output of the receive array can be represented as

x(t)＝As(t)+n(t) (1)

WhereinIs the reception of a vector of data,is a vector of data of the signal(s),middle β_p(t) and f_pRespectively reflection coefficient and doppler frequency.

X＝AS+N (2)

Wherein X ═ X (t)₁),…,x(t_J)]，S＝[s(t₁),…,s(t_J)]，N＝[n(t₁),…,n(t_J)]。

Based on receive-transmit steering vectorsThe structure of (1) shows that the transmit-receive steering vector satisfies

WhereinAndrespectively, a transformation matrix and a one-dimensional steering vector, expressed as

Wherein J_m＝[0_N×m,I_N,0_N×(M-m-1)]M is 0,1, …, M-1. From equation (4), we define the matrix F ═ G^HG, as shown below

By using the matrix G according to formula (3) and formula (6)^HThe two-dimensional steering vector can be converted to a one-dimensional steering vector for Q different elements, however, with G^HColor noise will be increased. To avoid additive color noise, the dimensionality reduction matrix may be defined as W ═ F^-1/2G^HSatisfies WW^H＝I_Q. Therefore, dimension-reduced received data can be obtained using WAs shown below

WhereinSatisfies the condition that B is ═ B (theta)₁),b(θ₂),…,b(θ_p)]，

2. And changing the augmented sample matrix of the received data after dimensionality reduction into a real domain by using a unitary transformation matrix, performing singular value decomposition and obtaining a corresponding model under a sparse representation frame.

The augmented sample matrix of the reduced-dimension received data is changed into a real domain as shown below

According to the formula (7), the dimension-reduced received data correspondingly contains a weight matrix F^1/2A linear array of (a). Therefore we consider an augmented sample matrixWherein gamma is_QIs a Q-switched matrix with 1 as the anti-diagonal element and 0 as the other element, (. DEG)^*Indicating a conjugate operation. Y is a central Hermite matrix and can be converted to a real-domain matrix

Wherein the unitary transformation matrix is defined as

By omitting U_2K+1Is easily obtained as a U in the center row and center column_2K. As can be seen from equation (8), the sample size doubled from J to 2J due to the combination of the pre-and post-average values. On the other hand, the steering matrix in equation (7)Satisfy the requirement ofWhereindiag[·]Representing a diagonalization operation. The result shows that the linear array with respect to the received data in equation (7) is a centrosymmetric array after the dimension reduction conversion. After a unitary transformation, the real-domain steering matrix can be represented asTherefore, through simple algebraic operation, equation (8) can be written as follows

Wherein S_Υ＝[Φ^*S ΦS^*Γ_J]U_2JIs a matrix of the real-domain signals,is a real-domain noise matrix.

Singular value decomposition is performed and corresponding models under a sparse representation framework are obtained, as shown below

For Y_ΥUsing Singular Value Decomposition (SVD) techniques, of

WhereinV_SIs formed by Y corresponding to P maximum singular values_ΥThe real domain right singular vectors of (a).

The signal model in equation (2) can be transformed into a sparse representation model based on sparsity corresponding to the entire spatial target. A series of possible positions is denoted by omega,(L>>p) representsA grid covering Ω. Thus, a transmitting complete dictionary and a receiving complete dictionary are denoted asConstruct a complete dictionary ofUnder the framework of sparse representation, the signal model in equation (2) can be written as

WhereinWith the same row support as S, i.e. matrixAre sparse. To estimateThe sparse representation model in equation (12) can be considered to minimize l₁Norm problem, expressed as

Wherein | · | purple₁And | · | non-conducting phosphor₂Respectively represent l₁Norm sum l₂And (4) norm.

WhereinAndwith the same row support, which means that the matrix isAre sparse.

3. Using real-field steering vectors (Each column of) and its corresponding noise subspace, a weight matrix is designed whose diagonal elements correspond to the real-domain MUSIC spectrum to solve the MMV problem.

The real domain complete dictionary can be divided into two parts:whereinIs guided by real-field steering vectors corresponding to possible targetsThe components of the composition are as follows,is composed of a dictionaryThe remaining real field steering vectors constitute. Thus, there are

Wherein, V_nIs the real-domain noise subspace, by pair Y_ΥAnd performing singular value decomposition to obtain the final product. When J → ∞ is reached, W_1,i→0，W_2,iIs greater than 0. Therefore, we define a weight matrix

Due to W_1,i/max(W₂)＜W_2,i/max(W₂) For MMV problems, the weight matrix W can well implement that a large weight is used to penalize those terms that are more likely to be zero in the sparse matrix, while a small weight is used to store the larger terms, which and iterative weighted minimization l for SMV problems₁The norm was studied consistently.

4. Design real-field weighted minimization₁And the norm framework obtains a recovery matrix by using a programming software package SOC (second order cone) calculation method, searches non-zero rows in the recovery matrix and realizes the estimation of the target DOA in the MIMO radar system.

Real-domain weighted minimization l₁The norm problem becomes

WhereinIs a regularization parameter, equation (17) can be calculated using a programming software package SOC (second order cone), such as SeDuMi. By mappingThe DOA estimate is obtained from solving equation (17).

In equation (17), the regularization parameterThe amount of error is set and plays an important role in the performance of the final DOA estimation. Regularization parameterIs selected byDue to W and U_k(k ═ Q,2J) are all orthogonal matrices, noise matrix N_ΥA real-domain gaussian distribution is also satisfied. Thus, the noise matrixApproximate a real-domain Gaussian distribution because of V_SOnly N_ΥA function of (a). Variance of passingThe standardization is carried out, and the standard,approximated as χ with one degree of freedom (M + N-1) P²And (4) distribution. By having a 99% confidence intervalUpper limit value of selecting regularization parameters of the present invention

Step one, establishing a receiving signal model of the single-base MIMO radar.

Assume a narrow-band monostatic MIMO radar system with M transmit antennas and N receive antennas, which are spatially Uniform Linear Arrays (ULA) with half a wavelength distance between elements. In a MIMO radar system, M orthogonal waves having the same bandwidth and center frequency are transmitted using M transmit antennas. Assume that there are P targets located in the same range of the far field of the array. Theta_pIndicating the angle of arrival (DOA) of the pth target. After using a matched filter, the output of the receive array can be represented as

x(t)＝As(t)+n(t) (18)

WhereinIs the reception of a vector of data,is a vector of data of the signal(s),middle β_p(t) and f_pRespectively reflection coefficient and doppler frequency.

Is a transmit-receive steering matrix in whichRepresenting the Kronecker product operation,is a vector of a direction of transmission,is the receive steering vector.Is a zero mean and covariance matrix of σ²I_MNIs generated from the complex random complex gaussian white noise vector. By collecting J snapshots, the received data in equation (18) becomes

X＝AS+N (19)

Wherein X ═ X (t)₁),…,x(t_J)]，S＝[s(t₁),…,s(t_J)]，N＝[n(t₁),…，n(t_J)]。

And step two, designing a dimension reduction matrix to carry out dimension reduction processing on the received data.

Based on receive-transmit steering vectorsThe structure of (1) shows that the transmit-receive steering vector satisfies

WhereinAnd(Q ═ M + N-1) are the transformation matrix and one-dimensional steering vector, respectively, and are represented as

Wherein J_m＝[0_N×m,I_N,0_N×(M-m-1)]M is 0,1, …, M-1. From equation (21), we define the matrix F ═ G^HG, as shown below

According to the formula (20) and the formula (23), by using the matrix G^HThe two-dimensional steering vector can be converted to a one-dimensional steering vector for Q different elements, however, with G^HColor noise will be increased. To avoid additive color noise, the dimensionality reduction matrix may be defined as W ═ F^-1/2G^HSatisfies WW^H＝I_Q. Therefore, dimension-reduced received data can be obtained using WAs shown below

WhereinSatisfies the condition that B is ═ B (theta)₁),b(θ₂),…,b(θ_p)]，

And step three, changing the augmented sample matrix of the received data after dimensionality reduction into a real domain by using a unitary transformation matrix.

According to the formula (24), the dimension-reduced received data correspondingly contains a weight matrix F^1/2A linear array of (a). Therefore we consider an augmented sample matrixWherein gamma is_QIs a Q-switched matrix with 1 as the anti-diagonal element and 0 as the other element, (. DEG)^*Indicating a conjugate operation. Y is a central Hermite matrix and can be converted to a real-domain matrix

Wherein the unitary transformation matrix is defined as

By omitting U_2K+1Is easily obtained as a U in the center row and center column_2K. As can be seen from equation (25), the sample size doubled from J to 2J due to the combination of the pre-and post-average values. On the other hand, the steering matrix in equation (24)Satisfy the requirement ofWhereindiag[·]Representing a diagonalization operation. The result shows that the linear array with respect to the received data in equation (24) is a centrosymmetric array after the dimension reduction conversion. After a unitary transformation, the real-domain steering matrix can be represented asTherefore, through simple algebraic operation, equation (25) can be written as follows

Wherein S_Υ＝[Φ^*S ΦS^*Γ_J]U_2JIs a matrix of the real-domain signals,is a real-domain noise matrix.

And fourthly, performing singular value decomposition on the real-domain augmentation sample matrix and obtaining a corresponding model under a sparse representation framework.

For Y_ΥUsing Singular Value Decomposition (SVD) techniques, of

WhereinV_SIs formed by corresponding to P maximum singular values, Y_ΥThe real domain right singular vectors of (a).

The signal model in equation (19) can be transformed into a sparse representation model based on sparsity corresponding to the entire spatial target. A series of possible positions is denoted by omega,(L>>p) represents a grid covering Ω. Thus, a transmitting complete dictionary and a receiving complete dictionary are denoted asConstruct a complete dictionary ofUnder the framework of sparse representation, the signal model in equation (19) can be written as

WhereinWith the same row support as S, i.e. matrixAre sparse. To estimateThe sparse representation model in equation (29) can be considered to minimize l₁Norm problem, expressed as

Wherein | · | purple₁And | · | non-conducting phosphor₂Respectively represent l₁Norm sum l₂And (4) norm.

WhereinAndwith the same row support, which means that the matrix isAre sparse.

And fifthly, aiming at the MMV problem, designing a weight matrix by utilizing the orthogonality of the real-domain steering vector and the corresponding noise subspace.

The real domain complete dictionary can be divided into two parts:whereinIs guided by real-field steering vectors corresponding to possible targetsThe components of the composition are as follows,is composed of a dictionaryThe remaining real field steering vectors constitute. Thus, there are

Wherein, V_nIs the real-domain noise subspace, by pair Y_ΥAnd performing singular value decomposition to obtain the final product. When J → ∞ is reached, W_1,i→0，W_2,iIs greater than 0. Therefore, we define a weight matrix

Due to W_1,i/max(W₂)＜W_2,i/max(W₂) For MMV problems, the weight matrix W can well implement that large weights are used to penalize those terms that are more likely to be zero in the sparse matrix, while small weights are used to store larger terms, which and iterative weighted minimization l for SMV problems₁The norm was studied consistently.

Step six, designing real domain weighted minimization₁And the norm framework is used for obtaining a recovery matrix and searching for a non-zero row in the recovery matrix to realize the estimation of the target DOA in the MIMO radar system.

Real-domain weighted minimization l₁The norm problem becomes

WhereinIs a regularization parameter, equation (34) can be calculated using a programming software package SOC (second order cone), such as SeDuMi. By mappingThe DOA estimate is obtained from solving equation (34).

In equation (34), the regularization parameterThe amount of error is set and plays an important role in the performance of the final DOA estimation. Regularization parameterIs selected byDue to W and U_k(k ═ Q,2J) are all orthogonal matrices, noise matrix N_ΥA real-domain gaussian distribution is also satisfied. Thus, the noise matrixApproximate a real-domain Gaussian distribution because of V_SOnly N_ΥA function of (a). Variance of passingThe standardization is carried out, and the standard,approximated as χ with one degree of freedom (M + N-1) P²And (4) distribution. By having a 99% confidence intervalUpper limit value of selecting regularization parameters of the present invention

The effects of the present invention can be illustrated by the following simulations:

simulation conditions and contents:

the present invention is combined with₁-SVD，RV l₁SVD and CRB were compared. Assuming a single-base MIMO radar system, where M is 5 and N is 5, the transmitting array and the receiving array are spatially uniform linear arrays with an array element distance of half a wavelength. For all methods in the simulation, it is assumed that the target number is known. In all methods, the spatial grid is uniform from-90 ° to 90 ° in the range of 0.1 °, and regularization is selectedThe confidence interval for the chemometric parameters was 99%.

(II) simulation results

1. Relationship between success probability and angle interval for distinguishing two unrelated targets by different algorithms

Fig. 2 shows the resolution versus separation angle for two unrelated targets. Where the fast beat number J is 50, SNR is 5dB and the uncorrelated target is assumed to come from θ₁＝0°，θ₂0 ° + Δ θ, Δ θ varies from 1 ° to 10 °. If at least two peaks occur in the spatial spectrum, and satisfyWhereinIs theta_iThen these two objectives can be considered to be resolved. As shown in FIG. 2, RV l₁-SVD algorithm is better than l₁-SVD algorithm. In addition, the invention enhances SNR gain through dimension reduction conversion, and designs the weight l₁Norm is better close to l₀Norm and reinforces sparse solution. Thus, the invention ratio l₁SVD and RV l₁The SVD algorithm has a higher resolution.

2. Root mean square error and signal-to-noise ratio relationship of different algorithms to three uncorrelated target angle estimates

FIG. 3 shows the Root Mean Square Error (RMSE) versus SNR for angle estimates for three uncorrelated targets, where the fast beat number J is 50, and assuming that the three uncorrelated targets are from θ₁＝-20°，θ₂＝-10°，θ₃10 deg.. As can be seen from FIG. 3, due to the real-domain conversion technique, RVl is in the low SNR region₁-SVD ratio l₁The SVD algorithm has a better angle estimation. In addition, the angle estimation performance of the invention is better than l₁SVD and RV l₁SVD and it is close to CRB due to the above mentioned advantages of the present invention.

3. Relation between root mean square error and correlation coefficient of different algorithms for two target angles

Fig. 4 shows the relationship of the estimated RMSE and the correlation coefficient for two target angles. Wherein the fast beat number J is 50, and SNR is 5 dB. Suppose two targets are from θ₁＝-20°，θ₂-10 ° and the correlation coefficient ranges from 0 to 1. As shown in FIG. 4, the present invention is robust to the variation of the correlation coefficient, and the ratio l₁SVD and RV l₁SVD has better angle estimation performance. This is because the invention incorporates a front-to-back spatial smoothing technique and weighting/₁Norm technique.

4. Root mean square error and fast beat number relation of different algorithms for three uncorrelated target angle estimates

FIG. 5 shows the RMSE versus snapshot count for three uncorrelated target angle estimates. Assuming SNR of 5dB, the three uncorrelated targets come from θ₁＝-20°，θ₂＝-10°，θ₃10 deg.. As shown in FIG. 5, the angle estimation performance ratio l of the present invention₁SVD and RV l₁The SVD algorithm works well, approaching the CRB in all snapshot ranges, which means that the invention works well for lower snapshot counts.

Claims (1)

1. Minimization l based on real domain weighting₁The DOA estimation method of the MIMO radar system of the norm method is characterized by comprising the following steps:

(1) the transmitting array transmits mutually orthogonal phase coding signals, the receiving end performs matched filtering processing to obtain received data, and dimension reduction processing is performed on the received data by using a dimension reduction matrix;

(2) changing an augmented sample matrix of the received data after dimensionality reduction into a real domain by using a unitary transformation matrix, performing singular value decomposition and obtaining a corresponding model under a sparse representation frame;

(3) designing a weight matrix of which diagonal elements correspond to a real-domain MUSIC spectrum by utilizing the orthogonality of a real-domain steering vector and a corresponding noise subspace thereof so as to solve the MMV problem;

(4) design real-field weighted minimization₁A norm framework, which is used for obtaining a recovery matrix by utilizing a programming software package SOC second-order cone calculation method, searching a non-zero row in the recovery matrix and realizing the estimation of a target DOA in the MIMO radar system;

in the step (1), the received data is subjected to dimensionality reduction according to the following steps:

(1.1) according to the structure of the transmitting-receiving guide vector of the monostatic MIMO radar system, the transmitting-receiving guide vector of the MIMO radar system satisfies the following conditions:

in the formula a_t(theta) and a_r(theta) are the transmit steering vector and the receive steering vector respectively,q is M + N-1, which is a transformation matrix and a one-dimensional steering vector respectively,

wherein,

J_m＝[0_N×m,I_N,0_N×(M-m-1)]，m＝0,1,...,M-1；

using matrix G^HCorresponding to Q different elements, converting the two-dimensional guide vector into a one-dimensional guide vector, namely performing dimension reduction processing;

(1.2) according to the transformation matrix, the dimensionality reduction matrix is W ═ F^-1/2G^HWherein

(1.3) obtaining dimension-reduced received data by using WThen there is

In the formulaSatisfies the condition that B is ═ B (theta)₁),b(θ₂),...,b(θ_p)]，S＝[s(t₁),...,s(t_J)]，N＝[n(t₁),...,n(t_J)]；s(t)＝[s₁(t),s₂(t),...,s_p(t)]^T，Middle β_p(t) and f_pRespectively reflection coefficient and doppler frequency, n (t) being a signal having a mean value of zero and a covariance matrix of σ²I_MNAdding random complex Gaussian white noise vector, M is the number of transmitting antennas, N is the number of receiving antennas, theta_pDenotes the angle of arrival of the pth target, P ═ 1, 2, …, P; in the step (2), a unitary transformation matrix is utilized according to the following steps, an augmented sample matrix of the received data after dimensionality reduction is changed into a real domain, singular value decomposition is carried out, and a corresponding model under a sparse representation frame is obtained:

(2.1) consider an augmented sample matrixWherein gamma is_QIs a Q-switched matrix with 1 as the anti-diagonal element and 0 as the other element, (. DEG)^*It is meant a conjugate operation of the two,y is the central hermitian matrix and can be converted to a real domain matrix,

wherein the unitary transformation matrix is

Steering matrixSatisfy the requirement ofdiag (-) denotes a diagonalization operation, in which the linear array with respect to the received data is centrosymmetric after the dimensionality reduction conversion,

after a unitary transformation, the real-domain steering matrix is represented asThrough the process of algebraic operation,written in the form of

Wherein S_Υ＝[Φ^*S ΦS^*Γ_J]U_2JIs a matrix of the real-domain signals,is a real-domain noise matrix;

(2.2) singular value decomposition and obtaining the corresponding model under the sparse representation framework, as shown below

For Y_ΥUsing singular value decomposition techniques, of

WhereinV_SIs formed by Y corresponding to P maximum singular values_ΥThe real domain right singular vector of (1);

(2.3) based on the sparsity corresponding to the entire spatial target, the signal model in X ═ AS + N is transformed into one sparse representation model; a series of possible positions is denoted by omega,denotes a grid covering Ω, P<<L, the transmit complete dictionary and the receive complete dictionary are denoted asConstruct a complete dictionary ofUnder the sparse representation framework, the signal model of X ═ AS + N is written AS

WhereinWith the same row support as S, i.e. matrixIs sparse;

is a transmit-receive steering matrix in whichRepresenting the Kronecker product operation,is a vector of a direction of transmission,

applying a sparse representation framework, and representing the real-domain one-dimensional complete dictionary as:

in the formulaUnder the framework of the sparse representation,

in the step (3), a weight matrix corresponding to diagonal elements and a real-domain MUSIC spectrum is designed by utilizing the orthogonality of the real-domain guide vector and a corresponding noise subspace thereof according to the following steps:

(3.1) dividing the real-domain one-dimensional complete dictionary into two parts:then there is

In the formulaIs guided by real-field steering vectors corresponding to possible targetsP is 1, 2, …, P,is composed of a dictionaryThe remaining real field steering vector component, V_nIs the real-domain noise subspace, by pair Y_ΥSingular value decomposition is carried out to obtain the product;

(3.2) according to the orthogonality of the real-domain steering vectors and the corresponding noise subspace, when J → ∞ W_1,i→0，W_2,i> 0, defining weight matrix

Due to W_1,i/max(W₂)＜W_2,i/max(W₂)，

In the step (4), the real-domain weighted minimization l is designed according to the following steps₁And (3) obtaining a recovery matrix by using a programming software package SOC second-order cone calculation method through a norm framework, searching non-zero rows in the recovery matrix, and estimating a target DOA in the MIMO radar system:

real-domain weighted minimization l₁Norm of

In the formulaIs a regularization parameter, and completes the mapping by utilizing the SOC second-order cone calculation of a programming software package