CN104251989B - Single base MIMO radar target Wave arrival direction estimating method based on compression stroke spectrum - Google Patents

Abstract

The present invention relates to Radar Technology field, a kind of application of more particularly to single base MIMO radar system, and in particular to single base MIMO radar target Wave arrival direction estimating method based on compression stroke spectrum.The present invention includes：Emission array launches mutually orthogonal phase-coded signal, and receiving terminal carries out matched filtering treatment using receiving array matched filter；Using dimensionality reduction matrix, taking the reception data obtained after matched filtering treatment soon to J carries out dimension-reduction treatment；The covariance matrix R of data Y is received after calculating dimension-reduction treatment, noise subspace is calculated and is conjugated intersection subspace collection subspace with it；Construction compression stroke spectral function, scans for compression stroke spectral function；False direction of arrival is excluded, the true direction of arrival of target is obtained.The present invention is in MIMO radar when carrying out spatial domain direction of arrival and searching for, it is to avoid traditional MUSIC algorithms 2-d direction finding Syndicating search, it is only necessary to one-dimensional space spectrum search, reduces computational complexity.

Description

Compressed space spectrum-based single-base MIMO radar target direction-of-arrival estimation method

Technical Field

The invention relates to the technical field of radar, in particular to application of a single-base MIMO radar system, and specifically relates to a target direction of arrival estimation method of a single-base MIMO radar based on a compressed spatial spectrum.

Background

In recent years, Multiple-Input Multiple-Output (MIMO) radar has attracted extensive attention of experts in the radar field due to its potential advantages over conventional phased array radar, and is rapidly becoming a popular research topic in the radar field. According to different configuration modes of an MIMO radar transmitting array and a MIMO radar receiving array, the MIMO radar can be divided into two main categories: one is statistical MIMO radar (IEEE Signal Processing Magazine, 2008, 25 (1): 116-. The statistical MIMO radar utilizes the spatial diversity technology to improve the detection performance of the radar, and the coherent MIMO radar utilizes the waveform diversity technology to obtain a virtual aperture larger than a real aperture, so that the coherent MIMO radar can obtain accurate direction-of-arrival estimation. The invention mainly relates to a target direction of arrival of a single-base coherent MIMO radar.

In the practical application of MIMO radar, the estimation of the direction of arrival of a target is an important aspect. Some direction-of-arrival Estimation algorithms have been proposed in MIMO radar, such as the rotation invariant subspace (Estimation of Signal parameters via arrival Estimation Technique, ESPRIT) algorithm (Electronics Letters: 2008, 44 (12): 770-. According to the methods, the arrival direction of the target is estimated by using the rotation invariant characteristic of the MIMO radar virtual steering vector, and part of the virtual array aperture is lost, so that the estimation of the final target arrival direction has certain deviation. While the multiple signal Classification (MUSIC) (IEEE transitions on Antennas and Propagation, 1986,34(3), 276) can obtain suboptimal direction of arrival estimation performance, two problems are faced when the method is directly applied to the direction of arrival estimation of MIMO radar: 1) two-dimensional direction-of-arrival parameter joint search is required; 2) and searching the direction of arrival of the whole airspace. Therefore, the application of the conventional MUSIC algorithm in the MIMO radar often causes too high operation complexity, and cannot meet the requirement of real-time signal processing in a real environment.

Disclosure of Invention

The invention aims to overcome the defects of the method and provides a novel method for estimating the direction of arrival of a single-base multi-MIMO radar based on a compressed spatial spectrum.

The method of the invention is realized by the following steps:

(1) the transmitting array transmits mutually orthogonal phase coding signals, and the receiving end performs matched filtering processing by using a receiving array matched filter until the number of snapshots reaches J;

the receiving array output expression involved is:

wherein P represents an unrelated target number, and P is 1,2, 3; theta_pThe direction of arrival of the corresponding target; a is_t(θ_p)＝[1,exp(jπsinθ_p),...,exp(jπ(Μ-1)sinθ_p)]^TFor transmitting steering vectors, a_r(θ_p)＝[1,exp(jπsinθ_p),...,exp(jπ(N-1)sinθ_p)]^TTo receive a steering vector;β_p(t) and f_pRespectively representing the reflection coefficient and the doppler frequency;denotes the zero mean and covariance matrices as σ²I_MNA gaussian white noise vector of;

in J fast beats, the received data obtained after the matched filtering process can be represented as:

X＝AS+N

in the formula,X＝[x(t₁),...,x(t_J)]，S＝[s(t₁),...,s(t_J)]，N＝[n(t₁),...,n(t_J)]is a Gaussian white noise matrix;

(2) performing dimensionality reduction processing on the received data obtained after the matched filtering processing under J snapshots by using a dimensionality reduction matrix to obtain received data Y after the dimensionality reduction processing;

the expression of the received data Y after the dimensionality reduction processing is as follows:

Y＝WX＝F^-(1/2)FBS+WN＝F^(1/2)BS+WN

wherein W is a dimensionality reduction matrix and has W ═ F^-(1/2)G^H(ii) a X is the received data output by the receiving array matched filter;

B＝[b(θ₁),b(θ₂),...,b(θ_p)]wherein b (theta)_p)＝[1,exp(jπsinθ_p),...,exp(jπ(M+N-2)sinθ_p)]^T；

(3) Calculating a covariance matrix R of the received data Y after the dimension reduction processing, obtaining a noise subspace by using eigenvalue decomposition, and calculating an intersection subspace of the noise subspace and a conjugate subspace thereof;

the expression of the covariance matrix R of the received data Y involved is:

the expression for eigenvalue decomposition of the covariance matrix is:

in the formula of U_sFor a signal subspace consisting of eigenvectors corresponding to P large eigenvalues, U_nIs a noise subspace composed of eigenvectors corresponding to the M + N-1-P small eigenvalues, Λ_sIs a diagonal matrix and whose diagonal elements consist of P large eigenvalues Λ_nThe matrix is a diagonal matrix, and the diagonal elements of the matrix are formed by small eigenvalues M + N-1-P;

noise subspace U of interest_nAnd its conjugate subspaceOf the intersection subspaceThe expression is as follows:

wherein E is a matrix formed by left singular eigenvectors, and E satisfies a singular value decomposition expression:

wherein,v is a matrix of left singular eigenvectors,a diagonal matrix composed of singular values;

(4) constructing a compressed space spectrum function, searching the compressed space spectrum function, and obtaining the true direction of arrival of the target by using the conjugate symmetry characteristic of the space spectrumAnd false direction of arrival

The expression of the compressed spatial spectrum function is:

(5) eliminating false direction of arrival by using the orthogonal characteristic of the real direction of arrival guide vector and the noise subspace, and obtaining the real direction of arrival of the target;

the expression of the orthogonal characteristic between the real direction of arrival guide vector and the noise subspace is as follows:

and obtaining the minimum P value meeting the formula, and the corresponding value is the real target arrival direction.

Compared with the prior art, the invention has the following characteristics:

1. when the MIMO radar searches the airspace direction of arrival, the method avoids the joint search of the two-dimensional direction of arrival of the traditional MUSIC algorithm, only needs one-dimensional space spectrum search, and reduces the operation complexity;

2. when the method is used for searching the direction of arrival of the airspace, the traditional MUSIC algorithm is prevented from searching the whole observation, only half of the observation airspace needs to be searched, and the direction of arrival is directly obtained by utilizing the symmetrical characteristic of the direction of arrival, so that the operation complexity is further reduced;

3. the method has better direction-of-arrival estimation performance than RD-ESPRIT, and has similar direction-of-arrival estimation performance to the traditional MUSIC algorithm.

Drawings

Fig. 1 is an overall frame diagram of the present invention.

FIG. 2 is a spatial spectrum diagram of the present invention and the MUSIC algorithm.

FIG. 3 is a graph of mean square error of direction of arrival estimation versus signal-to-noise ratio for different algorithms.

FIG. 4 is a graph of direction-of-arrival resolution probability versus signal-to-noise ratio for different algorithms.

FIG. 5 is a graph of operation time versus the number of transmit and receive array elements for different algorithms.

Detailed Description

The technical scheme of the invention is further explained by combining the accompanying drawings as follows:

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

A single-base MIMO radar is considered to be composed of M transmitting antennas and N receiving antennas, and a transmitting array and a receiving array of the single-base MIMO radar are both composed of uniform linear arrays with array element distance of half wavelength. In the monostatic MIMO radar, considering that a transmitting array and a receiving array are closely arranged, the directions Of Arrival Of targets with respect to the transmitting array and the receiving array are the same, and are collectively referred to as the Direction Of Arrival (DOA) Of the targets. At the transmitting end of the MIMO radar, a transmitting array transmits a group of orthogonal narrowband signals with the same bandwidth and center frequency. Consider P far-field uncorrelated objects located at an inward distance, where θ_p(P-1, 2, …, P) denotes the DOA of the P-th target relative to the transmit and receive arrays, then the receive array matched filter output may be expressed as

In the formulaβ_p(t) and f_pRespectively representing the reflection coefficient and the Doppler frequency a_t(θ_p)＝[1,exp(jπsinθ_p),...,exp(jπ(Μ-1)sinθ_p)]^TFor transmitting steering vectors, a_r(θ_p)＝[1,exp(jπsinθ_p),...,exp(jπ(N-1)sinθ_p)]^TTo receive steering vectors.Denotes the zero mean and covariance matrices as σ²I_MNGaussian white noise vector. Definition ofThe received signal in equation (1) may be expressed as x (t) as (t) + n (t). At J snapshots, the received signal can be represented as

X＝AS+N (2)

Wherein S ═ S (t)₁),...,s(t_J)]，N＝[n(t₁),...,n(t_J)]Is a gaussian white noise matrix.

According to transmit-receive steering vectorsStructure of (1) then

Where z is exp (j pi sin θ). As can be seen from equation (3), the transmit-receive steering of the monostatic MIMO radar contains only M + N-1 different elements, i.e., only M + N-1 different virtual array elements. The transmit-receive steering vector may be expressed as

Where G and b (theta) are the transformation matrices and corresponding virtual steering vectors,

b(θ)＝[1,exp(jπsinθ_p),...,exp(jπ(Μ+N-2)sinθ_p)]^T

in the formula

J_m＝[0_N×m,I_N,0_N×(M-m-1)]，m＝0,1,...,M-1 (6)

According to the structural characteristics of the transformation matrix in equation (5), we define the matrix F ═ G^HG is as follows

To avoid color noise, the dimensionality reduction matrix is defined as W ═ F^-(1/2)G^HSatisfies WW^H＝I_M+N-1. Processing the reception by using the dimensionality reduction matrix has

Y＝WX＝F^-(1/2)FBS+WN＝F^(1/2)BS+WN (8)

Wherein B ═ B (θ)₁),b(θ₂),...,b(θ_p)]. According to the formula (8), the received data after dimensionality reduction is equivalent to a weight F^(1/2)A uniform linear virtual array of.

And step two, calculating a covariance matrix of the dimension-reduced received data, obtaining a noise subspace by utilizing an eigenvalue decomposition technology, and calculating an intersection subspace of the noise subspace and a conjugate subspace thereof.

The covariance matrix of the reduced-dimension matrix is calculated as follows

The covariance matrix is subjected to eigenvalue decomposition, as shown below

In the formula of U_sThe signal subspace is composed of P eigenvectors corresponding to large eigenvalues, U_nThe noise subspace consists of eigenvectors corresponding to the small eigenvalues of M + N-1-P, Λ_sAnd Λ_nAre diagonal matrixes, and diagonal elements of the diagonal matrixes are respectively composed of P large eigenvalues and M + N-1-P small eigenvalues.

Obtaining a noise subspace U from equation (10)_nSolving U by SVD technique_nAndthe intersection subspace of (c). First, a matrix is definedThen carrying out singular value decomposition on the obtained product

Wherein E and V are respectively matrixes formed by left singular eigenvectors,a diagonal matrix of singular values. Intersection subspace of noise subspace and conjugate subspace thereofCan be obtained from the following formula

While equation (12) yields U_nAndof the intersection subspace

And step three, constructing a compressed space spectrum search function according to the double-orthogonality of the intersection subspace and the guide vector and the conjugate guide vector, searching the space spectrum function, and obtaining the true arrival direction and the false arrival direction of the target by utilizing the conjugate symmetric characteristic of the space spectrum.

As can be seen from the formula (12),is U_nAndthe intersection subspace of (c). Therefore, the temperature of the molten metal is controlled,

according to the orthogonality of the guide vector and the noise subspace and a weight matrix F^(1/2)The real value of (1) is

From the equation (14), it can be seen that the direction of arrival θ is true for each true direction of arrival_p(P ═ 1, 2.. times.p.) there is a false direction of arrival- θ in the conjugate noise subspace_p(P ═ 1, 2.., P). Combined formulae (13) and (14) then have

From equation (15), it can be seen that for the intersection subspace of the noise subspace and its conjugate subspaceThe steering vector and the conjugate steering vector are both orthogonal to the intersection subspaceThus constructing a compressed spatial spectral function as follows

If the formula (16) is carried out to observe the whole airspace at [ -90 DEG and 90 DEG]From the intersection subspaceThe characteristics of the orthogonal and steering vectors and the conjugate steering vector can obtain the real direction of arrival and the false direction of arrival of the target at the same time. Note the symmetry of real objects and artifacts, where we need only [0 °,90 ° ] for half the observation horizon]Or [ -90 °,0 ° ]]And performing spatial domain search, and then obtaining other directions of arrival by using conjugate characteristics, namely obtaining P real directions of arrival and P false directions of arrival.

And step four, eliminating the false direction of arrival by utilizing the orthogonal characteristic of the real direction of arrival guide vector and the noise subspace, and obtaining the real direction of arrival of the target.

2P directions of arrival theta are obtained by performing a search in half the observation space domain and the conjugate characteristics between the directions of arrival in equation (16)_p(P ═ 1.., 2P) (P true directions of arrival and P false directions of arrival). According to the fact that the steering vector corresponding to the true direction of arrival is orthogonal to the noise subspace, then

Finding the minimum P value in the formula (17) corresponds to the target direction of arrival, thereby realizing the target direction of arrival estimation of the invention.

The effect of the invention can be illustrated by the following operational complexity analysis and simulation:

operation complexity analysis

The operation complexity of the invention mainly focuses on the calculation of the covariance matrix R and the eigenvalue decomposition thereof, the eigenvalue decomposition of the matrix D and the search of the compressed space spectrum, therefore, the operation complexity of the invention is o { (M + N-1)²J+(M+N-1)³+(M+N-1-P)³+L/2[(M+N)(M+N-1+2P)]}. While the operation complexity of the MUSIC algorithm is mainly focused on the covariance matrix R_X＝1/LXX^HThe calculation and the eigenvalue decomposition of (2), and the whole observation space domainThe spatial spectrum search is carried out, so the operation complexity of the MUSIC algorithm is o { (MN)²J+(MN)³+ L [ (MN +1) (MN-P) }, where L is the total number of segmentation points in the entire observation space domain. Therefore, the invention has lower operation complexity than MUSIC algorithm.

Simulation conditions and contents:

consider a single base MIMO radar with 8 transmit elements and 8 receive elements. The transmitting array and the receiving array are both formed by uniform linear arrays with array element distance of half wavelength. Suppose there are 3 uncorrelated objects with directions of arrival θ₁＝10°，θ₂20 ° and θ₃At 40 deg., the sampling beat is 200. In most of the following experiments, the RD-ESPRIT, MUSIC algorithms were used to compare with the method of the present invention. The MUSIC algorithm and the airspace search step size of the invention are both 0.01 degrees. The root mean square error of the direction of arrival estimate is defined as

In the formulaIs the ith Monte Carlo test wave arrival angle theta_pQ200 is the number of monte carlo trials.

(III) simulation results

1. The invention and the entire spatial spectrum of MUSIC

Fig. 2 shows a spatial spectrum diagram of the present invention and the MUSIC algorithm searching the entire spatial domain. As can be seen from the figure, the MUSIC algorithm accurately estimates the directions of arrival of P targets, i.e., P peaks. In the invention, 2P peaks appear, and the peaks are symmetrical relative to 0 degree, namely P real target arrival directions and P false arrival directions. Therefore, P candidate directions of arrival can be obtained by searching a half observation space spectrum [0 degrees, 90 degrees ] or [ -90 degrees, 0 degrees ], and then other P candidate directions of arrival are obtained by utilizing the symmetry characteristic of the directions of arrival. And finally, eliminating the false direction of arrival by utilizing the orthogonal characteristic of the steering vector corresponding to the real direction of arrival and the noise subspace.

2. Mean square error versus signal-to-noise ratio for different algorithms

As can be seen from fig. 3, the direction of arrival estimation performance of the present invention is superior to RD-ESPRIT, while having similar direction of arrival estimation performance to MUSIC algorithm. However, the algorithm of the invention has the operation complexity far lower than that of MUSIC, has better signal real-time characteristic and has better prospect in practical application.

3. Direction-of-arrival resolution probability and SNR relationship of different algorithms

As can be seen from fig. 4, the direction-of-arrival resolution probability of the present invention is much greater than that of the RD-ESPRIT algorithm, while having a similar resolution probability as that of the MUSIC algorithm.

4. Relation between operation time of different algorithms and number of transmitting and receiving array elements

As can be seen from fig. 5, the operation time of the MUSIC algorithm increases rapidly with the increase of the number of the transmitting array elements and the receiving array elements, but the invention presents a process of increasing steadily, the operation time is much shorter than that of the MUSIC algorithm, which corresponds to the theoretical analysis result of the operation complexity, so the invention has good real-time characteristics.

Claims (1)

1. The single-base MIMO radar target direction-of-arrival estimation method based on the compressed spatial spectrum is characterized by comprising the following steps of:

(1) the transmitting array transmits mutually orthogonal phase coding signals, and the receiving end performs matched filtering processing by using a receiving array matched filter until the number of snapshots reaches J;

the receiving array output expression involved is:

$x\left(t\right)=\[a_t\left({\mathrm{\θ}}_1\right)\⊗a_r\left({\mathrm{\θ}}_1\right),...,a_t\left({\mathrm{\θ}}_p\right)\⊗a_r\left({\mathrm{\θ}}_p\right)\]s\left(t\right)+n\left(t\right)$

wherein p represents an unrelated target number, and p is 1,2, 3; theta_pThe direction of arrival of the corresponding target; a is_t(θ_p)＝[1,exp(jπsinθ_p),...,exp(jπ(Μ-1)sinθ_p)]^TFor transmitting steering vectors, a_r(θ_p)＝[1,exp(jπsinθ_p),...,exp(jπ(N-1)sinθ_p)]^TTo receive a steering vector;β_p(t) and f_pRespectively representing the reflection coefficient and the doppler frequency;denotes the zero mean and covariance matrices as σ²I_MNA gaussian white noise vector of;

in J fast beats, the received data obtained after the matched filtering process can be represented as:

X＝AS+N

in the formula,X＝[x(t₁),...,x(t_J)]，S＝[s(t₁),...,s(t_J)]，N＝[n(t₁),...,n(t_J)]is a Gaussian white noise matrix;

(2) performing dimensionality reduction processing on the received data obtained after the matched filtering processing under J snapshots by using a dimensionality reduction matrix to obtain received data Y after the dimensionality reduction processing;

the expression of the received data Y after the dimensionality reduction processing is as follows:

Y＝WX＝F^-(1/2)FBS+WN＝F^(1/2)BS+WN

wherein W is a dimensionality reduction matrix and has W ═ F^-(1/2)G^H(ii) a X is the received data output by the receiving array matched filter;

B＝[b(θ₁),b(θ₂),...,b(θ_p)]wherein b (theta)_p)＝[1,exp(jπsinθ_p),...,exp(jπ(M+N-2)sinθ_p)]^TG and b (θ) are transformation matrices and corresponding virtual steering vectors, J_m＝[0_N×m,I_N,0_N×(M-m-1)]，m＝0,1,...,M-1；

(3) Calculating a covariance matrix R of the received data Y after the dimension reduction processing, obtaining a noise subspace by using eigenvalue decomposition, and calculating an intersection subspace of the noise subspace and a conjugate subspace thereof;

the expression of the covariance matrix R of the received data Y involved is:

$R=\frac{1}{J}{\mathrm{YY}}^H$

the expression for eigenvalue decomposition of the covariance matrix is:

$R=U_s{\mathrm{\Λ}}_s{U}_s^H+U_n{\mathrm{\Λ}}_n{U}_n^H$

in the formula of U_sFor a signal subspace consisting of eigenvectors corresponding to P large eigenvalues, U_nIs a noise subspace composed of eigenvectors corresponding to the M + N-1-P small eigenvalues, Λ_sIs a diagonal matrix and whose diagonal elements consist of P large eigenvalues Λ_nThe diagonal matrix is formed by M + N-1-P small eigenvalues as diagonal elements;

noise subspace U of interest_nAnd its conjugate subspaceOf the intersection subspaceThe expression is as follows:

${\stackrel{\‾}{U}}_n=U_{n}E(M+N-1-2P)$

wherein E is a matrix formed by left singular eigenvectors, and E satisfies a singular value decomposition expression:

$D=E\stackrel{\‾}{\mathrm{\Λ}}{U}^H$

wherein,v is a matrix of left singular eigenvectors,a diagonal matrix composed of singular values;

(4) constructing a compressed space spectrum function, searching the compressed space spectrum function, and obtaining the true direction of arrival of the target by using the conjugate symmetry characteristic of the space spectrumAnd false direction of arrival

The expression of the compressed spatial spectrum function is:

$P_c=\frac{1}{{\[F^{(1/2)}b\left(\mathrm{\θ}\right)\]}^H{\stackrel{\‾}{U}}_n{\stackrel{\‾}{U}}_n^H{F}^{(1/2)}b\left(\mathrm{\θ}\right)}$

(5) eliminating false direction of arrival by using the orthogonal characteristic of the real direction of arrival guide vector and the noise subspace, and obtaining the real direction of arrival of the target;

the expression of the orthogonal characteristic between the real direction of arrival guide vector and the noise subspace is as follows:

$\left|\right|{\[F^{(1/2)}b\left({\mathrm{\θ}}_i\right)\]}^H{\stackrel{\‾}{U}}_n|{|}^2=0$

and obtaining the minimum P value meeting the formula, and the corresponding value is the real target arrival direction.