CN110579737B - Sparse array-based MIMO radar broadband DOA calculation method in clutter environment - Google Patents

Sparse array-based MIMO radar broadband DOA calculation method in clutter environment Download PDF

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CN110579737B
CN110579737B CN201910646812.6A CN201910646812A CN110579737B CN 110579737 B CN110579737 B CN 110579737B CN 201910646812 A CN201910646812 A CN 201910646812A CN 110579737 B CN110579737 B CN 110579737B
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doa
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CN110579737A (en
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何茜
任刚强
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University of Electronic Science and Technology of China
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/14—Systems for determining direction or deviation from predetermined direction
    • G01S3/143—Systems for determining direction or deviation from predetermined direction by vectorial combination of signals derived from differently oriented antennae
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/023—Interference mitigation, e.g. reducing or avoiding non-intentional interference with other HF-transmitters, base station transmitters for mobile communication or other radar systems, e.g. using electro-magnetic interference [EMI] reduction techniques
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
    • G01S7/414—Discriminating targets with respect to background clutter
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S2013/0236—Special technical features
    • G01S2013/0245—Radar with phased array antenna
    • G01S2013/0254—Active array antenna

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Abstract

The invention discloses a sparse array-based MIMO radar broadband DOA calculation method in a clutter environment, and belongs to the field of signal processing. Specifically WCSAB, in the method, clutter interference is suppressed by Capon beam forming, and then target DOA is estimated by a CS method by jointly utilizing different narrowband signal information. Considering that the DOA estimation performance is not only related to the beam forming weight value but also related to the sparse array structure, the invention provides a joint optimization problem of the beam forming weight value and the sparse array, and provides a simple algorithm for solving the optimization problem. The method provided by the invention can improve the performance of target DOA estimation in a clutter environment, including high resolution and low sidelobe, the sparse array reduces the system cost and complexity, the Bayesian Mean Square Error (BMSE) of the target DOA estimation is taken as a performance evaluation index, and the sparse array structure designed by the algorithm is similar to the optimal sparse array performance obtained by an exhaustive method and has better performance than a nested array and a co-prime array.

Description

Sparse array-based MIMO radar broadband DOA calculation method in clutter environment
Technical Field
The invention belongs to the field of signal processing, and particularly relates to a sparse array-based MIMO radar broadband DOA estimation problem in a clutter environment.
Background
The MIMO (Multiple Input Multiple Output) radar is a novel radar system that synchronously transmits signals by using Multiple transmitting antennas, receives echo signals by using Multiple receiving antennas, and processes them in a centralized manner. Compared with the traditional phased array radar, the MIMO radar has obvious advantages such as higher resolution, better target detection, positioning and tracking performance and better target parameter estimation and identification capability. The DOA estimation research is an important content in array signal processing, and the application of the DOA estimation research relates to the fields of radar, communication, sonar, radio astronomy, survey, earthquake, biomedicine and the like. At present, there are many classical DOA Estimation methods, such as Multiple Signal Classification (MUSIC), signal parameter Estimation based on rotation invariant technology (ESPRIT), and so on. In recent years, the theory of Compressive Sensing (CS) has gained wide attention of scholars at home and abroad, and compared with the traditional method, the CS-based MIMO radar DOA estimation has better estimation performance under the conditions of less sampling data and low signal-to-noise ratio.
According to the traditional array signal processing theory, in order to ensure the uniqueness of DOA estimation, the distance between adjacent array elements in the array is less than or equal to half wavelength of an incident signal, and the array meeting the condition is called a full array. The spatial resolution of the array is related to the array aperture, and increasing the resolution requires increasing the array aperture, which means that more antennas are required in a full array. However, due to the practical constraints of software and hardware resources, the number of antennas is usually limited. In order to increase the array aperture without increasing the number of antennas, sparse arrays have attracted a lot of attention. When the target is sparse in the observation space, the target DOA can be accurately estimated by the sparse array. However, in a clutter environment, sparsity of the target in the observation space may be destroyed, thereby causing degradation of DOA estimation performance.
Considering that broadband signals have the advantages of large information amount, strong anti-interference capability, high resolution and the like, representative broadband DOA estimation methods include an Incoherent Signal Subspace (ISSM), a Coherent Signal Subspace (CSSM) and the like. The ISSM divides the broadband signal into a plurality of narrow-band signals on a frequency band, then processes each narrow-band signal respectively, and finally averages the processing results of all the narrow-band signals to obtain a final estimation result. CSSM transforms the covariance matrix of narrowband signals of different frequencies to a reference frequency by focusing and then obtains the final result using a narrowband estimation method. However, CSSM requires an estimate of the target DOA and performance is greatly affected by the accuracy of the estimate.
Disclosure of Invention
The invention provides a sparse array-based MIMO radar broadband DOA estimation method in a clutter environment, in particular to a WCSAB (Wireless broadband Wireless application) method. Considering that the DOA estimation performance is not only related to the beam forming weight value but also related to the sparse array structure, the invention provides a joint optimization problem of the beam forming weight value and the sparse array, and provides a simple algorithm for solving the optimization problem.
The technical scheme of the invention is a sparse array-based MIMO radar broadband DOA calculation method in a clutter environment, which comprises the following steps:
step 1: assuming the position of the transmitting antenna is determined, the feasible region for placing the receiving antenna is [0 r ]For simplicity of analysis, the feasible fields are separated by an interval Δ r Discretization to N r A plurality of grid points, and N receiving antennas disposed on some of the grid points, N < N r ；
Step 2: establishing an MIMO radar echo signal model to obtain echo signal time domain sampling data
Figure GDA0002246415760000021
n＝1,...,N r And p = 1.. Times, L, where p represents a time domain snapshot and L is the number of snapshots;
and 3, step 3: for received signal
Figure GDA0002246415760000022
Performing an L-point discrete Fourier transform to obtain frequency domain data, i.e.
Figure GDA0002246415760000023
And N is r The data of each lattice point is expressed in vector form, i.e. y [ l ]]＝[y 1 [l],...,y Nr [l]] T Wherein p =1,.. And L, L =1,. And L;
and 4, step 4: discretizing the target angle observation area into G grid points theta 1 ,...,θ G K < G, where K represents the number of targets, the signal model is represented in sparse form:
y[l]＝Φ[l]x+c[l]+u[l]
wherein
Figure GDA0002246415760000024
Where a is r (θ,f l ) Indicating a received steering vector, a t (θ,f l ) Representing the transmit steering vector, s [ l ]]Representing a frequency domain transmitted signal, x = [ x = [ x ] 1 ,...,x G ] T Is K sparse, i.e. x has only K non-zero elements, and the values and positions of the non-zero elements are the target reflection systemNumber sum DOA, c [ l ]]Represents clutter u [ l ]]Representing noise;
and 5: will beam form weight vector w g,l Acting on y [ l]To obtain a beamforming output result:
Figure GDA0002246415760000025
will r is g,l (G = 1.., G, L = 1.., L) is expressed as a vector:
r＝[r 1,1 ,...,r G,1 ,...,r 1,L ,...,r G,L ] T
＝W r Φx+W r c+W r u
wherein the weight matrix W r ＝Diag{W 1 ,...,W l ,...,W L Is a block diagonal matrix;
and is provided with
Figure GDA0002246415760000026
Φ＝[Φ T [1],...,Φ T [L]] T ，c＝[c T [1],...,c T [L]] T Represents clutter, u = [) T [1],...,u T [L]] T Representing noise;
step 6: reconstructing a sparse vector x by basis pursuit desiccation based on the CS theory;
Figure GDA0002246415760000031
wherein eta is greater than or equal to 0 is a regularization parameter;
and 7: to the solution obtained in step 6
Figure GDA0002246415760000032
The values of the elements in the table are sorted from large to small, and the corresponding grid point of each sorted element is expressed as { theta (1) ,...,θ (G) Then the DOA estimation result can be expressed as;
Figure GDA00022464157600000314
and 8: based on minimum Bayes mean square error
Figure GDA0002246415760000033
Solving for optimal W r The following optimization problem is established
Figure GDA0002246415760000034
s.t.W r ＝Diag{W 1 ,...,W L }
Figure GDA0002246415760000035
||W|| 0 ＝N
W＝[w 1,1 ,...,w 1,L ,...,w G,1 ,...,w G,L ]
Wherein the DOA vector theta of the real target T Is random in nature and is not only easy to be recognized,
Figure GDA0002246415760000036
is expressed as a pair of theta T In the hope of expectation,
Figure GDA0002246415760000037
denotes theta T Mean square error of DOA estimation, w, when determined g,l Represents a weight vector, where G =1,. -, G, L =1, -, L;
and step 9: the problem provided by the step 8 is solved in an optimized way to obtain the optimal W r 。
Further, the specific method in step 9 is as follows:
step 1: initialization: the number of iterations j =1,
Figure GDA0002246415760000038
according to the formula
Figure GDA0002246415760000039
Calculating outBeamforming weight values
Figure GDA00022464157600000310
Wherein
Figure GDA00022464157600000311
R c (f l ) Is a clutter c [ l ]]The covariance matrix of (a); during each iteration, a set of lattice point selection vectors z is randomly generated 1 ,...,z α For a given z;
step 2: repeating the iterative process from the step 3 to the step 6:
and step 3: randomly generating a set of lattice point selection vectors z 1 ,...,z α }；
And 4, step 4: according to the formula w g,l ＝z⊙ξ g,l Computing
Figure GDA00022464157600000312
And form
Figure GDA00022464157600000313
According to the formula
Figure GDA0002246415760000041
Calculating r g,l R is to be g,l Expressed as a vector r;
will be provided with
Figure GDA0002246415760000042
And r into the formula
Figure GDA0002246415760000043
Obtaining x reconstruction results
Figure GDA0002246415760000044
And target DOA estimation result
Figure GDA0002246415760000045
According to the formula
Figure GDA0002246415760000046
Obtaining BMSE
Figure GDA0002246415760000047
And 5: minimum BMSE based derivation
Figure GDA0002246415760000048
Step 6: according to
Figure GDA0002246415760000049
Based on
Figure GDA00022464157600000410
Updating
Figure GDA00022464157600000411
Get the corresponding weight value
Figure GDA00022464157600000412
Let j = j +1; wherein
Figure GDA00022464157600000413
Is Dc [ l ]]The covariance matrix of (a) is determined,
Figure GDA00022464157600000414
and 7: when in use
Figure GDA00022464157600000415
Then, iteration stops and the optimal antenna selection is output
Figure GDA00022464157600000416
e 0 Is a threshold value set in advance.
The method provided by the invention can improve the performance of target DOA estimation in a clutter environment, including high resolution and low sidelobe, the sparse array reduces the system cost and complexity, the Bayesian Mean Square Error (BMSE) of the target DOA estimation is taken as a performance evaluation index, and the sparse array structure designed by the algorithm is similar to the optimal sparse array performance obtained by an exhaustive method and has better performance than a nested array and a co-prime array.
Drawings
FIG. 1 shows the results of BMSE ordering in ascending order for all possible sparse array configurations, and for comparison, FIG. 1 also shows the results for nested arrays (nested arrays) and co-prime arrays (co-prime arrays).
Fig. 2 (a) shows the optimal sparse array structure based on the minimum BMSE condition, and fig. 2 (b) shows the sparse array structure obtained by the proposed algorithm according to the present invention.
Fig. 3 shows DOA estimation results of different sparse array structures when using the WCSAB method.
FIG. 4 considers the single target case, DOA estimation results for different array structures using WCSAB and WCT (wideband capacitor technique) methods, respectively.
FIG. 5 shows the DOA estimation results of different array structures using WCSAB and WCT (wideband capacitor technology) methods, respectively, considering the dual target case.
Detailed Description
For convenience of description, the following definitions are first made:
bold capital letters represent matrices, bold lowercase letters represent vectors, (.) * For conjugation, (. Cndot) T For transposition, (·) H For the conjugate transposition, | x | | non-conducting phosphor 0 And | | x | calucing 1 Respectively representing l of the vector x 0 Norm and l 1 Norm, | W | count 0 Representing the number of non-zero rows of the matrix W, diag {. Cndot.) representing a block diagonal matrix, diag r {. Denotes the diagonal matrix after removing zero rows,
Figure GDA0002246415760000051
denotes the expectation with respect to theta, I N For an N-order unit array, 1 is a full 1 vector, and the symbol |, indicates a Hadamard product.
Consider a co-located MIMO radar system with both transmit and receive antennas placed on the horizontal axis of a two-dimensional cartesian coordinate system. Suppose there are M transmit antennas and the position on the horizontal axis is known as d t,m (M = 1.. Multidot.m). Hypothetical placementThe feasible region of the receiving antenna is [0, D ] r ]For simplicity of analysis, the feasible fields are separated by an interval Δ r Discretization to N r And grid points on which the receiving antennas are placed. Due to the constraint of the number of antennas, the radar system is assumed to be only N (N < N) r ) And a plurality of available receiving antennas. Order to
Figure GDA0002246415760000052
Representing a wideband signal transmitted by the m-th transmitting antenna in a frequency range of [ -B [ ] m /2,B m /2]Where p denotes time-domain snap, T s Indicating the sampling period and L the number of fast beats. Let DOA of K far-field point targets be theta T,k (K =1,.. K), then the signal received at the nth bin is
Figure GDA0002246415760000053
Wherein f is c Denotes the carrier frequency, beta k The reflection coefficient of the kth target is represented and assumed to be unknown. Let the first transmit antenna and the first lattice point be the reference, then τ Tt,m,k ＝(d t,m -d t,1 )sinθ T,k C represents the time delay of the signal from the m-th transmitting antenna to the k-th target relative to the reference array element, tau Tr,n,k ＝(n-1)Δ r sinθ T,k Representing the time delay of the signal from the kth target to the nth grid point relative to the first grid point. Q denotes the number of clutter scatterers, gamma q (Q = 1...., Q) represents the reflection coefficient of the clutter scatterers, and it is assumed that there is a gaussian random variable of independent co-distribution (iid) between them. Tau is Ct,m,q ＝(d t,m -d t,1 )sinθ C,q C represents the time delay of the signal from the m-th transmitting antenna to the q-th clutter scattering body relative to the reference array element, tau Cr,n,q ＝(n-1)Δ r sinθ C,q Representing the time delay of the signal from the qth clutter scatterer to the nth grid point, θ C,q Indicating the orientation of the q-th clutter scatterer relative to the array.
Figure GDA0002246415760000054
Is that the variance is σ 2 White gaussian noise.
By performing an L-point Discrete Fourier Transform (DFT) on the time domain discrete signal, the frequency point f can be obtained l ＝lf s Frequency domain data of (L = 1.., L), where f s Is the frequency sampling interval, f l ∈[-B/2,B/2]And is
Figure GDA0002246415760000061
The signal being at frequency f l At a DFT result of
Figure GDA0002246415760000062
Wherein s is m [l]And u n [l]Respectively representing the transmitted signals
Figure GDA0002246415760000063
And noise
Figure GDA0002246415760000064
DFT of (2). Order to
Figure GDA0002246415760000065
And
Figure GDA0002246415760000066
respectively expressed at an angle theta and a frequency f l A receive steering vector and a transmit steering vector. Will N r The signal received by each grid point is expressed as a vector
Figure GDA0002246415760000067
Wherein
Figure GDA0002246415760000068
Figure GDA0002246415760000069
Under the CS framework, to estimate DOA θ of K targets T,k (K = 1.. K.), discretizing the target angular observation region into G (K < G) grid points θ 1 ,...,θ G It is assumed that the dispersion error is negligible, i.e. the target falls exactly on the grid point. Then the formula (3) can be expressed as
y[l]＝Φ[l]x+c[l]+u[l] (4)
Wherein
Figure GDA00022464157600000610
Vector x = [ x = 1 ,...,x G ] T Is K sparse, i.e. x has only K non-zero elements, and the values and positions of the non-zero elements are the target reflection coefficient and DOA, which can be expressed as
Figure GDA00022464157600000611
CS theory estimates the target DOA using the sparsity of x, however, this sparsity is destroyed in clutter environments, thereby degrading the performance of DOA estimation. In order to suppress the interference of the spurious waves, a beam forming method is adopted at the receiving end. Order to
Figure GDA0002246415760000071
Is shown in the direction theta g Frequency f l The beamforming weight vector at (a) and the position of the non-zero element indicates the selection of the lattice point where the antenna is placed. Since there are only N available receive antennas, the weight vector is required to satisfy | | w g,l || 0 = N. The beamformed output is given by
Figure GDA0002246415760000072
Will r is g,l (G = 1.. G, G and L = 1.. G., L) is expressed as a vector GL × 1
Figure GDA0002246415760000073
Wherein phi = [ phi ] T [1],...,Φ T [L]] T ，c＝[c T [1],...,c T [L]] T ，u＝[u T [1],...,u T [L]] T ，W r ＝Diag{W 1 ,...,W L }，
Figure GDA0002246415760000074
According to equation (7), the DOA estimation problem can be converted into a sparse signal reconstruction problem, and based on the CS theory, the K sparse vector x can be reconstructed through base pursuit elimination (BPDN)
Figure GDA0002246415760000075
Wherein eta is more than or equal to 0 and is a regularization parameter, and for the optimization problem of the formula (8), a CVX tool package can be used for solving. Order to
Figure GDA0002246415760000076
The solution of the above formula is shown,
Figure GDA0002246415760000077
is the estimation result of the target DOA. Considering a target DOA vector θ T ＝[θ T,1 ,...,θ T,K ] T Is a random case, then the average estimation performance can be given by the Bayesian Mean Square Error (BMSE)
Figure GDA0002246415760000078
From the equation (9), the DOA estimated performance and the matrix W r In connection with, in order to optimize the performance, the following optimization problem is given
Figure GDA0002246415760000079
(10) Formula (II)The last two constraints in (A) are to ensure that w is for different g and l g,l The positions of the non-zero elements in (a) are the same. Due to w g,l The position of the non-zero element in the (10) expression indicates that the corresponding lattice point is selected to place the antenna, so that the formula is a joint optimization problem of the weighted value and the sparse array structure.
Considering that equation (10) is an NP-hard problem, a simple algorithm is proposed to solve the optimization problem. The algorithm firstly optimizes the sparse array structure when the weight is given, and then updates the weight for the next iteration. First, how to optimize the sparse array structure when the weight is given is explained. First, a lattice point selection vector is defined
Figure GDA0002246415760000081
Wherein z is n Belongs to {0,1}, and only if the element is 1, it means to select the corresponding lattice point to place the antenna, since there are only N available receiving antennas, it is required that z y 0 And (N). The weight value of the first iteration is given by the full array situation Capon beam forming
Figure GDA0002246415760000082
Wherein
Figure GDA0002246415760000083
R c (f l ) Is a clutter c [ l ]]The covariance matrix of (2). During each iteration, a set of lattice point selection vectors z is randomly generated 1 ,...,z α For a given z, there is
w g,l ＝z⊙ξ g,l (12)
For different z, different w can be obtained g,l And W r (W r From w g,l Composition) according to formula (9), BMSE and W r In this regard, it can therefore be seen that BMSE is also related to z, denoted as e (z). Based on minimum BMSE, the optimal lattice point selection vector z can be obtained op 。
Based on z op Updating xi g,l In the order of corresponding weight value
Figure GDA0002246415760000084
Xi is g,l In the formula z op The selected element value is updated by
Figure GDA0002246415760000085
Wherein
Figure GDA0002246415760000086
Is Dc [ l ]]The covariance matrix of (a) is determined,
Figure GDA0002246415760000088
when BMSE e (z) op ) Less than a certain threshold e 0 When so, the iteration stops. The detailed algorithm is given in table 1.
TABLE 1 iterative algorithm for solving optimization problem
Figure GDA0002246415760000087
Figure GDA0002246415760000091
In order to suppress the interference of the noise, a beam forming method is adopted at the receiving end.
Figure GDA0002246415760000092
Is shown in the direction theta g Frequency f l The position of the non-zero element represents the lattice point where the antenna is selected to be placed, and since there are only N available receiving antennas, the weight vector is required to satisfy | | w g,l || 0 = N. The array structure of the antenna should be the same for different g and l, i.e. w g,l The positions of the non-zero elements in (a) are the same. To represent this constraint, a matrix is constructed
W＝[w 1,1 ,...,w 1,L ,...,w G,1 ,...,w G,L ] (14)
And satisfy | | W | Liao 0 N, i.e. the number of non-zero rows of the matrix is N, by this constraint it is possible to satisfy the constraint for different g and l, w g,l The positions of the non-zero elements in (b) are the same. Weight vector w g,l Acting on received signals y [ l]Obtaining a beam forming output r according to the formula (6) g,l It is expressed as a G × 1 vector
Figure GDA0002246415760000093
From the above formula, it can be found that for different frequencies f l The sparsity of vector x is the same. In order to jointly utilize signal information of different frequencies, r is l (L = 1...., L) is expressed as a vector of GL × 1, i.e., formula (7). By converting the DOA estimation problem into the sparse signal reconstruction problem, the reconstruction result of the sparse vector x can be obtained according to the formula (8)
Figure GDA0002246415760000094
Then the
Figure GDA0002246415760000095
The position of the maximum K elements in the target DOA is the estimation result and is expressed as
Figure GDA0002246415760000101
For is to
Figure GDA0002246415760000102
The values of the elements in the table are sorted from big to small, and the corresponding lattice point of each sorted element is expressed as { theta [ [ theta ] ] (1) ,...,θ (G) Then the DOA estimation result can be expressed as
Figure GDA0002246415760000103
Full array beam forming weight vector xi g,l Can make the direction theta g Frequency f l The signal at the position passes through without distortion and simultaneously suppressesFor interference and noise in other directions, denoted as
Figure GDA0002246415760000104
The optimal solution of the above equation is equation (11).
Two simulation examples are given for sparse array-based MIMO radar broadband DOA estimation in a clutter environment, and the parameters are set as follows: suppose D r And 11 λ/2, wherein λ represents the wavelength corresponding to the highest frequency of the signal. Setting the feasible region where the receiving antenna can be placed by delta r And (= λ/2) is 12 grid points discrete at intervals. It is assumed that the number of transmit and receive antennas available for the MIMO radar system is M = N =6 and the transmit side array structure is definitely known.
To simplify the analysis, it is assumed that the transmitted signal bandwidths are the same, i.e. B m =200MHz (M = 1.. Gth, M), the carrier frequency is 1GHz.
The target angular field of view is discretized into 41 grid points-20 °, -19 °,20 °.
The clutter consists of 250 scatterers, distributed at angles of-90 °, -90 ° +180 °/250 °,90 °.
Defining a signal-to-noise ratio
Figure GDA0002246415760000105
And signal to noise ratio
Figure GDA0002246415760000106
Without loss of generality, assuming a target reflection coefficient of 1, SNR and SCR are set to-5 dB and-30 dB, respectively.
In simulation 1, it is assumed that the targets are uniformly and randomly distributed on the grid points after the angular observation domain is discretized. To ensure that the aperture of the array does not change, let
Figure GDA0002246415760000107
Then it shares
Figure GDA0002246415760000108
Different sparse array structures. FIG. 1 shows all possible sparse arraysThe results of the BMSEs in the column structure arranged in ascending order, the diamonds represent the optimal sparse array structure under the minimum BMSE condition, the squares represent the sparse array structure obtained according to the algorithm given in table 1, it can be seen that the performance of the two structures are similar, and the specific structures of the two sparse arrays are given in fig. 2. For comparison, fig. 1 also shows the results of a nested array (nested array) and a co-prime array (co-prime array), which are marked by asterisks and circles, respectively, and it can be seen that the performance of various sparse array structures is better than that of the nested array and the co-prime array. Assuming that there is only one target, DOA is-14 °, fig. 3 shows the DOA estimation results of the above four sparse array structures when using the WCSAB method. As can be seen from the figure, the optimal sparse array and the sparse array obtained by the algorithm can accurately estimate the target DOA, and the nested array and the co-prime array have errors in estimation.
In simulation 2, the performance of two wideband DOA estimation methods, WCSAB and WCT (wideband Capon technique), were compared. The WCT method belongs to one of ISSM, which uses Capon method to obtain corresponding DOA estimation result for each narrow-band signal, then averages all the results to obtain the final estimation result. Fig. 4 considers the single target case with a target DOA of 10 deg., fig. 5 considers the dual target case with target DOAs of 6 deg. and 10 deg.. In the figure, the solid line represents a full array structure at intervals of λ/2, the dotted line represents an optimal sparse array structure, and the dotted line represents a sparse array structure obtained according to an algorithm. As can be seen from fig. 4 and 5, compared to the full array structure, the two sparse arrays have narrower main lobe widths, i.e. the sparse arrays have higher resolution. But sparse arrays result in higher sidelobes and this problem is more severe in the dual target case. By comparison, it can be found that the side lobe of the WCSAB method is lower than the WCT. It can also be seen from fig. 5 that the WCSAB method can accurately estimate the target DOA in both sparse arrays, while the WCT estimates have errors. By contrast, the WCSAB method performed better.

Claims (2)

1. A MIMO radar broadband DOA calculation method based on sparse array in clutter environment comprises the following steps:
step 1: setting the position of the transmitting antennaThe feasible region for placing the receiving antenna is determined to be 0 r ]For simplicity of analysis, the feasible fields are separated by an interval Δ r Discretization to N r A plurality of grid points, and N receiving antennas disposed on some of the grid points, N < N r ；
And 2, step: establishing an MIMO radar echo signal model to obtain echo signal time domain sampling data
Figure FDA0003730310750000011
n＝1,...,N r And p =1, ·, L, where p represents time domain snapshots, L being the number of snapshots;
and step 3: for received signal
Figure FDA0003730310750000012
Performing an L-point discrete Fourier transform to obtain frequency domain data, i.e.
Figure FDA0003730310750000013
And N is r The data of the individual lattice points being represented in vector form, i.e.
Figure FDA0003730310750000014
Wherein p =1,.., L =1,.., L;
and 4, step 4: discretizing the target angle observation area into G grid points theta 1 ,...,θ G K < G, where K represents the number of targets, the signal model is represented in sparse form:
y[l]＝Φ[l]x+c[l]+u[l]
wherein
Figure FDA0003730310750000015
Where a is r (θ,f l ) Representing the received steering vector, f l Represents a frequency point, a t (θ,f l ) Representing the transmit steering vector, s [ l ]]Representing a frequency domain transmitted signal, x = [ x = [ x ] 1 ,...,x G ] T Is K sparse, i.e. x has only K non-zero elements, and the values and positions of the non-zero elements are the target reflection coefficient and DOA, c [ l [ ]]Represents clutter u [ l ]]To representNoise;
and 5: will beam form weight vector w g,l Acting on y [ l]To obtain a beamforming output result:
Figure FDA0003730310750000016
will r is g,l Expressed as a vector:
r＝[r 1,1 ,...,r G,1 ,...,r 1,L ,...,r G,L ] T
＝W r Φx+W r c+W r u
wherein the weight matrix W r ＝Diag{W 1 ,...,W l ,...,W L Is a block diagonal matrix, G = 1.., G, L = 1.., L;
and is provided with
Figure FDA0003730310750000017
Φ＝[Φ T [1],...,Φ T [L]] T ，c＝[c T [1],...,c T [L]] T Represents clutter, u = [) T [1],...,u T [L]] T Representing noise;
step 6: reconstructing a sparse vector x by base pursuit denoising based on a CS theory;
Figure FDA0003730310750000018
wherein eta is equal to or greater than 0 is a regularization parameter;
and 7: to the solution obtained in step 6
Figure FDA0003730310750000021
The values of the elements in the table are sorted from large to small, and the corresponding grid point of each sorted element is expressed as { theta (1) ,...,θ (G) Then the DOA estimation result can be expressed as;
Figure FDA0003730310750000022
and 8: based on minimum Bayes mean square error
Figure FDA0003730310750000023
Solving for optimal W r The following optimization problem is established
Figure FDA0003730310750000024
s.t.W r ＝Diag{W 1 ,...,W L }
Figure FDA0003730310750000025
||W|| 0 ＝N
W＝[w 1,1 ,...,w 1,L ,...,w G,1 ,...,w G,L ]
Wherein the DOA vector theta of the real target T Is random in nature and is not only easy to be recognized,
Figure FDA0003730310750000026
is expressed in the pair theta T In the hope of expectation,
Figure FDA0003730310750000027
denotes theta T Mean square error of DOA estimation, w, when determined g,l Represents a weight vector, where G =1,. -, G, L =1, -, L;
and step 9: the problem provided by the step 8 is solved in an optimized way to obtain the optimal W r 。
2. The method according to claim 1, wherein the method for calculating the MIMO radar wideband DOA based on the sparse array in the clutter environment comprises the following specific steps:
step 9.1: initialization: the number of iterations j =1,
Figure FDA0003730310750000028
according to the formula
Figure FDA0003730310750000029
Computing beamforming weight values
Figure FDA00037303107500000210
Wherein
Figure FDA00037303107500000211
R c (f l ) Is a clutter c]The covariance matrix of (a); during each iteration, a set of lattice point selection vectors z is randomly generated 1 ,...,z α For a given z;
step 9.2: repeating the iterative process from step 9.3 to step 9.6:
step 9.3: randomly generating a set of lattice point selection vectors z 1 ,...,z α }；
Step 9.4: according to the formula w g,l ＝z⊙ξ g,l Calculating out
Figure FDA00037303107500000212
And are formed by
Figure FDA00037303107500000213
According to the formula
Figure FDA00037303107500000214
Calculating r g,l R is to be g,l Expressed as a vector r;
will be provided with
Figure FDA0003730310750000031
And r into the formula
Figure FDA0003730310750000032
Obtaining x reconstruction results
Figure FDA0003730310750000033
And target DOA estimation result
Figure FDA0003730310750000034
According to the formula
Figure FDA0003730310750000035
Obtaining BMSE
Figure FDA0003730310750000036
Step 9.5: minimum BMSE based derivation
Figure FDA0003730310750000037
Step 9.6: according to
Figure FDA0003730310750000038
Based on
Figure FDA0003730310750000039
Updating
Figure FDA00037303107500000310
Get the corresponding weight value
Figure FDA00037303107500000311
Let j = j +1; wherein
Figure FDA00037303107500000312
Figure FDA00037303107500000313
Is Dc [ l ]]The covariance matrix of (a) is determined,
Figure FDA00037303107500000314
wherein,
Figure FDA00037303107500000315
z op selecting vectors for grid points, c [ l ]]Is clutter;
step 9.7: when the temperature is higher than the set temperature
Figure FDA00037303107500000316
Then, iteration stops and the optimal antenna selection is output
Figure FDA00037303107500000317
e 0 Is a preset threshold value.
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