CN110196410B - Array antenna main lobe interference suppression method and system - Google Patents
Array antenna main lobe interference suppression method and system Download PDFInfo
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Abstract
The invention discloses a method and a system for suppressing array antenna main lobe interference. The method comprises the following steps: acquiring an array antenna signal model; obtaining a high-precision covariance matrix by adopting a Taylor estimation method according to the array antenna signal model; determining an interference subspace according to the high-precision covariance matrix; acquiring a main lobe region subspace; determining a projection matrix by adopting a subspace intersection solving method according to the main lobe region subspace and the interference subspace; preprocessing the interference and noise signal according to the projection matrix to obtain a preprocessed covariance matrix; correcting the preprocessed covariance matrix by adopting a diagonal loading method to obtain a corrected covariance matrix; determining a self-adaptive weight vector according to the corrected covariance matrix; and determining an array output signal according to the self-adaptive weight vector. The method or the system can effectively inhibit the interference of a plurality of main lobes and keep good robustness under the condition of low snapshot.
Description
Technical Field
The invention relates to the field of main lobe interference, in particular to a method and a system for suppressing main lobe interference of an array antenna.
Background
With the increasing electronic countermeasure and the higher and higher requirement on the radar anti-interference performance, the phased array radar is widely applied by virtue of the flexible beam control performance. Adaptive Beam Forming (ABF) technology can realize forming null in unknown interference direction and better inhibit sidelobe interference. However, when interference enters the main lobe, the conventional ABF may form a null in the main lobe, which causes directional diagram distortion, and seriously affects the detection performance of the radar, for example, the angle measurement curve of the monopulse radar may be distorted, and the angle measurement accuracy thereof is greatly reduced.
In order to solve the above problems, researchers have proposed two main lobe interference suppression ideas. The 1 st type is a large-scale auxiliary array method, that is, the aperture of the antenna is enlarged by constructing a large-scale auxiliary array, so that the width of the main lobe of the antenna is reduced, and the main lobe interference is converted into side lobe interference to be suppressed. However, as the size of the antenna increases and the number of the array elements increases, the cost, power consumption and weight of the antenna also increase. Therefore, the auxiliary array method is not easy to be implemented in engineering. The 2 nd type is a data preprocessing method, namely, snapshot data received by an antenna is used for extracting relevant information of main lobe interference and constructing a preprocessing matrix to preprocess a received signal, so that the main lobe interference is suppressed. Compared with an auxiliary array method, the latter method has small hardware overhead and is easy to realize in engineering. However, the data preprocessing method has high requirements on algorithm design, and the output signal-to-interference-plus-noise ratio (SINR) obtained by applying different anti-interference algorithms has large difference.
The prior art proposes a main lobe interference suppression algorithm (BMP) based on blocking matrix preprocessing. The method utilizes the azimuth angle of the main lobe interference to construct a blocking matrix and carries out blocking matrix preprocessing on the received data. The method removes the main lobe interference and simultaneously reduces the degree of freedom of the antenna. The prior art proposes a main lobe interference suppression algorithm (EMP) based on feature projection matrix preprocessing. The method includes the steps that an interference-plus-noise covariance matrix (INCM) is subjected to characteristic decomposition, space domain signals are expanded on an energy domain, and an interference subspace and a noise subspace are obtained. The core of EMP is to extract eigenvector corresponding to main lobe interference from interference subspace and use the eigenvector to construct eigenprojection matrix to remove the main lobe interference. However, eigenprojection preprocessing can cause covariance matrix mismatch, causing a main beam offset of the pattern. In order to overcome the main beam offset, the prior art proposes an improved EMP algorithm, whose main idea is to perform covariance reconstruction, so that the beamforming performance is robust. But this method can only suppress single main lobe interference. In order to solve the problem of suppressing the interference of multiple main lobes, a main lobe interference suppression algorithm (SMF) based on subspace matrix filtering and covariance reconstruction is also proposed in the prior art. The method extracts the eigenvector corresponding to the main lobe interference by performing matrix filtering on the interference subspace. The matrix filter is essentially a spatial filter, and its function is to ensure that the signal in the main lobe region is not affected and to block the signal outside the main lobe region from passing through. And converting the convex problem into a convex problem, and solving an optimal filter matrix by using a cvx tool box. SMF is computationally complex and less robust in low snapshot conditions. The traditional sampling covariance matrix has larger estimation error under the condition of low snapshot, thereby causing the reduction of output SINR, and proposes to replace the traditional sampling covariance matrix by using a Taylor estimation method, thereby improving the estimation precision of the covariance matrix. The method effectively improves the output SINR under the condition of low snapshot. But the method has reduced effect when applied to a multi-main lobe interference environment.
Disclosure of Invention
The invention aims to provide an array antenna main lobe interference suppression method and system, which can effectively suppress a plurality of main lobe interferences and keep good robustness under a low snapshot condition.
In order to achieve the purpose, the invention provides the following scheme:
an array antenna main lobe interference suppression method comprises the following steps:
acquiring an array antenna signal model;
obtaining a high-precision covariance matrix by adopting a Taylor estimation method according to the array antenna signal model;
determining an interference subspace according to the high-precision covariance matrix;
acquiring a main lobe region subspace;
determining a projection matrix by adopting a subspace intersection solving method according to the main lobe region subspace and the interference subspace;
preprocessing the interference and noise signal according to the projection matrix to obtain a preprocessed covariance matrix;
correcting the preprocessed covariance matrix by adopting a diagonal loading method to obtain a corrected covariance matrix;
determining a self-adaptive weight vector according to the corrected covariance matrix;
and determining an array output signal according to the self-adaptive weight vector.
Optionally, the obtaining a high-precision covariance matrix by using a taylor estimation method according to the array antenna signal model specifically includes:
obtaining a high-precision covariance matrix by adopting a Taylor estimation method according to the array antenna signal model
Wherein,
piis the power of the i-th interference,
i is an identity matrix, a ═ a (θ) for the estimated noise power, respectively1),…,a(θp+q)]，a(θi) For steering vectors corresponding to the ith disturbance, θiThe direction of the incoming wave of the ith interference.
Optionally, the determining an interference subspace according to the high-precision covariance matrix specifically includes:
performing characteristic decomposition on the covariance matrix to obtain a decomposed covariance matrix
Determining an interference subspace according to the decomposed covariance matrix, wherein the interference subspace is formed by UsThe column vector of (1).
Optionally, the obtaining the main lobe region subspace specifically includes:
according to the main lobe interval, by using the formula H ═ integral-φa(θ)aH(theta) do theta and
determining a main lobe region subspace, the main lobe region subspace is formed by U1The column vector of (1);
wherein, ω isiFor the ith feature value, in descending order, viFor corresponding eigenvectors, Λ1Is front K2Diagonal matrix formed by large eigenvalues, U1Is Λ1Matrix of eigenvectors corresponding to medium eigenvalues, Λ2From the remaining M-K2A characteristic value component, U2Is Λ2And (5) a matrix formed by eigenvectors corresponding to the medium eigenvalues.
Optionally, the determining a projection matrix by using a subspace intersection solving method according to the main lobe region subspace and the interference subspace specifically includes:
performing singular value decomposition on the main lobe region subspace and the interference subspace to obtain a principal angle and a principal vector between the main lobe region subspace and the interference subspace;
determining a common vector of the main lobe region subspace and the interference subspace according to the principal angle and the principal vector, wherein the common vector is a vector corresponding to the main lobe interference;
determining a projection matrix B (I-GG) according to the vector corresponding to the main lobe interferenceH；
Wherein, G is a matrix formed by vectors corresponding to the main lobe interference, I is a unit matrix, and B is a projection matrix.
Optionally, the preprocessing the interference plus noise signal according to the projection matrix to obtain a preprocessed covariance matrix specifically includes:
obtaining a covariance matrix after projection preprocessing according to the projection matrix
Wherein R isYIs a pre-processed covariance matrix, uiFor corresponding feature vectors, λiIs the ith eigenvalue, B is the projectionAnd (4) matrix.
Optionally, the modifying the preprocessed covariance matrix by using a diagonal loading method to obtain a modified covariance matrix specifically includes:
correcting the preprocessed covariance matrix by adopting a diagonal loading method to obtain a corrected covariance matrix
Wherein,
for diagonal loading of factors, take
I is an identity matrix, RYIs the pre-processed covariance matrix,
is a modified covariance matrix.
Optionally, the determining an adaptive weight vector according to the modified covariance matrix specifically includes:
determining an adaptive weight vector according to the modified covariance matrix
Wherein, a (theta)s) As a guide vector of the desired signal, thetasW is the adaptive weight vector for the incoming direction of the desired signal.
An array antenna main lobe interference mitigation system comprising:
the first acquisition module is used for acquiring an array antenna signal model;
the Taylor estimation module is used for obtaining a high-precision covariance matrix by adopting a Taylor estimation method according to the array antenna signal model;
the interference subspace determination module is used for determining an interference subspace according to the high-precision covariance matrix;
the second acquisition module is used for acquiring a main lobe region subspace;
the projection matrix determining module is used for determining a projection matrix by adopting a subspace intersection solving method according to the main lobe region subspace and the interference subspace;
the preprocessing module is used for preprocessing the interference and noise signals according to the projection matrix to obtain a preprocessed covariance matrix;
the correcting module is used for correcting the preprocessed covariance matrix by adopting a diagonal loading method to obtain a corrected covariance matrix;
the adaptive weight vector determining module is used for determining an adaptive weight vector according to the corrected covariance matrix;
and the array output signal determining module is used for determining the array output signal according to the self-adaptive weight vector.
Optionally, the taylor estimation module specifically includes:
a Taylor estimation unit for obtaining a high-precision covariance matrix by using Taylor estimation method according to the array antenna signal model
Wherein,
pi is the power of the ith interference,
i is an identity matrix, a ═ a (θ) for the estimated noise power, respectively1),…,a(θp+q)]，a(θi) For steering vectors corresponding to the ith disturbance, θiThe direction of the incoming wave of the ith interference.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects: the invention provides an array antenna main lobe interference suppression method, which is a main lobe interference suppression algorithm based on intersection solving of Taylor estimation and subspace. And constructing a main lobe region subspace by using the priori knowledge, solving the intersection of the main lobe region subspace and the interference subspace and the vector corresponding to the main lobe interference, and further constructing a characteristic projection matrix. And correcting the covariance matrix after feature projection preprocessing by utilizing diagonal loading, and then solving the adaptive weight vector to inhibit side lobe interference. Compared with a sampling covariance matrix, the covariance matrix obtained by Taylor estimation has higher precision, the method can effectively inhibit the interference of a plurality of main lobes, has good robustness under the condition of low snapshot, and has higher output signal-to-interference-plus-noise ratio (SINR).
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
Fig. 1 is a flowchart of an array antenna main lobe interference suppression method according to the present invention;
fig. 2 is a structural diagram of the array antenna main lobe interference suppression system of the present invention;
FIG. 3 is an estimation error of a covariance matrix;
FIG. 4 is a spatial response plot of a subspace;
FIG. 5 is an error estimate of a vector corresponding to a mainlobe interference;
FIG. 6 is an adaptive array pattern;
fig. 7 is a graph of output SINR versus snapshot number under two main lobe interference conditions;
fig. 8 is a graph of output SINR versus snapshot number under a single main lobe interference condition.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide an array antenna main lobe interference suppression method and system, which can effectively suppress a plurality of main lobe interferences and keep good robustness under a low snapshot condition.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Example 1:
fig. 1 is a flowchart of an array antenna main lobe interference suppression method according to the present invention. As shown in fig. 1, a method for suppressing main lobe interference of an array antenna includes:
step 101: acquiring an array antenna signal model;
step 102: obtaining a high-precision covariance matrix by adopting a Taylor estimation method according to the array antenna signal model, which specifically comprises the following steps:
obtaining a high-precision covariance matrix by adopting a Taylor estimation method according to the array antenna signal model
Wherein,
piis the power of the i-th interference,
i is an identity matrix, a ═ a (θ) for the estimated noise power, respectively1),…,a(θp+q)]，a(θi) For steering vectors corresponding to the ith disturbance, θiThe direction of the incoming wave of the ith interference.
Step 103: determining an interference subspace according to the high-precision covariance matrix, specifically comprising:
performing characteristic decomposition on the covariance matrix to obtain a decomposed covariance matrix
Determining an interference subspace according to the decomposed covariance matrix, wherein the interference subspace is formed by UsThe column vector of (1).
Step 104: obtaining a main lobe region subspace, specifically comprising:
according to the main lobe interval, by using the formula H ═ integral-φa(θ)aH(theta) do theta and
determining a main lobe region subspace, the main lobe region subspace is formed by U1The column vector of (1);
wherein, ω isiFor the ith feature value, in descending order, viFor corresponding eigenvectors, Λ1Is front K2Diagonal matrix formed by large eigenvalues, U1Is Λ1Matrix of eigenvectors corresponding to medium eigenvalues, Λ2From the remaining M-K2A characteristic value component, U2Is Λ2And (5) a matrix formed by eigenvectors corresponding to the medium eigenvalues.
Step 105: determining a projection matrix by adopting a subspace intersection solving method according to the main lobe region subspace and the interference subspace, and specifically comprising the following steps:
performing singular value decomposition on the main lobe region subspace and the interference subspace to obtain a principal angle and a principal vector between the main lobe region subspace and the interference subspace;
determining a common vector of the main lobe region subspace and the interference subspace according to the principal angle and the principal vector, wherein the common vector is a vector corresponding to the main lobe interference;
determining a projection matrix B (I-GG) according to the vector corresponding to the main lobe interferenceH；
Wherein, G is a matrix formed by vectors corresponding to the main lobe interference, I is a unit matrix, and B is a projection matrix.
Step 106: preprocessing the interference and noise signal according to the projection matrix to obtain a preprocessed covariance matrix, which specifically comprises:
obtaining a covariance matrix after projection preprocessing according to the projection matrix
Wherein R isYIs a pre-processed covariance matrix, uiFor corresponding feature vectors, λiIs the ith eigenvalue, and B is the projection matrix.
Step 107: correcting the preprocessed covariance matrix by adopting a diagonal loading method to obtain a corrected covariance matrix, which specifically comprises the following steps:
correcting the preprocessed covariance matrix by adopting a diagonal loading method to obtain a corrected covariance matrix
Wherein,
for diagonal loading of factors, take
I is an identity matrix, RYIs the pre-processed covariance matrix,
is a modified covariance matrix.
Step 108: determining an adaptive weight vector according to the corrected covariance matrix, specifically comprising:
determining an adaptive weight vector according to the modified covariance matrix
Wherein, a (theta)s) As a guide vector of the desired signal, thetasW is the adaptive weight vector for the incoming direction of the desired signal.
Step 109: and determining an array output signal according to the self-adaptive weight vector.
The method is based on a main lobe interference suppression algorithm for intersection calculation of Taylor estimation and subspace, the method adopts the Taylor estimation to obtain a high-precision covariance matrix INCM, and characteristic decomposition is carried out on the covariance matrix INCM to obtain an interference subspace. And constructing a main lobe region subspace by using the priori knowledge, solving the intersection of the main lobe region subspace and the interference subspace and the vector corresponding to the main lobe interference, and further constructing a characteristic projection matrix. And correcting the covariance matrix after feature projection preprocessing by utilizing diagonal loading, and then solving the adaptive weight vector to inhibit side lobe interference. Compared with a sampling covariance matrix, the covariance matrix obtained by Taylor estimation has higher precision, the method can effectively inhibit the interference of a plurality of main lobes, has good robustness under the condition of low snapshot, and has higher output signal-to-interference-plus-noise ratio (SINR).
Example 2:
fig. 2 is a structural diagram of the array antenna main lobe interference suppression system of the present invention. As shown in fig. 2, an array antenna main lobe interference suppression system includes:
a first obtaining module 201, configured to obtain an array antenna signal model;
the Taylor estimation module 202 is used for obtaining a high-precision covariance matrix by adopting a Taylor estimation method according to the array antenna signal model;
an interference subspace determination module 203, configured to determine an interference subspace according to the high-precision covariance matrix;
a second obtaining module 204, configured to obtain a main lobe region subspace;
a projection matrix determining module 205, configured to determine a projection matrix by using a subspace intersection method according to the main lobe region subspace and the interference subspace;
a preprocessing module 206, configured to preprocess the interference plus noise signal according to the projection matrix, to obtain a preprocessed covariance matrix;
a correction module 207, configured to correct the preprocessed covariance matrix by using a diagonal loading method to obtain a corrected covariance matrix;
an adaptive weight vector determining module 208, configured to determine an adaptive weight vector according to the modified covariance matrix;
an array output signal determining module 209 is configured to determine an array output signal according to the adaptive weight vector.
The taylor estimation module 202 specifically includes:
a Taylor estimation unit for obtaining a high-precision covariance matrix by using Taylor estimation method according to the array antenna signal model
Wherein,
piis the power of the i-th interference,
i is an identity matrix, a ═ a (θ) for the estimated noise power, respectively1),…,a(θp+q)]，a(θi) For steering vectors corresponding to the ith disturbance, θiThe direction of the incoming wave of the ith interference.
Example 3:
an array antenna main lobe interference suppression method comprises the following steps:
step 301: acquiring an array antenna signal model;
consider a Uniform Linear Array (ULA) consisting of M array elements spaced one-half wavelength apart. Firstly, the antenna only receives signals and does not transmit signals, and the obtained snapshot data only contains interference and noise and does not contain expected signals and serves as training data. Assuming interference and interference, the interference and noise are independent of each other, and all signalsAre narrow-band far-field signals. Wherein the number of main lobe interference is p, the number of side lobe interference is q, and the incidence angle is theta in sequence1,…,θp+q. The training data received by the array is:
wherein a (theta)i) For steering vectors corresponding to the ith disturbance, θiThe direction of the incoming wave of the ith interference. si(t) is the complex envelope of the ith disturbance at time t. n (t) is a variance of
White gaussian noise. The theoretical INCM can be expressed as:
wherein p isiIs the power of the ith interference, I is the identity matrix, (. C)HIs known as Hermite. In practical situations, the theoretical INCM is difficult to obtain, and is often replaced by a sampling covariance matrix with a fast beat number K:
and then calculating an adaptive weight vector by utilizing Sampling Matrix Inversion (SMI):
wherein a (theta)s) As a guide vector of the desired signal, thetasIs the incoming wave direction of the desired signal. Although the sampling covariance matrix is the maximum likelihood estimate of the theoretical covariance matrix, the estimation error is large under low-snapshot conditions. Finally, the adaptive weight vector calculated by using the training data processes the actually received data (including the expected signal), and the signal y (t) output by the array can be expressed as:
Y(t)＝wHX(t) (4)
step 302: obtaining a high-precision covariance matrix by adopting a Taylor estimation method according to the array antenna signal model;
in order to reduce the estimation error of the covariance matrix under the condition of low snapshot, the basic measure is to find a covariance matrix estimation method with stronger robustness. Taylor estimation is a robust covariance matrix estimation method, and the expression is
Since in the array signal model, the covariance matrix has a known structure:
wherein a ═ a (θ)1),…,a(θp+q)]，P＝diag(p1,…,pp+q). Can be further simplified into
Wherein
The guide vector of the signal can be solved by the space spectrum estimation theory, so that only the matrix needs to be solved
An estimate is made, converting the problem into:
is solved by iterative algorithm
The iterative process is shown in table 1:
TABLE 1 Taylor estimation iterative Algorithm
In the first table, the first table shows,
in order to improve the calculation accuracy, the interference power is obtained by utilizing Capon spectrum estimation of a sampling covariance matrix as
Initial value of (2)
Therefore, it is
Obtaining a diagonal matrix through L iterations
The noise received by each array element is independently and equally distributed and follows Gaussian distribution. The noise power is replaced by the average of the estimated noise power:
finally, the covariance matrix after Taylor estimation is
Step 303: determining an interference subspace according to the high-precision covariance matrix;
firstly, the Taylor estimation is utilized to solve the high-precision covariance matrix, and the characteristic decomposition is carried out on the covariance matrix
Wherein
The ith characteristic value is arranged according to descending order. u. ofiIs the corresponding feature vector. u. of1,…,up+qOpening into an interference subspace, and a (theta)1),…,a(θp+q) The same subspace is spanned. Noise subspace is formed by up+q+1,…,uMAnd (5) stretching. Lambdas,ΛnDiagonal eigenvalue arrays, U, representing interference and noise, respectivelys,U1Respectively representing the corresponding interference eigenvector and the matrix formed by the noise eigenvector. First, the main lobe width BW can be obtained by using the geometrical structure of the ULA and the incoming wave direction of the desired signal0：
Where λ is the wavelength of the desired signal and d is the array element spacing. Then the main lobe interval is:
φ＝(θs-BW0/2,θs+BW0/2) (11)
step 304: acquiring a main lobe region subspace;
after the main lobe interval is determined, the main lobe region subspace is solved by using the following formulas (12) to (13):
H＝∫φa(θ)aH(θ)dθ (12)
where a (θ) represents the steering vector of the signal, and θ is the direction of arrival of the signal in the main lobe interval. The integral matrix H is subjected to a feature decomposition,
for the ith feature value, in descending order, viIs the corresponding feature vector. Lambda1Is front K2Diagonal matrix formed by large eigenvalues, U1A matrix of corresponding eigenvectors. Lambda2From the remaining M-K2A characteristic value component, U2A matrix of corresponding eigenvectors. H is obtained by integrating the pilot vector of the signal in the main lobe interval, so U1The feature vector in (a) may approximately span the main lobe region subspace.
Step 305: and determining a projection matrix according to the main lobe region subspace and the interference subspace. The method specifically comprises the following steps:
step 1: obtaining a projection matrix by utilizing a subspace intersection solving algorithm, wherein the subspace intersection solving algorithm comprises the following specific steps:
wherein K1＝p+q。
Step 2: performing singular value decomposition on the matrix C, and calculating principal angles and principal vectors of a main lobe region subspace and an interference subspace
THCV＝diag(cosθ1,…,cosθb) (15a)
UsT(:,1:b)＝[s1,…,sb] (15b)
U1V(:,1:b)＝[l1,…,lb] (15c)
Where b is min { K ═ min { (K)1,K2}. When cos theta is satisfiedkWhen 1, skOr lkThe vector is a common vector in the main lobe region subspace and the interference subspace, namely a vector corresponding to the main lobe interference.
And step 3: let τ be a constant close to 1. When cos theta is satisfiedkWhen t is greater than or equal to t, cos theta is approximately consideredk1. The subspace after intersection is therefore:
ran(U1)∩ran(Us)＝span{s1,…,sp}＝span{l1,…,lp} (16)
G＝[s1,…,sp]and forming a matrix for the vector corresponding to the main lobe interference. The projection matrix can thus be represented as
B＝I-GGH (17)
Wherein, G is a matrix formed by vectors corresponding to the main lobe interference. Carrying out characteristic projection preprocessing on the received data, wherein the processed data is as follows:
Y(t)＝BX(t) (18)
where x (t) is the actual received data. The computation complexity of the subspace intersection-solving algorithm is
Due to K1And K2Are all less than M, so the computational complexity is lower than SMF (O (M)3))。
Step 306: and preprocessing the interference and noise signals according to the projection matrix to obtain a preprocessed covariance matrix, and correcting the preprocessed covariance matrix by adopting a diagonal loading method to obtain a corrected covariance matrix.
Although the main lobe interference is removed by the characteristic projection preprocessing, a covariance matrix SINCM only containing side lobe interference and noise is obtained, but the covariance matrix can generate a certain degree of mismatch. Analyzing the SINCM mismatching mechanism, wherein the covariance matrix after feature projection preprocessing is as follows:
since G is a vector corresponding to the main lobe interference, therefore:
it can be seen that after the feature projection preprocessing, the feature vector corresponding to the main lobe interference is close to 0, and the covariance matrix is no longer full rank. Thus, calculating the adaptive weight vector using equation (3) results in a main beam offset. In order to eliminate the above-mentioned effects, the preprocessed covariance matrix must be corrected. The diagonal loading can effectively reduce the dispersion of small eigenvalues and reduce the distortion of the covariance matrix. The diagonally loaded covariance matrix can be expressed as:
wherein
For diagonal loading of factors, take
Step 307: determining an adaptive weight vector according to the corrected covariance matrix, wherein the adaptive weight vector can be calculated as follows:
step 308: determining an array output signal based on the adaptive weight vector, the array output signal being represented as:
Z(t)＝WHY(t)＝WHBX(t) (23)
according to the above, the method is divided into three parts, namely, a high-precision covariance matrix INCM is obtained by using Taylor estimation. Firstly, interference power is obtained by Capon spectrum estimation as an initial value. Secondly, the interference and noise power is solved iteratively. And finally, replacing the average value of the noise power with the noise power. Secondly, the subspace is used for solving the intersection to obtain a projection matrix. First, the INCM is subjected to feature decomposition to obtain an interference subspace. Then, the main lobe area subspace is obtained according to the prior information such as the incoming wave direction of the expected signal and the array geometric structure. And finally, obtaining a vector corresponding to the main lobe interference through the intersection of the main lobe region subspace and the interference subspace and calculating a projection matrix. And thirdly, utilizing the covariance matrix after diagonal loading correction preprocessing and calculating the self-adaptive weight vector. Firstly, the preprocessed covariance matrix is corrected by using the diagonal loading component. Then, an adaptive weight vector is calculated using the modified covariance matrix.
Example 4:
and selecting a uniform linear array with array element interval of half wavelength, wherein the number of the array elements is 16. Assuming that the incoming direction of the desired signal is 0 °, the signal-to-noise ratio (SNR) is 0 dB. The noise is white gaussian noise with zero mean and unit variance. The number of fast beats is 100 and the number of monte carlo simulations is 200. The main lobe interference has an incoming wave direction of (-4 °,5 °) and interference-to-noise ratios (INRs) of 10dB and 0dB, respectively. The incoming wave direction of the sidelobe interference is (-25 degrees, 35 degrees), and the INR is 5 dB. τ is 0.98, K2＝5。
The estimation error of the covariance matrix INCM has a large influence on the algorithm of the feature subspace class. Although the sampling covariance matrix is a maximum likelihood estimate of the theoretical INCM, the estimation error tends to be large under low snapshot conditions. The estimation error of the covariance matrix is calculated by using the standard mean square error (NMSE):
each set of experimental data is the average result of 200 monte carlo experiments, the iteration number L is 100, and the simulation result is shown in fig. 3. Fig. 3 shows the estimation error of the covariance matrix. The experiment compares the traditional sampling covariance matrix with the Taylor estimation method adopted by the invention. As can be seen from observing the simulation result of fig. 3, the estimation accuracy of the covariance matrix becomes higher and higher as the number of fast beats increases. Under the condition of low snapshot, the estimation error of the conventional sampling covariance matrix is large. The method can effectively improve the estimation precision of the covariance matrix under the condition of low snapshot by adopting a Taylor estimation method.
In order to verify whether the intersection of the main lobe region subspace and the interference subspace can obtain the vector corresponding to the main lobe interference, the following two groups of experiments are carried out. Experiment 1 separately solves the spatial response of the interference subspace, the main lobe region subspace and the post-intersection subspace. The formula for calculating the spatial response is:
where a (θ) is the steering vector of the signal, θ is the incoming wave direction of the signal, U UHAn orthogonal projection matrix for the respective subspace direction. FIG. 4 is a graph of the spatial response of a subspace. Fig. 4 shows the spatial response of three subspaces under the condition of L50. As can be seen from the simulation diagram, the subspace of the main lobe region can better protect the signals in the main lobe region and inhibit the signals outside the main lobe region, and the effect of spatial filtering is achieved. The spatial response of the subspace after intersection is only 1 in the main lobe interference direction, and the other directions approach to 0. Therefore, the common vector generated by the intersection of the two subspaces is the vector corresponding to the main lobe interference.
In a main lobe interference suppression algorithm based on feature projection preprocessing, the estimation accuracy of a vector corresponding to main lobe interference is important. According to the formula (24), the estimation error of the vector corresponding to the main lobe interference is:
wherein
For a matrix of vectors, U, corresponding to the estimated main lobe interferencemIs obtained by theoretical covariance matrix decompositionThe main lobe of (a) interferes with the corresponding vector. Experiment 2 compares the estimation errors of the vectors corresponding to the main lobe interference under the two methods, respectively. Fig. 5 shows an error estimation of a vector corresponding to a main lobe interference. Fig. 5 is an average of 200 monte carlo experiments under L ═ 100. It can be seen from observing fig. 5 that the estimation error of the vector corresponding to the mainlobe interference of the conventional sampling covariance matrix is large under the condition of low snapshot, but the method adopted by the invention has high estimation precision, does not obviously change along with the snapshot number, and has good robustness.
Fig. 6 is an adaptive array pattern, and fig. 6 shows the comparison results between the beam forming pattern of the method of the present invention and the beam forming pattern and the static pattern of the SMI method, the EMP method, the CMR method, the SMF method, and the CCTE method, respectively. Wherein the data used by the SMI method contains the desired signal, L50. As can be seen from the simulation diagram, SMI forms nulls in the main lobe interference direction, the side lobe level is significantly increased, and the main beam is severely distorted. EMP produces a significant main beam offset. Since the CMR can only suppress single main lobe interference, its directional pattern forms null in the other main lobe interference direction, and at the same time, directional pattern distortions such as main beam offset and side lobe level increase are generated. The SMF and CCTE methods and the method of the invention can effectively remove the interference of a plurality of main lobes. Compared with the other two methods, the method of the invention has lower side lobe level and the main beam directional diagram is very close to the static directional diagram (the main beam is not distorted).
In order to compare the output SINR of different algorithms, the output SINR is calculated by adopting a theoretical covariance matrix:
wherein w and B respectively represent adaptive weight vector and feature projection matrix obtained by different algorithms, PsIs the power of the desired signal. Where the SMI algorithm does not involve B. The expression of the optimal output SINR is:
SINRopt＝PsaH(θs)R′-1a(θs) (28)
where R' is the theoretical INCM without mainlobe interference.
Fig. 7 is a graph showing the variation of output SINR with snapshot number under two main lobe interference conditions, and fig. 8 is a graph showing the variation of output SINR with snapshot number under a single main lobe interference condition. The simulation conditions for the presence of a single main lobe interference are as follows: the incoming wave direction of the main lobe interference is 5 degrees, and the INR is 10 dB. The incoming wave direction of the sidelobe interference is-30 degrees, 20 degrees and 40 degrees, and the INR is 30dB, 40dB and 40dB in sequence. The number of monte carlo experiments is 200, and the number of iterations is 50, wherein the training data used by the SMI method contains the expected signal. As can be seen from the simulation diagram, as the number of fast beats increases, the output SINR of all the methods increases. The method has the highest output SINR and has good robustness under the condition of low snapshot number. Although the output SINR gradually approaches the proposed method as the number of snapshots increases, its robustness is inferior to the method proposed by the present invention. SMI is greatly influenced by the snapshot number, and the output SINR is very low under the condition of low snapshot. EMP produces a main beam offset and therefore the output SINR is low. Comparing fig. 7 and fig. 8, it can be seen that the CMR and CCTE algorithms perform well under a single main lobe interference condition, where the CCTE has the highest output SINR. However, in the multi-main lobe interference environment, the performance of both methods is significantly reduced, which is not the method proposed by the present invention.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. For the system disclosed by the embodiment, the description is relatively simple because the system corresponds to the method disclosed by the embodiment, and the relevant points can be referred to the method part for description.
The principles and embodiments of the present invention have been described herein using specific examples, which are provided only to help understand the method and the core concept of the present invention; meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (8)
1. An array antenna main lobe interference suppression method is characterized by comprising the following steps:
acquiring an array antenna signal model;
obtaining a high-precision covariance matrix by adopting a Taylor estimation method according to the array antenna signal model;
determining an interference subspace according to the high-precision covariance matrix;
acquiring a main lobe region subspace;
determining a projection matrix by adopting a subspace intersection solving method according to the main lobe region subspace and the interference subspace;
preprocessing the interference and noise signal according to the projection matrix to obtain a preprocessed covariance matrix;
correcting the preprocessed covariance matrix by adopting a diagonal loading method to obtain a corrected covariance matrix;
determining a self-adaptive weight vector according to the corrected covariance matrix;
determining an array output signal according to the self-adaptive weight vector;
the determining an interference subspace according to the high-precision covariance matrix specifically includes:
performing characteristic decomposition on the covariance matrix to obtain a decomposed covariance matrix
uiFor corresponding feature vectors, λiIs the ith characteristic value;
determining an interference subspace according to the decomposed covariance matrix, wherein the interference subspace is formed by UsThe column vector of (1);
the determining an adaptive weight vector according to the modified covariance matrix specifically includes:
determining an adaptive weight vector according to the modified covariance matrix
Wherein, a (theta)s) As a guide vector of the desired signal, thetasW is the incoming wave direction of the expected signal and is an adaptive weight vector;
determining an array output signal according to the adaptive weight vector specifically includes:
adopting a formula Z (t) W according to the adaptive weight vectorHY(t)＝WHBx (t), determining an array output signal;
wherein Z (t) is the array output signal, X (t) is the actual received data, W is the adaptive weight vector, (. DEG)HFor Hermite transpose, B is the projection matrix.
2. The array antenna main lobe interference suppression method according to claim 1, wherein the obtaining of the high-precision covariance matrix by using a taylor estimation method according to the array antenna signal model specifically includes:
obtaining a high-precision covariance matrix by adopting a Taylor estimation method according to the array antenna signal model
Wherein,
piis the power of the i-th interference,
i is an identity matrix, a ═ a (θ) for the estimated noise power, respectively1),…,a(θp+q)]，a(θi) For steering vectors corresponding to the ith disturbance, θiThe number of the main lobe interferences is p, and the number of the side lobe interferences is q.
3. The array antenna main lobe interference suppression method according to claim 1, wherein the obtaining of the main lobe region subspace specifically includes:
according to the main lobe interval, by using the formula H ═ integral-φa(θ)aH(theta) do theta and
determining a main lobe region subspace, the main lobe region subspace is formed by U1The column vector of (1);
wherein, ω isiFor the ith feature value, in descending order, viFor corresponding eigenvectors, Λ1Is front K2Diagonal matrix formed by large eigenvalues, U1Is Λ1Matrix of eigenvectors corresponding to medium eigenvalues, Λ2From the remaining M-K2A characteristic value component, U2Is Λ2And (5) a matrix formed by eigenvectors corresponding to the medium eigenvalues.
4. The array antenna main lobe interference suppression method according to claim 3, wherein the determining a projection matrix by using a subspace intersection method according to the main lobe region subspace and the interference subspace specifically includes:
performing singular value decomposition on the main lobe region subspace and the interference subspace to obtain a principal angle and a principal vector between the main lobe region subspace and the interference subspace;
determining a common vector of the main lobe region subspace and the interference subspace according to the principal angle and the principal vector, wherein the common vector is a vector corresponding to the main lobe interference;
determining a projection matrix B (I-GG) according to the vector corresponding to the main lobe interferenceH；
Wherein, G is a matrix formed by vectors corresponding to the main lobe interference, I is a unit matrix, and B is a projection matrix.
5. The array antenna main lobe interference suppression method according to claim 4, wherein the preprocessing the interference plus noise signal according to the projection matrix to obtain a preprocessed covariance matrix specifically comprises:
obtaining a covariance matrix after projection preprocessing according to the projection matrix
Wherein R isYIs a pre-processed covariance matrix, uiFor corresponding feature vectors, λiIs the ith eigenvalue, and B is the projection matrix.
6. The array antenna main lobe interference suppression method according to claim 5, wherein the modifying the preprocessed covariance matrix by using a diagonal loading method to obtain a modified covariance matrix specifically comprises:
correcting the preprocessed covariance matrix by adopting a diagonal loading method to obtain a corrected covariance matrix
Wherein,
for loading factors diagonally, take
I is an identity matrix, RYIs the pre-processed covariance matrix,
is a modified covariance matrix.
7. An array antenna main lobe interference mitigation system, comprising:
the first acquisition module is used for acquiring an array antenna signal model;
the Taylor estimation module is used for obtaining a high-precision covariance matrix by adopting a Taylor estimation method according to the array antenna signal model;
the interference subspace determination module is used for determining an interference subspace according to the high-precision covariance matrix;
the second acquisition module is used for acquiring a main lobe region subspace;
the projection matrix determining module is used for determining a projection matrix by adopting a subspace intersection solving method according to the main lobe region subspace and the interference subspace;
the preprocessing module is used for preprocessing the interference and noise signals according to the projection matrix to obtain a preprocessed covariance matrix;
the correcting module is used for correcting the preprocessed covariance matrix by adopting a diagonal loading method to obtain a corrected covariance matrix;
the adaptive weight vector determining module is used for determining an adaptive weight vector according to the corrected covariance matrix;
the array output signal determining module is used for determining an array output signal according to the self-adaptive weight vector;
the interference subspace determination module specifically includes:
a characteristic decomposition unit for performing characteristic decomposition on the covariance matrix to obtain a decomposed covariance matrix
uiFor corresponding feature vectors, λiIs the ith characteristic value;
an interference subspace determination unit, configured to determine an interference subspace according to the decomposed covariance matrix, where the interference subspace is formed by UsThe column vector of (1);
the adaptive weight vector determining module specifically includes:
an adaptive weight vector determining unit for determining an adaptive weight vector according to the modified covariance matrix
Wherein, a (theta)s) As a guide vector of the desired signal, thetasW is the incoming wave direction of the expected signal and is an adaptive weight vector;
the array output signal determining module specifically comprises:
an array output signal determining unit for adopting a formula Z (t) W according to the adaptive weight vectorHY(t)＝WHBx (t), determining an array output signal;
wherein Z (t) is the array output signal, X (t) is the actual received data, W is the adaptive weight vector, (. DEG)HFor Hermite transpose, B is the projection matrix.
8. The array antenna main lobe interference suppression system according to claim 7, wherein the taylor estimation module specifically includes:
a Taylor estimation unit for obtaining a high-precision covariance matrix by using Taylor estimation method according to the array antenna signal model
Wherein,
piis the power of the i-th interference,
i is an identity matrix, a ═ a (θ) for the estimated noise power, respectively1),…,a(θp+q)]，a(θi) For steering vectors corresponding to the ith disturbance, θiThe number of the main lobe interferences is p, and the number of the side lobe interferences is q.
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