CN109799486B - Self-adaptive sum and difference beam forming method - Google Patents
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Abstract
The invention belongs to the field of radars and discloses a sum and difference beam forming method. The method comprises the following steps: firstly, obtaining a difference beam zero-point constraint covariance matrix under an ideal condition, constructing an array error model, then calculating a zero-point constraint covariance mean matrix of the zero-point constraint covariance matrix by using the zero-point constraint covariance matrix and the array error vector, constructing a taper matrix to perform taper processing on the zero-point constraint covariance mean matrix, then constructing a low sidelobe zero-point alignment and beam constraint optimization model and a low sidelobe zero-point alignment difference beam constraint optimization model, solving the model to obtain a sum beam forming optimal weight vector and a difference beam forming optimal weight vector, and further obtaining a low sidelobe zero-point alignment difference beam. The invention can widen the width of the alignment zero while reducing the sidelobe level of the sum and difference beams, thereby improving the anti-interference performance of the radar in the target parameter estimation.
Description
Technical Field
The invention relates to the technical field of radars, in particular to a self-adaptive sum and difference beam forming method.
Background
The radar plays a very important role in target detection and tracking, and with the development of radar technology, phased array radars are increasingly applied to practical engineering projects. At present, increasingly severe and complex working environments put higher requirements on the performance of the radar: the radar also has the capability of self-adaptive interference suppression while finishing the functions of searching, intercepting, tracking, guiding and the like.
The sum and difference beam angle measurement technology has the advantages of simplicity, reliability, small operand, high data rate and the like, so that the sum and difference beam angle measurement technology is widely applied to phased array radars to estimate relevant parameters of targets and has important military and civil values. The sum and difference angle measurement is to form a sum beam and a difference beam at the output end by a certain method, wherein the sum beam is generally called to form a main lobe in the target direction, the difference beam is called to form a null in the target direction, a certain value is obtained by the ratio of the sum beam to the difference beam, and then the target angle is found by looking up a table. When the sum and difference beam angle measurement technology is used in the phased array radar, external interference can affect the performance of beam forming. For the interference with the known position, the influence of the interference on the performance of the radar array can be greatly reduced by generating the beam zero point at the corresponding angle. However, in many cases, the location of the disturbance is unknown. To solve this problem, adaptive null-forming techniques including adaptive digital beam-forming (ADBF) and space-time adaptive processing (STAP) techniques have been proposed. The self-adaptive zero point forming technology enables a directional diagram null point of the radar antenna to be aligned to the interference direction in a self-adaptive mode on the premise of ensuring the large gain receiving of the expected signal, so that the interference is restrained or the strength of the interference signal is reduced. Relevant researches show that when the zero point (except the center zero point) of the difference beam is positioned at the position of the sum beam zero point, the radar has higher output signal-to-interference-and-noise ratio and strong anti-interference performance. However, in an actual scenario, array errors including cell amplitude and phase errors, cell position errors, and inter-cell mutual coupling inevitably exist, in this case, the sum and difference beam nulls deviate from the ideal position, the misalignment phenomenon is more serious, and it is difficult to align the sum and difference beam nulls by the existing adaptive beam forming method. Meanwhile, array errors can also cause the elevation of the sidelobe level of the sum and difference beams, so that the self-adaptive interference suppression performance of the radar array is greatly reduced.
Disclosure of Invention
Embodiments of the present invention provide an adaptive sum and difference beam forming method, which is capable of forming a sum and difference beam with low side lobe null alignment in the presence of a cell amplitude and phase error, a cell position error, and an array error including inter-cell coupling.
In order to achieve the above purpose, the embodiment of the invention adopts the following technical scheme:
And 2, constructing an array error vector model of the phased array radar.
And 3, calculating a zero point constraint covariance mean matrix of the zero point constraint covariance matrix by using the zero point constraint covariance matrix and the array error vector.
And 4, constructing a tapering matrix, and tapering the zero constraint covariance mean matrix by using the tapering matrix to obtain the zero constraint covariance mean matrix after tapering.
Step 6, solving the low sidelobe zero alignment and beam constraint optimization model to obtain a sum beam forming optimal weight vector, and calculating the low sidelobe zero alignment and beam by using the sum beam forming optimal weight vector; and solving the low sidelobe zero alignment difference beam constraint optimization model to obtain a difference beam forming optimal weight vector, and calculating the low sidelobe zero alignment difference beam by using the difference beam forming optimal weight vector.
The invention constructs a generalized array error model, namely uniformly expressing the amplitude-phase error, the position error and the coupling among array elements of the excitation current as the amplitude error and the phase error of each array element response, considering the array error model into the construction of a zero point constraint covariance matrix, and further performing matrix taper processing on the preliminarily estimated zero point constraint covariance matrix, so that the width of an alignment zero point can be widened while the sum-difference beam sidelobe level is reduced, and the anti-interference performance of the radar in the target parameter estimation is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic flow chart of a method for adaptive sum-difference beamforming according to an embodiment of the present invention;
FIG. 2 is a graph of the sum and difference beams obtained in an ideal case and the sum and difference beams obtained in the presence of array errors;
FIG. 3 is a sum beam pattern and a partial magnified view obtained using the method provided by an embodiment of the present invention in the presence of array errors; wherein (a) is the sum beam pattern obtained using the method provided by the embodiments of the present invention in the presence of array errors, (b) is a magnified detail view around 10 °, and (c) is a magnified detail view around 42 °;
FIG. 4 is a diagram of a poor beam pattern and a partially enlarged view obtained using the method provided by an embodiment of the present invention in the presence of array errors; wherein (a) is a poor beam pattern obtained using the method provided by the embodiments of the present invention in the presence of array errors, (b) is a partial enlarged view around 10 °, and (c) is a partial enlarged view around 42 °.
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.
Fig. 1 is a schematic flow chart of a method for forming adaptive sum and difference beams according to an embodiment of the present invention, and referring to fig. 1, the method for forming adaptive sum and difference beams according to the embodiment of the present invention includes the following steps:
Further, step 1 specifically includes:
(1.1) obtaining difference beams of phased array radar in ideal situation
Wherein w △-ideal The order of a weight vector of a difference beam under an ideal condition is 2 Mx 1, superscript H represents conjugate transpose operation, a (theta) is a steering vector of the phased array radar, and the order is 2 Mx 1; l. the △ A coning weight vector for reducing the side lobe level of the difference beam, the order is 2 Mx 1; as an example, the number of array elements is Ma Ji and 2M is the number of array elements of the phased array radar.
(1.2) computing the set of initial nulls for the difference beam in the ideal case
N is the number of initial zeros, and the initial zeros are stored in the initial zero column vector
Wherein, θ initial Is N x 1, and is,
η is the radiation field strength of the radar antenna.
(1.3) defining the angular dimension sampling interval Δ θ Removing the first element in the initial zero column vector to form
Removing the Nth element in the initial zero column vector to form
Order to
Find out the
Is greater than the angle dimension sampling interval delta θ And placing these elements in said
The sequence numbers in the sequence are arranged from small to large and then stored in a column vector B d Performing the following steps; b is d (q) is the column vector B d The q element of (1); q =1,2, …, P.
(1.4) reacting the theta initial The elements in (1) are divided into P +1 groups, and the group consisting of the elements in group 1 is
The set of elements in the m-th group is
The set of elements of group P +1 is
And removing therefrom the first
And calculating the average value of the rest P groups, and forming the set of difference beam zero points in the ideal case by using the obtained P average values 1 ,θ 2 ,…,θ P }，θ 1 ,<θ 2 <…<θ P (ii) a Wherein m =2,3, …, P.
(1.5) using all zeros in the difference beam zero set in the ideal case, computing a zero-constrained covariance matrix R in the ideal case,
wherein, the order of R is 2 Mx 2M, theta p The p-th zero point in the zero point set of the difference beam under the ideal condition; p is the {1,2, …, P }, a (theta) p ) The order of the array steering vector of the p-th zero point is 2M multiplied by 1.
And 2, constructing an array error vector model of the phased array radar.
Further, the method for constructing the array error vector model of the phased array radar specifically comprises the following steps: constructing array error vectors of L phased array radars: the ith array error vector comprises error models of 2M array elements, and the error model of the mth array element in the error models of the 2M array elements of the ith array error vector is
Further obtain the first array error vector e l ，e l ＝[e 1 l ,e 2 l ,…,e 2M l ]。
Wherein L is ∈ {1,2, …, L }, e l The order of (2M) is 2M multiplied by 1, M =1, …,2M and 2M are the number of array elements of the phased array radar, alpha m l Representing the amplitude response error of the m-th array element in the ith array error vector
Obedience mean 0 and variance
A gaussian distribution of (d); beta is a m l Indicating the phase response error of the m-th array element in the ith array error vector
Obedience mean is 0 and variance is
A gaussian distribution of (a).
And 3, calculating a zero point constraint covariance mean matrix of the zero point constraint covariance matrix by using the zero point constraint covariance matrix and the array error vector.
Further, step 3 specifically includes:
(3.1) calculating zero point constraint covariance matrixes under L error conditions: the first zero constraint covariance matrix in the presence of errors is
Wherein, a e (θ p )＝e l ⊙a(θ p ) The order is 2 Mx 1; e.g. of the type l Is the ith array error vector; e l ＝e l (e l ) H Is the l-th error matrix, E l The order of (a) is 2M × 2M; l is from {1,2, …, L }.
(3.2) calculating the zero point constraint covariance mean matrix of the zero point constraint covariance matrix under the condition of L errors
Wherein the content of the first and second substances,
of order 2M×2M。
And step 4, constructing a tapering matrix, and tapering the zero point constraint covariance mean matrix by using the tapering matrix to obtain the zero point constraint covariance mean matrix after tapering.
Preferably, step 4 specifically comprises:
constructing a tapering matrix T, wherein the element of the a-th row and the b-th column of the tapering matrix T is T ab ＝exp[-(a-b) 2 ξ]Tapering the zero point constraint covariance mean matrix by using a tapering matrix to obtain the zero point constraint covariance mean matrix after tapering
Wherein exp [. Cndot. ] represents an exponential function with a natural number e as the base, a and b are respectively in the group of {1,2, …,2M }, the order of the tapering matrix T is 2M multiplied by 2M, xi is the tapering coefficient, and xi is larger than 0.
Further, step 5 specifically includes:
(5.1) constructing a low sidelobe null alignment and beam constraint optimization model:
constraint (w) Σ ') H (a(θ 0 )⊙l Σ ) =1 beam pointing to ensure sum beam in optimization problem is θ 0 ，w Σ ' is a sum beamforming weight vector, θ 0 Is a target angle,/ Σ Are tapered weight vectors used to reduce sum beam sidelobe levels.
(5.2) construction ofAnd (3) a low side lobe zero alignment difference beam constraint optimization model:
wherein the constraint (w) △ ') H C＝f T In the optimization problem to ensure the difference beam is in theta 0 Form a zero point, w △ ' is a difference beam forming weight vector, C = [ (a (theta) = 0 )⊙l Σ ) T ,(b(θ 0 )⊙l △ ) T ] T ，f＝[0,1] T ，b(θ 0 )＝a(θ 0 )⊙b △ ，
1 M Is a column vector with elements of all 1 and the order of 2M multiplied by 1,l △ The order of the tapering weight vector for reducing the difference beam sidelobe level is 2M × 1.
Step 6, solving the low side lobe zero alignment and beam constraint optimization model to obtain a sum beam forming optimal weight vector, forming the optimal weight vector by using the sum beam, and calculating the low side lobe zero alignment and beam; and solving the low sidelobe zero alignment difference beam constraint optimization model to obtain a difference beam forming optimal weight vector, forming the optimal weight vector by using the difference beam, and calculating the low sidelobe zero alignment difference beam.
Further, step 6 specifically includes:
(6.1) solving a low sidelobe zero alignment and beam constraint optimization model: obtaining the optimal weight vector w of sum beam forming Σ ：
The order is 2 MX 1; computing low sidelobe null alignment and beam Y Σ ：Y Σ ＝(w Σ ) H a(θ)。
(6.2) solving a low sidelobe zero alignment difference beam constraint optimization model: obtaining the optimal weight vector w of the difference beam forming △ ：
The order is 2 MX 1; calculating low sidelobe zerosPoor spot alignment beam Y △ ：Y △ ＝(w △ ) H a(θ)。
The invention constructs a generalized array error model, namely uniformly expressing the amplitude-phase error, the position error and the coupling among array elements of the excitation current as the amplitude error and the phase error of each array element response, considering the array error model into the construction of a zero point constraint covariance matrix, and further performing matrix taper processing on the preliminarily estimated zero point constraint covariance matrix, so that the width of an alignment zero point can be widened while the sum-difference beam sidelobe level is reduced, and the anti-interference performance of the radar in the target parameter estimation is improved.
Further, the beneficial effects of the invention are verified by simulation experiments as follows:
simulation conditions are as follows: in the ith array error vector
Obedience mean 0 and variance
Of the gaussian distribution, wherein the variance σ 1 Satisfies the conditions
Beta in the ith array error vector 1 l ,β 2 l ,…,β 2M l Obedience mean is 0 and variance is
Of the gaussian distribution, wherein the variance σ 2 Satisfies the conditions
Referring to fig. 2, case1 is the sum and difference beams in the ideal Case, case2 is the sum and difference beams in the presence of amplitude response errors and phase response errors, and in both cases, the sum beam uses-35 dB chebyshev amplitude tapering weights and the difference beam does not use amplitude tapering weights. As can be seen from fig. 2, in the presence of array errors, the null misalignment between the sum beam and the difference beam is severe, the side lobe level of the sum beam is raised by 13dB, and the side lobe level of the difference beam is raised by 4dB, compared with the ideal case.
Fig. 3 is a sum beam obtained by the method of the present invention in the presence of an amplitude response error and a phase response error. Wherein (a) is the sum beam pattern obtained using the method provided by the embodiments of the present invention in the presence of array errors, (b) is a magnified detail view around 10 °, and (c) is a magnified detail view around 42 °. FIG. 3 (a) is obtained by comparing the analysis with FIG. 2, and the covariance matrix is constrained based on the zero point
The obtained weight vector forms a sum beam, and the sidelobe level of the sum beam is reduced by 7dB. To pair
The matrix tapering process is performed and the sidelobe level of the sum beam is reduced by 3dB. See and use with reference to FIGS. 3 (b) and 3 (c)
Obtained sum beam, using
The null of the resulting sum beam is further broadened.
Fig. 4 shows a difference beam obtained by the method of the present invention in the presence of an amplitude response error and a phase response error. Wherein (a) is a poor beam pattern obtained using the method provided by the embodiments of the present invention in the presence of array errors, (b) is a partial enlarged view around 10 °, and (c) is a partial enlarged view around 42 °. FIG. 4 (a) is obtained by comparing the analysis of FIG. 2 with the covariance matrix based on the zero point constraint
The side lobe level of the difference beam formed by the obtained weight vector is reduced2dB lower. To pair
The matrix tapering process is performed and the sidelobe level of the sum beam is reduced by 3.7dB. See and use with reference to FIGS. 4 (b) and 4 (c)
Obtained difference beam comparison, using
The null of the obtained difference beam is further broadened.
As can be seen from fig. 3 and 4, the sum and difference beams obtained by the method can widen the width of the alignment zero while reducing the sidelobe level of the sum and difference beams, thereby improving the anti-interference performance of the radar in the target parameter estimation.
Those of ordinary skill in the art will understand that: all or part of the steps for implementing the method embodiments may be implemented by hardware related to program instructions, and the program may be stored in a computer readable storage medium, and when executed, the program performs the steps including the method embodiments; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily think of the changes or substitutions within the technical scope of the present invention, and shall cover the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (6)
1. A sum and difference beamforming method, comprising the steps of:
step 1, obtaining a difference beam of a phased array radar under an ideal condition, calculating a set of difference beam zeros under the ideal condition, and calculating a zero constraint covariance matrix under the ideal condition according to the set of difference beam zeros;
the step 1 specifically comprises:
(1.1) obtaining difference beams of phased array radar in ideal situation
Wherein w △-ideal The order of a weight vector of a difference beam under an ideal condition is 2 Mx 1, the superscript H represents conjugate transpose operation, a (theta) is a guide vector of the phased array radar, and the order is 2 Mx 1; l. the △ The order of the tapered weight vector used for reducing the side lobe level of the difference beam is 2 Mx 1; an element number of the phased array radar is as high as Ma Ji, and 2M is;
(1.2) computing the set of initial nulls for the difference beam in the ideal case
N =1,2, … N, N being the number of initial zeros stored in the initial zero column vector
Wherein, θ initial The dimension of (a) is N x 1,
eta is the radiation field intensity of the radar antenna;
(1.3) defining the angular dimension sampling interval Δ θ Removing the first element in the initial zero column vector to form
Removing the Nth element in the initial zero column vector to form
Order to
Find out the
Is larger than the angular dimension sampling interval delta θ And placing these elements in said
The sequence numbers in the sequence are arranged from small to large and then stored in a column vector B d Performing the following steps; b is d (q) is the column vector B d The q element of (1); q =1,2, …, P;
(1.4) reacting the theta initial The elements in (1) are divided into P +1 groups, and the group consisting of the elements in group 1 is
The set of elements in the m-th group is
The set of elements of group P +1 is
And removing therefrom the first
And calculating the average value of the rest P groups, and forming the set of difference beam zero points in the ideal situation by using the obtained P average values 1 ,θ 2 ,…,θ P }，θ 1 ,<θ 2 <…<θ P (ii) a Wherein m =2,3, …, P;
(1.5) calculating a null-constrained covariance matrix R in the ideal case using all nulls in the difference beam null set in the ideal case,
wherein, the order of R is 2 Mx 2M, theta p In the null set for the difference beam in the ideal caseThe p-th zero point; p is the {1,2, …, P }, a (theta) p ) The array steering vector of the p-th zero point is an order of 2 Mx 1;
step 2, constructing an array error vector model of the phased array radar;
step 3, calculating a zero point constraint covariance mean matrix of the zero point constraint covariance matrix by using the zero point constraint covariance matrix and the array error vector;
step 4, constructing a tapering matrix, and tapering the zero constraint covariance mean matrix by using the tapering matrix to obtain the zero constraint covariance mean matrix after tapering;
step 5, constructing a low-sidelobe zero alignment and beam constraint optimization model and a low-sidelobe zero alignment difference beam constraint optimization model according to a target optimization criterion by using the zero constraint covariance mean matrix after the tapering processing; the optimization criterion is that the array of the phased array radar can radiate minimum energy from an expected zero point under the condition of meeting an expected target-oriented undistorted response;
step 6, solving the low sidelobe zero alignment and beam constraint optimization model to obtain a sum beam forming optimal weight vector, and calculating the low sidelobe zero alignment and beam by using the sum beam forming optimal weight vector; and solving the low sidelobe zero alignment difference beam constraint optimization model to obtain a difference beam forming optimal weight vector, and calculating the low sidelobe zero alignment difference beam by using the difference beam forming optimal weight vector.
2. The method according to claim 1, wherein step 2 is specifically:
constructing array error vectors of L phased array radars: the ith array error vector comprises error models of 2M array elements, and the error model of the mth array element in the error models of the 2M array elements of the ith array error vector is
Further obtain the first array error vector e l ，e l ＝[e 1 l ,e 2 l ,…,e 2M l ]；
Wherein L is ∈ {1,2, …, L }, e l The order of (2M) is 2M multiplied by 1, M =1, …,2M and 2M are the number of array elements of the phased array radar, alpha m l Representing the amplitude response error of the m-th array element in the ith array error vector
Obey mean 0 and variance
A gaussian distribution of (d); beta is a m l Indicating the phase response error of the m-th array element in the ith array error vector, beta in the ith array error vector 1 l ,β 2 l ,…,β 2M l Obedience mean 0 and variance
A gaussian distribution of (a).
3. The method according to claim 1, wherein step 3 specifically comprises:
(3.1) calculating zero point constraint covariance matrixes under L error conditions: the first zero constraint covariance matrix in the presence of errors is
Wherein, a e (θ p )＝e l ⊙a(θ p ) The order is 2 Mx 1; e.g. of a cylinder l Is the l-th array error vector; e l ＝e l (e l ) H Is the l-th error matrix, E l The order of (a) is 2M × 2M; l belongs to {1,2, …, L };
(3.2) calculating the zero point constraint covariance mean matrix of the zero point constraint covariance matrixes under the L error conditions
Wherein the content of the first and second substances,
the order of (2M) is 2 M.times.2M.
4. The method according to claim 1, wherein step 4 is specifically: constructing a tapering matrix T, wherein the element of the a-th row and the b-th column of the tapering matrix T is T ab ＝exp[-(a-b) 2 ξ]Tapering the zero point constraint covariance mean matrix by using the tapering matrix to obtain the zero point constraint covariance mean matrix after tapering
Wherein exp [. Cndot. ] represents an exponential function with a natural number e as a base, a and b ∈ {1,2, …,2M }, the order of the tapering matrix T is 2M multiplied by 2M, ξ is a tapering coefficient, and ξ is greater than 0.
5. The method according to claim 1, wherein the step 5 specifically comprises:
(5.1) constructing a low sidelobe null alignment and beam constraint optimization model:
constraint (w) Σ ') H (a(θ 0 )⊙l Σ ) =1 beam pointing to ensure sum beam in optimization problem is θ 0 ，w Σ ' is a sum beamforming weight vector,θ 0 is a target angle,/ Σ A tapering weight vector for reducing sum beam sidelobe levels;
(5.2) constructing a low sidelobe null alignment difference beam constraint optimization model:
wherein the constraint (w) △ ') H C＝f T In the optimization problem to ensure the difference beam is in theta 0 Form a zero point, w △ ' is a difference beam forming weight vector, C = [ (a (theta) = 0 )⊙l Σ ) T ,(b(θ 0 )⊙l △ ) T ] T ，f＝[0,1] T ，b(θ 0 )＝a(θ 0 )⊙b △ ，
1 M Is a column vector with elements of all 1 and the order of 2M multiplied by 1,l △ The order of the tapering weight vector for reducing the difference beam sidelobe level is 2M × 1.
6. The method according to claim 1, wherein the step 6 specifically comprises:
(6.1) solving the low side lobe zero alignment and beam constraint optimization model to obtain an optimal weight vector w formed by a sum beam Σ ：
The order is 2 MX 1; computing low sidelobe null alignment and beam Y Σ ：Y Σ ＝(w Σ ) H a(θ)；
(6.2) solving the low sidelobe null alignment difference beam constraint optimization model: obtaining the optimal weight vector w of the difference beam forming △ ：
The order is 2 MX 1; computing low sidelobe null alignment difference beam Y △ ：Y △ ＝(w △ ) H a(θ)。
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