CN109799486A - A kind of adaptive and difference beam forming method - Google Patents
A kind of adaptive and difference beam forming method Download PDFInfo
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Abstract
The invention belongs to field of radar, disclose a kind of and difference beam forming method.This method comprises the following steps: obtaining difference beam zeros constrained covariance matrix ideally first, construct array error model, then the zeros constrained covariance matrix and the array error vector are utilized, calculate the zeros constrained covariance Mean Matrix of the zeros constrained covariance matrix, it constructs taper matrix and taper processing is carried out to zeros constrained covariance Mean Matrix, then the alignment of building low sidelobe zero point and wave beam Constraint Anchored Optimization and low sidelobe zero point are aligned difference beam Constraint Anchored Optimization, solving model obtains forming optimal weight vector with the optimal weight vector of Wave beam forming and difference beam, further obtain low sidelobe zero point alignment difference beam.The present invention broadening can be aligned the width of zero point while reducing and difference beam sidelobe level, to improve interference free performance of the radar in target component estimation.
Description
Technical field
The present invention relates to Radar Technology fields, more particularly to a kind of adaptive and difference beam forming method.
Background technique
Radar plays very important role in target detection and tracking, with the development of Radar Technology, phased array
Radar has been applied to more and more in actual engineering project.Currently, property of the increasingly severe complicated working environment to radar
More stringent requirements are proposed for energy: radar should also have adaptive while completing and the functions such as searching for, intercept and capture, track, guide
The ability of AF panel.
There are simple and reliable, the advantages such as operand is small, data transfer rate is high with difference beam angle measurement technique, therefore be widely used
The relevant parameter that target is estimated in phased-array radar, has important military and civilian value.So-called and poor angle measurement, is to pass through
Some way makes output end formation and wave beam and difference beam and wave beam are i.e. usually said to form main lobe in target direction, and poor
Wave beam is to form null in target direction, and then the value by obtaining a certain determination with difference beam ratio is tabled look-up again finds out target angle
Degree.When in phased-array radar using with difference beam angle measurement technique, extraneous interference can have an impact the performance of Wave beam forming.
Interference can be greatly lowered to radar array performance by generating beam null in respective angles in interference for known location
Influence.However, the position interfered in many cases, is unknown.In order to solve this problem, it proposes including adaptive
Adaptive causing zero_point including digital beam froming (ADBF) and space-time adaptive processing (STAP) technology.Adaptive zero
Point forms technology under the premise of guaranteeing that desired signal large gain is received, is adaptively aligned the directional diagram null of radar antenna
The direction of interference, to inhibit interference or reduce the intensity of interference signal.Correlative study show when difference beam zero point (in
Except heart zero point) be located at and beam null position when, radar output Signal to Interference plus Noise Ratio with higher, strong anti-interference performance.So
And in actual scene, it is inevitably present including unit amplitude phase error, cell position error and inter-element mutual coupling
Array error, the position under ideal conditions can be deviateed with difference beam zero point in this case, it is more tight to be misaligned phenomenon
Weight is difficult to make to be aligned with difference beam zero point by existing Adaptive beamformer method.Meanwhile array error can also cause and
Difference beam sidelobe level is raised, to cause being greatly lowered for the adaptive interference mitigation performance of radar array.
Summary of the invention
The embodiment of the present invention provides a kind of adaptive and difference beam forming method, can there are unit amplitude phase error,
In the case where array error including cell position error and inter-element mutual coupling, wave that low sidelobe zero point is aligned and poor is formed
Beam.
In order to achieve the above objectives, the embodiment of the present invention adopts the following technical scheme that
Step 1, the difference beam for obtaining ideally phased-array radar, calculates the collection of difference beam zero point ideally
It closes, and zeros constrained covariance matrix ideally is calculated according to the set of the difference beam zero point.
Step 2, the array error vector model of phased-array radar is constructed.
Step 3, using the zeros constrained covariance matrix and the array error vector, the zeros constrained association is calculated
The zeros constrained covariance Mean Matrix of variance matrix.
Step 4, taper matrix is constructed, and the zeros constrained covariance Mean Matrix is carried out using the taper matrix
Taper processing obtains taper treated zeros constrained covariance Mean Matrix.
Step 5, it is constructed low using taper treated zeros constrained covariance Mean Matrix according to objective optimization criterion
The alignment of secondary lobe zero point and wave beam Constraint Anchored Optimization and low sidelobe zero point are aligned difference beam Constraint Anchored Optimization；The Optimality Criteria
It can be under conditions of meeting expectation target guiding undistorted response, from spoke from desired zero point for the array of the phased-array radar
The energy of injection is minimum.
Step 6, the low sidelobe zero point alignment and wave beam Constraint Anchored Optimization are solved, is obtained and the optimal power arrow of Wave beam forming
Amount calculates the alignment of low sidelobe zero point and wave beam using the described and optimal weight vector of Wave beam forming；Solve the low sidelobe zero point pair
Neat difference beam Constraint Anchored Optimization, obtains difference beam and forms optimal weight vector, form optimal weight vector using the difference beam, counts
It calculates low sidelobe zero point and is aligned difference beam.
The present invention constructs the array error model of broad sense, i.e., by the amplitude phase error of exciting current, location error and battle array
Coupling between member is collectively expressed as the range error and phase error of each array element response, and the array error model is taken into account zero
In point constraint covariance matrix building, by carrying out further matrix cone to the zeros constrained covariance matrix gone out according to a preliminary estimate
Processing is cut, the width of alignment zero point can be broadened while reducing and difference beam sidelobe level, to improve radar in target
Interference free performance in parameter Estimation.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with
It obtains other drawings based on these drawings.
Fig. 1 is a kind of adaptive and difference beam forming method flow diagram that inventive embodiments provide；
Fig. 2 be ideally obtain and difference beam and there are array error in the case where obtain and difference beam；
Fig. 3 be there are array error in the case where using method provided in an embodiment of the present invention obtain and beam pattern
And partial enlarged view；The sum obtained in the case that wherein (a) is there are array error using method provided in an embodiment of the present invention
Beam pattern is (b) partial enlarged view near 10 °, is (c) partial enlarged view near 42 °；
Fig. 4 be there are array error in the case where the difference beam directional diagram that is obtained using method provided in an embodiment of the present invention
And partial enlarged view；The difference obtained in the case that wherein (a) is there are array error using method provided in an embodiment of the present invention
Beam pattern is (b) partial enlarged view near 10 °, is (c) partial enlarged view near 42 °.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
Fig. 1 is a kind of adaptive and difference beam forming method flow diagram provided in an embodiment of the present invention, referring to Fig.1,
A kind of adaptive and difference beam forming method provided in an embodiment of the present invention, comprising the following steps:
Step 1, the difference beam for obtaining ideally phased-array radar, calculates the collection of difference beam zero point ideally
It closes, and zeros constrained covariance matrix ideally is calculated according to the set of difference beam zero point.
Further, step 1 specifically includes:
(1.1) difference beam of ideally phased-array radar is obtainedWherein
wΔ-idealFor the weight vector of ideally difference beam, order is 2M × 1, and subscript H indicates that conjugate transposition operation, a (θ) are array
The steering vector of radar, order are 2M × 1；lΔFor the taper weight vector for reducing difference beam sidelobe level, order be 2M ×
1；⊙ is Hadamard product, and 2M is the element number of array of array radar.
(1.2) the set θ of the ideally initial zero of difference beam is calculatedinitial={ θn init|fΔ-ideal(θn init)≤
η }, n=1,2 ... N, N are the number of initial zero, and initial zero is stored in initial zero column vectorIn, wherein θinitialDimension be N × 1,η is radar day
The radiation field intensity of line.
It defines angle and ties up sampling interval Δθ, first element removed in the initial zero column vector formedThe n-th element removed in the initial zero column vector is formedIt enablesIt finds out describedIn be greater than the angle dimension sampling interval Δ θ member
Element, and by these elements describedIn serial number arrange from small to large after be stored in column vector BdIn；Bd(q) it is sweared for the column
Measure BdQ-th of element；Q=1,2 ..., P；
(1.4) by the θinitialIn element be divided into P+1 group, the collection that the 1st group of element is constituted is combined intoThe collection that element in m group is constituted is combined intoP+1 group
Element constitute collection be combined intoAnd remove thereinGroup calculates the average value of remaining P group, utilizes
Resulting P average value constitutes the set { θ of the ideally difference beam zero point1, θ2..., θP, θ1, < θ2< ... < θP；
Wherein, m=2,3 ..., P.
(1.5) using all zero points in difference beam zero point set ideally, zero point ideally is calculated
Covariance matrix R is constrained,
Wherein, the order of R is 2M × 2M, θpFor p-th of zero point in the zero point set of ideally difference beam；p∈
{ 1,2 ..., P }, a (θp) be p-th of zero point array steering vector, order be 2M × 1.
Step 2, the array error vector model of phased-array radar is constructed.
Further, the array error vector model of phased-array radar is constructed specifically: the battle array of L phased-array radar of building
Column error vector: first of array error vector includes the error model of 2M array element, 2M battle array of first of array error vector
The error model of m-th of array element is in the error model of memberFurther obtain first of array error arrow
Measure el, el=[e1 l, e2 l..., e2M l]。
Wherein, l ∈ { 1,2 ..., L }, elOrder be 2M × 1, m=1 ..., 2M, 2M is the array element of phased-array radar
Number, αm lThe amplitude response error of m-th of array element in first of array error vector is indicated, in first of array error vectorObeying mean value is 0, and variance isGaussian Profile；βm lM-th gust is indicated in first of array error vector
The phase response error of member, the β in first of array error vector1 l, β2 l..., β2M lObeying mean value is 0, and variance is
Gaussian Profile.
Step 3, using zeros constrained covariance matrix and array error vector, the zero of zeros constrained covariance matrix is calculated
Point constraint covariance Mean Matrix.
Further, step 3 specifically includes:
(3.1) there are the zeros constrained covariance matrixes under error condition for calculating L: there are first under error condition
Zeros constrained covariance matrix is
Wherein, ae(θP)=el⊙a(θP), order is 2M × 1；elFor first of array error vector；El=el(el)HIt is
L error matrix, ElOrder be 2M × 2M；L ∈ { 1,2 ..., L }.
(3.2) there are the zeros constrained covariance Mean Matrixes of zeros constrained covariance matrix under error condition for calculating L
Wherein,Order be 2M × 2M.
Step 4, taper matrix is constructed, and zeros constrained covariance Mean Matrix is carried out at taper using taper matrix
Reason obtains taper treated zeros constrained covariance Mean Matrix.
Preferably, step 4 specifically:
Taper matrix T is constructed, the element of a row b column of taper matrix T is tab=exp [- (a-b)2ξ], utilize taper
Matrix carries out taper processing to zeros constrained covariance Mean Matrix, obtains taper treated zeros constrained covariance mean value square
Battle array
Wherein, exp [] is represented using natural number e as the exponential function at bottom, a, b ∈ { 1,2 ..., 2M }, taper matrix T
Order be 2M × 2M, ξ be taper coefficient, ξ > 0.
Step 5, it is constructed low using taper treated zeros constrained covariance Mean Matrix according to objective optimization criterion
The alignment of secondary lobe zero point and wave beam Constraint Anchored Optimization and low sidelobe zero point are aligned difference beam Constraint Anchored Optimization；Optimality Criteria is phase
The array for controlling battle array radar can be under conditions of meeting expectation target and being oriented to undistorted response, the energy that gives off from desired zero point
Amount is minimum.
Further, step 5 specifically includes:
(5.1) alignment of building low sidelobe zero point and wave beam Constraint Anchored Optimization:About
Beam condition (w∑′)H(a(θ0)⊙l∑)=1 is used to guarantee in optimization problem with the beam position of wave beam to be θ0, w∑' be and wave beam
Form weight vector, θ0For target angle, l∑For for for reducing the taper weight vector with beam side lobe levels.
(5.2) building low sidelobe zero point is aligned difference beam Constraint Anchored Optimization:Wherein constrain
Condition (wΔ′)HC=fT is used to guarantee difference beam in θ in optimization problem0Place forms zero point, wΔ' it is that difference beam forms weight vector,
C=[(a (θ0)⊙l∑)T, (b (θ0)⊙lΔ)T]T, f=[0, l]T, b (θ0)=a (θ0)⊙bΔ,1MFor member
Element is all 1 column vector, and order is 2M × 1, lΔFor the taper weight vector for reducing difference beam sidelobe level, order be 2M ×
1。
Step 6, solve low sidelobe zero point alignment and wave beam Constraint Anchored Optimization, obtain with the optimal weight vector of Wave beam forming,
Using with the optimal weight vector of Wave beam forming, calculate low sidelobe zero point alignment and wave beam；Solve low sidelobe zero point alignment difference beam about
Beam Optimized model obtains difference beam and forms optimal weight vector, forms optimal weight vector using difference beam, calculates low sidelobe zero point pair
Neat difference beam.
Further, step 6 specifically includes:
(6.1) alignment of low sidelobe zero point and wave beam Constraint Anchored Optimization are solved:, it obtains and the optimal weight vector of Wave beam forming
w∑:Order is 2M × 1；Calculate the alignment of low sidelobe zero point and wave beam Y∑: Y∑=(w∑)Ha(θ)。
(6.2) it solves low sidelobe zero point and is aligned difference beam Constraint Anchored Optimization: obtaining difference beam and form optimal weight vector wΔ:Order is 2M × 1；It calculates low sidelobe zero point and is aligned difference beam YΔ: YΔ=(wΔ)Ha(θ)。
The present invention constructs the array error model of broad sense, i.e., by the amplitude phase error of exciting current, location error and battle array
Coupling between member is collectively expressed as the range error and phase error of each array element response, and the array error model is taken into account zero
In point constraint covariance matrix building, by carrying out further matrix cone to the zeros constrained covariance matrix gone out according to a preliminary estimate
Processing is cut, the width of alignment zero point can be broadened while reducing and difference beam sidelobe level, to improve radar in target
Interference free performance in parameter Estimation.
Further, the above-mentioned beneficial effect of the present invention is verified below by way of emulation experiment:
Simulated conditions: in first of array error vectorObeying mean value is 0, and variance isGauss
Distribution, wherein variances sigma1Meet conditionβ in first of array error vector1 l, β2 l..., β2M lIt obeys equal
Value is 0, and variance isGaussian Profile, wherein variances sigma2Meet condition
Referring to Fig. 2, Case1 be ideally and difference beam, Case2 be that there are amplitude response error and phase responses
In the case where error and difference beam, in the case of two kinds and wave beam is all made of the weighting of -35dB Chebyshev amplitude taper, poor wave
Beam does not use amplitude taper to weight.From Figure 2 it can be seen that there are in the case of array error, relative to ideally with wave beam with
The zero point of difference beam is misaligned that phenomenon is serious, and has raised 13dB with the sidelobe level of wave beam, and the sidelobe level of difference beam is raised
4dB.
Fig. 3 be there are in the case where amplitude response error and phase response error, using the method for the present invention it is obtained and
Wave beam.Obtained in the case that wherein (a) is there are array error using method provided in an embodiment of the present invention and beam direction
Figure is (b) partial enlarged view near 10 °, is (c) partial enlarged view near 42 °.Fig. 3 (a) and Fig. 2 comparative analysis
It is available, using based on zeros constrained covariance matrixThe weight vector acquired is formed by and wave beam, sidelobe level drop
Low 7dB.It is rightThe sidelobe level for carrying out the processing of matrix taper and wave beam reduces 3dB again.It can referring to Fig. 3 (b) and Fig. 3 (c)
See and usesIt is obtained to be compared with wave beam, it usesObtained and wave beam zero point is further broadened.
Fig. 4 is there are in the case where amplitude response error and phase response error, using the method for the present invention difference obtained
Wave beam.The difference beam direction obtained in the case that wherein (a) is there are array error using method provided in an embodiment of the present invention
Figure is (b) partial enlarged view near 10 °, is (c) partial enlarged view near 42 °.Fig. 4 (a) and Fig. 2 comparative analysis
It is available, using based on zeros constrained covariance matrixThe weight vector acquired is formed by difference beam, sidelobe level drop
Low 2dB.It is rightThe sidelobe level for carrying out the processing of matrix taper and wave beam reduces 3.7dB again.Referring to Fig. 4 (b) and Fig. 4 (c)
It can be seen that with usingDifference beam obtained is compared, and is usedThe zero point of difference beam obtained is further broadened.
By Fig. 3 and Fig. 4 as it can be seen that using the obtained and difference beam of the present invention can reduce and difference beam sidelobe level it is same
Shi Zhankuan is aligned the width of zero point, to improve interference free performance of the radar in target component estimation.
Those of ordinary skill in the art will appreciate that: realize that all or part of the steps of above method embodiment can pass through
The relevant hardware of program instruction is completed, and program above-mentioned can be stored in a computer readable storage medium, the program
When being executed, step including the steps of the foregoing method embodiments is executed；And storage medium above-mentioned includes: ROM, RAM, magnetic disk or light
The various media that can store program code such as disk.
More than, only a specific embodiment of the invention, but scope of protection of the present invention is not limited thereto, and it is any to be familiar with
Those skilled in the art in the technical scope disclosed by the present invention, can easily think of the change or the replacement, and should all cover
Within protection scope of the present invention.Therefore, protection scope of the present invention should be subject to the protection scope in claims.
Claims (7)
1. a kind of and difference beam forming method, characteristic value are, comprising the following steps:
Step 1, the difference beam for obtaining ideally phased-array radar, calculates the set of difference beam zero point ideally,
And zeros constrained covariance matrix ideally is calculated according to the set of the difference beam zero point；
Step 2, the array error vector model of phased-array radar is constructed；
Step 3, using the zeros constrained covariance matrix and the array error vector, the zeros constrained covariance is calculated
The zeros constrained covariance Mean Matrix of matrix；
Step 4, taper matrix is constructed, and taper is carried out to the zeros constrained covariance Mean Matrix using the taper matrix
Processing obtains taper treated zeros constrained covariance Mean Matrix；
Step 5, low sidelobe is constructed according to objective optimization criterion using taper treated zeros constrained covariance Mean Matrix
Zero point alignment and wave beam Constraint Anchored Optimization and low sidelobe zero point are aligned difference beam Constraint Anchored Optimization；The Optimality Criteria is institute
The array for stating phased-array radar can give off from desired zero point under conditions of meeting expectation target guiding undistorted response
Energy it is minimum；
Step 6, low sidelobe zero point alignment and wave beam Constraint Anchored Optimization are solved, obtain with the optimal weight vector of Wave beam forming,
Using the described and optimal weight vector of Wave beam forming, the alignment of low sidelobe zero point and wave beam are calculated；Solve the low sidelobe zero point alignment
Difference beam Constraint Anchored Optimization obtains difference beam and forms optimal weight vector, forms optimal weight vector using the difference beam, calculates
Low sidelobe zero point is aligned difference beam.
2. the method according to claim 1, wherein the step 1 specifically includes:
(1.1) difference beam of ideally phased-array radar is obtainedWherein wΔ-ideal
For the weight vector of ideally difference beam, order is 2M × 1, and subscript H indicates that conjugate transposition operation, a (θ) are the array thunder
The steering vector reached, order are 2M × 1；lΔFor the taper weight vector for reducing difference beam sidelobe level, order is 2M × 1；
⊙ is Hadamard product, and 2M is the element number of array of array radar；
(1.2) the set θ of the ideally initial zero of difference beam is calculatedinitial={ θn init|fΔ-ideal(θn init)≤η }, n
=1,2 ... N, N are the number of initial zero, and the initial zero is stored in initial zero column vectorIn, wherein θinitialDimension be N × 1,η is radar antenna
Radiation field intensity；
(1.3) it defines angle and ties up sampling interval Δθ, first element removed in the initial zero column vector formedThe n-th element removed in the initial zero column vector is formedIt enablesIt finds out describedIn be greater than the angle tie up sampling interval ΔθMember
Element, and by these elements describedIn serial number arrange from small to large after be stored in column vector BdIn；Bd(q) it is sweared for the column
Measure BdQ-th of element；Q=1,2 ..., P；
(1.4) by the θinitialIn element be divided into P+1 group, the collection that the 1st group of element is constituted is combined into
The collection that element in m group is constituted is combined intoThe collection that the element of P+1 group is constituted is combined intoAnd remove thereinGroup calculates the average value of remaining P group, is constituted using resulting P average value
Set { the θ of the ideally difference beam zero point1, θ2..., θP, θ1, < θ2< ... < θP；Wherein, m=2,3 ...,
P；
(1.5) using all zero points in the difference beam zero point set ideally, zero point ideally is calculated
Covariance matrix R is constrained,
Wherein, the order of R is 2M × 2M, θpFor p-th of zero point in the zero point set of the ideally difference beam；P∈
{ 1,2 ..., P }, a (θp) be p-th of zero point array steering vector, order be 2M × 1.
3. the method according to claim 1, wherein the step 2 specifically:
Construct the array error vector of the L phased-array radars: first of array error vector includes the error mould of 2M array element
Type, the error model of m-th of array element is in the error model of 2M array element of first of array error vectorFurther obtain first of array error vector el, el=[e1 l, e2 l..., e2M l]；
Wherein, l ∈ { 1,2 ..., L }, elOrder be 2M × 1, m=1 ..., 2M, 2M be phased-array radar element number of array,
αm lThe amplitude response error of m-th of array element in first of array error vector is indicated, in first of array error vectorObeying mean value is 0, and variance isGaussian Profile Gaussian Profile；βm lIt indicates in first of array error vector
The phase response error of m-th of array element, the β in first of array error vector1 l, β2 l..., β2M lObeying mean value is 0, side
Difference isGaussian Profile.
4. the method according to claim 1, wherein the step 3 specifically includes:
(3.1) there are the zeros constrained covariance matrixes under error condition for calculating L: there are first of zero points under error condition
Constraining covariance matrix is
Wherein, ae(θp)=el⊙a(θp), order is 2M × 1；elFor first of array error vector；El=el(el)HIt is
L error matrix, ElOrder be 2M × 2M；L ∈ { 1,2 ..., L }；
(3.2) there are the zeros constrained covariance Mean Matrixes of zeros constrained covariance matrix under error condition for described L of calculating
Wherein,Order be 2M × 2M.
5. the method according to claim 1, wherein the step 4 specifically:
Taper matrix T is constructed, the element of a row b column of the taper matrix T is tab=exp [- (a-b)2ξ], using described
Taper matrix carries out taper processing to the zeros constrained covariance Mean Matrix, obtains taper treated zeros constrained association side
Poor Mean Matrix
Wherein, exp [] is represented using natural number e as the exponential function at bottom, a, b ∈ { 1,2 ..., 2M }, the rank of taper matrix T
Number is 2M × 2M, and ξ is taper coefficient, ξ > 0.
6. the method according to claim 1, wherein the step 5 specifically includes:
(5.1) alignment of building low sidelobe zero point and wave beam Constraint Anchored Optimization:Constrain item
Part (w∑′)H(a(θ0)⊙lΣ)=1 is used to guarantee in optimization problem with the beam position of wave beam to be θ0, w∑' be and Wave beam forming
Weight vector, θ0For target angle, l∑For for for reducing the taper weight vector with beam side lobe levels；
(5.2) building low sidelobe zero point is aligned difference beam Constraint Anchored Optimization:Wherein constraint condition
(wΔ′)HC=fTIt is used to guarantee difference beam in θ in optimization problem0Place forms zero point, wΔ' it is that difference beam forms weight vector, C=
[(a(θ0)⊙l∑)T, (b (θ0)⊙lΔ)T]T, f=[0,1]T, b (θ0)=a (θ0)⊙bΔ,lMIt is complete for element
For 1 column vector, order is 2M × 1, lΔFor the taper weight vector for reducing difference beam sidelobe level, order is 2M × 1.
7. the method according to claim 1, wherein the step 6 specifically includes:
(6.1) the low sidelobe zero point alignment and wave beam Constraint Anchored Optimization are solved:, it obtains and the optimal weight vector of Wave beam formingOrder is 2M × 1；Calculate the alignment of low sidelobe zero point and wave beam YΣ: YΣ=(wΣ)Ha(θ)；
(6.2) it solves the low sidelobe zero point and is aligned difference beam Constraint Anchored Optimization: obtaining difference beam and form optimal weight vectorOrder is 2M × 1；It calculates low sidelobe zero point and is aligned difference beam YΔ: YΔ=(wΔ)Ha
(θ)。
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