CN104750944A - Rapid planar sparse array synthesis method - Google Patents

Abstract

The invention discloses a rapid planar sparse array synthesis method. The method has the advantages that a conventional planar array synthesis constraint optimization model is converted into an unconstraint optimization problem by constructing a Lagrange function, so that calculation ill-posed problems in the iterative optimization process of a planar array are avoided, an array weight vector can be updated by the aid of closed-form solution in each time of iteration, planar array synthesis problems can be solved without an optimization tool, the method is more universal and transportability, an inverse matrix in the closed-form solution is quite large in scale as a two-dimensional space angle sample number of the planar array is increased in a quadratic manner, the inversion problem of the large-scale matrix is solved by introducing a conjugate gradient method, and convergence of planar array synthesis is accelerated, so that the method is higher in real-time performance and particularly applicable to occasions with high requirements on array optimization real-time performance and universality.

Description

One is plane thinned array integrated approach fast

Technical field

The present invention relates to one plane thinned array integrated approach fast.

Background technology

In recent years, planar array antenna is listed in the fields such as radar, communication, guidance and satellite broadcasting television and is widely applied.In order to reduce software and hardware complexity and the cost of system, in Practical Project, usually requiring that planar array can reach large array aperture to obtain high spatial resolution with the least possible bay number, keep lower minor level simultaneously.Therefore, adopt non-homogeneous sparse planar array to be an effective solution, and the sparse layout of array element often cause the minor level of directional diagram to improve.

The object of Synthesis of Antenna Arrays is while the minor level that maintenance is lower, makes aerial array that minimum array number can be adopted to meet the desired radiation characteristic requirement by optimization element position and energisation mode thereof.Element position and the excitation of comprehensive inhomogeneous plane array are nonlinearity optimization problems comprising multiple unknown quantity.Along with the development of computer technology, the intelligent optimization algorithms such as genetic algorithm, simulated annealing, particle cluster algorithm and ant group algorithm are widely used in array synthetic, but these traditional optimized algorithm essence are all the natural algorithms based on randomness, when for Solving Large Scale Sparse array, their search time can become very tediously long, to such an extent as to needs long time could obtain array optimization result.

Sparse and the discrete characteristic of spatial distribution of thinned array and the theoretical equivalent of the sparse signal of latest developments, therefore, Synthesis of Antenna Arrays can be regarded as the problem of space sparse signal reconfiguring in fact.In recent years, many scholar's research are had based on iteration weighting l ₁the Synthesis of Antenna Arrays method of norm minimum, the method can obtain the higher aerial array of sparse degree with less iterations, but the method needs to use convex Optimization Software to solve l in each iteration ₁norm minimum problem, the meeting consuming time of array synthetic is long.

In prior art, such as: burnish gilding roc, Gong Pengcheng, Cai Jingye, Zhu Xueyong computer engineering with application periodical deliver in 2014 " based on iteration weighting l ₁the thinned array of norm is comprehensive " give the weighing vector closed solutions of sparse linear array in each iteration, avoid Optimization Software and solve, accelerate convergence, thus realize the rapid integrated of sparse linear array.The major calculations amount of the array weight vectors closed solutions of the method concentrates on matrix inversion aspect; but the matrix size that needs are inverted is relevant with the space angle hits of desired orientation figure; when being applied to plane thinned array and being comprehensive; because its desired orientation figure is the two-dimensional directional figure comprising position angle and the angle of pitch; thus cause space angle hits to increase in square formula; therefore when planar array is comprehensive the scale of finding the inverse matrix can be far longer than linear array comprehensive time finding the inverse matrix, thus the meeting consuming time causing planar array comprehensive is veryer long.

In addition, the applicant on November 17th, 2014 submit to, application number be 2014106546300 patent application disclose a kind of based on L _1/2the sparse linear array optimization method of norm.This patent provides a kind of array synthetic method towards linear array, and the method needs by using optimization tool, and such as convex optimization tool solves linear array synthtic price index, and therefore the meeting consuming time of array synthetic is long.The present invention provides one array synthetic method fast towards planar array, utilize closed solutions to upgrade array weight vectors, without the need to the synthtic price index using optimization tool to solve planar array, accelerate the speed of array synthetic.

Summary of the invention

For the problems referred to above, the invention provides one plane thinned array integrated approach fast, avoid occurring calculating pathosis problem in planar array iterative optimization procedure, without the need to the synthtic price index using optimization tool to solve planar array, thus have more versatility and portability, in addition, the speed of convergence that planar array is comprehensive can be accelerated, thus have more real-time.

For realizing above-mentioned technical purpose, reach above-mentioned technique effect, the present invention is achieved through the following technical solutions:

One is plane thinned array integrated approach fast, comprises the steps:

S01: according to given planar array lateral length and longitudinal length, arranges the initialization planar array that an array element is evenly arranged, according to array number determination array weight vectors W and the weighting matrix Z of initialization planar array; The planar array stream shape matrix A be made up of all direction parameter u and v sampled point is jointly determined by the hits of initialization array elements number, position angle and the angle of pitch;

S02: Constraint Anchored Optimization comprehensive for planar array is converted into unconstrained optimize model by structure Lagrangian function, and utilize plural differentiate and get null value to obtain the closed solutions of the array weight vectors in each iteration, wherein, in the matrix inversion operation of closed solutions, method of conjugate gradient is introduced to promote algorithm accelerating convergence;

S03: the l judging the difference of array weight vectors before and after optimizing ₁whether norm is less than the error minimum value ξ of setting:

If the l of the difference of array weight vectors before and after optimizing ₁norm is greater than error minimum value ξ, then produce new array weight matrix by following formula,

Z＝diag{z _k}

Be back to step S02, z in above formula _k=| w _k| ², represent in diag () and vector carried out diagonalization operation;

If the l of the difference of array weight vectors before and after optimizing ₁norm is less than ξ, then iteration optimization stops, and enters step S04;

S04: the array weight vectors obtained step S03 carries out the weighting matrix that data rearrangement operation that vector converts matrix to obtains planar array, the position at the element place being greater than setting excitation minimum value in weighting matrix is defined as the element position of plane thinned array, its element value is the excitation range value of this array element, final element position and the excitation range value obtaining the planar array comprehensively.

The invention has the beneficial effects as follows:

One, by structure Lagrangian function, the Constraint Anchored Optimization of conventional plane array synthetic is converted into unconstrained optimization problem, thus avoids occurring calculating pathosis problem in planar array iterative optimization procedure;

Two, this method can utilize closed solutions to upgrade array weight vectors in each iteration, without the need to the synthtic price index using optimization tool to solve planar array, thus has more versatility and portability;

Three, because the two-dimensional space angular samples number of planar array causes the scale of finding the inverse matrix in closed solutions very large in a square formula growth, the present invention introduces the inversion problem that conjugate gradient method solves extensive matrix, to accelerate the comprehensive speed of convergence of planar array, thus have more real-time.

Under the constraint conditions such as given planar array scale and peak sidelobe, maximum sparse planar array can be obtained fast, provide element position and excitation amplitude thereof simultaneously, required array synthetic time decreased more than 30%, is specially adapted to array optimization real-time and the higher occasion of versatility requirement.

Accompanying drawing explanation

Fig. 1 is the process flow diagram of a kind of plane fast of the present invention thinned array integrated approach;

Fig. 2 is the present invention is 5 λ and longitudinal length 5 λ at given planar array lateral length, peak sidelobe adopts plane thinned array integrated approach optimization fast to obtain afterwards element position distribution plan under being less than the condition of-20dB;

Fig. 3 is the normalization beam directional diagram under Fig. 2 provides element position and optimizes excitation;

Fig. 4 is the present invention is 8 λ and longitudinal length 8 λ at given planar array lateral length, peak sidelobe adopts plane thinned array integrated approach optimization fast to obtain afterwards element position distribution plan under being less than the condition of-24d;

Fig. 5 is the normalization beam directional diagram under Fig. 4 provides element position and optimizes excitation.

Embodiment

Below in conjunction with accompanying drawing and specific embodiment, technical solution of the present invention is described in further detail, can better understand the present invention to make those skilled in the art and can be implemented, but illustrated embodiment is not as a limitation of the invention.

One is plane thinned array integrated approach fast, and its overall flow as shown in Figure 1, comprises the steps:

S01: determine initialization array weight vectors and weighting matrix:

According to given planar array lateral length and longitudinal length, the initialization planar array that an array element is evenly arranged is set, according to array number determination array weight vectors W and the weighting matrix Z of initialization planar array; The planar array stream shape matrix A be made up of all direction parameter u and v sampled point is jointly determined by the hits of initialization array elements number, position angle and the angle of pitch.

Step S01 specifically comprises the steps:

According to given planar array lateral length and longitudinal length, arrange the initialization planar array that an array element is evenly arranged, its horizontal array element distance is d _x, longitudinal array element distance is d _y, its horizontal array number is M, and longitudinal array number is N, preferably, and the horizontal array element distance d of initialization planar array _xwith longitudinal array element distance d _ybetween (1/8-1/2) λ, wherein, λ represents wavelength, then the weighting matrix of planar array is:

$\tilde{W}=\left[\begin{array}{cccc}{w}_{11}& w_{12}& ...& w_{1M}\\ w_{21}& w_{22}& ...& w_{2M}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ w_{N1}& w_{N2}& ...& w_{\mathrm{NM}}\end{array}\right],$

Because quick plane array synthetic method proposed by the invention carries out computing based on vector, therefore need first by weighting matrix vectorization by row, obtains the array weight vectors W=[w after changing ₁₁w ₁₂w _1Mw _n1w _n2w _nM] ^t, wherein, [] ^trepresent the transposition of vector.

Wherein, initialization array weight vectors W is complete 1 vectors in MN rank, then corresponding initialization array weight matrix Z is MN rank unit matrixs.

Suppose direction parameter u ∈ [-1 1], v ∈ [-1 1], wherein for position angle, θ is the angle of pitch, and direction parameter u is equal interval sampling L in span [-1 1] _xpoint, can be expressed as direction parameter v is equal interval sampling L in span [-1 1] _ypoint, can be expressed as then in conjunction with the total array number MN of initialization, the planar array stream shape matrix A be made up of all direction parameter u and v sampled point can be determined,

$A={\left[\begin{array}{ccc}a(u_1,v_1)& a(u_1,v_2)\·\·\·a(u_1,v_{L_y})...a(u_{L_x},v_1)& a(u_{L_x},v_2)\·\·\·a(u_{L_x},v_{L_y})\end{array}\right]}^2---\left(1\right)$

In formula,

$a(u_i,v_j)={[e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}(d_x{u}_i+d_y{v}_j)}{e}^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}(d_x{u}_i+{2d}_y{v}_j)}\·\·\·e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}(d_x{u}_i+{\mathrm{Md}}_y{v}_j)}\·\·\·e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}({\mathrm{Nd}}_x{u}_i+d_y{v}_j)}{e}^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}({\mathrm{Nd}}_x{u}_i+{2d}_y{v}_j)}\·\·\·e^{j\frac{2\mathrm{\π}}{\mathrm{\λ}}({\mathrm{Nd}}_x{U}_i+{\mathrm{Md}}_y{v}_j)}]}^T$ For sampled point u _i, v _j, i ∈ [1,2 ... L _x], j ∈ [1,2 ... L _y] corresponding planar array guiding vector.

S02: utilize closed solutions to upgrade weighing vector:

By structure Lagrangian function, Constraint Anchored Optimization comprehensive for planar array is converted into unconstrained optimize model, and utilize plural differentiate and get null value to obtain the closed solutions of the array weight vectors in each iteration, wherein, in the matrix inversion operation of closed solutions, method of conjugate gradient is introduced to promote algorithm accelerating convergence.

Step S02 specifically comprises the steps:

According to the constraint condition of given planar array, such as, the constraint conditions such as the scale of planar array, required peak sidelobe value, are formed and expect two dimensional beam pattern matrix carried out the operation of vectorization by row and generated expectation beam pattern vector F _d, then the sparse optimization problem of plane adopts l ₁optimized model is expressed as follows:

$\begin{array}{cc}\underset{w}{\min }f\left(W\right)={\left|\right|W\left|\right|}_1& s.t.{\left|\right|F_d-\mathrm{AW}\left|\right|}_2^2<\mathrm{\&epsiv;}---\left(2\right)\end{array}$

Wherein, || || ₁be expressed as the l of vector ₁norm; || || ₂be expressed as the l of vector ₂norm; ε represents acceptable error, and s.t. is the abbreviation of subject to, the affined meaning.

By the method constructing Lagrangian function, constrained optimization problem (2) is converted to unconstrained optimization problem:

$\underset{w,z}{\min }f(W,Z)={\left|\right|F_d-\mathrm{AW}\left|\right|}_2^2+\mathrm{\&alpha;}\underset{k=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}{z}_k{\left|w_k\right|}_1---\left(3\right)$

Unconstrained optimization objective function f (W, Z) is launched:

$\begin{array}{c}f(W,Z)={\left|\right|F_d-\mathrm{AW}\left|\right|}_2^2+\mathrm{\&alpha;}\underset{k=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}{z}_k{\left|w_k\right|}_1\\ =({F_d}^H{F}_d-{F_d}^H\mathrm{AW}-W^H{A}^H{F}_d+W^H{A}^H\mathrm{AW})+\mathrm{\&alpha;}\underset{k=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}{z}_k{\left|w_k\right|}_1\end{array}---\left(4\right)$

Wherein, () ^hfor conjugate transpose, α is the Lagrange factor, z _kbe one group of weighted value, z _k=| w _k| ², in order to obtain the expression formula of array weight vectors, above formula (4) is to W ^hcarry out asking partial derivative, can obtain

$\frac{\&PartialD;f(W,Z)}{{\&PartialD;W}^H}=(A^H\mathrm{AW}-A^H{F}_d)+\mathrm{\&alpha;}{Z}^{-1}W---\left(5\right)$

Wherein, Z be one by weighting coefficient z _kthe diagonal matrix of composition, i.e. Z=diag{z _k, wherein, represent in diag () and vector is carried out diagonalization operation.Order following nonlinear equation can be obtained:

(A ^HAW-A ^HF _d)+αZ ^-1W＝0 (6)

Solving equation (6), can obtain the expression formula of array weight vectors W:

W＝(A ^HA+αZ ^-1) ^-1A ^HF _d＝ZA ^H(αI+AZA ^H) ^-1F _d(7)

Wherein, I is unit matrix, note matrix G=(α I+AZA ^h), vectorial Y=G ^-1f _d.Due to the existence of Lagrangian function factor-alpha, can ensure that matrix G still keeps reversible after each iteration, thus avoid the phenomenon occurring ill-condition matrix in interative computation process.

The scale of matrix G is relevant with space angle hits; space angle due to plane thinned array is that two dimension angular is as position angle and the angle of pitch; compare the linear array that space angle is one dimension angle; its space angle hits can increase in square formula; therefore when planar array is comprehensive, the scale of matrix G can be very large; thus cause inverting of matrix G can be consuming time long, therefore in whole planar array optimizing process, larger one piece of time overhead is above the inversion operation of extensive matrix G in each iteration optimization.According to expression formula Y=G ^-1f _d, can solving of vectorial Y be regarded as system of linear equations GY=F _dsolve, then method of conjugate gradient can be utilized to accelerate the solution efficiency of system of linear equations, thus solve the problem of extensive matrix inversion, improve the real-time of algorithm.

Method of conjugate gradient is with conjugate direction some algorithms as the direction of search, process a kind of important Mathematical method in large-scale symmetric positive definite linear equation at present, it combines conjugacy with method of steepest descent, construct one group of conjugate direction about matrix G according to the gradient at known point place, and carry out searching for along this direction and obtain the minimal point of objective function.Method of conjugate gradient has the feature of quadratic terminability, makes system of linear equations GY=F _dsolve can Fast Convergent.Therefore the present invention introduces the inversion problem that conjugate gradient method solves extensive matrix G, can accelerate the speed of convergence that planar array is comprehensive, thus improves the real-time of array synthetic.

More new formula is as follows to introduce the array weight vectors after conjugate gradient:

$\left\{\begin{array}{c}\mathrm{GY}=F_d\\ W=\mathrm{ZAY}\end{array}\right.---\left(8\right)$

In formula (8), conjugate gradient is utilized to solve system of linear equations GY=F _d, thus obtain the value of vectorial Y, and then utilize second formula in formula (8) to calculate new array weight vectors W.

S03: the l judging the difference of array weight vectors before and after optimizing ₁whether norm is less than the error minimum value ξ of setting:

If the l of the difference of array weight vectors before and after optimizing ₁norm is greater than error minimum value ξ, then show that the sparse degree that this suboptimization obtains thinned array does not also reach requirement, need optimize further.New array weight matrix Z is produced by formula (9):

Z＝diag{z _k} (9)

Be back to step S02, continue iteration optimization, produce new array weight vectors W, z in above formula _k=| w _k| ², vector is carried out diagonalization operation by diag () expression.

If the l of the difference of array weight vectors before and after optimizing ₁norm is less than ξ, then iteration optimization stops, and the array weight vectors of acquisition has been under specified criteria can try to achieve one most sparse solution, enters step S04.

Preferably, the scope of error minimum value ξ is 10 ^-5-10 ^-4between.

S04: element position and the excitation of determining plane thinned array:

The array weight vectors obtained step S03 carries out the weighting matrix that data rearrangement operation that vector converts matrix to obtains planar array, and the operating process that vector converts matrix to is by weighting matrix in step S01 the inverse process of vectorization operation by row, the operation being converted to matrix by vector is reduced into weighting matrix corresponding to planar array.

The position at the element place being greater than setting excitation minimum value in weighting matrix is defined as the element position of plane thinned array, its element value is the excitation range value of this array element, final element position and the excitation range value obtaining the planar array comprehensively.

The embodiment of a kind of thinned array of plane fast integrated approach that the present invention proposes can provide further by following emulation embodiment and result:

Emulation embodiment 1:

The lateral length that arranging needs comprehensive planar array is 5 λ and longitudinal length is 5 λ, wherein, horizontal array element distance be λ/ ₄, longitudinal array element distance be λ/ ₄, then the horizontal array number of initialization planar array is M=21, and longitudinal array number is N=21, then initialization array number i.e. comprehensive front array number is 441, requires that the beam peak sidelobe level of plane thinned array is less than-20dB.According to the method according to array element distance being the full battle array arrangement in λ/2, then need antenna element number to be 121, the quick plane thinned array integrated approach adopting the present invention to propose is optimized, wherein u _xand v _ysample to be spaced apart 0.05 in span [-1 1] respectively, Lagrange factor α=71.5, error minimum value ξ=10 ^-5, the plane thinned array array number after comprehensive is 68, and planar array degree of rarefication reaches 56.20%, can save 53 antenna elements.Planar array element position distribution after comprehensive as shown in Figure 2, combine comprehensive after element position and the two dimensional beam directional diagram that formed of excitation as shown in Figure 3.As can be seen from Figure 3 the inventive method obtains the directional diagram that maximum thinned array formed and substantially to meet the expectation radiation characteristic.

Emulation embodiment 2:

In order to verify the validity of the inventive method further, under the constraint conditions such as different given planar array scales and peak sidelobe, again carry out planar array comprehensive.Constraint condition arranges as follows: planar array lateral length is 8 λ and longitudinal length 8 λ, its horizontal array element distance is λ/4, longitudinal array element distance is λ/4, the horizontal array number of initialization planar array is M=33, longitudinal array number is N=33, then initialization array number is 1089, requires that the beam peak sidelobe level optimized is less than-24dB.According to being the method that full battle array arrangement is carried out in λ/2 according to array element distance, then need antenna element number to be 289, and the quick plane thinned array integrated approach adopting the present invention to propose only needs 165 bays, the degree of rarefication of array reaches 57.09%, save 124 antenna elements, wherein u _xand v _ysample to be spaced apart 0.04 in span [-1 1] respectively, Lagrange factor α=27.5, error minimum value ξ=10 ^-4.The distribution of concrete element position as shown in Figure 4, combines two dimensional beam directional diagram that the element position comprehensively and excitation value thereof formed as shown in Figure 5, substantially meets the desired beam radiation characteristic as shown in Figure 5.

Above emulation experiment all completes in MATLAB 2012b, and allocation of computer is: Intel (R) Core (TM) i5-4570 processor, dominant frequency be 3.2GHz, in save as 4GB.In emulation embodiment 1: do not introduce conjugate gradient method when utilizing closed solutions to calculate weighing vector in each iteration and directly carry out matrix inversion, then the planar array composite demand time is 21.1s, and introduce the problem that method of conjugate gradient solves extensive matrix inversion in weighing vector closed solutions, planar array comprehensively only needs 12.9s just can obtain maximum sparse planar array, and the optimization time saves 38.86%.In emulation embodiment 2: when not introducing conjugate gradient method, planar array integrated approach needs 95.1s, and introduce method of conjugate gradient back plane array synthetic method and only need 66.0s just can obtain the plane thinned array met the demands, the time saves 30.60%.Therefore the inventive method can promote algorithm accelerating convergence after introducing method of conjugate gradient, thus realizes the rapid integrated of plane thinned array, improves the real-time that planar array is comprehensive.

The invention has the beneficial effects as follows:

One, by structure Lagrangian function, the Constraint Anchored Optimization of conventional plane array synthetic is converted into unconstrained optimization problem, thus avoids occurring calculating pathosis problem in planar array iterative optimization procedure;

Two, this method can utilize closed solutions to upgrade array weight vectors in each iteration, without the need to the synthtic price index using optimization tool to solve planar array, thus has more versatility and portability;

Three, because the two-dimensional space angular samples number of planar array causes the scale of finding the inverse matrix in closed solutions very large in a square formula growth, the present invention introduces the inversion problem that conjugate gradient method solves extensive matrix, to accelerate the comprehensive speed of convergence of planar array, thus have more real-time.

Under the constraint conditions such as given planar array scale and peak sidelobe, maximum sparse planar array can be obtained fast, provide element position and excitation amplitude thereof simultaneously, required array synthetic time decreased more than 30%, is specially adapted to array optimization real-time and the higher occasion of versatility requirement.

These are only the preferred embodiments of the present invention; not thereby the scope of the claims of the present invention is limited; every utilize instructions of the present invention and accompanying drawing content to do equivalent structure or equivalent flow process conversion; or be directly or indirectly used in the technical field that other are relevant, be all in like manner included in scope of patent protection of the present invention.

Claims (5)

1. a plane thinned array integrated approach fast, is characterized in that, comprise the steps:

S01: according to given planar array lateral length and longitudinal length, arranges the initialization planar array that an array element is evenly arranged, according to array number determination array weight vectors W and the weighting matrix Z of initialization planar array; The planar array stream shape matrix A be made up of all direction parameter u and v sampled point is jointly determined by the hits of initialization array elements number, position angle and the angle of pitch;

S02: Constraint Anchored Optimization comprehensive for planar array is converted into unconstrained optimize model by structure Lagrangian function, and utilize plural differentiate and get null value to obtain the closed solutions of the array weight vectors in each iteration, wherein, in the matrix inversion operation of closed solutions, method of conjugate gradient is introduced to promote algorithm accelerating convergence;

S03: the l judging the difference of array weight vectors before and after optimizing ₁whether norm is less than the error minimum value ξ of setting:

If the l of the difference of array weight vectors before and after optimizing ₁norm is greater than error minimum value ξ, then produce new array weight matrix Z by following formula,

Z＝diag{z _k}

Be back to step S02, z in above formula _k=| w _k| ², vector is carried out diagonalization operation by diag () expression;

If the l of the difference of array weight vectors before and after optimizing ₁norm is less than ξ, then iteration optimization stops, and enters step S04;

S04: the array weight vectors obtained step S03 carries out the weighting matrix that data rearrangement operation that vector converts matrix to obtains planar array, the position at the element place being greater than setting excitation minimum value in weighting matrix is defined as the element position of plane thinned array, its element value is the excitation range value of this array element, final element position and the excitation range value obtaining the planar array comprehensively.

2. one according to claim 1 plane thinned array integrated approach fast, it is characterized in that, step S01 specifically comprises the steps:

According to given planar array lateral length and longitudinal length, arrange the initialization planar array that an array element is evenly arranged, its horizontal array element distance is d _x, longitudinal array element distance is d _y, its horizontal array number is M, and longitudinal array number is N, then the weighting matrix of planar array is:

$\tilde{W}=\left[\begin{array}{cccc}{w}_{11}& w_{12}& ...& w_{1M}\\ w_{21}& w_{22}& ...& w_{2M}\\ .& .& & .\\ .& .& & .\\ .& .& & .\\ w_{N1}& w_{N2}& ...& w_{\mathrm{NM}}\end{array}\right],$

By weighting matrix vectorization by row, obtains the array weight vectors W=[w after changing ₁₁w ₁₂... w _1M... w _n1w _n2... w _nM] ^t, wherein, [] ^trepresent the transposition of vector, initialization array weight vectors is complete 1 vectors in MN rank, then corresponding initialization array weight matrix Z is MN rank unit matrixs;

Suppose direction parameter u ∈ [-1 1], v ∈ [-1 1], wherein for position angle, θ is the angle of pitch, and direction parameter u is equal interval sampling L in span [-1 1] _xpoint, can be expressed as direction parameter v is equal interval sampling L in span [-1 1] _ypoint, can be expressed as then in conjunction with the total array number MN of initialization, the planar array stream shape matrix A be made up of all direction parameter u and v sampled point can be determined,

$A={\left[\begin{array}{ccc}a(u_1,v_1)& a(u_1,v_2)...a(u_1,v_{L_y})...a(u_{L_x},v_1)& a(u_{L_x},v_2)...a(u_{L_x},v_{L_y})\end{array}\right]}^T---\left(1\right)$

In formula,

$a(u_i,v_j)={[e^{j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(d_x{u}_i+d_y{v}_j)}{e}^{j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(d_x{u}_i+2d_y{v}_j)}...e^{j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(d_x{u}_i+M{d}_y{v}_j)}...e^{j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}(N{d}_x{u}_i+d_y{v}_j)}{e}^{j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}({\mathrm{Nd}}_x{u}_i+2d_y{v}_j)}...e^{j\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}({\mathrm{Nd}}_x{u}_i+{\mathrm{Md}}_x{u}_i+{\mathrm{Md}}_y{v}_j)}]}^T$ For sampled point u _i, v _j, i ∈ [1,2 ... L _x], j ∈ [1,2 ... L _y] corresponding planar array guiding vector.

3. one according to claim 2 plane thinned array integrated approach fast, is characterized in that, in step S01, and the horizontal array element distance d of initialization planar array _xwith longitudinal array element distance d _ybetween (1/8-1/2) λ, wherein, λ represents wavelength.

4. one according to claim 2 plane thinned array integrated approach fast, it is characterized in that, step S02 specifically comprises the steps:

According to the constraint condition of given planar array, formed and expect two dimensional beam pattern matrix carried out the operation of vectorization by row and generated expectation beam pattern vector F _d, then the sparse optimization problem of plane adopts l ₁optimized model is expressed as follows:

$\begin{array}{cc}\underset{w}{\min }f\left(W\right)={\left|\right|W\left|\right|}_1& s.t.{\left|\right|F_d-\mathrm{AW}\left|\right|}_2^2<\mathrm{\&epsiv;}\end{array}---\left(2\right)$

Wherein, || || ₁be expressed as the l of vector ₁norm; || || ₂be expressed as the l of vector ₂norm; ε represents acceptable error, and s.t. is the abbreviation of subject to, the affined meaning;

By the method constructing Lagrangian function, constrained optimization problem (2) is converted to unconstrained optimization problem:

$\underset{w,z}{\min }f(W,Z)={\left|\right|F_d-\mathrm{AW}\left|\right|}_2^2+\mathrm{\&alpha;}\underset{k=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}{z}_k{\left|w_k\right|}_1---\left(3\right)$

Unconstrained optimization objective function f (W, Z) is launched:

$\begin{array}{c}f(W,Z)={\left|\right|F_d-\mathrm{AW}\left|\right|}_2^2+\mathrm{\&alpha;}\underset{k=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}{z}_k{\left|w_k\right|}_1\\ =({F_d}^H{F}_d-{F_d}^H\mathrm{AW}-W^H{A}^H{F}_d+W^H{A}^H\mathrm{AW})+\mathrm{\&alpha;}\underset{k=1}{\overset{\mathrm{NM}}{\mathrm{\&Sigma;}}}{z}_k{\left|w_k\right|}_1\end{array}---\left(4\right)$

Wherein, () ^hfor conjugate transpose, α is the Lagrange factor, z _kbe one group of weighted value, in order to obtain the expression formula of array weight vectors, above formula (4) is to W ^hcarry out asking partial derivative, can obtain

$\frac{\&PartialD;f(W,Z)}{\&PartialD;W^H}=(A^H\mathrm{AW}-A^H{F}_d)+\mathrm{\&alpha;}{Z}^{-1}W---\left(5\right)$

Wherein, Z be one by weighting coefficient z _kthe diagonal matrix Z=diag{z of composition _k, order following nonlinear equation can be obtained:

(A ^HAW-A ^HF _d)+αZ ^-1W＝0 (6)

Solving equation (6), can obtain the expression formula of array weight vectors W:

W＝(A ^HA+αZ ^-1) ^-1A ^HF _d＝ZA ^H(αI+AZA ^H) ^-1F _d(7)

Wherein, I is unit matrix, note matrix G=(α I+AZA ^h), vectorial Y=G ^-1f _d,

More new formula is as follows to introduce the array weight vectors after conjugate gradient:

$\left\{\begin{array}{c}\mathrm{GY}=F_d\\ W=Z{A}^{H}Y\end{array}\right.---\left(8\right)$

Array weight matrix Z is updated to formula (8), calculates new array weight vectors W.

5. one according to claim 1 plane thinned array integrated approach fast, is characterized in that, in step S03, the scope of error minimum value ξ is 10 ^-5-10 ^-4between.