CN104182636A - Fast implementation method for comprehensive minor lobes of array antenna radiation field and scattered field - Google Patents

Abstract

The invention discloses a fast implementation method for comprehensive minor lobes of an array antenna radiation field and a scattered field. The fast implementation method comprises the following steps of (1) determining structure parameters, electromagnetic working parameters and array surface distribution parameters of an array antenna; (2) determining an initial sparse arrangement scheme of the array antenna to obtain a sparse arrangement matrix of array antenna units; (3) calculating phase difference between the radiation field and a radiation field actinal surface of the array antenna; (4) calculating a radiation pattern function of the array antenna and calculating the maximum minor lobe level of the radiation field of the array antenna under the sparse arrangement scheme; (5) calculating a scattering pattern function of the array antenna and calculating the maximum minor lobe level of the radiation field of the array antenna under the sparse arrangement scheme; and (6) judging whether the radiation field and the scattered field simultaneously meet the requirement on low minor lobes or not under the sparse arrangement scheme of the array antenna until the optimum sparse arrangement scheme by which the requirements on the low minor lobes of the radiation field and the scattered field of the array antenna can be met simultaneously is obtained. By the fast implementation method, the low minor lobe performance of the radiation field of the array antenna and the low minor lobe performance of the scattered field of the array antenna can be simultaneously realized.

Description

A kind of array antenna radiation field and the comprehensive Sidelobe Fast implementation of scattered field

Technical field

The invention belongs to antenna technical field, implementation method when being specifically related to array antenna radiation field and scattered field Sidelobe.

Background technology

Stealth technology is occupied very consequence in modern war, has obtained attention and the development of increasing country.Along with the development of Stealthy Technology and the application of new material, (Radar Cross Section, RCS) is very little for the RCS of target self, thereby antenna has become the main contributions person of its platform RCS carrying.Array antenna can form the radiation characteristic that is different from general separate antenna, especially can form the much better than radiation of ratio separate antenna of pointing to certain segment space, and because its reliability is high, function is many, detection and the advantage such as tracking power is strong, be widely used in various radar systems, and become the main flow that current radar develops, particularly in advanced person's airborne the synthetical electronics information system, obtain application well.Under increasingly serious military struggle, development has particularly important that the array antenna of high-gain, high Stealth Fighter just highlights.

The scattered field of array antenna comprises antenna mode scattering field and structural mode scattering field, and both using array plane as reflecting surface, scattering peak value appears in the mirror-reflection direction using arrival bearing as incident direction.That aims at for fear of specular scattering peak value that detection radar causes is detected threat, and inclination mounting means has become the main flow mounting means of stealthy array antenna.This mounting means has been avoided the threat that is detected that specular scattering peak value causes.Meanwhile, make the main lobe of array antenna structure schema entry and antenna mode scattering field depart from arrival bearing, thereby reach stealthy object, and its radiance can be ensured by feed amplitude and the phase place of controlling each unit.Can be in the situation that ensureing radiance, avoid mirror-reflection peak value to aim at detection radar and caused array antenna to be detected threat.But, that has caused although tilt to install to have avoided mirror-reflection peak value to aim at detection radar is detected threat,, now in array, the secondary lobe of scattered field and scattering peak value become the main contributions person of tilted-putted RCS of Array Antenna, become the chief threat that array antenna is detected.Simultaneously, low sidelobe antenna has good in electronically jamproof ability, the secondary lobe performance of array antenna is an important indicator of array radar system, it has determined the anti-interference of radar and anti-clutter ability to a great extent, low or super low sidelobe array antenna is the generally requirement of modern radar, is to be badly in need of one of gordian technique solving.

Therefore, no matter from the angle of radar detection performance, or consider from the angle of stealthy effect, all should adopt suitable method pair array radiation field of aerial and the secondary lobe of scattered field to control.

Chinese scholars is more deep to the research of radiation field Sidelobe performance at present, but the Sidelobe performance study of scattered field is less.Realize general amplitude weighting, phase weighting and the Density Weighted method of adopting for radiation field Sidelobe both at home and abroad.Wherein, amplitude weighting makes each unit of phased array antenna will connect the attenuator of different weights, has additionally increased the complexity of cost and the feed of system.And the scattering problems of array antenna cannot adopt amplitude weighting method to reduce minor level, it is limited that phase weighting method realizes the effect of Sidelobe, because only depend on phase weighting to be difficult to obtain better Sidelobe performance index, and phase weighting can not be used for realizing the Sidelobe of array antenna scattered field, the fractal antenna unit interval that constant amplitude unequal-interval array in Density Weighted obtains is to front structural design, heat dissipation design, and the engineering construction such as processes has brought very large difficulty, Sparse Array Sidelobe implementation method in Density Weighted not only can be for realize the Sidelobe of radiation field and scattered field simultaneously, and compare with the full battle array with identical bore, almost there is identical main lobe width, with respect to the identical array of number of unit Sparse Array there is the resolution of narrower main lobe and Geng Gao, the full battle array of cost ratio is low simultaneously, this method is adopted by some large-scale high-performance phased array antenna.Therefore, provide a kind of sparse arrangement of antenna element, the Sidelobe that comes simultaneously to form fast Sparse Array radiation field of aerial and scattered field combination property becomes this area technical matters urgently to be resolved hurrily at present.

Summary of the invention

While the object of the invention is to tilt to install for stealthy array antenna, the secondary lobe of scattered field becomes the chief threat that it is detected, simultaneously radiation field Sidelobe has determined the anti-interference and anti-clutter ability of array antenna, only there is the implementation method of array antenna radiation field Sidelobe in existing research, and pair array antenna scattering field Sidelobe performance is difficult to the deficiency realizing.For this reason, the present invention is analyzing the relative merits of array antenna radiation field Sidelobe implementation method, and the restriction of these methods in scattered field Sidelobe is realized, propose based on the sparse array antenna radiation field of arranging of antenna element and the comprehensive Sidelobe Fast implementation of scattered field.The method, by changing the arrangement form of array antenna unit, can realize the Sidelobe performance of array antenna radiation field and scattered field simultaneously.

The technical solution that realizes the object of the invention is:

A kind of array antenna radiation field and the comprehensive Sidelobe Fast implementation of scattered field, comprise following process:

(1) according to the version of the equidistant rectangular grid array antenna of plane, determine array antenna structure parameter, electromagnetism running parameter, and front layout parameter;

(2) according to array antenna structure parameter and front layout parameter, provide the initial sparse arrangement of array antenna, obtain the sparse matrix of arranging of array antenna unit;

(3), according to the structural parameters of array antenna and electromagnetism running parameter, utilize the array antenna unit parameter of arranging, the radiation field of computing array antenna and scattered field actinal surface phase differential;

(4) associated matrix array antenna radiation field actinal surface phase differential, and the sparse matrix of arranging of array antenna unit, the antenna pattern function of computing array antenna, and calculate the maximum sidelobe levels of array antenna radiation field under this sparse arrangement according to array antenna antenna pattern function;

(5) associated matrix array antenna scattered field actinal surface phase differential, and the sparse matrix of arranging of array antenna unit, the scattering pattern function of computing array antenna, and calculate the maximum sidelobe levels of array antenna scattered field under this sparse arrangement according to array antenna scattering pattern function;

(6), according to array antenna design objective, judge whether radiation field and the scattered field under the sparse arrangement of this array antenna meets Sidelobe requirement simultaneously; If meet, the sparse arrangement of this array antenna is the sparse arrangement of optimum that simultaneously realizes array antenna radiation field and scattered field Sidelobe; Otherwise, according to last radiation field and scattered field maximum sidelobe levels value, upgrade the sparse matrix of arranging of array antenna unit by the method for crossover and mutation, and repeating step (3) is to step (6) until meet the demands.

Further, in step (1), described definite array antenna structure parameter, comprising front grid line number, columns and horizontal, longitudinal grid distance; Described definite array antenna electromagnetism running parameter, comprising central task frequency, incident wave frequency; Described definite array antenna front layout parameter, comprises the sparse rate of front.

Further, described step (2) provides the initial sparse arrangement of array antenna, determines each grid place in original array antenna and whether places antenna element, obtains the sparse matrix of arranging of array antenna unit, carries out according to the following procedure:

(2a) establish total M × N grid in equidistant rectangular grid array antenna, wherein laterally grid number is M, and longitudinally grid number is N; This grid point value is designated as to 1 if place antenna element on some grids, this grid point value is designated as to 0 if do not place antenna element, the each grid point value of sequential storage of numbering according to the grid of equidistant matrix grid array antenna according to this, thus the sparse matrix of arranging of array antenna unit obtained;

(2b) establishing the sparse matrix of arranging of array antenna unit is F, the sparse rate of front is ξ, get the sparse matrix F of arranging of original array antenna element (0) [0,1] matrix for the capable N row of the random M generating, and the grid of equidistantly not placing antenna element in grid battle array is counted N ⁰count N with the grid of placing antenna element ¹ratio meet

$\frac{N^1}{N^1+N^0}=\mathrm{\ξ}.$

Further, the grid of not placing antenna element in equidistant grid battle array is counted N ⁰for being the number of 0 element in matrix; Place the grid of antenna element and count N ¹for being the number of 1 element in matrix.

Further, described step (3) is carried out according to the following procedure:

(3a) establish in the array antenna battle array of equidistant rectangular grid arrangement, observation point P is with respect to the direction at coordinate system O-xyz place be expressed as (cos φ with direction cosine _x, cos φ _y, cos φ _z), obtain observation point P and with respect to the angle of coordinate axis and the pass of direction cosine be

(3b) establish the horizontal and vertical grid distance of array antenna that equidistant rectangular grid arranges and be respectively d _xand d _y, the antenna element that adjacent two grids (i, j) and (i-1, j-1) locate is the space quadrature along x-axis, y-axis and z-axis at target place be respectively

$\left\{\begin{array}{c}\mathrm{\Δ}{\mathrm{\Φ}}_x^{i,j}=k_r\·d_x\·\cos {\mathrm{\φ}}_x\\ \mathrm{\Δ}{\mathrm{\Φ}}_y^{i,j}=k_r\·d_y\·\cos {\mathrm{\φ}}_y\\ \mathrm{\Δ}{\mathrm{\Φ}}_z^{i,j}=0\end{array}\right.$

Wherein, k _r=2 π/λ _rfor space wave constant; λ _rfor antenna electromagnetic wavelength;

(3c) antenna element at (m, n) individual grid place is with respect to the radiation field phase differential ΔΦ of the antenna element at (1,1) individual grid place ^r _mnfor

$\begin{array}{c}\mathrm{\Δ}{{\mathrm{\Φ}}^r}_{\mathrm{mn}}=\mathrm{\Δ}{\mathrm{\Φ}}_x^{m,n}+\mathrm{\Δ}{\mathrm{\Φ}}_y^{m,n}+\mathrm{\Δ}{\mathrm{\Φ}}_z^{m,n}\\ =k_r\·[(m-1)\·d_x\·\cos {\mathrm{\φ}}_x+(n-1)\·d_y\·\cos {\mathrm{\φ}}_y]\end{array};$

Scattered field phase differential in array antenna between antenna element is the twice of phase differential between radiation field-based antenna unit, in equidistant rectangular grid array antenna, (m, n) antenna element at individual grid place is with respect to the scattered field phase differential ΔΦ of the antenna element at (1,1) individual grid place ^s _mnfor

$\begin{array}{c}\mathrm{\Δ}{{\mathrm{\Φ}}^s}_{\mathrm{mn}}=2\·(\mathrm{\Δ}{\mathrm{\Φ}}_x^{m,n}+\mathrm{\Δ}{\mathrm{\Φ}}_y^{m,n}+\mathrm{\Δ}{\mathrm{\Φ}}_z^{m,n})\\ =2\·k_r\·[(m-1)\·d_x\·\cos {\mathrm{\φ}}_x+(n-1)\·d_y\·\cos {\mathrm{\φ}}_y]\end{array}$

Wherein, k _s=2 π/λ _sfor scattered field space wave constant, λ _sfor radar detection wave-wave long; the antenna element that represents respectively (m, n) individual grid place is the space quadrature along x-axis, y-axis and z-axis with respect to the antenna element at (1,1) individual grid place;

(3d) by equidistant rectangular grid array antenna, the antenna element at each grid place is with respect in array the (1,1) the antenna element radiation field phase differential at individual grid place and scattered field phase differential, become the form of matrix according to the sequential storage of array antenna grid numbering, obtain radiation field actinal surface phase differential and the scattered field actinal surface phase differential of array antenna.

Further, step (4) is carried out according to the following procedure:

(4a) according to array antenna electromagnetic wave superposition principle and directional diagram product theorem, the array antenna radiation field phase differential ΔΦ that utilizes step (3c) to obtain ^r _mn, and the sparse matrix F of arranging of array antenna unit that obtains of step (2b) _mn, the antenna pattern function that obtains the lower equidistant rectangular grid array antenna of the t time sparse arrangement F of array antenna (t) is

In formula, I _mnit is the exciting current of antenna element in battle array; for the radiating element factor; for radiation array factor; According to the interference of electromagenetic wave radiation and superposition principle, in the time of computing array antenna radiation characteristics, only need to calculate radiation array factor ;

(4b) draw and obtain its antenna pattern according to antenna pattern function, and calculate the radiation field maximum sidelobe levels PSLL under the t time sparse arrangement F of array antenna (t) _r.

Further, described step (4b) is calculated the radiation field maximum sidelobe levels PSLL under the t time sparse arrangement F of array antenna (t) _rrealize by following manner:

I) array antenna minor level is field intensity value corresponding to each flex point in antenna pattern, for plane, for obtaining the flex point of antenna pattern function, makes radiation array factor first order derivative be zero, second derivative is less than zero,

Wherein, θ ^p=[θ ¹, θ ²... θ ^p] be position angle corresponding to each flex point except main lobe in radiation array factor directional diagram, P is the flex point sum in radiation array factor directional diagram;

II) each secondary lobe of obtaining accordingly in antenna pattern is

Thereby the maximum sidelobe levels obtaining in antenna pattern is

Wherein be under the t time sparse arrangement F of array antenna (t) the position angle that plane radiation field maximum sidelobe levels is corresponding.

Further, step (5) is carried out according to the following procedure:

(5a) analyzing known array radar scattering cross-section according to the computing formula of RCS and antenna element phase differential is

$\mathrm{\σ}=\underset{r\→\∞}{\lim }\left\{4\mathrm{\π}{r}^2\frac{{\left|{\stackrel{\→}{E}}^s\right|}^2}{{\left|{\stackrel{\→}{E}}^i\right|}^2}\right\}=\underset{r\→\∞}{\lim }\left\{4\mathrm{\π}{r}^2\frac{{\left|{\stackrel{\→}{E}}_E^{\mathrm{se}}\right|}^2\·{\left|{\stackrel{\→}{E}}_a^s\right|}^2}{{\left|{\stackrel{\→}{E}}^i\right|}^2}\right\}=\underset{r\→\∞}{\lim }\{4\mathrm{\π}{r}^2\frac{{\left|{\stackrel{\→}{E}}_E^{\mathrm{se}}\right|}^2}{{\left|{\stackrel{\→}{E}}^i\right|}^2}\·{\left|{\stackrel{\→}{E}}_a^s\right|}^2\}$

Wherein, the scattering unit factor ${\mathrm{\σ}}_e=\underset{r\→\∞}{\lim }\left\{4\mathrm{\π}{r}^2\frac{{\left|{\stackrel{\→}{E}}_e^s\right|}^2}{{\left|{\stackrel{\→}{E}}^i\right|}^2}\right\},$ Scattering array factor is ${\mathrm{\σ}}_a=\underset{r\→\∞}{\lim }{\left|{\stackrel{\→}{E}}_a^s\right|}^2;$

(5b) the array antenna scattered field phase differential ΔΦ that utilizes step (3c) to obtain ^s _mn, and the sparse matrix F of arranging of array antenna unit that obtains of step (2b) _mn, obtain under the t time sparse arrangement F of array antenna (t), equidistantly the scattering pattern function of rectangular grid array antenna is

According to the interference of electromagenetic wave radiation and superposition principle, in the time of computing array antenna scattering characteristic, only need to calculate scattering array factor ;

(5c) draw and obtain its scattering directional diagram according to scattering pattern function, and calculate the scattered field maximum sidelobe levels PSLL under the t time sparse arrangement F of array antenna (t) _s.

Further, described step (5c) is calculated the scattered field maximum sidelobe levels PSLL under the t time sparse arrangement F of array antenna (t) _scarry out according to the following procedure:

I) array antenna scattered field minor level is field intensity value corresponding to each flex point in scattering directional diagram, for plane, for obtaining the flex point of scattering pattern function, makes scattering array factor first order derivative be zero, second derivative is less than zero,

Wherein, θ ^q=[θ ¹, θ ²... θ ^q] be incident angle corresponding to each flex point except main lobe in scattering array factor directional diagram, Q is the flex point sum in scattering array factor directional diagram;

II) each secondary lobe of obtaining accordingly in scattering directional diagram is

Thereby the maximum sidelobe levels obtaining in scattering directional diagram is

Wherein be under the t time sparse arrangement F of array antenna (t) incident angle corresponding to in-plane scatter field maximum sidelobe levels.

Further, step (6) judges that whether radiation field and the scattered field under the sparse arrangement of this array antenna meets Sidelobe requirement simultaneously, carries out according to the following procedure:

If (6a) meet simultaneously

$\left\{\begin{array}{c}{\mathrm{PSLL}}_r\≤{\mathrm{PSLL}}_r^C\\ {\mathrm{PSLL}}_s\≤{\mathrm{PSLL}}_s^C\end{array}\right.$

The sparse arrangement of this array antenna is the sparse arrangement of optimum that simultaneously realizes array antenna radiation field and scattered field Sidelobe, wherein with be respectively the design objective of array antenna radiation field and scattered field Sidelobe in engineering;

If (6b) do not meet the demands, upgrade the sparse matrix of arranging of array antenna unit by the method for crossover and mutation respectively;

The crossing-over rate G and the variation multiplying power H that define F (t) under the sparse matrix of arranging of the t time sparse arrangement of antenna are respectively

$G={({\mathrm{\ω}}_1\·|\frac{{\mathrm{PSLL}}_r^C}{{\mathrm{PSLL}}_r\left[F\left(t\right)\right]}|\×100\%,{\mathrm{\ω}}_2\·|\frac{{\mathrm{PSLL}}_s^C}{{\mathrm{PSLL}}_s\left[F\left(t\right)\right]}|\×100\%)}_{\max }$

According to probability G by the sparse matrix F of arranging (t) | _{m × N}in before (1-G) % capable, front (1-G) % column matrix element and rear (1-G) % is capable, rear (1-G) % column matrix element switch, if front (1-G) % matrix element and rear (1-G) % matrix element have overlapping,, by the negate of overlay elements value, become 1 element by 0 element in matrix; Simultaneously, by H, 2H...nH (nH<M) in matrix OK, the matrix element negate of H, 2H...nH (nH<N) row, thus the sparse matrix of arranging that obtains the t+1 time sparse arrangement of antenna is F (t+1) | _{m × N}; Wherein, ω ₁, ω ₂, ω ₃, ω ₄for weighting coefficient.

The present invention compared with prior art, has following characteristics:

1. become and tilted to install the chief threat that array antenna is detected for scattered field secondary lobe, and radiation field Sidelobe performance is for the importance of its antijamming capability, the present invention arranges by changing the sparse of antenna element in array antenna, has realized the Sidelobe performance of array antenna radiation field and scattered field simultaneously.Overcome the implementation method that existing research only exists array antenna radiation field Sidelobe, and pair array antenna scattering field Sidelobe performance is difficult to the deficiency realizing.

2. the present invention is by analyzing the relative merits of array antenna radiation field Sidelobe implementation method, and scattered field Sidelobe realize in restriction, find the method that can simultaneously realize radiation field and scattering Sidelobe, for array antenna radiation and scattering property comprehensively found new thinking and method, simultaneously for the development of high-gain, high Stealth Fighter array antenna provides structural design scheme basis.

Brief description of the drawings

Fig. 1 is the process flow diagram of technical solution of the present invention.

Fig. 2 is equidistant rectangular grid array antenna schematic diagram.

Fig. 3 is the sparse scheme iterative process of array antenna unit.

Fig. 4 is the array antenna first quartile 3D antenna pattern under the sparse scheme of optimum array antenna unit.

Fig. 5 is array antenna radiation field E face and H face directional diagram under the sparse scheme of optimum array antenna unit.

Fig. 6 is array antenna scattered field RCS directional diagram under the sparse scheme of optimum array antenna unit.

Embodiment

Below in conjunction with drawings and Examples, the present invention will be further described.

With reference to Fig. 1, based on the sparse array antenna radiation field of arranging of antenna element and the comprehensive Sidelobe Fast implementation of scattered field, concrete steps are as follows:

Step 1, determines structural parameters, the electromagnetism running parameter of array antenna and front layout parameter

1.1) obtain the structural parameters of array antenna, comprising the equidistant structural parameters of rectangular grid array antenna, comprising the horizontal grid of front count M, longitudinally grid is counted N and lateral cell spacing d _x, longitudinal grid distance d _y, as shown in Figure 2;

1.2) obtain the electromagnetism running parameter of array antenna, comprise the frequency of operation f of this array antenna _rthe antenna wavelength λ of frequency computation part according to this _r, incident wave frequency f when this antenna of radar illumination _sthe incident wave wavelength X of this antenna of radar illumination of frequency computation part according to this _s;

1.3) obtain the front layout parameter of array antenna, comprise the sparse rate ξ of front.

Step 2, determines the sparse arrangement that array antenna is initial, obtains the sparse matrix of arranging of array antenna unit

2.1) this grid point value is designated as to 1 if place antenna element on some grids of certain equidistant rectangular grid array antenna, this grid point value is designated as to 0 if do not place antenna element, the each grid point value of sequential storage of numbering according to the grid of equidistant matrix grid array antenna according to this, thus the sparse matrix F of arranging of array antenna unit obtained;

2.2) get the sparse matrix F of arranging of original array antenna element (0) [0,1] matrix for the capable N row of the random M generating, and the grid of equidistantly not placing antenna element in grid battle array is counted N ⁰the grid of (being to be the number of 0 element in matrix) and placement antenna element is counted N ¹the ratio of (being to be the number of 1 element in matrix) meets

$\frac{N^1}{N^1+N^0}=\mathrm{\&xi;}---\left(1\right).$

Step 3, the radiation field of computing array antenna and scattered field actinal surface phase differential

3.1) establish in the array antenna battle array of equidistant rectangular grid arrangement, observation point P is with respect to the direction at coordinate system O-xyz place be expressed as (cos φ with direction cosine _x, cos φ _y, cos φ _z).Obtaining observation point P with respect to the angle of coordinate axis and the pass of direction cosine is

3.2) establish the horizontal and vertical grid distance of array antenna that equidistant rectangular grid arranges and be respectively d _xand d _y, the antenna element that adjacent two grids (i, j) and (i-1, j-1) locate is the space quadrature along x-axis, y-axis and z-axis at target place be respectively

$\left\{\begin{array}{c}\mathrm{\&Delta;}{\mathrm{\&Phi;}}_x^{i,j}=k_r\&CenterDot;d_x\&CenterDot;\cos {\mathrm{\&phi;}}_x\\ \mathrm{\&Delta;}{\mathrm{\&Phi;}}_y^{i,j}=k_r\&CenterDot;d_y\&CenterDot;\cos {\mathrm{\&phi;}}_y\\ \mathrm{\&Delta;}{\mathrm{\&Phi;}}_z^{i,j}=0\end{array}\right.---\left(3\right)$

Wherein, k _r=2 π/λ _rfor space wave constant; λ _rfor antenna electromagnetic wavelength;

3.3) antenna element at (m, n) individual grid place is with respect to the radiation field phase differential ΔΦ of the antenna element at (1,1) individual grid place ^r _mnfor

$\begin{array}{c}\mathrm{\&Delta;}{{\mathrm{\&Phi;}}^r}_{\mathrm{mn}}=\mathrm{\&Delta;}{\mathrm{\&Phi;}}_x^{m,n}+\mathrm{\&Delta;}{\mathrm{\&Phi;}}_y^{m,n}+\mathrm{\&Delta;}{\mathrm{\&Phi;}}_z^{m,n}\\ =k_r\&CenterDot;[(m-1)\&CenterDot;d_x\&CenterDot;\cos {\mathrm{\&phi;}}_x+(n-1)\&CenterDot;d_y\&CenterDot;\cos {\mathrm{\&phi;}}_y]\end{array}---\left(4\right)$

From the scattering mechanism of array antenna, the scattered field phase differential in array antenna between antenna element is the twice of phase differential between radiation field-based antenna unit., in equidistant rectangular grid array antenna, the antenna element at (m, n) individual grid place is with respect to the scattered field phase differential ΔΦ of the antenna element at (1,1) individual grid place ^s _mnfor

$\begin{array}{c}\mathrm{\&Delta;}{{\mathrm{\&Phi;}}^s}_{\mathrm{mn}}=2\&CenterDot;(\mathrm{\&Delta;}{\mathrm{\&Phi;}}_x^{m,n}+\mathrm{\&Delta;}{\mathrm{\&Phi;}}_y^{m,n}+\mathrm{\&Delta;}{\mathrm{\&Phi;}}_z^{m,n})\\ =2\&CenterDot;k_r\&CenterDot;[(m-1)\&CenterDot;d_x\&CenterDot;\cos {\mathrm{\&phi;}}_x+(n-1)\&CenterDot;d_y\&CenterDot;\cos {\mathrm{\&phi;}}_y]\end{array}---\left(5\right)$

Wherein, k _s=2 π/λ _sfor scattered field space wave constant, λ _sfor radar detection wave-wave long; the antenna element that represents respectively (m, n) individual grid place is the space quadrature along x-axis, y-axis and z-axis with respect to the antenna element at (1,1) individual grid place;

3.4) by equidistant rectangular grid array antenna, the antenna element at each grid place is with respect in array the (1,1) the antenna element radiation field phase differential at individual grid place and scattered field phase differential, become the form of matrix according to the sequential storage of array antenna grid numbering, can obtain radiation field actinal surface phase differential and the scattered field actinal surface phase differential of array antenna.

Step 4, the radiation field maximum sidelobe levels under computing array radiation field of aerial pattern function and now unit arrangement

4.1) according to array antenna electromagnetic wave superposition principle and directional diagram product theorem, the array antenna radiation field phase differential ΔΦ that utilizes formula (4) to obtain ^r _mn, and the sparse matrix F of arranging of array antenna unit that obtains of step (2.2) _mn, can obtain under the t time sparse arrangement F of array antenna (t), equidistantly the antenna pattern function of rectangular grid array antenna is

In formula, I _mnit is the exciting current of antenna element in battle array; for the radiating element factor; for radiation array factor; According to the interference of electromagenetic wave radiation and superposition principle, in the time of computing array antenna radiation characteristics, only need to calculate radiation array factor ;

4.2) draw and obtain its antenna pattern according to antenna pattern function, and calculate the radiation field maximum sidelobe levels PSLL under the t time sparse arrangement F of array antenna (t) _r;

Array antenna minor level is field intensity value corresponding to each flex point in antenna pattern.For plane, for obtaining the flex point of antenna pattern function, makes radiation array factor first order derivative be zero, second derivative is less than zero,

Wherein, θ ^p=[θ ¹, θ ²... θ ^p] be position angle corresponding to each flex point except main lobe in radiation array factor directional diagram, P is the flex point sum in radiation array factor directional diagram;

Each secondary lobe that can obtain accordingly in antenna pattern is

Thereby the maximum sidelobe levels obtaining in antenna pattern is

Wherein be under the t time sparse arrangement F of array antenna (t) the position angle that plane radiation field maximum sidelobe levels is corresponding.

Step 5, the scattered field maximum sidelobe levels under computing array antenna scattering field pattern function and now unit arrangement

5.1) analyzing known array radar scattering cross-section according to the computing formula of RCS and antenna element phase differential is:

$\mathrm{\&sigma;}=\underset{r\&RightArrow;\&infin;}{\lim }\left\{4\mathrm{\&pi;}{r}^2\frac{{\left|{\stackrel{\&RightArrow;}{E}}^s\right|}^2}{{\left|{\stackrel{\&RightArrow;}{E}}^i\right|}^2}\right\}=\underset{r\&RightArrow;\&infin;}{\lim }\left\{4\mathrm{\&pi;}{r}^2\frac{{\left|{\stackrel{\&RightArrow;}{E}}_E^{\mathrm{se}}\right|}^2\&CenterDot;{\left|{\stackrel{\&RightArrow;}{E}}_a^s\right|}^2}{{\left|{\stackrel{\&RightArrow;}{E}}^i\right|}^2}\right\}=\underset{r\&RightArrow;\&infin;}{\lim }\{4\mathrm{\&pi;}{r}^2\frac{{\left|{\stackrel{\&RightArrow;}{E}}_E^{\mathrm{se}}\right|}^2}{{\left|{\stackrel{\&RightArrow;}{E}}^i\right|}^2}\&CenterDot;{\left|{\stackrel{\&RightArrow;}{E}}_a^s\right|}^2\}---\left(11\right)$

The definition scattering unit factor ${\mathrm{\&sigma;}}_e=\underset{r\&RightArrow;\&infin;}{\lim }\left\{4\mathrm{\&pi;}{r}^2\frac{{\left|{\stackrel{\&RightArrow;}{E}}_e^s\right|}^2}{{\left|{\stackrel{\&RightArrow;}{E}}^i\right|}^2}\right\},$ Scattering array factor is ${\mathrm{\&sigma;}}_a=\underset{r\&RightArrow;\&infin;}{\lim }{\left|{\stackrel{\&RightArrow;}{E}}_a^s\right|}^2;$

5.2) the array antenna scattered field phase differential ΔΦ that utilizes formula (5) to obtain ^s _mn, and the sparse matrix F of arranging of array antenna unit that obtains of step (2.2) _mn, can obtain under the t time sparse arrangement F of array antenna (t), equidistantly the scattering pattern function of rectangular grid array antenna is:

According to the interference of electromagenetic wave radiation and superposition principle, in the time that calculating antenna scattering characteristic, research only needs to calculate scattering array factor ;

5.3) draw and obtain its scattering directional diagram according to scattering pattern function, and calculate the scattered field maximum sidelobe levels PSLL under the t time sparse arrangement F of array antenna (t) _s:

Array antenna scattered field minor level is field intensity value corresponding to each flex point in scattering directional diagram.For plane, for obtaining the flex point of scattering pattern function, makes scattering array factor first order derivative be zero, second derivative is less than zero,

Wherein, θ ^q=[θ ¹, θ ²... θ ^q] be incident angle corresponding to each flex point except main lobe in scattering array factor directional diagram, Q is the flex point sum in scattering array factor directional diagram;

Each secondary lobe that can obtain accordingly in scattering directional diagram is

Thereby the maximum sidelobe levels obtaining in scattering directional diagram is

Wherein be under the t time sparse arrangement F of array antenna (t) incident angle corresponding to in-plane scatter field maximum sidelobe levels.

Step 6, judges whether radiation field and the scattered field under the sparse arrangement of this array antenna meets Sidelobe requirement simultaneously

6.1) if meet simultaneously

$\left\{\begin{array}{c}{\mathrm{PSLL}}_r\&le;{\mathrm{PSLL}}_r^C\\ {\mathrm{PSLL}}_s\&le;{\mathrm{PSLL}}_s^C\end{array}\right.---\left(17\right)$

The sparse arrangement of this array antenna is the sparse arrangement of optimum that can simultaneously realize array antenna radiation field and scattered field Sidelobe, wherein with be respectively the design objective of array antenna radiation field and scattered field Sidelobe in engineering;

6.2), if do not meet the demands, upgrade the sparse matrix of arranging of array antenna unit by the method for crossover and mutation respectively;

The crossing-over rate G and the variation multiplying power H that define F (t) under the sparse matrix of arranging of the t time sparse arrangement of antenna are respectively:

$G={({\mathrm{\&omega;}}_1\&CenterDot;|\frac{{\mathrm{PSLL}}_r^C}{{\mathrm{PSLL}}_r\left[F\left(t\right)\right]}|\&times;100\%,{\mathrm{\&omega;}}_2\&CenterDot;|\frac{{\mathrm{PSLL}}_s^C}{{\mathrm{PSLL}}_s\left[F\left(t\right)\right]}|\&times;100\%)}_{\max }---\left(18\right)$

According to probability G by the sparse matrix F of arranging (t) | _{m × N}in before (1-G) % capable, front (1-G) % column matrix element and rear (1-G) % is capable, rear (1-G) % column matrix element switch, if it is overlapping that front (1-G) % matrix element and rear (1-G) % matrix element have, by the negate of overlay elements value (becoming 1 element by 0 element in matrix).Simultaneously, by H, 2H...nH (nH<M) in matrix OK, the matrix element negate of H, 2H...nH (nH<N) row, thus the sparse matrix of arranging that obtains the t+1 time sparse arrangement of antenna is F (t+1) | _{m × N}.Wherein, ω ₁, ω ₂, ω ₃, ω ₄for weighting coefficient, in the present invention, get ω ₁=ω ₂=1, ω ₃=ω ₄=2.

Advantage of the present invention can further illustrate by following emulation experiment:

1. determine structural parameters and the electromagnetic parameter of array antenna, and front layout parameter

(1.1) this experiment is with frequency of operation f _r=3GHz, wavelength X _rcertain airborne radar of=100mm is example, gets in equidistant rectangular grid array antenna and has 20 × 20 grids, considers that this experimental array antenna is for onboard radar system, and therefore, in 20 × 20 grids, getting front bore D is 10 λ _r(1000mm), x, equidistant 0.5 λ of y direction _r(50mm).Getting antenna element is half-wave doublet.Consider that this operating frequency of antenna found out by non-partner, get radar detection ripple frequency f _sfor the central task frequency of this radiation field of aerial, i.e. f _s=f _r=3GHz, incides this array with Ψ angle (pi/2≤Ψ≤pi/2).And suppose that the exciting current of Antenna aperture adopts the even weighting of constant amplitude homophase, i.e. I _mn=1;

(1.2) according to the conventional sparse rate of thinned array in engineering reality, in this experiment, getting the sparse rate of front is ξ=67%.

2. determine that the initial bare cloth scheme of array antenna obtains the sparse matrix of arranging of array antenna unit

Get the sparse matrix F of arranging of original array antenna element (0) [0,1] matrix for the capable N row of the random M generating, and in sparse matrix, be that 1 element is 67% of the total element of whole matrix.In Matlab software, according to the random sparse matrix of arranging of array antenna initial cell generating of front bare cloth rate ξ be

3. computing array radiation pattern function, radiation field maximum sidelobe levels value, and scattered field pattern function, and scattered field maximum sidelobe levels value.

(3.1) according to formula (6), can obtain array antenna antenna pattern function, calculate the array antenna radiation field maximum sidelobe levels under this antenna element bare cloth scheme according to formula (7)～formula (12);

(3.2) according to formula (12), can obtain array antenna scattered field pattern function, calculate the array antenna scattered field maximum sidelobe levels under this antenna element bare cloth scheme according to formula (13)～formula (16).

4. optimum array antenna unit bare cloth scheme and electrical property result

Upgrade respectively unit bare cloth matrix the double counting of array antenna by crossover and mutation according to formula (18) and formula (19), convergence process as shown in Figure 3, upgrade through 400 times, while being t=400, the optimum array antenna unit bare cloth matrix F (400) that is simultaneously realized radiation field and scattered field Sidelobe performance is:

Obtain array antenna radiation field gain 3D directional diagram (first quartile) and E face and H face directional diagram as shown in Figure 4 and Figure 5 according to this array antenna unit bare cloth matrix computations, scattered field directional diagram as shown in Figure 6.Concrete data are more as shown in table 1.

Radiation field and the scattered field maximum sidelobe levels value of table 1 optimal antenna unit under arranging

Can find out from the data of Fig. 4～Fig. 6 and table 1, under this array antenna unit bare cloth matrix, this array antenna radiation field E face and be respectively-24.98dB of H face maximum sidelobe levels and-23.18dB, scattered field secondary lobe all-below 25dBsm.Visible under this array antenna unit bare cloth scheme, array antenna radiation field and scattered field have been realized Sidelobe performance simultaneously.

Above-mentioned emulation experiment can be found out, can arrange by the unit that changes array antenna according to the inventive method, thereby realize the Sidelobe performance of array antenna radiation field and scattered field simultaneously, method of the present invention is also comprehensively providing of array antenna radiation and scattering property new thinking and method simultaneously, for the development of high-gain, high Stealth Fighter array antenna provides structural design scheme basis.

Claims (10)

1. the comprehensive Sidelobe Fast implementation of array antenna radiation field and scattered field, is characterized in that, comprises following process:

(1) according to the version of the equidistant rectangular grid array antenna of plane, determine array antenna structure parameter, electromagnetism running parameter, and front layout parameter;

(2) according to array antenna structure parameter and front layout parameter, provide the initial sparse arrangement of array antenna, obtain the sparse matrix of arranging of array antenna unit;

(3), according to the structural parameters of array antenna and electromagnetism running parameter, utilize the array antenna unit parameter of arranging, the radiation field of computing array antenna and scattered field actinal surface phase differential;

(4) associated matrix array antenna radiation field actinal surface phase differential, and the sparse matrix of arranging of array antenna unit, the antenna pattern function of computing array antenna, and calculate the maximum sidelobe levels of array antenna radiation field under this sparse arrangement according to array antenna antenna pattern function;

(5) associated matrix array antenna scattered field actinal surface phase differential, and the sparse matrix of arranging of array antenna unit, the scattering pattern function of computing array antenna, and calculate the maximum sidelobe levels of array antenna scattered field under this sparse arrangement according to array antenna scattering pattern function;

(6), according to array antenna design objective, judge whether radiation field and the scattered field under the sparse arrangement of this array antenna meets Sidelobe requirement simultaneously; If meet, the sparse arrangement of this array antenna is the sparse arrangement of optimum that simultaneously realizes array antenna radiation field and scattered field Sidelobe; Otherwise, according to last radiation field and scattered field maximum sidelobe levels value, upgrade the sparse matrix of arranging of array antenna unit by the method for crossover and mutation, and repeating step (3) is to step (6) until meet the demands.

2. the comprehensive Sidelobe Fast implementation of array antenna radiation field according to claim 1 and scattered field, it is characterized in that, in step (1), described definite array antenna structure parameter, comprising front grid line number M, columns and horizontal, longitudinal grid distance; Described definite array antenna electromagnetism running parameter, comprising central task frequency, incident wave frequency; Described definite array antenna front layout parameter, comprises the sparse rate of front.

3. the comprehensive Sidelobe Fast implementation of array antenna radiation field according to claim 1 and scattered field, it is characterized in that, described step (2) provides the initial sparse arrangement of array antenna, determine each grid place in original array antenna and whether place antenna element, obtain the sparse matrix of arranging of array antenna unit, carry out according to the following procedure:

(2a) establish total M × N grid in equidistant rectangular grid array antenna, wherein laterally grid number is M, and longitudinally grid number is N; This grid point value is designated as to 1 if place antenna element on some grids, this grid point value is designated as to 0 if do not place antenna element, the each grid point value of sequential storage of numbering according to the grid of equidistant matrix grid array antenna according to this, thus the sparse matrix of arranging of array antenna unit obtained;

(2b) establishing the sparse matrix of arranging of array antenna unit is F, the sparse rate of front is ξ, get the sparse matrix F of arranging of original array antenna element (0) [0,1] matrix for the capable N row of the random M generating, and the grid of equidistantly not placing antenna element in grid battle array is counted N ⁰count N with the grid of placing antenna element ¹ratio meet

$\frac{N^1}{N^1+N^0}=\mathrm{\&xi;}.$

4. the comprehensive Sidelobe Fast implementation of array antenna radiation field according to claim 3 and scattered field, is characterized in that, equidistantly in grid battle array, does not place the grid of antenna element and counts N ⁰for being the number of 0 element in matrix; Place the grid of antenna element and count N ¹for being the number of 1 element in matrix.

5. the comprehensive Sidelobe Fast implementation of array antenna radiation field according to claim 1 and scattered field, is characterized in that, described step (3) is carried out according to the following procedure:

(3a) establish in the array antenna battle array of equidistant rectangular grid arrangement, observation point P is with respect to the direction at coordinate system O-xyz place be expressed as (cos φ with direction cosine _x, cos φ _y, cos φ _z), obtain observation point P and with respect to the angle of coordinate axis and the pass of direction cosine be

(3b) establish the horizontal and vertical grid distance of array antenna that equidistant rectangular grid arranges and be respectively d _xand d _y, the antenna element that adjacent two grids (i, j) and (i-1, j-1) locate is the space quadrature along x-axis, y-axis and z-axis at target place be respectively

$\left\{\begin{array}{c}\mathrm{\&Delta;}{\mathrm{\&Phi;}}_x^{i,j}=k_r\&CenterDot;d_x\&CenterDot;\cos {\mathrm{\&phi;}}_x\\ \mathrm{\&Delta;}{\mathrm{\&Phi;}}_y^{i,j}=k_r\&CenterDot;d_y\&CenterDot;\cos {\mathrm{\&phi;}}_y\\ \mathrm{\&Delta;}{\mathrm{\&Phi;}}_z^{i,j}=0\end{array}\right.$

Wherein, k _r=2 π/λ _rfor space wave constant; λ _rfor antenna electromagnetic wavelength;

(3c) antenna element at (m, n) individual grid place is with respect to the radiation field phase differential ΔΦ of the antenna element at (1,1) individual grid place ^r _mnfor

$\begin{array}{c}\mathrm{\&Delta;}{{\mathrm{\&Phi;}}^r}_{\mathrm{mn}}=\mathrm{\&Delta;}{\mathrm{\&Phi;}}_x^{m,n}+\mathrm{\&Delta;}{\mathrm{\&Phi;}}_y^{m,n}+\mathrm{\&Delta;}{\mathrm{\&Phi;}}_z^{m,n}\\ =k_r\&CenterDot;[(m-1)\&CenterDot;d_x\&CenterDot;\cos {\mathrm{\&phi;}}_x+(n-1)\&CenterDot;d_y\&CenterDot;\cos {\mathrm{\&phi;}}_y]\end{array};$

Scattered field phase differential in array antenna between antenna element is the twice of phase differential between radiation field-based antenna unit, in equidistant rectangular grid array antenna, (m, n) antenna element at individual grid place is with respect to the scattered field phase differential ΔΦ of the antenna element at (1,1) individual grid place ^s _mnfor

$\begin{array}{c}\mathrm{\&Delta;}{{\mathrm{\&Phi;}}^s}_{\mathrm{mn}}=2\&CenterDot;(\mathrm{\&Delta;}{\mathrm{\&Phi;}}_x^{m,n}+\mathrm{\&Delta;}{\mathrm{\&Phi;}}_y^{m,n}+\mathrm{\&Delta;}{\mathrm{\&Phi;}}_z^{m,n})\\ =2\&CenterDot;k_r\&CenterDot;[(m-1)\&CenterDot;d_x\&CenterDot;\cos {\mathrm{\&phi;}}_x+(n-1)\&CenterDot;d_y\&CenterDot;\cos {\mathrm{\&phi;}}_y]\end{array};$

Wherein, k _s=2 π/λ _sfor scattered field space wave constant, λ _sfor radar detection wave-wave long; the antenna element that represents respectively (m, n) individual grid place is the space quadrature along x-axis, y-axis and z-axis with respect to the antenna element at (1,1) individual grid place;

(3d) by equidistant rectangular grid array antenna, the antenna element at each grid place is with respect in array the (1,1) the antenna element radiation field phase differential at individual grid place and scattered field phase differential, become the form of matrix according to the sequential storage of array antenna grid numbering, obtain radiation field actinal surface phase differential and the scattered field actinal surface phase differential of array antenna.

6. according to the array antenna radiation field described in claim 3-5 and the comprehensive Sidelobe Fast implementation of scattered field, it is characterized in that, step (4) is carried out according to the following procedure:

(4a) according to array antenna electromagnetic wave superposition principle and directional diagram product theorem, the array antenna radiation field phase differential ΔΦ that utilizes step (3c) to obtain ^r _mn, and the sparse matrix F of arranging of array antenna unit that obtains of step (2b) _mn, the antenna pattern function that obtains the lower equidistant rectangular grid array antenna of the t time sparse arrangement F of array antenna (t) is

In formula, I _mnit is the exciting current of antenna element in battle array; for the radiating element factor; for radiation array factor; According to the interference of electromagenetic wave radiation and superposition principle, in the time of computing array antenna radiation characteristics, only need to calculate radiation array factor ;

(4b) draw and obtain its antenna pattern according to antenna pattern function, and calculate the radiation field maximum sidelobe levels PSLL under the t time sparse arrangement F of array antenna (t) _r.

7. the comprehensive Sidelobe Fast implementation of array antenna radiation field according to claim 6 and scattered field, it is characterized in that, described step (4b) is calculated the radiation field maximum sidelobe levels PSLL under the t time sparse arrangement F of array antenna (t) _rrealize by following manner:

I) array antenna minor level is field intensity value corresponding to each flex point in antenna pattern, for plane, for obtaining the flex point of antenna pattern function, makes radiation array factor first order derivative be zero, second derivative is less than zero,

Wherein, θ ^p=[θ ¹, θ ²... θ ^p] be position angle corresponding to each flex point except main lobe in radiation array factor directional diagram, P is the flex point sum in radiation array factor directional diagram;

II) each secondary lobe of obtaining accordingly in antenna pattern is

Thereby the maximum sidelobe levels obtaining in antenna pattern is

Wherein be under the t time sparse arrangement F of array antenna (t) the position angle that plane radiation field maximum sidelobe levels is corresponding.

8. the comprehensive Sidelobe Fast implementation of array antenna radiation field according to claim 1 and scattered field, is characterized in that, step (5) is carried out according to the following procedure:

(5a) analyzing known array radar scattering cross-section according to the computing formula of RCS and antenna element phase differential is

$\mathrm{\&sigma;}=\underset{r\&RightArrow;\&infin;}{\lim }\left\{4\mathrm{\&pi;}{r}^2\frac{{\left|{\stackrel{\&RightArrow;}{E}}^s\right|}^2}{{\left|{\stackrel{\&RightArrow;}{E}}^i\right|}^2}\right\}=\underset{r\&RightArrow;\&infin;}{\lim }\left\{4\mathrm{\&pi;}{r}^2\frac{{\left|{\stackrel{\&RightArrow;}{E}}_E^{\mathrm{se}}\right|}^2\&CenterDot;{\left|{\stackrel{\&RightArrow;}{E}}_a^s\right|}^2}{{\left|{\stackrel{\&RightArrow;}{E}}^i\right|}^2}\right\}=\underset{r\&RightArrow;\&infin;}{\lim }\{4\mathrm{\&pi;}{r}^2\frac{{\left|{\stackrel{\&RightArrow;}{E}}_E^{\mathrm{se}}\right|}^2}{{\left|{\stackrel{\&RightArrow;}{E}}^i\right|}^2}\&CenterDot;{\left|{\stackrel{\&RightArrow;}{E}}_a^s\right|}^2\}$

Wherein, the scattering unit factor ${\mathrm{\&sigma;}}_e=\underset{r\&RightArrow;\&infin;}{\lim }\left\{4\mathrm{\&pi;}{r}^2\frac{{\left|{\stackrel{\&RightArrow;}{E}}_e^s\right|}^2}{{\left|{\stackrel{\&RightArrow;}{E}}^i\right|}^2}\right\},$ Scattering array factor is ${\mathrm{\&sigma;}}_a=\underset{r\&RightArrow;\&infin;}{\lim }{\left|{\stackrel{\&RightArrow;}{E}}_a^s\right|}^2;$

(5b) the array antenna scattered field phase differential ΔΦ that utilizes step (3c) to obtain ^s _mn, and the sparse matrix F of arranging of array antenna unit that obtains of step (2b) _mn, obtain under the t time sparse arrangement F of array antenna (t), equidistantly the scattering pattern function of rectangular grid array antenna is

According to the interference of electromagenetic wave radiation and superposition principle, in the time of computing array antenna scattering characteristic, only need to calculate scattering array factor ;

(5c) draw and obtain its scattering directional diagram according to scattering pattern function, and calculate the scattered field maximum sidelobe levels PSLL under the t time sparse arrangement F of array antenna (t) _s.

9. the comprehensive Sidelobe Fast implementation of array antenna radiation field according to claim 8 and scattered field, it is characterized in that, described step (5c) is calculated the scattered field maximum sidelobe levels PSLL under the t time sparse arrangement F of array antenna (t) _scarry out according to the following procedure:

I) array antenna scattered field minor level is field intensity value corresponding to each flex point in scattering directional diagram, for plane, for obtaining the flex point of scattering pattern function, makes scattering array factor first order derivative be zero, second derivative is less than zero,

Wherein, θ ^q=[θ ¹, θ ²... θ ^q] be incident angle corresponding to each flex point except main lobe in scattering array factor directional diagram, Q is the flex point sum in scattering array factor directional diagram;

II) each secondary lobe of obtaining accordingly in scattering directional diagram is

Thereby the maximum sidelobe levels obtaining in scattering directional diagram is

Wherein be under the t time sparse arrangement F of array antenna (t) incident angle corresponding to in-plane scatter field maximum sidelobe levels.

10. the comprehensive Sidelobe Fast implementation of array antenna radiation field according to claim 1 and scattered field, it is characterized in that, step (6) judges that whether radiation field and the scattered field under the sparse arrangement of this array antenna meets Sidelobe requirement simultaneously, carries out according to the following procedure:

If (6a) meet simultaneously

$\left\{\begin{array}{c}{\mathrm{PSLL}}_r\&le;{\mathrm{PSLL}}_r^C\\ {\mathrm{PSLL}}_s\&le;{\mathrm{PSLL}}_s^C\end{array}\right.$

The sparse arrangement of this array antenna is the sparse arrangement of optimum that simultaneously realizes array antenna radiation field and scattered field Sidelobe, wherein with be respectively the design objective of array antenna radiation field and scattered field Sidelobe in engineering;

If (6b) do not meet the demands, upgrade the sparse matrix of arranging of array antenna unit by the method for crossover and mutation respectively;

The crossing-over rate G and the variation multiplying power H that define F (t) under the sparse matrix of arranging of the t time sparse arrangement of antenna are respectively

$G={({\mathrm{\&omega;}}_1\&CenterDot;|\frac{{\mathrm{PSLL}}_r^C}{{\mathrm{PSLL}}_r\left[F\left(t\right)\right]}|\&times;100\%,{\mathrm{\&omega;}}_2\&CenterDot;|\frac{{\mathrm{PSLL}}_s^C}{{\mathrm{PSLL}}_s\left[F\left(t\right)\right]}|\&times;100\%)}_{\max }$

According to probability G by the sparse matrix F of arranging (t) | _{m × N}in before (1-G) % capable, front (1-G) % column matrix element and rear (1-G) % is capable, rear (1-G) % column matrix element switch, if front (1-G) % matrix element and rear (1-G) % matrix element have overlapping,, by the negate of overlay elements value, become 1 element by 0 element in matrix; Simultaneously, by H, 2H...nH (nH<M) in matrix OK, the matrix element negate of H, 2H...nH (nH<N) row, thus the sparse matrix of arranging that obtains the t+1 time sparse arrangement of antenna is F (t+1) | _{m × N}; Wherein, ω ₁, ω ₂, ω ₃, ω ₄for weighting coefficient.