CN108920767A - The double constraint lobe array antenna optimum design methods of cosecant quadratic sum synthesis phase - Google Patents
The double constraint lobe array antenna optimum design methods of cosecant quadratic sum synthesis phase Download PDFInfo
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Abstract
The invention discloses a kind of double constraint lobe array antenna optimum design methods of cosecant quadratic sum synthesis phase, mainly solve the problems, such as that existing antenna cosecant square lobe is unable to angle measurement and the low elevation angle measuring angle by comparing amplitude precision of pen shape lobe is not high.Implementation step is：Determine array antenna geometric configuration and horizontal direction array element spacing and pitch orientation array element spacing, array antenna geometric configuration selects rectangular element grid；Determine antenna aperture and orientation, pitching array number；Bay type is selected, the lobe of bay is designed；The wave beam under the conditions of cosecant square lobe and phase restriction is designed, array antenna is constructed using global optimization probability search method and optimization design problem solves；Amplitude and phase are motivated according to array element, design feeding network；Bay and feeding network are integrated, optimize each port phase of feeding network, are finely adjusted to array beams directional diagram, meet the requirement of synthesis wave beam cosecant square lobe and synthesis phase.
Description
Technical field
The present invention relates to a kind of double constraint lobe array antenna optimum design methods of cosecant quadratic sum synthesis phase, belong to battle array
The technical field of column signal processing.
Background technique
The angle of volumetric radar measurement target generallys use pencil beam, carries out than width or Monopulse estimation.Using pen
The antenna of shape wave beam, azimuth beamwidth and the product of pitching beam angle are smaller, and antenna gain is higher, detect the distance of target
It is remoter, but the spatial angle range that wave beam is covered is also smaller.In the case where azimuth beamwidth is certain, covering is caused all to be bowed
The wave beam number in elevation angle airspace increases, the data transfer rate decline of searching sector.Air target search radar, in order to make sustained height not
The target detection of same distance detection probability having the same sets up meter cosecant square lobe, i.e. antenna gainFormula
In, K is constant,For pitch orientation angle, big airspace covering and high search data transfer rate are realized.
In recent years, the tracking and guidance instruction of low target become the problem of very paying close attention to both at home and abroad, and key is low faces upward
Angle height-finding technique.Current low Elevation height uses pencil beam dualbeam measuring angle by comparing amplitude method.In signal-to-noise ratio 12dB, can reach
Angle measurement accuracy be about 1/10th of beam angle, need two to be radiated at 0 ° of elevation angle or more and be offset from the pen shape of fixed angle
Wave beam.Multiple pencil beam scanning covering elevations angle detect airspace, and the survey for completing different height target is high, the data transfer rate of searching sector
It is limited by elevation beamwidth and elevation angle coverage area.Cosecant square lobe can cover whole elevations angle model with single pass
It encloses, but without the ability of measuring angle by comparing amplitude and Monopulse estimation.Design synthesis phase with elevation angle linear change cosecant square lobe,
Using the phase information of cosecant square lobe, the height of target is indicated, can take into account the requirement of elevation angle covering and elevation angle angle measurement.It adopts
With the 2 or 3 cosecant square lobes with out of phase characteristic, 2 or 3 cosecant square lobes are extracted by signal processing
The phase of output, can high-acruracy survey target the elevation angle.
Cosecant square lobe is realized by antenna figuration.The each array element of array antenna is by choosing suitable excitation width
Degree, phase and element position, comprehensive cosecant square wave beam, key out are the design of feeding network.When bay position
Fixed, selecting array element excitation amplitude and phase is the key that realize cosecant square lobe.In antenna lobe general field, modern intelligence
Energy optimization algorithm, such as particle swarm algorithm, genetic algorithm and simulated annealing, opposite traditional algorithm, such as Fourier transform, labor
Gloomy Wood is fertile hereby to integrate scheduling algorithm, there is unrivaled superiority.
Summary of the invention
Technical problem to be solved by the invention is to provide a kind of double constraint lobe array days of cosecant quadratic sum synthesis phase
Line optimum design method, core technology are to optimize battle array using modern intelligence optimization algorithm (global optimization probability search method)
Array antenna array element motivates amplitude and phase, realizes the cosecant square lobe array antenna under synthesis phase constraint, solves cosecant
The double constraint lobe array antenna design problems of quadratic sum synthesis phase.
The present invention uses following technical scheme to solve above-mentioned technical problem：
The present invention provides a kind of double constraint lobe array antenna optimum design methods of cosecant quadratic sum synthesis phase, including such as
Lower specific steps：
Step 1 is covered according to orientation, pitching airspace, determines array antenna geometric configuration and horizontal direction array element spacing
With pitch orientation array element spacing；
Step 2, according to the requirement of antenna gain, azimuth beamwidth, pitching lobe cosecant square, determine antenna aperture and
Orientation, pitching array number；
Step 3, selection bay type, design the lobe of bay, in radar working frequency range, meet low-voltage
The requirement of standing-wave ratio, i.e. impedance matching, bay directional diagram are denoted asWherein θ indicates orientation angle,Expression is bowed
It faces upward to angle；
Wave beam under step 4, design cosecant square lobe and synthesis phase constraint condition, using global optimization probabilistic search
Algorithm solves the construction and optimization design problem of array antenna, specially：
(4.1) according to the requirement of antenna gain, azimuth beamwidth, pitching cosecant square lobe, the array antenna phase is determined
The shaped-beam of prestige, the optimization problem with minimum mean square error criterion construction array antenna design are：
Wherein, In、It respectively indicates the cosecant square lobe with 3 with out of phase characteristic, design cosecant square
Lobe and the first beam-forming network of synthesis phase constraint, the second beam-forming network, n-th of third beam-forming network
The excitation of bay, n=0,1 ..., Ms- 1, MsIndicate pitching to array number；The beam pattern of first beam-forming networkThe beam pattern of second beam-forming network
The beam pattern of third beam-forming networkK indicates wave number, k=2 π/λ, λ table
Oscillography is long, dzIndicate pitch orientation array element spacing；Indicate the main lobe and ideal of the beam pattern of the i-th beam-forming network
The error of cosecant chi square function,
Indicate the value range of ideal cosecant chi square function,Indicate pitching to wave cover minimum angle of elevation,Indicate pitching to wave
Beam covers maximum elevation,It is the value range of ideal cosecant chi square function for beam pattern main lobe regionAngle dis-crete sample values, Q to be taken angle value number,Indicate i-th of wave beam shape
At the maximum value of the beam pattern of network, max () indicates maximizing；[ψ1,ψ2] it is bay designed by step 3
Beam angle,For the difference of angle corresponding to angle corresponding to the array beams major lobe of directional diagram and the first minor lobe；EMSL is
It is expected that maximum sidelobe level, the beam pattern phase of the i-th beam-forming network areArg () table
The main value argument for giving instructions in reply several, () ' indicate to take first derivative, (), " expression took second dervative；σ is empirical value, and value indicates
Antenna phase center spacing size；Min () expression is minimized；
(4.2) using the optimization problem in global optimization probability search method solution procedure (4.1), array element excitation width is obtained
Degree and phase；
Step 5 solves obtained array element excitation amplitude and phase according to step 4, designs feeding network；
Step 6, bay and feeding network are integrated, optimize each port phase of feeding network, i.e. the excitation of adjustment array element
Phase, array beams directional diagram is finely adjusted, meet synthesis wave beam cosecant square lobe and synthesis phase requirement, wave beam
Exporting result isWherein,I-th of array after indicating fine tuning phase optimization
Beam pattern.
As further technical solution of the present invention, array antenna geometric configuration selects rectangular element grid, battle array in step 1
First position is uniformly distributed, horizontal direction array element spacingPitch orientation array element spacingWherein, λminIndicate minimum operation wavelength, θ3dBWithRespectively indicate orientation and pitching to
3dB beam angle, θmaxIndicate orientation maximum scan angle,Indicate pitching to wave cover maximum elevation.
As further technical solution of the present invention, the optimization problem in step (4.1) is turned with linear weight sum method
It is changed to single-object problem：
As further technical solution of the present invention, single-object problem is solved using genetic algorithm.
As further technical solution of the present invention, solution procedure is as follows：
Optimization problem is converted to computer code using real coding by (4.2a), specially：
Optimization problem parametric variable is In、Value is plural number, total 3MsA variable is [0,1] with value range
6MsA real variableReplacement, wherein xm, m=1 ..., MsAnd xm, m=3Ms+1,…,4MsRespectively indicate first wave
The array element that beam forms network motivates amplitude and phase, xm, m=Ms+1,…,2MsAnd xm, m=4Ms+1,…,5MsRespectively indicate
The array element of two beam-forming networks motivates amplitude and phase, xm, m=2Ms+1,…,3MsAnd xm, m=5Ms+1,…,6MsTable respectively
The array element excitation amplitude and phase for showing third beam-forming network, then have
Population Size is arranged in (4.2b), creates initial population, and calculating target function value, i.e. fitness functionValue；
(4.2c) distributes fitness value, carries out Fitness analysis, carries out genetic manipulation, that is, selects, intersects, variation, realizing
Target global optimization probabilistic search；
The judgement of (4.2d) termination condition, fitness function value deviation reaches error margin or algorithm reaches maximum hereditary generation
Number, algorithm terminate；Otherwise, fitness function value is recalculated, the optimizing search for (4.2c) progress next round that gos to step.
The invention adopts the above technical scheme compared with prior art, has the following technical effects：
(1) wide elevation angle covering and high precision angle-measuring：Cosecant square lobe realizes wide elevation coverage covering, 2 or 3 tools
There is the cosecant square wave beam of out of phase characteristic to export, while the wide elevation angle covers, by phase bit comparison, it can be achieved that the wide elevation angle
The high-precision of range is without fuzzy angle measurement；Angle measurement accuracy is more related than phase slope of a curve with different beams, unrelated with beam angle, solution
The problem of wide elevation angle covering determined with high-precision measurement of elevation；
(2) antenna hardware cost is saved：Angle measurement or pulse and difference beam angle measurement, angle measurement essence are compared using dualbeam amplitude
Degree is about 1/10th of beam angle；It improves angle measurement accuracy to need to increase antenna aperture, implies the antenna scale that increases, it is active
The cost of phased array antenna greatly increases；And this method only needs to design the two cosecant square lobes bigger than phase slope, is not required to
Increase the bore of array antenna, antenna hardware cost can be saved.
Detailed description of the invention
Fig. 1 is general flow chart of the invention；
Fig. 2 is geometrical model of the aerial array used in the present invention in cartesian coordinate system；
Fig. 3 is the flow chart that global optimization probability search method used in the present invention i.e. genetic algorithm solves；
Fig. 4 is the power waves of the first beam-forming network of the present invention, the second beam-forming network, third beam-forming network
Shu Fangxiang analogous diagram；
Fig. 5 is the Error Graph of the cosecant square lobe that the method for the present invention obtains and ideal cosecant chi square function；
Fig. 6 is the first beam-forming network of the invention and the second beam-forming network, the second beam-forming network and third
Phase dygoram between beam-forming network, wherein (a) be the first beam-forming network and the second beam-forming network it
Between phase dygoram, (b) be phase dygoram between the second beam-forming network and third beam-forming network；
Fig. 7 is the powerbeam direction analogous diagram of beam-forming network of the present invention with amplitude and phase error；
Fig. 8 is first beam-forming network and second beam-forming network of the present invention with amplitude and phase error, the
Phase dygoram between two beam-forming networks and third beam-forming network, wherein (a) is the first beam-forming network
Phase dygoram between the second beam-forming network is (b) the second beam-forming network and third beam-forming network
Between phase dygoram.
Specific embodiment
Embodiments of the present invention are described below in detail, the example of the embodiment is shown in the accompanying drawings.Below by
The embodiment being described with reference to the drawings is exemplary, and for explaining only the invention, and is not construed as limiting the claims.
Those skilled in the art can understand that unless otherwise defined, all terms used herein (including skill
Art term and scientific term) there is meaning identical with the general understanding of those of ordinary skill in fields of the present invention.Also
It should be understood that those terms such as defined in the general dictionary should be understood that have in the context of the prior art
The consistent meaning of meaning will not be explained in an idealized or overly formal meaning and unless defined as here.
Technical solution of the present invention is described in further detail with reference to the accompanying drawing：
The present invention provides a kind of double constraint lobe array antenna optimum design methods of cosecant quadratic sum synthesis phase, realizes
Step is as shown in Figure 1.
Step 1 is covered according to orientation, pitching airspace, determines array antenna geometric configuration and horizontal direction array element spacing
With pitch orientation array element spacing.
(1.1) detecting low-altitude objective, measures the azimuth and the elevation angle of target, and array antenna geometric configuration selects rectangular element
Grid, element position are uniformly distributed；
(1.2) geometrical model referring to Fig. 2 bay in cartesian coordinate system, array element are arranged in y-z plane, water
Square d is denoted as to array element spacingy.Phase sweeper mechanism is used according to orientation, front maximum scan angle is ± θmax, wherein 0 ° of <
θmax≤90°.By the engineering estimation formula of bay spacing, do not occur graing lobe within the scope of scan sector, determines horizontal direction
Array element spacing meetsWherein λminIndicate minimum operation wavelength, θ3dBIndicate orientation 3dB wave
Beam width；
(1.3) pitch orientation array element spacing is denoted as dz, pitching is to using broad beam scanning covering, wave cover maximum elevation
ForBy the engineering estimation formula of bay spacing, do not occur graing lobe within the scope of scan sector,
Determine that pitch orientation array element spacing meetsWhereinIndicate pitching to 3dB beam angle,Indicate pitching to wave cover maximum elevation.
Step 2, according to the requirement of antenna gain, azimuth beamwidth, pitching lobe cosecant square, determine antenna aperture and
Orientation, pitching array number, orientation array number are denoted as Ns, pitching is denoted as M to array numbers。
Step 3, selection bay type, design the lobe of bay, in radar working frequency range, meet low-voltage
The requirement of standing-wave ratio, i.e. impedance matching, bay directional diagram are denoted asWherein θ indicates orientation angle,Expression is bowed
It faces upward to angle.
Wave beam under step 4, design cosecant square lobe and synthesis phase constraint condition, using global optimization probabilistic search
Algorithm solves the construction and optimization design problem of array antenna, and specific step is as follows：
(4.1) according to the requirement of antenna gain, azimuth beamwidth, pitching cosecant square lobe, the array antenna phase is determined
The shaped-beam of prestige, with the optimization problem of minimum mean square error criterion construction array antenna design, particular content includes：
(4.1a) has the cosecant square lobes of out of phase characteristic with 3, designs cosecant square lobe and synthesis phase
The first beam-forming network, the second beam-forming network, third beam-forming network of constraint, array beams directional diagram distinguish table
State for：
Wherein, In、Respectively indicate the first beam-forming network, the second beam-forming network, third Wave beam forming
The excitation (including amplitude and phase) of n-th of bay of network, n=0,1 ..., Ms- 1, k=2 π/λ indicate wave number, and λ is
Wavelength.
(4.1b) according to the main lobe of minimum mean square error criterion array of designs beam pattern, the first beam-forming network,
Second beam-forming network, third beam-forming network beam pattern main lobe and ideal cosecant chi square function error
For：
Wherein,Indicate the value range of ideal cosecant chi square function,Indicate pitching to wave cover most
The small elevation angle,Indicate pitching to wave cover maximum elevation,Indicate i-th of beam-forming network
Beam pattern maximum value, max () indicate maximizing.Error functionDiscrete sampling mean square error be：
Wherein,For beam pattern main lobe region, i.e., the value range of ideal cosecant chi square functionAngle dis-crete sample values, Q is is taken angle value number.According to minimum mean square error criterion, bay is calculated
Excitation In、 So that mean square error EiReach minimum, i.e.,：Wherein min () is indicated
It minimizes.
(4.1c) applies the constraint of beam pattern secondary lobe, the first beam-forming network, the second beam-forming network, third wave
The beam pattern sidelobe level and radar system of beam formation network it is expected that the difference of maximum sidelobe level is：
Wherein, [ψ1,ψ2] be step 3 designed by bay beam angle,It is right for beam pattern main lobe
The difference of angle corresponding to the angle answered and the first minor lobe, can be practical selected according to engineering, and EMSL is it is expected maximum sidelobe level value.
Within the scope of beam pattern secondary lobe, constraint conditionPerseverance is set up and is equivalent toI.e.
(4.1d) applies the constraint of beam pattern main lobe phase, the first beam-forming network, the second beam-forming network, the
The main lobe phase of three beam-forming networks is expressed as respectivelyWherein, arg
() indicates that the main value argument of plural number, range are -180 °~180 °.In beam pattern main lobe coverage areaIt is interior, the
Meet line between one beam-forming network and the second beam-forming network, the second beam-forming network and third beam-forming network
The constraint relationship of property phase difference, formulation are：
Wherein, () ' expression is about angleFirst derivative, () " indicate about angleSecond dervative, σ be warp
Constant is tested, value indicates antenna phase center spacing size, it is higher to be worth bigger expression angle measurement sensitivity, but without fuzzy angle measurement
Range is smaller, conversely, indicating big without fuzzy measurable angle range, but angle measurement sensitivity is low.
In conclusion as follows with the optimization problem of minimum mean square error criterion construction array antenna design：
This is a multi-objective optimization question, and it is excellent that multi-objective optimization question is converted to single goal with linear weight sum method
Change problem is：
(4.2) above-mentioned optimization problem is solved using global optimization probability search method, referring to Fig. 3, using genetic algorithm as work
Tool, solution procedure are as follows：
Above-mentioned practical problem is converted to computer code using real coding by (4.2a) representation.Above-mentioned optimization is asked
Topic parametric variable is In、Value is plural number, total 3MsA variable take value range as the 6M of [0,1]sA real variableReplacement, wherein xm, m=1 ..., MsAnd xm, m=3Ms+1,…,4MsRespectively indicate the first beam-forming network
Array element motivates amplitude and phase, xm, m=Ms+1,…,2MsAnd xm, m=4Ms+1,…,5MsRespectively indicate the second Wave beam forming net
The array element of network motivates amplitude and phase, xm, m=2Ms+1,…,3MsAnd xm, m=5Ms+1,…,6MsRespectively indicate third wave beam shape
Amplitude and phase are motivated at the array element of network, then are had
Population Size is arranged in (4.2b), creates initial population, and calculating target function value, i.e. fitness functionValue.
(4.2c) distributes fitness value, carries out Fitness analysis, carries out genetic manipulation, that is, selects, intersects, variation, realizing
Target global optimization probabilistic search.
The judgement of (4.2d) termination condition, fitness function value deviation reaches error margin or algorithm reaches maximum hereditary generation
Number, algorithm terminate；Otherwise, fitness function value is recalculated, the optimizing search for (4.2c) progress next round that gos to step.
Step 5 motivates amplitude and phase according to the array element that genetic algorithm in step 4 solves, and designs feeding network.
Step 6, bay and feeding network are integrated, optimize each port phase of feeding network, i.e. the excitation of adjustment array element
Phase, array beams directional diagram is finely adjusted, meet synthesis wave beam cosecant square lobe and synthesis phase requirement, wave beam
Exporting result isWherein, subscript i indicates i-th of beam-forming network,Table
I-th of array beams directional diagram after showing fine tuning phase optimization.
Effect of the invention is further illustrated by following emulation experiment：
1. experiment condition：Certain Ku band broadband Digital Array Radar, rectangular surfaces battle array, array number are 64 × 16.Orientation battle array
First number is 64, and orientation scanning angle range is -45 °~45 °, and horizontal direction array element spacing is selected as 0.56 λmin, wherein λmin
Indicate minimum operation wavelength.Pitching to array number be 16, pitching to beam coverage be 0 °~30 °, between pitch orientation array element
Away from being selected as 0.6 λmin。
2. emulation content：
Emulation 1 is based on following simulation parameter, and it is [0,1] that bay, which motivates amplitude value range, and array element excitation phase takes
Being worth range is [0 °, 360 °], it is expected that maximum sidelobe level is -20dB, the value range of ideal cosecant chi square function be [6 °,
40 °], genetic algorithm parameter setting is as follows：Population Size is 100, and elite number is 5, and intersecting offspring's ratio is 0.8, it is maximum into
Changing algebraical sum and stopping algebra is 500, and ranking functions are grade sequence, selects function for random consistent selection, intersecting function is
Dispersion intersects, and variation function uses function constraint TSP question.Fig. 4 gives the first wave beam obtained based on the method for the present invention
The powerbeam directional diagram of network, the second beam-forming network, third beam-forming network is formed, Fig. 5 gives present invention side
The Error Graph of cosecant square lobe that method obtains and ideal cosecant chi square function, (a) and (b) is set forth based on this in Fig. 6
The first beam-forming network and the second beam-forming network, the second beam-forming network and the third wave beam shape that inventive method obtains
At the phase dygoram between network.Meanwhile linear fit curve is given in Fig. 6.
Emulation 2, the wave beam network based on above-mentioned design, due to production technology etc., wave beam net during actual processing
Network can generate amplitude and phase error.Therefore, the phase error of the range error of addition ± 0.5dB and ± 5 ° in simulations, into
100 Monte Carlo Experiments of row.Fig. 7 gives the powerbeam direction of the beam-forming network with amplitude and phase error
Figure.(a) in Fig. 8 and the first beam-forming network and the second wave beam shape with amplitude and phase error (b) is set forth
At the phase dygoram between network, the second beam-forming network and third beam-forming network.
3. analysis of simulation result：
From fig. 4, it can be seen that wave beam network designed by the present invention has cosecant square lobe in [6 °, 40 °] range.
The cosecant square lobe that the method for the present invention that Fig. 5 is provided obtains and the Error Graph of ideal cosecant chi square function further explain
The degree of closeness of the two illustrates that method proposed by the invention is correct feasible.
Phase dygoram between wave beam network shown in fig. 6 shows the first beam-forming network and the second wave beam shape
At having approximately linear phase relation, and the first wave beam between network, the second beam-forming network and third beam-forming network
Forming phase difference fitting a straight line slope between network and the second beam-forming network is approximately 26, the second beam-forming network and the
Phase difference fitting a straight line slope is approximately 5.5 between three beam-forming networks.
The powerbeam directional diagram of beam-forming network shown in Fig. 7 with amplitude and phase error and shown in Fig. 8
Phase dygoram between beam-forming network, in the range error and ± 5 ° of phase error of ± 0.5dB, this hair
Bright designed beam-forming network still has cosecant square lobe and linear phase difference, and demonstrate the method for the present invention has
Effect property, operation and processing to beam-forming network have directive significance.
The invention discloses a kind of double constraint lobe array antenna optimum design methods of cosecant quadratic sum synthesis phase, mainly
Solve the problems, such as that existing antenna cosecant square lobe is unable to angle measurement and the low elevation angle measuring angle by comparing amplitude precision of pen shape lobe is not high.It is realized
Step is：1. covering according to orientation, pitching airspace, array antenna geometric configuration and horizontal direction array element spacing and pitching are determined
Direction array element spacing, array antenna geometric configuration select rectangular element grid；2. according to antenna gain, azimuth beamwidth, bowing
The requirement for facing upward lobe cosecant square determines antenna aperture and orientation, pitching array number；3. selecting bay type, day is designed
The lobe of linear array member meets the requirement of low-voltage standing-wave ratio in radar working frequency range；4. designing cosecant square lobe and phase about
Wave beam under the conditions of beam, constructs array antenna using global optimization probability search method and optimization design problem solves；5. piece
Amplitude and phase are motivated according to array element, design feeding network；6. bay and feeding network are integrated, optimize each end of feeding network
Mouth phase, is finely adjusted array beams directional diagram, meets the requirement of synthesis wave beam cosecant square lobe and synthesis phase.
The present invention utilizes the double constraint lobe array antennas of intelligent optimization algorithm optimization design cosecant quadratic sum synthesis phase, solution
It has determined cosecant square lobe high precision angle-measuring problem, has reduced the complexity of radar antenna, save hardware cost, in conjunction with dynamic mesh
Mark detection (MTD) signal processing technology, realizes the covering of the wide elevation angle and elevation angle high precision angle-measuring, can be widely used for security against air attack,
The three-dimensional radars such as battle reconnaissance.
The above, the only specific embodiment in the present invention, but scope of protection of the present invention is not limited thereto, appoints
What is familiar with the people of the technology within the technical scope disclosed by the invention, it will be appreciated that expects transforms or replaces, and should all cover
Within scope of the invention.Therefore, the scope of protection of the invention shall be subject to the scope of protection specified in the patent claim.
Claims (5)
1. the double constraint lobe array antenna optimum design methods of cosecant quadratic sum synthesis phase, which is characterized in that including having as follows
Body step：
Step 1 is covered according to orientation, pitching airspace, is determined array antenna geometric configuration and horizontal direction array element spacing and is bowed
Face upward direction array element spacing；
Step 2, according to the requirement of antenna gain, azimuth beamwidth, pitching lobe cosecant square, determine antenna aperture and side
Position, pitching array number；
Step 3, selection bay type, design the lobe of bay, in radar working frequency range, meet low-voltage standing wave
The requirement of ratio, i.e. impedance matching, bay directional diagram are denoted asWherein θ indicates orientation angle,Indicate pitching to
Angle；
Wave beam under step 4, design cosecant square lobe and synthesis phase constraint condition, using global optimization probability search method
Construction and optimization design problem to array antenna solve, specially：
(4.1) according to the requirement of antenna gain, azimuth beamwidth, pitching cosecant square lobe, determine that array antenna is desired
Shaped-beam, the optimization problem with minimum mean square error criterion construction array antenna design are：
Wherein, In、Respectively indicate cosecant square lobe, the design cosecant square lobe with 3 with out of phase characteristic
With synthesis phase constraint the first beam-forming network, the second beam-forming network, third beam-forming network n-th of antenna
The excitation of array element, n=0,1 ..., Ms- 1, MsIndicate pitching to array number；The beam pattern of first beam-forming networkThe beam pattern of second beam-forming network
The beam pattern of third beam-forming networkK indicates wave number, k=2 π/λ, λ table
Oscillography is long, dzIndicate pitch orientation array element spacing；Indicate the main lobe and ideal of the beam pattern of the i-th beam-forming network
The error of cosecant chi square function,
Indicate the value range of ideal cosecant chi square function,Indicate pitching to wave cover minimum angle of elevation,Indicate pitching to wave
Beam covers maximum elevation,Q is the value range that beam pattern main lobe region is ideal cosecant chi square functionAngle dis-crete sample values, Q to be taken angle value number,Indicate i-th of wave beam shape
At the maximum value of the beam pattern of network, max () indicates maximizing；[ψ1,ψ2] it is bay designed by step 3
Beam angle,For the difference of angle corresponding to angle corresponding to the array beams major lobe of directional diagram and the first minor lobe；EMSL is
It is expected that maximum sidelobe level, the beam pattern phase of the i-th beam-forming network areArg () table
The main value argument for giving instructions in reply several, () ' indicate to take first derivative, (), " expression took second dervative；σ is empirical value, and value indicates
Antenna phase center spacing size；Min () expression is minimized；
(4.2) using the optimization problem in global optimization probability search method solution procedure (4.1), obtain array element excitation amplitude and
Phase；
Step 5 solves obtained array element excitation amplitude and phase according to step 4, designs feeding network；
Step 6, bay and feeding network are integrated, optimize each port phase of feeding network, the i.e. phase of adjustment array element excitation
Position, is finely adjusted array beams directional diagram, meets the requirement of synthesis wave beam cosecant square lobe and synthesis phase, wave beam output
As a result it isWherein,I-th of array beams after indicating fine tuning phase optimization
Directional diagram.
2. the double constraint lobe array antenna optimum design methods of cosecant quadratic sum synthesis phase according to claim 1,
It is characterized in that, array antenna geometric configuration selects rectangular element grid in step 1, and element position is uniformly distributed, horizontal direction battle array
First spacingPitch orientation array element spacingWherein, λminTable
Show minimum operation wavelength, θ3dBWithOrientation and pitching are respectively indicated to 3dB beam angle, θmaxIndicate that orientation maximum is swept
Angle is retouched,Indicate pitching to wave cover maximum elevation.
3. the double constraint lobe array antenna optimum design methods of cosecant quadratic sum synthesis phase according to claim 1,
It is characterized in that, the optimization problem in step (4.1) is converted into single-object problem with linear weight sum method：
4. the double constraint lobe array antenna optimum design methods of cosecant quadratic sum synthesis phase according to claim 3,
It is characterized in that, single-object problem is solved using genetic algorithm.
5. the double constraint lobe array antenna optimum design methods of cosecant quadratic sum synthesis phase according to claim 4,
It is characterized in that, solution procedure is as follows：
Optimization problem is converted to computer code using real coding by (4.2a), specially：
Optimization problem parametric variable is In、Value is plural number, total 3MsA variable take value range as the 6M of [0,1]sIt is a
Real variable x1,…,Replacement, wherein xm, m=1 ..., MsAnd xm, m=3Ms+1,…,4MsRespectively indicate the first wave beam shape
Amplitude and phase, x are motivated at the array element of networkm, m=Ms+1,…,2MsAnd xm, m=4Ms+1,…,5MsRespectively indicate the second wave
The array element that beam forms network motivates amplitude and phase, xm, m=2Ms+1,…,3MsAnd xm, m=5Ms+1,…,6MsRespectively indicate
The array element of three beam-forming networks motivates amplitude and phase, then has
Population Size is arranged in (4.2b), creates initial population, and calculating target function value, i.e. fitness function
Value；
(4.2c) distributes fitness value, carries out Fitness analysis, carries out genetic manipulation, that is, selects, intersects, variation, realizing target
Global optimization probabilistic search；
The judgement of (4.2d) termination condition, fitness function value deviation reaches error margin or algorithm reaches maximum genetic algebra, calculates
Method terminates；Otherwise, fitness function value is recalculated, the optimizing search for (4.2c) progress next round that gos to step.
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