CN111291493B - Design method for airborne early warning conformal array pitching detection beam forming - Google Patents

Design method for airborne early warning conformal array pitching detection beam forming Download PDF

Info

Publication number
CN111291493B
CN111291493B CN202010107411.6A CN202010107411A CN111291493B CN 111291493 B CN111291493 B CN 111291493B CN 202010107411 A CN202010107411 A CN 202010107411A CN 111291493 B CN111291493 B CN 111291493B
Authority
CN
China
Prior art keywords
array
early warning
theta
scan
conformal
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202010107411.6A
Other languages
Chinese (zh)
Other versions
CN111291493A (en
Inventor
曾元琛
李娜
段宝岩
钟旺
张烁
孙梓涵
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Xidian University
Original Assignee
Xidian University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Xidian University filed Critical Xidian University
Priority to CN202010107411.6A priority Critical patent/CN111291493B/en
Publication of CN111291493A publication Critical patent/CN111291493A/en
Application granted granted Critical
Publication of CN111291493B publication Critical patent/CN111291493B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00—Details of, or arrangements associated with, antennas
    • H01Q1/27—Adaptation for use in or on movable bodies
    • H01Q1/28—Adaptation for use in or on aircraft, missiles, satellites, or balloons
    • H01Q1/285—Aircraft wire antennas
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q21/00—Antenna arrays or systems
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
    • Y02T10/40—Engine management systems

Abstract

The invention belongs to the technical field of antennas, and particularly relates to a design method for airborne early warning conformal array pitching detection beam forming. By the method, on one hand, optimization variables are reduced in the optimization process to accelerate the optimization speed, and on the other hand, the introduced amplitude control variables can reduce the level of the side lobes of the whole array, which is very beneficial to the detection of the airborne early warning radar. Meanwhile, the smooth change of the optimized unit excitation is beneficial to the design of a feed network, so that the corresponding construction cost is greatly reduced. The method can be used for early warning radar pitching surface detection beam forming design, array side lobe improvement and array feed network design simplification.

Description

Design method for airborne early warning conformal array pitching detection beam forming
Technical Field
The invention belongs to the technical field of antennas, and particularly relates to a design method for pitching detection beam forming of an airborne early-warning conformal array, which can be used for realizing pitching beam forming design of an early-warning conformal radar during detection, improving array side lobes and simplifying array feed network design.
Background
The early warning radar is the most main detection equipment and information source on the early warning machine, and the detection objects of the early warning radar are generally airplane targets flying at different heights and sea ships. When detecting an object, the shape of a pitch plane detection beam needs to be designed to avoid the occurrence of signal attenuation areas and false objects caused by reflection. The application of beamforming enables coverage of the primary airspace while reducing the effects of reflections from the ground, etc.
Antenna beamforming methods are generally divided into: only the excitation phase of the antenna elements is adjusted and the amplitude and phase of the antenna elements are weighted simultaneously. The Taylor and Chebyshev integrated method is the simplest and intuitive analysis method in an antenna array, but the Taylor and Chebyshev integrated method usually has requirements on the array element spacing when being applied, and an effective solution is often difficult to obtain when the shape of the antenna array is complex or the scale is large. In recent years, intelligent optimization algorithms are widely applied to array forming. For example, the amplitude and the phase of the array are updated by utilizing a particle swarm algorithm, a genetic algorithm and the like to complete array shaping. However, most of these shaping methods do not consider the aperture efficiency of the array, and the optimized amplitude oscillates. On the one hand, the amplitude of the high oscillation will make it difficult to feed the array; on the other hand, when the planar linear array is excited uniformly, the aperture efficiency is 1; when the Taylor weighting method is adopted, tapered cutting exists in the unit excitation amplitude obtained through optimization, and the aperture efficiency of the array is smaller than 1. Although the side lobes are greatly reduced compared to uniform excitation, these methods mostly reduce the side lobe levels at the expense of aperture efficiency. Therefore, array aperture efficiency and side lobe level need to be comprehensively considered in conformal array shaping. And the introduction of bernstein polynomials provides a method for obtaining lower sidelobes with less aperture efficiency reduction. For example, Boeringer D W, Werner D H. effective-constrained parameter mapping of a modified bernstein multinomial for a conformal array excitation synthesis [ J ]. IEEE Transactions on Antennas and Propagation,2005, 53(8): 2662-. And utilizing two one-dimensional correction Bernstein modes to respectively synthesize directional diagrams of the cylindrical conformal area arrays with different wave beams on the pitching surface and the azimuth surface.
However, the current improvement on the bernstein polynomial, whether applied to a conformal linear array or an area array, ignores the relation between units in each row of the array and limits the further reduction of side lobes, and the optimized maximum value of the excitation amplitude of each row of the units is the same and is 1, so that the 'personality' of the excitation of different rows of the array is ignored. Therefore, the modified bernstein polynomial is applied with attention to the relation of the excitation amplitude between each row of the array elements and how to improve the array side lobe again so as to meet the requirement of low side lobe of radar.
Disclosure of Invention
The invention aims to provide a design method for forming a pitching detection beam of an airborne early warning conformal array, which can reduce optimization variables in an optimization process and accelerate optimization speed, can reduce the level of a whole array side lobe, greatly reduces corresponding construction cost, improves the array side lobe and simplifies the design of an array feed network.
The invention aims to realize the method for designing the pitching detection beam forming of the airborne early warning conformal array, which is characterized by at least comprising the following steps of:
step (1), according to the general expression of the aperture efficiency of the early warning radar planar array, deducing the aperture efficiency expression of the conformal array:
the step (1) comprises the following steps: general expression of array pitch surface field strength
Figure 2
Wherein:
f nθ (θ) represents a polarization component of the element vector pattern in the θ direction;
I n is the excitation amplitude, phi, of the nth array element n Is the excitation phase;
k is the spatial propagation constant, k is 2 pi/λ, λ is the wavelength;
r n is the position vector of the nth array element;
r is the unit vector in the far field direction;
combining a coordinate system rotation method to obtain a far field of the pitching surface of the conformal array, wherein the expression is
Figure 1
Wherein:
T n (theta) is a rotation matrix of the nth array element in the theta directionThe array may be converted in two steps: the far-field viewing direction theta in the global coordinate system o-xyz is first translated to its local coordinate system per cell
Figure BDA0002388834230000033
Is shown in
Figure BDA0002388834230000034
Finally, directional diagram function in unit local coordinate system
Figure BDA0002388834230000035
F is obtained by rotating and transforming the coordinate system into a global coordinate system nθ (θ n )。
On the basis of formula (1), a general expression of aperture efficiency of a planar array can be defined as:
Figure BDA0002388834230000041
wherein:
G(θ scan ) Representing the gain at the respective scan angle;
G max (θ scan ) Represents the maximum gain on pitch;
obtaining G (theta) in conformal array with complete matching of far field by adopting coordinate system rotation method scan ) And G max (θ scan ) Can be respectively represented by formulas (4) and (5):
Figure BDA0002388834230000042
Figure BDA0002388834230000043
wherein:
T n (θ scan ) Indicating the nth array element at the scan angle theta scan A rotation matrix of (d);
E(θ scan ) Is given by formula (2);
Figure BDA0002388834230000044
exciting the maximum amplitude for the array elements under the corresponding scanning angle;
normalized input power P of the entire array in Can be given by the excitation coefficient of each unit, i.e.
Figure BDA0002388834230000045
When P is in When 1, the maximum amplitude of excitation of the array element in equations (2) and (6) can be expressed as
Figure BDA0002388834230000046
And (3), the joint vertical type (4), the joint vertical type (5) and the joint vertical type (7) can obtain a general aperture efficiency expression of the conformal array.
Step (2), defining a beam shape required by the pitching surface detection of the early warning radar;
the step (2) comprises the following steps: when the height of the airplane is unchanged, the pitching surface cosecant shaped beam antenna can receive electric wave signals with equal strength for targets positioned at different inclination distances;
the gain expression of the change of an antenna used by the conformal array of the computer-mounted early warning radar along with the pitch angle theta in the pitching plane is as follows:
Figure BDA0002388834230000051
wherein:
θ l is the upper limit of the pitch angle;
θ m the lower limit of the pitch angle;
step (3), introducing an amplitude control variable Am into the modified Bernstein polynomial to reduce an optimization variable and reduce a side lobe level;
the step (3) comprises the following steps: 5 with C 1 、C 2 、A、N 1 And N 2 The modified bernstein polynomial for the parameter may be expressed as:
Figure BDA0002388834230000052
in order to complete the shaping of the array with a plurality of rows of array elements, an amplitude control variable Am is introduced into each row based on the formula (9), so that each modified bernstein polynomial is changed from the original 5 control parameters to 6, as shown in the following formula:
Figure BDA0002388834230000061
wherein:
C 1 、C 2 represents a value at an end of the polynomial, and 0. ltoreq.C 1 、C 2 ≤1；
Taking a unimodal peak value by a polynomial when u is A;
N 1 、N 2 more than or equal to 0, and is used for controlling the gentle degree of the curve;
the introduced amplitude control variable Am can control the peak value of the curve;
when only the amplitude of the array element is optimized, the excitation phase phi is kept n When the array element spacing is not changed when the array element spacing is 0, the direction diagram of the pitching surface of the conformal array can be expressed as
Figure BDA0002388834230000062
Thus, the largest side lobe of the array can be represented as
Figure BDA0002388834230000063
Wherein:
θ sl representing a side valve region;
the maximum side lobe of the array after introducing the magnitude control variable Am is approximately
Figure BDA0002388834230000064
In the formula (13), Am is less than or equal to 1, so that a lower side lobe can be obtained more easily after an amplitude control variable is introduced, which is very beneficial to the detection of the airborne early warning radar.
Step (4), defining a description function of the pitching detection beam and determining a fitted objective function;
θ 1 the following region is the region, so only the maximum side lobe level of this portion is considered to be limited as low as possible for θ 1 Dividing the area into 3 sections for fitting;
the step (4) is divided into 3 sections for fitting, and comprises the following steps:
a first stage: over theta 1 The area adopts an oblique line a 1 (θ 1 ) Fitting, controlling the slope of the pitch beam to meet the required half-power lobe width requirement;
and a second stage: the target function adopts a cosecant curve a through a sky area of the maximum radiation value 2 (θ 2 )；
A third stage: outside the desired pitch range, i.e. high pitch region, the objective function is set to a line a with a larger slope for faster signal attenuation 3 (θ 3 )；
Theta is given by the formula (13) 1 The maximum side lobe level of the side lobe region S below the angle is:
Figure BDA0002388834230000071
for theta 1 And in the above areas, respectively obtaining the root mean square value RMS of the beam shape actually obtained by shaping and 3 fitting curves:
Figure BDA0002388834230000072
wherein:
num represents the total number of sampling points of the region to be fitted on the actually obtained beam shape;
P 1 (θ 1 ) Representing the first segment of the actual resulting beam curve;
P 2 (θ 2 ) Representing the actual resulting beam curve of the second segment;
P 3 (θ 3 ) Representing the actual resulting beam profile of the third segment.
Step (5), optimizing an objective function by adopting the following optimization model to obtain an objective detection curve; find X ═ C 1 ,C 2 ,N 1 ,N 2 ,A,Am] T
Figure BDA0002388834230000081
Figure BDA0002388834230000082
Figure BDA0002388834230000083
p(u)≥0 (18)
Figure BDA0002388834230000084
Figure BDA0002388834230000085
Figure BDA0002388834230000086
In the formula:
design variable X ═ C 1 ,C 2 ,N 1 ,N 2 ,A,Am] T Is a description of an objective functionA parameter;
the objective function f (x) is a function of the negative side lobe levels and the fitted curve, with the aim of transforming the optimization problem into a standard optimization model;
constraints (16) and constraints (17) are to ensure that the basic excitation function characteristics are satisfied;
constraints (18), constraints (19) and constraints (20) are to ensure that the modified bernstein polynomial maintains basic shape properties;
the constraint (21) is to ensure that the side lobe levels meet the requirements;
and (6) writing a firefly algorithm by adopting Matlab software to solve the optimization model in the step (5) to obtain a design variable X.
The principle and the beneficial effects of the invention are as follows: the invention provides an improvement aiming at the problems in the prior art, namely the invention discloses a design method for airborne early warning conformal array pitching detection beam forming. The core of the design method is to introduce an amplitude control variable into the modified Bernstein polynomial. By the method, on one hand, optimization variables are reduced in the optimization process to accelerate the optimization speed, and on the other hand, the introduced amplitude control variables can reduce the level of the side lobes of the whole array, which is very beneficial to the detection of the airborne early warning radar. Meanwhile, the smooth change of the optimized unit excitation is beneficial to the design of a feed network, so that the corresponding construction cost is greatly reduced. The method can be used for early warning radar pitching surface detection beam forming design, array side lobe improvement and array feed network design simplification.
Firstly, obtaining a far-field directional pattern of the conformal array antenna according to an electromagnetic field theory, and deducing a caliber efficiency expression of the conformal array by combining a general expression of the caliber efficiency of the planar array on the basis; secondly, introducing an amplitude control variable set into the corrected Bernstein polynomial and deducing the relation between the amplitude control variable and the array side lobe level; and finally, obtaining the excitation amplitude of the array by optimizing each control parameter in the corrected Bernstein polynomial by taking the shape of a far-field directional diagram required by the pitching surface detection of the airborne early warning radar as a target to complete the shaping design.
The invention discloses a design method for forming an airborne early warning conformal array pitching detection beam, which has the following beneficial effects: by the design method, the detection and shaping design of the pitching plane of the airborne early warning conformal array is realized under the condition of ensuring lower array side lobe level and smaller aperture efficiency loss, the fluctuation degree of the array excitation amplitude is reduced, the design of the feed network is simplified, and the manufacturing cost of the feed network is reduced.
Drawings
The following detailed description of embodiments of the invention refers to the accompanying drawings in which:
FIG. 1 is an airborne early warning radar distance-height overlay in accordance with the present invention;
FIG. 2 is a diagram of the beam shape required for pitching detection of the airborne early warning radar according to the present invention;
FIG. 3 is a schematic diagram of an airborne conformal array layout in accordance with the present invention;
FIG. 4 is a schematic diagram of a Bernstein polynomial curve controlled by different amplitude control variables according to the present invention;
fig. 5 is a comparison of the far field normalized power pattern and the target curve optimized by the present invention.
The specific implementation mode is as follows:
as shown in fig. 1, the method for designing beamforming for detecting a pitching plane of an airborne early warning conformal array includes:
step (1), according to the general expression of the aperture efficiency of the early warning radar planar array, deducing the aperture efficiency expression of the conformal array:
general expression of array pitch surface field strength
Figure BDA0002388834230000101
Wherein: f. of nθ (θ) represents a polarization component of the element vector pattern in the θ direction;
I n is the excitation amplitude, phi, of the nth array element n Is the excitation phase;
k is the space propagation constant, k is 2 pi/lambda, lambda is the wavelength;
r n is the position vector of the nth array element;
r is the unit vector in the far field direction;
obtaining the far field of the pitching surface of the conformal array by combining a coordinate system rotation method, wherein the expression is
Figure BDA0002388834230000102
Wherein:
T n (theta) is a rotation matrix of the nth array element in the theta direction, and the matrix can be converted by two steps: the far-field viewing direction theta in the global coordinate system o-xyz is first translated to its local coordinate system per cell
Figure BDA0002388834230000111
Is shown in
Figure BDA0002388834230000112
Finally, directional diagram function in unit local coordinate system
Figure BDA0002388834230000113
F is obtained by rotating and transforming the coordinate system into a global coordinate system nθ (θ n )。
On the basis of the formula (1), a general expression of aperture efficiency of a planar array can be defined as
Figure BDA0002388834230000114
Wherein:
G(θ scan ) Representing the gain at the respective scan angle;
G max (θ scan ) Represents the maximum gain on pitch;
obtaining G (theta) in conformal array with complete matching of far field by adopting coordinate system rotation method scan )G max (θ scan ) Can be respectively represented by formulas (4) and (5):
Figure BDA0002388834230000115
Figure BDA0002388834230000116
wherein:
T n (θ scan ) Indicating the nth array element at the scan angle theta scan A rotation matrix of (d);
E(θ scan ) Is given by formula (2);
Figure BDA0002388834230000117
exciting the maximum amplitude for the array elements under the corresponding scanning angle;
normalized input power P of the entire array in Can be given by the excitation coefficient of each unit, i.e.
Figure BDA0002388834230000118
When P is present in When 1, the maximum amplitude of excitation of the array element in equations (2) and (6) can be expressed as
Figure BDA0002388834230000121
And (3), the joint vertical type (4), the joint vertical type (5) and the joint vertical type (7) can obtain a general aperture efficiency expression of the conformal array.
Step (2), defining the wave beam shape required by the pitching detection of the early warning radar
When the height of the airplane is unchanged, the cosecant shaped beam antenna on the pitching surface can receive radio wave signals with equal strength for targets positioned at different inclined distances.
The gain expression of the antenna used by the airborne conformal array in the pitch plane along with the change of the pitch angle theta is as follows:
Figure BDA0002388834230000122
wherein:
θ l is the upper limit of the pitch angle;
θ m is the lower limit of the pitch angle;
when the airborne early warning radar is used for detecting a pitching plane, the power requirement in a required direction is met as much as possible, so that the occurrence of a signal attenuation area, a false target caused by reflection and the reduction of power directly irradiating on the ground are avoided. For this purpose, the probe beam shown in FIG. 2 should satisfy the following requirements
1. The peak of the pitch surface beam should be in the target direction;
2. at theta 1 The proximity of the corners (angle at which the downward illumination detection distance is R) should be cut off rapidly to reduce the energy of the lobe illumination to ground. This requires an over theta 1 The slope of the beam shape at the corners is as great as possible, theta 1 The ground illumination area is as follows;
3. classical cosecant forming is adopted in a main empty detection area, and the characteristic that the beam in the cosecant shape can receive electric wave signals with equal strength for targets positioned at different inclined distances is utilized, so that stable communication is facilitated;
4. in high elevation areas, the signal should decay faster to prevent the signal from reaching areas of no interest.
And (3) introducing an amplitude control variable Am into the modified Bernstein polynomial to reduce an optimization variable and reduce a side lobe level
5 with C 1 、C 2 、A、N 1 And N 2 The modified Bernstein polynomial for the parameter may be expressed as
Figure BDA0002388834230000131
In order to complete the shaping of the array with a plurality of rows of array elements, an amplitude control variable Am is introduced into each row on the basis of the formula (9), and a curve of different amplitude control variables under the condition of the same other parameters is shown in fig. 4. Thus, each modified bernstein polynomial is changed from the original 5 control parameters to 6, as shown in the following equation:
Figure BDA0002388834230000132
wherein:
C 1 、C 2 represents a value at an end of the polynomial, and 0. ltoreq.C 1 、C 2 ≤1；
Taking a unimodal peak value by a polynomial when u is A;
N 1 、N 2 not less than 0, for controlling the gentle degree of the curve;
the introduced amplitude control variable Am can control the peak value of the curve;
when only the amplitude of the array element is optimized, the excitation phase phi is kept n When the array element spacing is not changed when the array element spacing is 0, the direction diagram of the pitching surface of the conformal array can be expressed as
Figure BDA0002388834230000141
Thus, the largest side lobe of the array can be represented as
Figure BDA0002388834230000142
Wherein:
θ sl representing a side valve region;
the maximum side lobe of the array after introducing the magnitude control variable Am is approximately
Figure BDA0002388834230000143
In the formula (13), Am is less than or equal to 1, so that a lower side lobe can be obtained more easily after an amplitude control variable is introduced, which is very beneficial to the detection of the airborne early warning radar.
Step (4), defining description function of pitching detection beam and determining fitted objective function
θ 1 The following region is a region, and therefore only the maximum side lobe level of this portion is considered to be limited as low as possible. For theta 1 And the above region is divided into 3 segments for fitting. A first stage: over theta 1 The area adopts an oblique line a 1 (θ 1 ) Fitting, controlling the slope of the pitch beam to meet the required half-power lobe width requirement; and a second stage: the target function adopts a cosecant curve a through a sky area of the maximum radiation value 2 (θ 2 ) (ii) a A third stage: outside the desired pitch range, i.e. high pitch region, the objective function is set to a line a with a larger slope for faster signal attenuation 3 (θ 3 )。
Theta is given by the formula (13) 1 The maximum side lobe level of the side lobe region S below the angle is:
Figure BDA0002388834230000151
for theta 1 And in the above regions, respectively obtaining the root mean square value RMS of the beam shape obtained by forming practice and 3 fitting curves:
Figure BDA0002388834230000152
wherein:
num represents the total number of sampling points of the region to be fitted on the actually obtained beam shape;
P 1 (θ 1 ) Representing the first segment of the actual resulting beam curve;
P 2 (θ 2 ) Representing the actual resulting beam curve of the second segment;
P 3 (θ 3 ) Representing the actual resulting beam curve of the third segment;
and (5) optimizing the objective function by adopting the following optimization model to obtain the target detection curve. Find X ═ C 1 ,C 2 ,N 1 ,N 2 ,A,Am] T
Figure BDA0002388834230000153
Figure BDA0002388834230000154
Figure BDA0002388834230000155
p(u)≥0 (18)
Figure BDA0002388834230000156
Figure BDA0002388834230000157
Figure BDA0002388834230000161
In the formula:
design variable X ═ C 1 ,C 2 ,N 1 ,N 2 ,A,Am] T Is a description parameter of the objective function;
the objective function f (x) is a function of the negative sidelobe level and the fitted curve, with the aim of transforming the optimization problem into a standard optimization model;
constraints (16) and constraints (17) are to ensure that the basic excitation function characteristics are satisfied;
constraints (18), constraints (19) and constraints (20) are to ensure that the modified bernstein polynomial maintains basic shape characteristics;
the constraint (21) is to ensure that the side lobe levels meet the requirements;
and (6) writing a firefly algorithm by adopting Matlab software to solve the optimization model in the step (5) to obtain a design variable X.
The advantages of the present invention can be further illustrated by the following numerical simulation experiments:
1. the number of simulation parameter populations is set to 30, the number of iteration steps is set to 2000, the algorithm is executed for 15 times, and the optimization result is averaged. The dipole array is adopted, the array form is shown in fig. 3, the number of the array elements is 3 rows and 9 columns, the array elements are uniformly arranged, the array element spacing d is 0.6 lambda, the working frequency f is 3GHz, and the wave beam points to 0 deg. The dimension of the problem to be optimized is thus 18. The maximum side lobe level CSL given in equation (21) is-20 dB.
2. Emulated content and results
The present invention provides a numerical simulation result of an objective function. Under the simulation example, each control parameter in the formula (10) is optimized according to a target curve; then, obtaining the excitation amplitude of each unit in the array through uniform sampling; finally, a far-field power normalized directional diagram is obtained by using the excitation amplitudes, as shown in fig. 5.
Table 1 shows the optimized values of the control parameters of the modified bernstein polynomial, and the excitation amplitude of each unit is obtained by uniform sampling according to the data in table 1. The far field pattern of the airborne conformal array is then calculated as shown in fig. 5. Wherein, the solid line represents the far-field directional diagram of the pitching surface based on the given optimization model, and the dashed line is a three-segment curve fitted. As can be seen from FIG. 5, the first and second curves substantially satisfy the target to be fitted, and the third beam has reached a high elevation region, the lower the sidelobe of the region, the better, so that the optimization result of the third section shown in FIG. 5 can be considered to satisfy the condition. In conclusion, the established optimization model can well complete the wave beams required by the airborne conformal array pitching surface detection.
TABLE 1 modified Bernstein polynomial parameters after optimization
Figure BDA0002388834230000171
The embodiments of the present invention have been described in detail. However, the present invention is not limited to the above-described embodiments, and various changes can be made within the knowledge of those skilled in the art without departing from the spirit of the present invention.

Claims (5)

1. A design method for airborne early warning conformal array pitching detection beam forming is characterized by at least comprising the following steps:
step (1), according to the general expression of the aperture efficiency of the early warning radar planar array, deducing the aperture efficiency expression of the conformal array:
step (2), defining a beam shape required by the pitching surface detection of the early warning radar;
step (3), introducing an amplitude control variable Am to a modified Bernstein polynomial to reduce an optimization variable and reduce a side lobe level;
step (4), defining a description function of the pitching detection beam and determining a fitted objective function;
θ 1 the following region is the region, so only the maximum side lobe level of this portion is considered to be limited as low as possible for θ 1 Dividing the area into 3 sections for fitting;
step (5), optimizing an objective function by adopting the following optimization model to obtain an objective detection curve;
and (6) writing a firefly algorithm by adopting Matlab software to solve the optimization model in the step (5) to obtain a design variable X.
2. The design method for airborne pre-warning conformal array pitch detection beamforming as claimed in claim 1, wherein: the step (1) comprises the following steps:
general expression for array pitch field strength:
Figure FDA0002388834220000011
wherein:
f nθ (θ) represents a polarization component of the element vector pattern in the θ direction;
I n is the excitation amplitude of the n-th array elementValue phi n Is the excitation phase;
k is the spatial propagation constant, k is 2 pi/λ, λ is the wavelength;
r n is the position vector of the nth array element;
r is the unit vector in the far field direction;
obtaining the far field of the pitching surface of the conformal array by combining a coordinate system rotation method, wherein the expression is
Figure FDA0002388834220000021
Wherein:
T n (theta) is a rotation matrix of the nth array element in the theta direction, and the matrix can be converted by two steps: the far-field viewing direction theta in the global coordinate system o-xyz is first translated to its local coordinate system per cell
Figure FDA0002388834220000022
Is shown in
Figure FDA0002388834220000023
Finally, directional diagram function in unit local coordinate system
Figure FDA0002388834220000024
F is obtained by rotating and transforming the coordinate system into a global coordinate system nθ (θ n )；
On the basis of formula (1), a general expression of aperture efficiency of a planar array can be defined as:
Figure FDA0002388834220000025
wherein:
G(θ scan ) Representing the gain at the respective scan angle;
G max (θ scan ) Represents the maximum gain in pitch;
by rotation of a coordinate systemMethod for obtaining G (theta) in conformal array with complete matching of far field scan ) And G max (θ scan ) Can be respectively represented by formulas (4) and (5):
Figure FDA0002388834220000031
Figure FDA0002388834220000032
wherein:
T n (θ scan ) Indicating the nth array element at the scan angle theta scan A rotation matrix of (d);
E(θ scan ) Is given by formula (2);
Figure FDA0002388834220000033
exciting the maximum amplitude for the array elements under the corresponding scanning angle;
normalized input power P of the entire array in Can be given by the excitation coefficient of each unit, i.e.
Figure FDA0002388834220000034
When P is present in When 1, the maximum amplitude of excitation of the array element in equations (2) and (6) can be expressed as
Figure FDA0002388834220000035
And (3), the joint vertical type (4), the joint vertical type (5) and the joint vertical type (7) can obtain a general aperture efficiency expression of the conformal array.
3. The design method for airborne pre-warning conformal array pitch detection beamforming as claimed in claim 1, wherein: the step (3) comprises the following stepsThe method comprises the following steps: 5 with C 1 、C 2 、A、N 1 And N 2 The modified bernstein polynomial for the parameter may be expressed as:
Figure FDA0002388834220000036
in order to complete the shaping of the array with multiple rows of array elements, an amplitude control variable Am is introduced into each row based on the formula (9), so that each modified bernstein polynomial is changed from the original 5 control parameters to 6, as shown in the following formula:
Figure FDA0002388834220000041
wherein:
C 1 、C 2 represents a value at an end of the polynomial, and 0. ltoreq.C 1 、C 2 ≤1；
Taking a unimodal peak value by a polynomial when u is A;
N 1 、N 2 not less than 0, for controlling the gentle degree of the curve;
the introduced amplitude control variable Am can control the peak value of the curve;
when only the amplitude of the array element is optimized, the excitation phase phi is kept n When the array element spacing is not changed when the array element spacing is 0, the direction diagram of the pitching surface of the conformal array can be expressed as
Figure FDA0002388834220000042
Thus, the largest side lobe of the array can be represented as
Figure FDA0002388834220000043
Wherein:
θ sl representing a side valve region;
the maximum side lobe of the array after introducing the magnitude control variable Am is approximately
Figure FDA0002388834220000051
In the formula (13), Am is less than or equal to 1, so that a lower side lobe can be obtained more easily after an amplitude control variable is introduced, which is very beneficial to the detection of the airborne early warning radar.
4. The design method for airborne pre-warning conformal array pitch detection beamforming as claimed in claim 1, wherein: the step (4) is divided into 3 sections for fitting, and comprises the following steps:
a first stage: over theta 1 The area adopts an oblique line a 1 (θ 1 ) Fitting, controlling the slope of the pitch beam to meet the required half-power lobe width requirement;
and a second stage: the object function adopts a cosecant curve a through a sky area of the maximum radiation value 2 (θ 2 )；
A third stage: outside the desired pitch range, i.e. high pitch region, the objective function is set to a line a with a larger slope for faster signal attenuation 3 (θ 3 )；
Theta is given by the formula (13) 1 The maximum side lobe level of the side lobe region S below the angle is:
Figure FDA0002388834220000052
for theta 1 And in the above areas, respectively obtaining the root mean square value RMS of the beam shape actually obtained by shaping and 3 fitting curves:
Figure FDA0002388834220000053
wherein:
num represents the total number of sampling points of the region to be fitted on the actually obtained beam shape;
P 1 (θ 1 ) Representing a first segment of an actual resulting beam curve;
P 2 (θ 2 ) Representing the actual resulting beam curve of the second segment;
P 3 (θ 3 ) Representing the actual resulting beam profile of the third segment.
5. The design method for airborne pre-warning conformal array pitch detection beamforming as claimed in claim 1, wherein: the step (5) comprises the following steps: find X ═ C 1 ,C 2 ,N 1 ,N 2 ,A,Am] T
Figure FDA0002388834220000061
Figure FDA0002388834220000062
Figure FDA0002388834220000063
p(u)≥0 (18)
Figure FDA0002388834220000064
Figure FDA0002388834220000065
Figure FDA0002388834220000066
In the formula:
design variable X ═ C 1 ,C 2 ,N 1 ,N 2 ,A,Am] T Is a description parameter of the objective function;
the objective function f (x) is a function of the negative sidelobe level and the fitted curve, with the aim of transforming the optimization problem into a standard optimization model;
constraints (16) and constraints (17) are to ensure that the basic excitation function characteristics are satisfied;
constraints (18), constraints (19) and constraints (20) are to ensure that the modified bernstein polynomial maintains basic shape characteristics;
the constraint (21) is to ensure that the side lobe levels meet the requirements.
CN202010107411.6A 2020-02-21 2020-02-21 Design method for airborne early warning conformal array pitching detection beam forming Active CN111291493B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010107411.6A CN111291493B (en) 2020-02-21 2020-02-21 Design method for airborne early warning conformal array pitching detection beam forming

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010107411.6A CN111291493B (en) 2020-02-21 2020-02-21 Design method for airborne early warning conformal array pitching detection beam forming

Publications (2)

Publication Number Publication Date
CN111291493A CN111291493A (en) 2020-06-16
CN111291493B true CN111291493B (en) 2022-09-13

Family

ID=71018007

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010107411.6A Active CN111291493B (en) 2020-02-21 2020-02-21 Design method for airborne early warning conformal array pitching detection beam forming

Country Status (1)

Country Link
CN (1) CN111291493B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2023055262A1 (en) * 2021-09-29 2023-04-06 Saab Ab Method for operating wide-band aesa

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104793187B (en) * 2015-04-21 2017-08-04 南京理工大学 A kind of digital shaped-beam design method of Digital Array Radar
CN107017468A (en) * 2017-03-17 2017-08-04 西安电子科技大学 A kind of cell layout of conformal array antenna of fuselage and Electromagnetic Desigu Method
CN108920767B (en) * 2018-06-07 2019-09-10 河海大学 The double constraint lobe array antenna optimum design methods of cosecant quadratic sum synthesis phase

Also Published As

Publication number Publication date
CN111291493A (en) 2020-06-16

Similar Documents

Publication Publication Date Title
CN106654601B (en) Grating lobe-free wide-angle scanning hybrid array ultra-sparse layout method
CN113032989B (en) Sparse array optimization method for minimizing array element number by constraining directivity coefficient
CN103646144A (en) Aperiodic array antenna design method
CN106779161B (en) Array layout optimization method of distributed three-dimensional array under pneumatic shape constraint
CN114357767B (en) Sum and difference beam sparse array synthesis method for wide-bandwidth angular beam scanning
CN108736158B (en) Ground ultra-low side flap design method
CN111276822B (en) Antenna pattern main lobe controllable antenna array design method
CN111291493B (en) Design method for airborne early warning conformal array pitching detection beam forming
CN115084874A (en) Beam scanning array optimization design method based on heterogeneous subarray non-uniform layout
CN116244940A (en) Dual-beam ultra-wideband array antenna optimization layout method
EP1250726B1 (en) Antenna arrangement and method for side-lobe suppression
CN112016662B (en) Array directional diagram synthesis method based on hybrid differential evolution algorithm and weighted total least square method
CN114709616B (en) Ultra-wideband strong coupling antenna array edge effect suppression method based on amplitude and phase regulation
CN114386271A (en) Method for synthesizing random array antenna directional diagram considering mutual coupling effect
Panduro et al. Energy Patterns of UWB antenna arrays with low side lobe level during beam-scanning
CN115133291A (en) Irregular antenna subarray, phased array antenna and design method of phased array antenna
CN116227590A (en) Terahertz phased array sidelobe suppression method and device based on improved genetic algorithm
Li et al. Unequally spaced linear antenna arrays synthesis based on genetic algorithm
CN114510879A (en) Phase configuration method for arbitrary interval linear array end-fire enhancement
Zeng et al. Shaped elevation beam design for airborne conformal array detection
CN112949193A (en) Numerical method and system for directional diagram of subarray-level sparse array antenna
Zhai et al. PSO algorithm combined with parallel higher-order MoM to compensate the influence of radome on antennas
CN113328263B (en) Shaping method and system for realizing null-free beam falling of linear array antenna
Zhao et al. Hybrid alternate projection algorithm and its application for practical conformal array pattern synthesis
CN117648871A (en) Distributed array grating lobe suppression method based on subarray layout and sparse optimization

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant