CN109343004B - Iterative feed phase calculation method for improving beam pointing accuracy of planar phased array antenna - Google Patents

Iterative feed phase calculation method for improving beam pointing accuracy of planar phased array antenna Download PDF

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CN109343004B
CN109343004B CN201811084409.0A CN201811084409A CN109343004B CN 109343004 B CN109343004 B CN 109343004B CN 201811084409 A CN201811084409 A CN 201811084409A CN 109343004 B CN109343004 B CN 109343004B
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CN109343004A (en
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张仁李
卞子懿
盛卫星
马晓峰
韩玉兵
崔杰
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Nanjing University of Science and Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/66—Radar-tracking systems; Analogous systems
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications

Abstract

The invention discloses an iterative phase-feed calculation method for improving the pointing accuracy of a planar phased array antenna beam. Firstly, determining the coordinates of each array element by taking the central symmetry point of a planar phased array antenna as an original point, and numbering all the array elements in sequence according to the central symmetry characteristic; taking the first half array elements, and calculating theoretical phase-feed values and actual phase-feed values of the array elements in sequence, wherein the actual phase-feed values are obtained by carrying quantization or truncating quantization of the theoretical phase-feed values, and the selection of a quantization mode follows the principle of minimizing the accumulated beam pointing error of the calculated phase-feed array elements; and finally completing phase feeding of the second half of array elements according to the central symmetry characteristic. The invention effectively improves the beam pointing accuracy of the planar phased array antenna, simultaneously has moderate computation amount and complexity of phase calculation, and meets the requirement of rapid beam scanning and tracking in a phased array antenna system.

Description

Iterative feed phase calculation method for improving beam pointing accuracy of planar phased array antenna
Technical Field
The invention belongs to the field of phased array antennas, and relates to an array element iterative phase-feeding calculation method for improving the beam pointing accuracy of a planar phased array antenna.
Background
Phased array antennas are widely used in radar systems to achieve fast scanning in space and target detection. The beam pointing of the phased array antenna is controlled by adjusting the excitation current of each array element, including the amplitude and phase of the excitation current. The phase shifter is a key device for adjusting the phase of an array element, and comprises an analog phase shifter and a digital phase shifter, wherein the digital phase shifter is widely adopted due to the advantages of high integration level, low power consumption, stable phase shift value and the like. However, the phase feeding accuracy of the digital phase shifter is limited by the number of bits of the phase shifter, and only provides a minimum amount of phase shift stepped by an integer multiple of the phase shift, and the resulting error between the actual and theoretical feed phases is called a feed error. The phase feed error causes beam pointing error, i.e. the actual beam pointing deviates from the intended beam pointing.
At present, a plurality of experts and scholars at home and abroad deeply research the problem of improving the beam pointing accuracy of the planar phased array antenna. Conventional phase-feed calculation methods include carry, round-off and round-off methods, however, such methods cause large periodic beam pointing errors. Guo Yanchang et al propose a random phase feeding method and a proper random phase feeding method, including a pre-phase feeding method, a binary possible value method, a proper pre-phase feeding method, a proper binary possible value method and the like, destroy the periodic error of the traditional phase feeding method, and eliminate the beam pointing error from the statistical angle. However, the phase feeding result of the random phase feeding method has randomness and instability, and the phase feeding value is often calculated for many times and a phase feeding scheme with the optimal performance is selected from the phase feeding value. In order to obtain a more stable phase feeding result, a random phase feeding calculation method based on an intelligent optimization algorithm is proposed by the director and the like, a global better solution is obtained through random search and multiple iterations, however, the method has the problems of large calculation amount and high calculation complexity, and the rapid phase feeding requirement in an actual system is difficult to meet. Chris Hemmi et al propose a two-dimensional quantization method that takes advantage of the extra degree of freedom of the array elements orthogonal to the beam scanning direction to improve pointing accuracy, but lacks versatility for general planar arrays.
Disclosure of Invention
The invention aims to provide an iterative phase-feed calculation method for realizing high-precision beam pointing by utilizing the central symmetry of a planar phased array antenna.
The technical solution for realizing the invention is as follows: an iterative phase-feed calculation method for improving the beam pointing accuracy of a planar phased array antenna comprises the following steps:
step 1, a spatial rectangular coordinate system is established by taking a central symmetry point of a planar phased array antenna as an origin, taking a plane array as an xoy plane and taking a vertical plane array upwards as a z axis, wherein the total number of planar phased array elements is 2N and the planar phased array elements are sequentially numbered from No.0 to No. (2N-1), the coordinates of No. i array elements and No. (2N-1-i) array elements are in odd symmetry with respect to the origin, and i is more than or equal to 0 and less than or equal to (N-1);
step 2, for the preset beam pointing and working wavelength, taking the first half of array elements, namely No. 0-No. (N-1) array elements, sequentially calculating the theoretical phase feed value of No. i array elements from i =0 to i = (N-1), and calculating the actual phase feed value according to the theoretical phase feed value, specifically, the theoretical phase feed value is obtained by carrying quantization or truncation quantization, and the selection of the quantization mode follows the principle of minimizing the accumulated beam pointing error of the calculated phase feed array elements;
step 3, completing the phase-feeding calculation of the second half array elements according to the central symmetry characteristic, namely No.N-No. (2N-1) array elements, which specifically comprises the following steps: the actual feed values of the No. i array elements and No. (2N-1-i) array elements which are centrosymmetric about the origin are opposite numbers, and N is less than or equal to i and less than or equal to (2N-1).
Compared with the prior art, the invention has the following remarkable advantages: (1) The invention is a deterministic phase feed calculation method, and the phase feed result is stable; (2) The invention improves the beam pointing precision of the planar phased array by sequentially iterating and feeding the phase of the array elements; (3) The phase calculation method has moderate complexity and calculation amount, and meets the requirements of fast beam scanning and tracking in a phased array system.
The present invention is described in further detail below with reference to the attached drawing figures.
Drawings
Fig. 1 is a flow chart of array element iteration phase-feeding calculation for improving the pointing accuracy of a planar phased array beam.
Fig. 2 is a planar phased array element layout.
FIG. 3 is a diagram of spatial coordinate system definition and off-axis angle, rotation angle, beam pointing error definition.
Fig. 4 is a schematic array element numbering diagram.
Fig. 5 is the antenna pattern after the phase feeding of the method, wherein the predetermined beam pointing direction is configured to be (0 ° ) in fig. 5 (a), and the predetermined beam pointing direction is configured to be (40 ° ) in fig. 5 (b).
FIG. 6 shows the corresponding beam pointing errors γ for the planar phased array at different beam scanning angles after phase feeding of the method, where the predetermined beam pointing configuration is
Figure GDA0003962412950000021
And theta 0 And the angle is 0-40 degrees, and 0.01 degrees is used as steps.
Detailed Description
An iterative phase-feed calculation method for improving the beam pointing accuracy of a planar phased array antenna comprises the following steps:
step 1, establishing a space rectangular coordinate system shown in fig. 3 by taking a central symmetric point of a planar phased array antenna as an origin, a plane array as an xoy plane and a vertical array surface upward as a z axis, wherein the total number of planar phased array elements is 2N and the planar phased array elements are sequentially numbered from No.0 to No. (2N-1), the coordinates of No. i array elements and No. (2N-1-i) array elements are in odd symmetry with respect to the origin, and i is more than or equal to 0 and less than or equal to (N-1);
step 2, for the preset beam pointing and working wavelength, taking the first half of array elements, namely No. 0-No. (N-1) array elements, sequentially calculating the theoretical phase feed value of No. i array elements from i =0 to i = (N-1), and calculating the actual phase feed value according to the theoretical phase feed value, specifically, the theoretical phase feed value is obtained by carrying quantization or truncation quantization, and the selection of the quantization mode follows the principle of minimizing the accumulated beam pointing error of the calculated phase feed array elements;
the specific steps of calculating the theoretical phase feeding value of the No. i array element from i =0 to i = (N-1) in the first half of the array elements, namely, the No.0 to the No. (N-1) array elements, and calculating the actual phase feeding value according to the theoretical phase feeding value are as follows:
step 2-1, calculating the theoretical phase-feed value of the No.i array element, specifically comprising
When the planar phased array antenna has an operating wavelength of λ and the predetermined beam is directed to
Figure GDA0003962412950000031
Theoretical phase-feed value phi of No.i array element theo,i Comprises the following steps:
Figure GDA0003962412950000032
wherein k =2 π/λ, (x) i ,y i ) Is the coordinate of No.i array element, i is more than or equal to 0 and less than or equal to N-1, theta 0 Is the off-axis angle at which the predetermined beam is directed,
Figure GDA0003962412950000033
is rotation of a predetermined beam pointing directionAn angle;
step 2-2, quantizing the theoretical phase-feed value of No.i array element into integral multiple of the minimum phase-shifting step of the digital phase shifter according to a carry method or a truncation method, thereby obtaining the actual phase-feed value phi i The method specifically comprises the following steps:
Figure GDA0003962412950000034
wherein
Figure GDA0003962412950000035
Meaning that the rounding is done up for x,
Figure GDA0003962412950000036
meaning rounding down on x, Δ is the minimum phase shift step of the digital phase shifter, Δ =2 pi/2 for a digital phase shifter with Q bits Q ；
The feed error of the No. i array element is expressed as:
δφ i ＝φ i -φ theo,i
the actual phase-feed value and phase-feed error obtained by quantizing theoretical phase-feed value according to carry method are respectively recorded as phi carry,i ，δφ carry,i The actual phase-fed value and phase-fed error quantized by truncation method are respectively recorded as phi truncate,i ，δφ truncate,i ；
Step 2-3, calculating accumulated beam pointing errors gamma caused by the array elements from No.0 to No. i and the array elements from No. (2N-1-i) to No. (2N-1) which are symmetric around the origin in the central mode i The method specifically comprises the following steps:
according to the central symmetry characteristic, the actual feed phase value of the No. i array element is opposite to the actual feed phase value of the No. (2N-1-i) array element which is centrosymmetric about the origin; accumulated beam pointing error gamma caused by No. 0-No. i array elements and No. (2N-1-i) -No. (2N-1) array elements which are centrosymmetric about the origin i Expressed as:
Figure GDA0003962412950000041
wherein the beam pointing error gamma i Defined as the angle between the intended beam pointing direction and the actual beam pointing direction, δ θ i Defined as the difference in off-axis angle between the intended beam pointing direction and the actual beam pointing direction,
Figure GDA0003962412950000042
defined as the difference in rotation angle between the intended beam pointing direction and the actual beam pointing direction, expressed in particular as:
Figure GDA0003962412950000043
wherein, the actual phase feeding value and phase feeding error of No. 0-No. (i-1) array elements and the array elements which are centrosymmetric about the origin are determined, and the coefficient p 1 ,q 1 ,p 2 And q is 2 Is given a value of
Figure GDA0003962412950000044
Determining the working wavelength lambda and the array element coordinates, specifically:
Figure GDA0003962412950000051
wherein k =2 π/λ,
Figure GDA0003962412950000052
at a predetermined pointing angle, x n Is the abscissa, y, of the No. n array element n Ordinate of No. n array element, I n The excitation amplitude of the No. n array element.
By quantizing phi by carry theo,i The resulting accumulated beam pointing error is denoted as gamma carry,i Quantization of phi by rounding theo,i The resulting accumulated beam pointing error is noted as gamma truncate,i 。
Step 2-4, selecting the quantization method which minimizes the accumulated beam pointing error caused by the calculated feed phase array element as phi theo,i The actual quantization method specifically includes:
comparison of gamma carry,i And gamma truncate,i If γ is carry,i ＜γ truncate,i Then the actual phase-feed value of the No.i array element is from phi theo,i Carry quantization is obtained, i.e.
Figure GDA0003962412950000053
Otherwise, the actual phase-feed value of No.i array element is phi theo,i Truncated quantization to obtain
Figure GDA0003962412950000054
Step 3, finishing the phase feeding calculation of the second half array elements according to the centrosymmetric characteristic, namely, no.N-No. (2N-1) array elements, which specifically comprises the following steps: the actual feed values of the No. i array elements and No. (2N-1-i) array elements which are centrosymmetric about the origin are opposite numbers, and N is less than or equal to i and less than or equal to (2N-1).
Example 1
As shown in fig. 1, the iterative phase-feed calculation method for improving the beam pointing accuracy of a planar phased array antenna of the present invention includes the following steps:
simulation conditions are as follows: the planar phased array antenna with the centrosymmetric characteristic is arranged as shown in fig. 2, and is a triangular grid planar phased array composed of 182 (14 × 13) array elements, the centrosymmetric point of the planar phased array is point a, the distance d =0.56 λ between any two adjacent array elements, λ is the working wavelength, a 6-bit digital phase shifter is connected behind each array element, and the amplitude of the excitation current of each array element is 1.
Step 1, firstly, a space rectangular coordinate system shown in fig. 3 is established by taking a central symmetry point A of a planar phased array as an origin, taking a front surface as an xoy plane and taking a vertical front surface upward as a z axis. The total array element number of the planar phased array is 182, and the array elements are numbered from No.0 to No.181 in sequence as shown in FIG. 4, wherein the coordinates of the No. i array element and the No. (181-i) array element are in odd symmetry with respect to the origin, and i is more than or equal to 0 and less than or equal to 90.
Step 2, pointing to the preset beam
Figure GDA0003962412950000061
And working wavelength lambda, taking the first half array elements, namely No.0 to No.90 array elements, and sequentially from i =0 to i =90And calculating the actual phase-feed value of No.i, and specifically comprising the following steps:
(1) Calculating the theoretical phase-feed value phi of No.i array element theo,i By the formula:
Figure GDA0003962412950000062
wherein k =2 π/λ, (x) i ,y i ) Is the coordinate of No.i array element, i is more than or equal to 0 and less than or equal to 90, theta 0 Is the off-axis angle at which the predetermined beam is directed,
Figure GDA0003962412950000063
is the rotation angle of the predetermined beam pointing, specifically defined as shown in fig. 3;
(2) Quantizing the theoretical phase-feed value of No.i array element into integer multiple of the minimum phase-shift step of the digital phase shifter by a carry method or a truncation method, thereby obtaining the actual phase-feed value phi i The method specifically comprises the following steps:
actual phase-fed value phi of No.i array element when quantizing according to carry method carry,i And phase error delta phi carry,i Is composed of
Figure GDA0003962412950000064
δφ carry,i ＝φ carry,i -φ theo,i
Actual phase-feeding value phi of No.i array element when quantization is carried out according to truncation method truncate,i And phase error delta phi truncate,i Is composed of
Figure GDA0003962412950000065
δφ truncate,i ＝φ truncate,i -φ theo,i
Wherein the minimum phase shift step of the digital phase shifter is delta =2 pi/2 6 。
(3) Calculating the results of No. 0-No. i array elements and No. (181-i) -No. 181 array elements which are centrosymmetric about the originAccumulated beam pointing error gamma of i And the actual phase feeding values and phase feeding errors of the array elements with the numbers of No. 0-No. (i-1) and the array elements which are in central symmetry with the origin are determined.
Separately computing quantization phi by carry method theo,i Resulting accumulated beam pointing error gamma carry,i And quantizing phi by truncation theo,i Resulting accumulated beam pointing error gamma truncate,i By the formula
Figure GDA0003962412950000071
Wherein
Figure GDA0003962412950000072
Figure GDA0003962412950000073
k＝2π/λ，
Figure GDA0003962412950000074
At a predetermined pointing angle, x n Is the abscissa, y, of the No. n array element n Ordinate of No. n array element, I n The excitation amplitude of the No. n array element.
(4) Comparison of gamma carry,i And gamma truncate,i If γ is carry,i ＜γ truncate,i Then the actual phase-feeding value of No.i array element is from phi theo,i Carry quantization is obtained, i.e.
Figure GDA0003962412950000075
Otherwise, the actual phase-feed value of No.i array element is phi theo,i Truncated quantization to obtain
Figure GDA0003962412950000076
(5) i = i +1, repeating steps 2-1-2-4, and calculating the actual phase-feed value of the No. i array element until i = N-1.
Step 3, finishing the phase feeding calculation of the second half array elements according to the central symmetry characteristic, namely No. 91-No. 181 array elements, specifically: the actual feed phase values of the No. i array element and the No. (181-i) array element which is centrosymmetric about the origin are opposite numbers, phi i ＝-φ 181-i ，i＝91,92,...,181。
By calculation, when the predetermined beam directions are respectively configured to be (0 ° ) and (40 °,40 °), the antenna pattern fed by the method is as shown in fig. 5, the actual beam directions thereof are respectively (0 ° ) and (39.99 °,40 °), the off-axis angle deviation between the predetermined beam direction and the actual beam direction is within 0.01 °, and the rotation angle deviation between the predetermined beam direction and the actual beam direction is also within 0.01 °.
When the predetermined beam is pointed
Figure GDA0003962412950000081
Wherein
Figure GDA0003962412950000082
And theta 0 And = 0-40 degrees, when the 0.01 degrees are used as steps, the beam pointing error gamma of the planar phased array antenna fed by the method is shown in fig. 6, and the included angle between the preset beam pointing direction and the actual beam pointing direction is within 0.0106 degrees.
Therefore, the invention can effectively improve the beam pointing accuracy of the planar phased array antenna, has moderate complexity of the phase calculation method, and meets the requirements of rapid beam scanning and tracking in a phased array system.

Claims (3)

1. An iterative feed phase calculation method for improving the beam pointing accuracy of a planar phased array antenna is characterized by comprising the following steps of:
step 1, establishing a space rectangular coordinate system by taking a central symmetrical point of a planar phased array antenna as an original point, a plane array surface as an xoy plane and a vertical plane array surface upward as a z axis, wherein the total number of planar phased array elements is 2N and the planar phased array elements are numbered from No.0 to No. (2N-1), the coordinates of No. i array elements and No. (2N-1-i) array elements are in odd symmetry relative to the original point, and i is more than or equal to 0 and less than or equal to (N-1);
step 2, for the preset beam direction and working wavelength, taking the first half of array elements, namely, no.0 to No. (N-1) array elements, sequentially calculating theoretical phase feeding values of the no.i array elements from i =0 to i = (N-1), and calculating actual phase feeding values according to the theoretical phase feeding values, specifically, obtaining the theoretical phase feeding values through carry quantization or truncate quantization, wherein the selection of the quantization mode follows the principle of minimizing the accumulated beam direction error of the calculated phase feeding array elements, the first half of array elements in step 2, namely, no.0 to No. (N-1) array elements, sequentially calculating the theoretical phase feeding values of the no.i array elements from i =0 to i = (N-1), and calculating the actual phase feeding values according to the theoretical phase feeding values, and the specific steps are as follows:
step 2-1, calculating a theoretical phase-feed value of the No.i array element, specifically:
when the planar phased array antenna has an operating wavelength of λ and the predetermined beam is directed to
Figure FDA0003962412940000011
Theoretical phase-feed value phi of No.i array element theo,i Comprises the following steps:
Figure FDA0003962412940000012
wherein k =2 π/λ, (x) i ,y i ) Is the coordinate of No.i array element, i is more than or equal to 0 and less than or equal to N-1, theta 0 Is the off-axis angle at which the predetermined beam is directed,
Figure FDA0003962412940000013
is the rotation angle of the predetermined beam pointing;
step 2-2, quantizing the theoretical phase-feed value of No.i array element into integral multiple of minimum phase-shifting step of digital phase shifter by carry method or truncation method, thereby obtaining actual phase-feed value phi i The method specifically comprises the following steps:
Figure FDA0003962412940000014
wherein
Figure FDA0003962412940000015
Meaning that the rounding is done up for x,
Figure FDA0003962412940000016
meaning rounding down on x, Δ is the minimum phase shift step of the digital phase shifter, Δ =2 pi/2 for a digital phase shifter with Q bits Q ；
The feed error of the No. i array element is expressed as:
δφ i ＝φ i -φ theo,i
the actual phase-fed value and phase-fed error obtained by quantizing the theoretical phase-fed value by the carry method are respectively recorded as phi carry,i ，δφ carry,i The actual phase-fed value and phase-fed error quantized by truncation method are respectively recorded as phi truncate,i ，δφ truncate,i ；
Step 2-3, calculating accumulated beam pointing errors gamma caused by array elements No. 0-No. i and array elements No. (2N-1-i) -No. (2N-1) which are centrosymmetric about the origin i The method specifically comprises the following steps:
according to the central symmetry characteristic, the actual feed phase value of the No. i array element is opposite to the actual feed phase value of the No. (2N-1-i) array element which is centrosymmetric about the origin; accumulated beam pointing error gamma caused by No. 0-No. i array elements and No. (2N-1-i) -No. (2N-1) array elements which are centrosymmetric about the origin i Expressed as:
Figure FDA0003962412940000021
wherein the beam pointing error gamma i Defined as the angle between the intended beam pointing direction and the actual beam pointing direction, δ θ i For the off-axis angular difference between the intended beam pointing direction and the actual beam pointing direction,
Figure FDA0003962412940000022
is the difference in rotation angle between the predetermined beam pointing direction and the actual beam pointing direction;
by quantizing phi by carry method theo,i The resulting accumulated beam pointing error is denoted as gamma carry,i Quantization of phi by truncation theo,i The resulting accumulated beam pointing error is denoted as gamma truncate,i ；
Step 2-4, selecting the quantization method which minimizes the accumulated beam pointing error caused by the calculated feed phase array element as phi theo,i The actual quantization method specifically includes:
comparison of gamma carry,i And gamma truncate,i If γ is carry,i ＜γ truncate,i Then the actual phase-feeding value of No.i array element is from phi theo,i Carry quantization is obtained, i.e.
Figure FDA0003962412940000023
Otherwise, the actual phase-feed value of the No.i array element is phi theo,i Truncated quantization to obtain
Figure FDA0003962412940000024
Step 3, completing the phase-feeding calculation of the second half array elements according to the central symmetry characteristic, namely No.N-No. (2N-1) array elements, which specifically comprises the following steps: the actual feed phase value of the No. i array element is opposite to the actual feed phase value of the No. (2N-1-i) array element which is centrosymmetric about the origin, and N is less than or equal to i and less than or equal to (2N-1).
2. The iterative phase-feed calculation method for improving beam pointing accuracy of a planar phased array antenna according to claim 1, wherein an off-axis angle difference δ θ between a predetermined beam pointing direction and an actual beam pointing direction i Difference in rotation angle between the intended beam pointing direction and the actual beam pointing direction
Figure FDA0003962412940000031
The concrete expression is as follows:
Figure FDA0003962412940000032
no. 0-No. (i-1) array elements and related elements thereofThe actual phase-feed value and phase-feed error of the array element which is point-symmetric to the center are determined, and the coefficient p 1 ,q 1 ,p 2 And q is 2 Is given a value of
Figure FDA0003962412940000033
Determination of the working wavelength lambda and the coordinates of the array elements, I n The excitation amplitude of the No. n array element.
3. The iterative phase-feed calculation method for improving the beam pointing accuracy of a planar phased array antenna according to claim 2, wherein the coefficient p is 1 ,q 1 ,p 2 And q is 2 The method comprises the following specific steps:
Figure FDA0003962412940000034
wherein k =2 π/λ,
Figure FDA0003962412940000035
at a predetermined pointing angle, x n Is the abscissa, y, of the No. n array element n Is the ordinate of No. n array element, I n The excitation amplitude of the No. n array element.
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