CN116244940A - Dual-beam ultra-wideband array antenna optimization layout method - Google Patents

Dual-beam ultra-wideband array antenna optimization layout method Download PDF

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CN116244940A
CN116244940A CN202310161926.8A CN202310161926A CN116244940A CN 116244940 A CN116244940 A CN 116244940A CN 202310161926 A CN202310161926 A CN 202310161926A CN 116244940 A CN116244940 A CN 116244940A
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树玉泉
刘颜回
付野
刘泱
姚志会
黄杰
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University of Electronic Science and Technology of China
CETC 54 Research Institute
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Abstract

The invention belongs to the technical field of antennas, provides a double-beam ultra-wideband array antenna optimization layout method, and relates to array antenna pattern synthesis and antenna array element position optimization. The method comprises the following steps: step 1, initializing and laying out planar array antenna units by adopting a Fermat spiral array layout method; and 2, performing continuous perturbation optimization on the array element positions by adopting an iterative convex optimization method, and minimizing the maximum sidelobe level of the dual-beam with the beam pointing to different directions in the range of ultra-wideband working frequency (the ratio of the highest working frequency point to the lowest working frequency point is more than 3) to obtain an optimization target. And setting maximum sidelobe level constraint, array element position perturbation amplitude constraint and minimum unit spacing constraint in the optimization process. The invention can integrate the planar array with ultra-wideband and dual-beam scanning performance by optimizing the antenna unit layout, and can effectively control the minimum unit spacing to meet the practical application requirements.

Description

Dual-beam ultra-wideband array antenna optimization layout method
Technical Field
The invention belongs to the technical field of antennas, and particularly relates to an optimized layout method of a dual-beam ultra-wideband array antenna.
Background
The ultra-wideband array antenna can realize effective radiation in the case that the ratio of the highest operating frequency point to the lowest operating frequency point is more than 3, so that it is widely used in wireless communication systems and radar systems. However, designing a high performance ultra wideband array antenna is often faced with a dilemma, namely the choice of minimum cell spacing. In one aspect, half wavelength of the highest frequency point is selected as the minimum cell pitch, such as a tight coupling technique. Although the technology can realize extremely large working bandwidth, the technology needs more channels and has difficult active standing-wave ratio suppression. On the other hand, a half wavelength of the lowest frequency point is selected as the minimum cell pitch, but this results in a high frequency grating lobe being introduced into the array pattern. Therefore, most of the current methods further optimize the positions of the array antenna elements by using a sparse array layout method. For example: the document 1 uses the characteristics of the Bessel function of the first class to represent array factors, and provides a design method for analyzing and calculating the radius of a ring and the number of elements in the ring.
Although the method can comprehensively meet the design index requirements of the dual-beam ultra-wideband array antenna, the method searches parameters affecting the layout of the antenna units within a certain reasonable value range, so that the positions of the antenna units capable of realizing the optimal radiation performance are found analytically. However, despite the faster solution speed of the above method, the limited solution range results in limited optimization performance of the algorithm. Meanwhile, how to ensure broadband and beam scanning performance in the optimization process, and considering the minimum unit distance, avoiding physical overlapping between antenna array elements is also a great challenge. Finally, in the existing ultra-wideband array synthesis method, only a sparse array layout method is adopted to synthesize the single-beam linear array, and the sparse array layout method is used for synthesizing the dual-beam ultra-wideband planar array, and the method for realizing minimum unit spacing control is few.
Chinese patent CN202110281818.5 discloses a method for scanning and arranging an array at a large angle without grating lobes in an array with an ultra-large pitch, the whole array antenna is first divided into an i, an ii and an iii plane array regions according to the x-axis, the plane arrays of the plane array regions i and iii are subjected to oblique angle arrangement, the whole two-dimensional plane array is subjected to shape adjustment, the space utilization is increased, and the experimental result shows that the method can realize an ultra-wideband grating lobe free sparse array with frequency more than 3 times. However, the planar ultra-wideband array synthesized by the method is used for searching parameters influencing the layout analytically, and the optimized array element layout result still has a further optimization space.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method for optimizing the layout of a dual-beam ultra-wideband array antenna, which adopts the Fermat spiral layout as the initial layout of the array and ensures that the array meets the minimum unit spacing required; and finally, performing continuous perturbation optimization on the array element positions by adopting an iterative convex optimization method, and minimizing the maximum sidelobe level of the dual-beam with the beam pointing to different directions in the range of ultra-wideband working frequency (the ratio of the highest working frequency point to the lowest working frequency point is more than 3) as an optimization target. And setting maximum sidelobe level constraint, array element position perturbation amplitude constraint and minimum unit spacing constraint in the optimization process. The optimized array element layout can realize the dual-beam planar array with ultra-wideband and beam scanning performance, and the minimum unit spacing required is met to meet the practical application requirement.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
the method for optimizing layout of the dual-beam ultra-wideband array antenna comprises the following steps:
(1) Determining the number of array elements of the planar array antenna and the minimum array element spacing, and initializing and laying out the array elements of the planar array antenna by adopting a Fermat spiral array layout method;
(2) Performing perturbation optimization on the array element positions by adopting an iterative convex optimization method, in an ultra-wideband working frequency range, minimizing the maximum sidelobe level of the dual-beam with the beam pointing to different directions as an optimization target, and setting the maximum sidelobe level constraint, the array element position perturbation magnitude constraint and the minimum array element spacing constraint in the optimization process; the ultra-wideband working frequency is that the ratio of the highest working frequency point to the lowest working frequency point is more than 3.
Further, in step 1, an initial layout is performed on array elements of the planar array antenna by adopting a fischer spiral array layout method, which specifically comprises the following steps:
in a polar coordinate system, n=1 based on the N-th, n=1, of the fermat spiral planar array
Figure BDA0004094485840000031
Figure BDA0004094485840000032
in the formula ,
Figure BDA0004094485840000033
for golden angle, normalization factor->
Figure BDA0004094485840000034
d min The position information under the polar coordinate system of the antenna array elements is converted into rectangular coordinate system position information of an xoy plane through formulas (3) and (4) for the minimum unit distance, namely half wavelength of the lowest frequency point, wherein N is the number of the array elements of the planar array antenna;
x n ＝ρ n cos(φ n ) (3)
y n ＝ρ n sin(φ n ) (4)
based on the array element positions obtained in the formulas (3) and (4), the expression of the array factor of the dual-beam planar array of K frequency points is shown as (5) in the k=1
Figure BDA0004094485840000035
wherein ,
Figure BDA0004094485840000036
x n and yn Respectively representing the positions of the nth antenna element in the array in the x-axis and the y-axis,
Figure BDA0004094485840000037
active element patterns, theta and +.>
Figure BDA0004094485840000038
Representing the direction of observation measured from the z and x axes, beta k ＝2πf k C represents the wavenumber in free space at the kth frequency point, and f k ＝f L +(f H -f L )*k/K，f L and fH Respectively representing the lowest and highest frequency points of the working frequency points,/->
Figure BDA0004094485840000041
and
Figure BDA0004094485840000042
and />
Figure BDA0004094485840000043
and />
Figure BDA0004094485840000044
The desired pointing directions of the two beams are indicated, respectively, and u and v represent the abscissa and ordinate, respectively, of the spherical coordinate system after projection onto the xoy plane.
Further, the step 2 specifically includes:
adopting an iterative convex optimization method to perform continuous perturbation optimization on the array element position, and in an ultra-wideband working frequency range, minimizing the maximum sidelobe level of the dual-beam with the beam pointing to different directions as an optimization target, and reducing the peak level of a grating lobe/sidelobe region on the basis of controllable minimum spacing to obtain the optimal planar array antenna array element layout; wherein the basic principle of the perturbation method is to locate the array element x in the formula (5) n and yn Becomes x n +Δx n and yn +Δy n ，Δx n and Δyn Representing the position perturbation quantity of the array element in the x and y directions respectively, and expanding the array element into a linear expression through a first-order Taylor, and ensuring that three constraint conditions of side lobe level constraint, position perturbation amplitude constraint and minimum spacing constraint of double beams are met in the optimization process, wherein the specific constraint conditions are set as follows:
1) Side lobe level constraint for dual beams: in the ultra-wideband working frequency range, a set auxiliary variable epsilon is introduced to restrict the dual-wave beam directional diagram to be in the k frequency point side lobe area
Figure BDA0004094485840000045
The value of (2) is smaller than epsilon;
2) Position perturbation amplitude constraint: for n=1, …, N satisfies |β H Δx n|≤μ and |βH Δy n |≤μ，β H For the free space wave number of the highest frequency in the working frequency band, mu is a set value, and mu determines the amplitude of the position perturbation;
3) Minimum pitch constraint: in the perturbation process, the distance between any two antenna array elements p and q is required to be larger than the set minimum unit distance d min ，p&q＝1,…,N&p is not equal to q and p is not equal to q;
finally, the array synthesis problem is expressed as formula (6), the solution is carried out by an iterative convex optimization method, and the optimization objective of the L iterations is to minimize the peak level of the grating\side lobe region;
Figure BDA0004094485840000051
where ε constrains the peak level of the array pattern for the introduced auxiliary variable,
Figure BDA0004094485840000052
side lobe region representing kth frequency point, dual beams are directed to +.>
Figure BDA0004094485840000053
and />
Figure BDA0004094485840000054
(x p ，y p) and (xq ，y q ) The coordinates of the antenna array elements p and q, respectively, theta a &θ b ∈{0°,θ max The 2 pitch angles {0 }, θ, respectively, to which the dual beams considered in the optimization process are directed max }，θ max For the maximum pitch angle considered, +.>
Figure BDA0004094485840000055
4 azimuth angles which respectively indicate the directions of the double wave beams considered in the optimization process are {0 °,45 °,90 °,135 ° }; when the constraint conditions are met, performing multi-step perturbation on the array element position through an iterative convex optimization method, and reducing the peak level of the grating lobe/side lobe region; iteratively solving the position perturbation quantity delta x in the x and y directions at each step n and Δyn After that, x is n and yn Becomes x n +Δx n and yn +Δy n And updating the array element position, and obtaining the optimized array layout when the peak level of the grating lobe/side lobe region of the new array is unchanged and the array layout is also unchanged.
The invention can integrate the planar array with ultra-wideband and dual-beam scanning performance by optimizing the antenna unit layout, and can effectively control the minimum unit spacing to meet the practical application requirements.
Drawings
Fig. 1 is a flow chart of the technical scheme of the invention.
Fig. 2 is an initial antenna element position based on the fermat spiral array layout method.
Fig. 3 is a side lobe peak level during an optimization process for array antenna element position using iterative convex optimization.
Fig. 4 is an array antenna element position after iterative convex optimization.
Fig. 5 is an array pattern for a 3GHz frequency bin dual beam profile pointing normal and pitch and azimuth angles of 45 degrees.
Fig. 6 is an array pattern for a 13GHz frequency bin dual beam profile pointing normal and pitch and azimuth angles of 45 degrees.
Detailed Description
The present invention will be further described in detail below with reference to the accompanying drawings, in order to make the objects, technical solutions and advantages of the present invention more apparent.
The invention is further explained below in connection with an example. The design target is as follows: the working frequency ranges from 3Hz to 13GHz, and the lowest frequency f L =3 GHz and f H =13 GHz; consider 2 frequency points k=2, and the maximum angle of the dual beam at pitch angle is θ max =45°; a sparse planar array of grating lobes/side lobe regions with the peak level of the grating lobes/side lobe regions remaining unchanged.
As shown in fig. 1, the following steps are performed:
step 1: and (5) performing initial layout by adopting a Fermat spiral array layout method. In a polar coordinate system, n=1 based on the N-th, n=1, of the fermat spiral planar array
Figure BDA0004094485840000061
Figure BDA0004094485840000062
Where the number of array elements n=140,
Figure BDA0004094485840000063
is the golden angle, is normalizedChemical factor
Figure BDA0004094485840000064
When d min ＝λ L 2=0.05m is the minimum cell pitch (half the wavelength of the lowest operating frequency point). And converting the position information of the antenna array element in the polar coordinate system into rectangular coordinate system position information of the xoy plane through formulas (3) and (4). Fig. 2 shows the antenna element positions achieved based on the fermat spiral array layout method.
x n ＝p n cos(φ n ) (3)
y n ＝p n sin(φ n ) (4)
Based on the array element positions obtained by the formulas (3) and (4), the expression of the dual-beam planar array factor of K frequency points is shown as (5) at k=1.
Figure BDA0004094485840000071
wherein ,
Figure BDA0004094485840000072
x n and yn Respectively representing the positions of the nth antenna element in the array in the x-axis and the y-axis,
Figure BDA0004094485840000073
active element patterns, theta and +.>
Figure BDA0004094485840000074
Representing the direction of observation measured from the z and x axes, beta k ＝2πf k C represents the wavenumber in free space at the kth frequency point, and f k ＝f L +(f H -f L )*k/K，f L and fH Respectively representing the lowest and highest frequency points of the working frequency points,/->
Figure BDA0004094485840000075
and
Figure BDA0004094485840000076
and />
Figure BDA0004094485840000077
and />
Figure BDA0004094485840000078
The desired pointing directions of the two beams are indicated, respectively, and u and v represent the abscissa and ordinate, respectively, of the spherical coordinate system after projection onto the xoy plane.
Step 2: continuous perturbation optimization is carried out on array element positions by adopting an iterative convex optimization method, the maximum sidelobe level of the dual-beam in different directions pointed by beams in ultra-wideband working frequency (the ratio of the highest working frequency point to the lowest working frequency point is more than 3) is minimized as an optimization target, and the peak level of grating lobes/sidelobe areas is reduced to the greatest extent on the basis of controllable minimum spacing, so that the optimal planar array antenna unit layout is obtained. The basic principle of the perturbation method is to locate the array element in the position x in the method (5) n and yn Becomes x n +Δx n and yn +Δy n ，Δx n and Δyn Represents the position perturbation quantity of the array element in the x and y directions respectively, and is developed into a linear expression through first-order Taylor. In addition, in the optimization process, three constraint conditions of side lobe level constraint, position perturbation amplitude constraint and minimum spacing constraint of the double beams need to be guaranteed to be met, and the specific constraint conditions are set as follows:
1) Side lobe level constraint for dual beams: in the range of ultra-wideband working frequency (the ratio of the highest working frequency point to the lowest working frequency point is more than 3), in order to ensure that the peak level of double beams with different beam directions in different angles in the optimization process in a grating lobe/side lobe area is reduced to the greatest extent, an auxiliary variable epsilon is introduced, and the double-beam directional diagram is restrained in a kth frequency point side lobe area
Figure BDA0004094485840000085
The value of (2) is smaller than epsilon.
2) Position perturbation amplitude constraint: to ensure the approximation accuracy of the position perturbation, N satisfies |β for each of n=1, 2, … H Δx n|≤μ and |βH Δy n |≤μ，β H The magnitude of μ determines the magnitude of the position perturbation for the free space wavenumber of the highest frequency in the operating band, set to μ=1.4 m m.
3) Minimum pitch constraint: in order to reduce the difficulty of antenna element design, the practicality of antenna array layout is improved, and the smaller the antenna element coupling is expected in the range of the working frequency band, the minimum spacing constraint needs to be satisfied for the array element spacing in the actual antenna array layout process. Thus, when the minimum cell spacing d between array elements is set min After =50mm (half wavelength of lowest operating frequency point), the distance between any two antenna elements p and q during perturbation needs to be larger than the set minimum element spacing d min (half wavelength of lowest operating frequency point), p&q＝1,…,N&p+.q and p+.q.
Finally, this array synthesis problem can be expressed as equation (6), solved by iterative convex optimization method, at the first = 1..the optimization objective of L iterations is to minimize the peak level of the grating\side lobe region;
Figure BDA0004094485840000081
where ε constrains the peak level of the array pattern for the introduced auxiliary variable,
Figure BDA0004094485840000082
side lobe region representing kth frequency point, dual beams are directed to +.>
Figure BDA0004094485840000083
and />
Figure BDA0004094485840000084
(x p ，y p) and (xq ，y q ) The coordinates of the antenna array elements p and q, respectively, theta a &θ b ∈{0°,θ max The 2 pitch angles {0 }, θ, respectively, to which the dual beams considered in the optimization process are directed max }，θ max For the maximum pitch angle considered, +.>
Figure BDA0004094485840000091
4 azimuth angles which respectively indicate the directions of the double wave beams considered in the optimization process are {0 °,45 °,90 °,135 ° }; when the constraint conditions are met, performing multi-step perturbation on the array element position through an iterative convex optimization method, and reducing the peak level of the grating lobe/side lobe region; iteratively solving the position perturbation quantity delta x in the x and y directions at each step n and Δyn After that, x is n and yn Becomes x n +Δx n and yn +Δy n And updating the array element position, and obtaining the optimized array layout when the peak level of the grating lobe/side lobe region of the new array is unchanged and the array layout is also unchanged. Fig. 3 shows the peak level values of the grating lobe/side lobe regions of the perturbation results at each step, after about 70 iterations, the peak level of the grating lobe/side lobe regions was reduced to about-15.43 dB, then remained essentially unchanged, and after iterative convex optimization the peak level of the grating lobe/side lobe regions was reduced by a total of 4.26dB. Figure 4 shows the array position after iterative convex optimization. FIGS. 5 and 6 show the direction of the dual beam at the 3GHz and 13GHz frequency points, respectively, in normal direction>
Figure BDA0004094485840000092
The peak levels of the grating lobe/side lobe regions at this time were-14.28 dB and-10.68 dB, respectively. />

Claims (3)

1. The method for optimizing the layout of the dual-beam ultra-wideband array antenna is characterized by comprising the following steps of:
(1) Determining the number of array elements of the planar array antenna and the minimum array element spacing, and initializing and laying out the array elements of the planar array antenna by adopting a Fermat spiral array layout method;
(2) Performing perturbation optimization on the array element positions by adopting an iterative convex optimization method, in an ultra-wideband working frequency range, minimizing the maximum sidelobe level of the dual-beam with the beam pointing to different directions as an optimization target, and setting the maximum sidelobe level constraint, the array element position perturbation magnitude constraint and the minimum array element spacing constraint in the optimization process; the ultra-wideband working frequency is that the ratio of the highest working frequency point to the lowest working frequency point is more than 3.
2. The ultra-wideband sparse planar array synthesis method according to claim 1, wherein in step 1, a fischer spiral array layout method is adopted to perform initialization layout on planar array antenna array elements, specifically:
in a polar coordinate system, n=1 based on the N-th, n=1, of the fermat spiral planar array
Figure FDA0004094485830000011
Figure FDA0004094485830000012
in the formula ,
Figure FDA0004094485830000013
for golden angle, normalization factor->
Figure FDA0004094485830000014
d min The position information under the polar coordinate system of the antenna array elements is converted into rectangular coordinate system position information of an xoy plane through formulas (3) and (4) for the minimum unit distance, namely half wavelength of the lowest frequency point, wherein N is the number of the array elements of the planar array antenna;
x n ＝ρ n cos(φ n ) (3)
y n ＝ρ n sin(φ n ) (4)
based on the array element positions obtained in the formulas (3) and (4), the expression of the array factor of the dual-beam planar array of K frequency points is shown as (5) in the k=1
Figure FDA0004094485830000021
wherein ,
Figure FDA0004094485830000022
x n and yn Respectively representing the positions of the nth antenna element in the array in the x-axis and the y-axis,
Figure FDA0004094485830000023
active element patterns, theta and +.>
Figure FDA0004094485830000024
Representing the direction of observation measured from the z and x axes, beta k ＝2πf k C represents the wavenumber in free space at the kth frequency point, and f k ＝f L +(f H -f L )*k/K，f L and fH Respectively representing the lowest and highest frequency points of the working frequency points,/->
Figure FDA0004094485830000025
and
Figure FDA0004094485830000026
and />
Figure FDA0004094485830000027
and />
Figure FDA0004094485830000028
The desired pointing directions of the two beams are indicated, respectively, and u and v represent the abscissa and ordinate, respectively, of the spherical coordinate system after projection onto the xoy plane.
3. The method for optimizing layout of a dual-beam ultra-wideband array antenna of claim 2, wherein step 2 is specifically:
adopting an iterative convex optimization method to continuously micro-scale the array element positionDisturbance optimization, namely, in an ultra-wideband working frequency range, minimizing the maximum sidelobe level of the dual-beam with the beam pointing to different directions into an optimization target, and reducing the peak level of a grating lobe/sidelobe region on the basis of controllable minimum spacing to obtain the optimal array element layout of the planar array antenna; wherein the basic principle of the perturbation method is to locate the array element x in the formula (5) n and yn Becomes x n +Δx n and yn +Δy n ，Δx n and Δyn Representing the position perturbation quantity of the array element in the x and y directions respectively, and expanding the array element into a linear expression through a first-order Taylor, and ensuring that three constraint conditions of side lobe level constraint, position perturbation amplitude constraint and minimum spacing constraint of double beams are met in the optimization process, wherein the specific constraint conditions are set as follows:
1) Side lobe level constraint for dual beams: in the ultra-wideband working frequency range, a set auxiliary variable epsilon is introduced to restrict the dual-wave beam directional diagram to be in the k frequency point side lobe area
Figure FDA0004094485830000029
The value of (2) is smaller than epsilon;
2) Position perturbation amplitude constraint: for n=1, …, N satisfies |β H Δx n|≤μ and |βH Δy n |≤μ，β H For the free space wave number of the highest frequency in the working frequency band, mu is a set value, and mu determines the amplitude of the position perturbation;
3) Minimum pitch constraint: in the perturbation process, the distance between any two antenna array elements p and q is required to be larger than the set minimum unit distance d min ，p&q＝1,…,N&p is not equal to q and p is not equal to q;
finally, the array synthesis problem is expressed as formula (6), the solution is carried out by an iterative convex optimization method, and the optimization objective of the L iterations is to minimize the peak level of the grating\side lobe region;
Figure FDA0004094485830000031
wherein ε is the introduction ofIs used to constrain the peak levels of the array pattern,
Figure FDA0004094485830000032
side lobe region representing kth frequency point, dual beams are directed to +.>
Figure FDA0004094485830000033
and />
Figure FDA0004094485830000034
(x p ，y p) and (xq ，y q ) The coordinates of the antenna array elements p and q, respectively, theta a &θ b ∈{0°,θ max The 2 pitch angles {0 }, θ, respectively, to which the dual beams considered in the optimization process are directed max }，θ max For the maximum pitch angle considered, +.>
Figure FDA0004094485830000035
4 azimuth angles which respectively indicate the directions of the double wave beams considered in the optimization process are {0 °,45 °,90 °,135 ° }; when the constraint conditions are met, performing multi-step perturbation on the array element position through an iterative convex optimization method, and reducing the peak level of the grating lobe/side lobe region; iteratively solving the position perturbation quantity delta x in the x and y directions at each step n and Δyn After that, x is n and yn Becomes x n +Δx n and yn +Δy n And updating the array element position, and obtaining the optimized array layout when the peak level of the grating lobe/side lobe region of the new array is unchanged and the array layout is also unchanged. />
CN202310161926.8A 2023-02-24 2023-02-24 Dual-beam ultra-wideband array antenna optimization layout method Pending CN116244940A (en)

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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116632561A (en) * 2023-07-19 2023-08-22 南京纳特通信电子有限公司 Design method of thin-fabric high-gain antenna array and storage medium
CN117078863A (en) * 2023-08-30 2023-11-17 电子科技大学 Rapid beam forming method of heterogeneous array antenna

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN116632561A (en) * 2023-07-19 2023-08-22 南京纳特通信电子有限公司 Design method of thin-fabric high-gain antenna array and storage medium
CN116632561B (en) * 2023-07-19 2023-09-19 南京纳特通信电子有限公司 Design method of thin-fabric high-gain antenna array and storage medium
CN117078863A (en) * 2023-08-30 2023-11-17 电子科技大学 Rapid beam forming method of heterogeneous array antenna

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