Rapid synthesis method for array directional diagram with radome effect

Abstract

The invention discloses a method for rapidly synthesizing an array pattern with a radome effect, and relates to the field of array antenna synthesis. According to the method, an active unit pattern is used for considering the influence of the radome effect on an array pattern. In order to improve the comprehensive efficiency of an array directional diagram, an active unit directional diagram expansion technology is adopted, and an initial antenna housing-array antenna integrated system directional diagram which cannot be subjected to acceleration calculation by directly using fast Fourier transform originally is converted into an initial antenna housing-array antenna integrated system directional diagram. And converting into an extended virtual array directional diagram capable of performing accelerated calculation by efficiently utilizing fast Fourier transform. By alternately applying the fast Fourier forward transform and the fast Fourier inverse transform to the directional diagram and the excitation of the virtual array, fast synthesis of the array directional diagram with the radome effect is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of array antennas, and particularly to a fast synthesis method for array pattern with radome effect. Background Art

[0002] Phased array technology has been widely used in high-performance electronic systems such as communication, sensing, and radar due to its flexible beamforming ability. However, in practical applications, to ensure the stability and reliability of the antenna array and prevent it from being eroded by harsh external environments such as weather changes and physical collisions, the antenna array is usually used in conjunction with a radome. Although the radome provides necessary protection, it inevitably affects the radiation performance of the antenna array. To suppress the negative impact of the radome on the performance of the phased array antenna, that is, the so-called "radome effect", researchers have developed various techniques to optimize the parameters of the radome, such as adjusting its shape and thickness distribution. However, the degree of freedom of this optimization is often limited because the design of the radome also needs to meet other key requirements such as mechanical strength and electromagnetic scattering. Given the above limitations, a more flexible and effective alternative is to consider the array antenna and the radome as an integrated system, and then optimize the excitation amplitude and phase of the array elements.

[0003] Based on the radome-array antenna integrated system, some studies have proposed the method of directly solving by the method of moments. Although this technique can optimize the pattern performance of the array near the dielectric body, it often uses an ideal point source model and ignores the complexity of the actual antenna element structure. To more accurately consider the mutual coupling between antenna elements and the radome effect, researchers have applied the active element pattern to array synthesis. In these techniques, stochastic optimization algorithms are often used to find the optimized excitation amplitude and phase to improve the array pattern performance. For example, Chinese Patent No. 202310738753.1 discloses an integrated pattern synthesis method for a radome-phased array system, which takes the radome and the phased array antenna as a whole and uses an improved simulated annealing algorithm to optimize the feeding amplitude and phase of the phased array antenna, thereby realizing the accurate synthesis of the array pattern. However, as a classification of stochastic optimization algorithms, the optimization process of the simulated annealing algorithm still requires a large number of iterative calculations, and each iteration requires complex complex multiplication operations for the array pattern and excitation. As the array size increases, this computational burden will be further aggravated, greatly increasing the time cost in practical applications. Summary of the Invention

[0004] Aiming at the deficiencies in the prior art, the present invention provides a fast synthesis method for array pattern with radome effect.

[0005] The present invention includes the following steps:

[0006] 1) Determine the size and material of the radome, as well as the number, element form, and element spacing of the array elements according to the system application requirements, and set the upper and lower bounds of the array pattern.

[0007] 2) Based on the active element pattern expansion method, obtain the relationship between the actual excitation of the radome-array antenna integrated system and the extended virtual array excitation.

[0008] 3) Perform the inverse Fourier transform on the extended virtual array excitation to quickly calculate the extended virtual array pattern.

[0009] 4) Find the region where the extended virtual array pattern exceeds the preset boundary limit, correct the amplitude value of the pattern in this region so that it is between the upper and lower bounds, and keep the phase unchanged.

[0010] 5) Perform the fast Fourier transform on the corrected extended virtual array pattern to obtain the excitation of the extended virtual array.

[0011] 6) Based on the relationship between the actual excitation of the radome-array antenna integrated system and the extended virtual array excitation, further calculate the actual excitation of the radome-array antenna integrated system.

[0012] 7) Repeat steps 2 to 6, and exit the loop when the array pattern of the radome-array antenna integrated system meets the preset requirements.

[0013] In step 2), the active element pattern expansion method includes: the active element pattern g n (u) of each element in the radome-array antenna integrated system can be approximated as the virtual subarray pattern obtained by exciting itself and several nearby identical elements. This approximation process can be mathematically expressed as:

[0014]

[0015] where u ∈ [-1, 1], n = 1, 2... N, j is the imaginary unit, β = 2π / λ, λ is the wavelength, and d is the element spacing. g s (u) represents the element pattern of the extended virtual array, specifically the mean value of the active element patterns of all elements in the radome-array antenna integrated system. To approximate the edge elements in the radome-array antenna integrated system, Q / 2 virtual elements are added around the initial planar array to form an extended virtual array. The length of this extended virtual array is (N + Q). c nq represents the coupling coefficient of the (n + q)-th virtual element in the extended virtual array to the n-th actual element in the radome-array antenna integrated system, and this coupling coefficient can be solved by minimizing the mean square error.

[0016]

[0017] wherein

[0018] c n = [c n,-Q / 2 , c n,-Q / 2+1 , …, c n,Q x 2 T

[0019] g n = [g n (u 1 ), g n (u 2 ), …, g n (u k )] T

[0020]

[0021] The coupling coefficient c nq The vector c n can be obtained by c n = (Z H Z) -1 Z H g n Since for different g n , the matrix Z is invariant. Therefore, (Z H Z) -1 Z H only needs to be calculated once.

[0022] In step 2), the relationship between the actual excitation and the extended virtual array excitation of the radome-array antenna integrated system is:

[0023] a = Cw

[0024] wherein, a = [a 0 , a 1 , …, a L-1 ) T is the excitation vector corresponding to L elements in the extended virtual array, and L = N + Q is the total number of elements in the extended virtual array; w = [w 0 ,..., w N-1 ) T is the excitation vector of the actual N elements of the radome-array antenna integrated system; the matrix C is the coupling coefficient matrix, and the coupling coefficient of its l-th row and n-th column is specifically

[0025]

[0026] In step 3), the expression of the extended virtual array pattern is​

[0027]

[0028] Among them, the excitation a l and the array pattern f(u) have a Fourier transform relationship. When the excitation vector a is known, f(u) can be quickly calculated by performing an inverse Fourier transform on the excitation, thus avoiding the weighted summation process. When the array pattern f(u) is given, the excitation vector a can be quickly obtained by performing a fast Fourier transform on f(u).

[0029] The present invention uses the active element pattern to consider the effects of the radome-array antenna integrated system on the radome effect and element mutual coupling on the array pattern. To improve the efficiency of array pattern synthesis, the present invention adopts a technique for expanding the active element pattern, which successfully transforms the initial array pattern of the radome-array antenna integrated system that cannot be directly accelerated by the fast Fourier transform into an extended virtual array pattern that can be accelerated by efficiently using the fast Fourier transform. By alternately applying the fast Fourier forward transform and inverse transform to the virtual array pattern and the excitation, the present invention realizes the fast synthesis of the array pattern with the radome effect.

[0030] The advantages and beneficial effects of the present invention are as follows: The present invention can accurately consider the radome effect, and at the same time, in the process of array pattern synthesis, it cleverly uses the fast Fourier transform technology to realize the fast synthesis of the array pattern, greatly saving the time cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The drawings described herein are used to provide a further understanding of the embodiments of the present invention, form a part of this application, and do not limit the embodiments of the present invention. In the drawings:

[0032] Figure 1 is a flowchart of a method for fast synthesis of an array pattern with a radome effect provided by an embodiment of the present invention;

[0033] Figure 2 is a schematic diagram of the geometric structure of a radome-array antenna integrated system provided by an embodiment of the present invention;

[0034] Figure 3 is the array pattern provided by an embodiment of the present invention;

[0035] Figure 4 is Figure 3 the corresponding excitation normalized amplitude distribution diagram;

[0036] Figure 5 is Figure 3 the corresponding excitation phase distribution diagram. DETAILED DESCRIPTION OF THE INVENTION

[0037] The terms used in the various embodiments of the present invention are for the purpose of describing specific embodiments only and are not intended to limit the various embodiments of the present invention. As used herein, the singular forms are intended to include the plural forms as well, unless the context clearly indicates otherwise. Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the various embodiments of the present invention pertain. The terms (such as those defined in a commonly used dictionary) will be interpreted as having the same meaning as the contextual meaning in the relevant technical field and will not be interpreted as having an idealized meaning or an overly formal meaning, unless clearly defined in the various embodiments of the present invention.

[0038] To make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention will be further described in detail below with reference to embodiments and the accompanying drawings. The illustrative embodiments and descriptions thereof of the present invention are only for explaining the present invention and do not limit the present invention.

[0039] Referring to the process Figure 1 , a specific embodiment of the present invention is given, and its implementation steps are as follows:

[0040] Step 1: According to the system application requirements, set the number of array elements of the uniform linear array to 12, the antenna element to a dipole antenna, the center frequency to 9.82 GHz, the array is arranged along the x-axis, and the adjacent element spacing is 15.275 mm (half wavelength at the center frequency). Figure 2 A schematic diagram of the geometric structure of the radome-array antenna integrated system in this example is given, where the relative dielectric constant ε of the radome r = 3.48, the thickness is 2.8 mm, the loss tanδ = 0.003, the radome is 46 mm away from the array plane, and the radome length is 200 mm. Set the maximum pointing angle of the array to the array normal, and the maximum sidelobe level to -35 dB.

[0041] Step 2: Perform full-wave simulation on the radome-array antenna integrated system and export the active element pattern g n (u) of each element. By approximating the active element pattern of each element as the virtual subarray pattern obtained by exciting itself and several adjacent identical elements, the relationship between the actual excitation of the radome-array antenna integrated system and the extended virtual array excitation is obtained.

[0042] The process of expanding the active element pattern can be expressed by a mathematical formula as

[0043]

[0044] Where u = sinθ, n = 1, 2…N, j is the imaginary unit, β = 2π / λ, λ is the wavelength, and d is the array element spacing. s (u) represents the unit pattern of the extended virtual array, specifically the average of the active unit patterns of all array elements in the radome-array antenna integrated system. nq It represents the coupling coefficient of the (n+q)th virtual array element in the extended virtual array to the nth actual array element in the radome-array antenna integrated system. In order to approximate the edge array elements in the radome-array antenna integrated system, Q / 2 virtual array elements are added around the initial planar array to form an extended virtual array. The length of the extended virtual array is (N+Q). The value of Q can be determined by referring to the active unit pattern approximation error formula.

[0045]

[0046] The error formula describes the relationship between the approximate accuracy of the active unit pattern and the size of the virtual subarray (Q+1). Its variation curve is as follows: Figure 3 As shown. Figure 3 It can be seen that as Q increases, the approximation accuracy becomes more accurate and the error becomes smaller; however, the increase in Q will increase the calculation time. In order to take into account both calculation efficiency and accuracy, Q is set to 6 in this example. Coupling coefficient c nq It can be solved by minimizing the mean square error

[0047]

[0048] in

[0049] c n =[c n,-Q / 2 ,c n,-Q / 2+1 ,…,c n,Q / 2 ] T

[0050] g n =[g n (u 1 ),g n (u 2 ),…,g n (u k )] T

[0051]

[0052] Coupling coefficient c nq The vector composed of c n You can use c n =(Z H Z) -1 Z H g nObtained by solving

[0053] The relationship between the actual excitation of the radome-array antenna integrated system and the extended virtual array excitation can be expressed as:

[0054] a = Cw

[0055] where a = [a 0 , a 1 , …, a L-1 T is the extended virtual array excitation, and L = N + Q is the total number of array elements of the extended virtual array; w = [w 0 ,..., w N-1 T is the actual excitation of the radome-array antenna integrated system; the matrix C is the coupling coefficient matrix, and the coupling coefficient of its l-th row and n-th column is specifically

[0056]

[0057] After initializing the excitation w of the radome-array antenna integrated system, the excitation a of the extended virtual array can be obtained through a = Cw, and vice versa.

[0058] Step 3: Convert the array pattern synthesis of the initial radome-array antenna integrated system into the array pattern synthesis of the extended virtual array, and quickly calculate the extended virtual array pattern by performing the inverse Fourier transform on the extended virtual array excitation a, including

[0059] The array pattern of the initial radome-array antenna integrated system is

[0060]

[0061] Due to the influence of the mutual coupling between the radome and the array elements, the active element patterns g n (u) of each unit are often different, resulting in the inability to use the traditional fast Fourier transform to accelerate the calculation of f(u) in the above formula. After replacing g n (u) with the active element pattern expansion formula in Step 2, the pattern of the extended virtual array can be obtained

[0062]

[0063] Obviously, there is a Fourier transform relationship between the pattern of the extended virtual array and the excitation. Discretely sampling the pattern of the extended virtual array in the u space, that is, u = mΔu, where Δu = λ / (Md), m = -M / 2,..., M / 2 - 1 (M ≥ L), we can obtain

[0064] ​​

[0065] where g' m = g s (mΔu)e jπQm / M . At this time, the accelerated calculation of the summation of the above formula can be realized by performing an M-point inverse Fourier transform on the extended sequence {a l ; l = 0, 1,..., M - 1} obtained by the zero-padding technique.

[0066] Step 4: Find the region where the extended virtual array pattern exceeds the preset boundary limit, correct the pattern amplitude value in this region so that it is between the upper and lower bounds, and keep the phase unchanged.

[0067] Step 5: After obtaining the corrected extended virtual array pattern, the excitation of the extended virtual array can be quickly calculated by performing an M-point fast Fourier transform on the following formula.

[0068]

[0069] Once the excitation vector a of the extended virtual array is obtained, based on the relationship a = Cw between the actual excitation w of the radome-array antenna integrated system and the excitation a of the extended virtual array, the actual excitation w of the radome-array antenna integrated system = (C H C) -1 C H a can be obtained.

[0070] Step 6: Repeat Steps 2 to 5, and exit the loop when the array pattern of the radome-array antenna integrated system meets the requirements or the number of iterations reaches the upper limit.

[0071] Figure 3 is a comparison diagram of the array pattern synthesized by the method proposed in the present invention and the array pattern simulated by the electromagnetic simulation software. It can be seen from the figure that the synthesized pattern obtained by the method proposed in the present invention coincides with the simulated pattern and both meet the given boundary requirements. Figure 4 and Figure 5 respectively give the corresponding excitation normalized amplitude distribution and phase distribution. In this example, when using the method proposed in the present invention on a computer with Intel Core i5-2400 (main frequency 3.10 GHz), the total time consumed for the full process of pattern synthesis is about 0.1 second. This result fully verifies the effectiveness of the method proposed in the present invention, which can realize the rapid synthesis of the array pattern with radome effect.

[0072] The above-described embodiments are only a specific implementation method of the present invention and should not be construed as a limitation on the scope of the present invention. Those skilled in the art of the present technology can make other improvements and changes within the framework of the present invention.

Claims

1. A method for rapid synthesis of array patterns with radome effect, characterized in that The steps include: 1) According to the system application requirements, determine the size and material of the radome, as well as the number of array elements, unit form, array element spacing, and set the upper and lower limits of the array pattern; 2) Based on the active unit pattern expansion method, the relationship between the actual excitation of the radome-array antenna integrated system and the extended virtual array excitation is obtained; 3) performing an inverse Fourier transform on the extended virtual array excitation, thereby quickly calculating the extended virtual array pattern; 4) Find the area where the extended virtual array pattern exceeds the preset boundary limit, correct the pattern amplitude value of the area so that it is between the upper and lower bounds, and keep the phase unchanged; 5) performing fast Fourier transform on the corrected extended virtual array pattern to obtain the excitation of the extended virtual array; 6) Based on the relationship between the actual excitation of the radome-array antenna integrated system and the extended virtual array excitation, the actual excitation of the radome-array antenna integrated system is further calculated; 7) Repeat steps 2 to 6, and exit the loop when the array pattern of the radome-array antenna integrated system meets the preset requirements.

2. A method for rapidly synthesizing array patterns including radome effect as claimed in claim 1, characterized in that The method of expanding the active unit pattern in step 2) can be mathematically expressed as: Among them, g n (u) is the active unit radiation pattern of each element in the radome-array antenna integrated system, which is approximately the virtual sub-array radiation pattern obtained by exciting itself and several identical elements nearby, u∈[-1,1], n=1,2...N, j is the imaginary unit, β=2π / λ, λ is the wavelength, and d is the element spacing, g s (u) represents the unit radiation pattern of the extended virtual array, which is the average of the active unit radiation patterns of all elements in the radome-array antenna integrated system. In order to approximate the edge elements in the radome-array antenna integrated system, Q / 2 virtual elements are added around the initial planar array to form an extended virtual array. The length of the extended virtual array is (N+Q). c nq It represents the coupling coefficient of the (n+q)th virtual array element in the extended virtual array to the nth actual array element in the radome-array antenna integrated system, and the coupling coefficient can be solved by minimizing the mean square error. in c n =[c n,-Q2 ,c n,-Q2+1 ,…,c n,Q2 ] T g n =[g n (u1),g n (u2),…,g n (u k )] T Coupling coefficient c nq The vector composed of c n You can use c n =(Z H Z) -1 Z H g n The solution is that for different g n , the matrix Z is unchanged, so (Z H Z) -1 Z H Only needs to be calculated once.

3. A method for rapidly synthesizing array patterns including radome effect as claimed in claim 1, characterized in that In step 2), the relationship between the actual excitation of the radome-array antenna integrated system and the extended virtual array excitation is: a=Cw Where a=[a0,a1,…,a L-1 ] T is the excitation vector corresponding to L array elements in the extended virtual array, L = N + Q is the total number of array elements in the extended virtual array; w = [w0, ..., w N-1 ] T is the excitation vector of the actual N array elements of the radome-array antenna integrated system; the matrix C is the coupling coefficient matrix, and the coupling coefficient of its lth row and nth column is specifically 4. A method for rapidly synthesizing array patterns including radome effect as claimed in claim 1, characterized in that In step 3), the extended virtual array pattern is expressed as: Among them, the incentive a l There is a Fourier transform relationship between the excitation vector a and the array pattern f(u); when the excitation vector a is known, f(u) can be quickly calculated by performing an inverse Fourier transform on the excitation, thereby avoiding the weighted summation process. When the array pattern f(u) is given, the excitation vector a can be quickly obtained by performing a fast Fourier transform on f(u).

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