Irregular subarray division design method for low-sidelobe wide-angle scanning array antenna

Abstract

The invention discloses an irregular subarray division design method for a low-sidelobe wide-angle scanning array antenna, and solves the problem that the optimization time is long due to the slow speed of calculating the sidelobe level in the prior art. The method comprises the steps of discretizing an array plane into an array element set, performing permutation and combination on array elements in the array element set to obtain a sub-array position combination set, and constructing a dictionary matrix; converting a sub-array division problem into a set coverage problem, solving a binary selection vector to enable the dictionary matrix and the binary selection vector to obtain a whole-row vector, and further obtaining a candidate sub-array combination set of a coverage array surface; constructing an irregular subarray division design model, and screening the candidate subarray combination set to obtain an optimal subarray division result; optimizing the excitation amplitude of the optimal sub-array division result by using the optimal sub-array division result and adopting a grey wolf optimization algorithm so as to reduce the sidelobe level of the directional diagram; according to the method, direct calculation of the sidelobe level is replaced, so that the calculation efficiency is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of antenna design, and in particular to an irregular sub-array division design method for a low sidelobe wide-angle scanning array antenna. Background Art

[0002] The phased array antenna system can realize real-time regulation of the excitation amplitude and phase of each element in the array. Therefore, it has been widely used in many fields such as communication and radar. However, the high cost of transceiver components limits the popularization and application of phased array antennas. In order to reduce the cost of phased array antennas, scholars have proposed the sub-array division method, which aims to reduce the number of devices to achieve cost reduction.

[0003] However, if the regular sub-array division method is adopted, the phase centers of the sub-arrays of the array antenna will be periodically arranged with a large spacing (exceeding the operating wavelength), and grating lobes will appear during scanning. To suppress the appearance of grating lobes, the sub-array spacing can be reduced or the periodic arrangement of the sub-array phase centers can be broken. If the sub-array spacing is reduced, serious mutual coupling effects will be generated. Therefore, breaking the periodic arrangement of the sub-array phase centers is a feasible method to suppress the appearance of grating lobes. Thus, the irregular sub-array division method has been proposed. At the same time, considering the design difficulty of the sub-array feeding network in actual engineering, multi-connected domino sub-arrays similar to Tetris are usually used to design the transmitting antenna.

[0004] According to the scanning performance requirements of the array beam, typical sub-array structures can currently be divided into limited field of view scanning structures and broadband wide-angle scanning structures. The broadband wide-angle scanning structure adopts phase delay at the element level and time delay at the sub-array level. This architecture can not only reduce the number of required time delay modules, but also reduce the pattern loss caused by beam squint, and achieve broadband wide-angle scanning performance.

[0005] The sidelobe level is one of the important parameters in the comprehensive evaluation index of the antenna array pattern. However, the broadband wide-angle scanning structure usually calculates the sidelobe level relatively slowly, resulting in a long optimization time. Summary of the Invention

[0006] By providing an irregular sub-array division design method for a low sidelobe wide-angle scanning array antenna, the present invention solves the problem that the calculation speed of the sidelobe level in the prior art is relatively slow, resulting in a long optimization time, and realizes the replacement of directly calculating the sidelobe level, thereby improving the calculation efficiency.

[0007] The present invention provides an irregular sub-array division design method for a low sidelobe wide-angle scanning array antenna, and the method includes:

[0008] Discretize the array surface into an array element set, perform permutations and combinations on the array elements in the array element set to obtain a set of sub-array position combinations, and construct a dictionary matrix according to the array element set and the set of sub-array position combinations;

[0009] Transform the sub-array partitioning problem into a set covering problem, and solve the binary selection vector so that the dictionary matrix and the binary selection vector obtain a full one-row vector, thereby obtaining a set of candidate sub-array combinations that cover the array surface;

[0010] Construct an irregular sub-array partitioning design model, screen the set of candidate sub-array combinations, and obtain the optimal sub-array partitioning result;

[0011] Using the optimal sub-array partitioning result, adopt the gray wolf optimization algorithm to optimize the excitation amplitude of the optimal sub-array partitioning result to reduce the sidelobe level of the radiation pattern.

[0012] In a possible implementation, the array elements corresponding to each sub-array position combination in the set of sub-array position combinations are physically adjacent in the array surface.

[0013] In a possible implementation, the dictionary matrix is a binary matrix; where, when the element L(m,n) in the dictionary matrix is 1, it means that the nth array element belongs to the mth sub-array position combination; when the element L(m,n) in the dictionary matrix is 0, it means that the nth array element does not belong to the mth sub-array position combination.

[0014] In a possible implementation, the dictionary matrix uniquely covers each array element in the array element set.

[0015] In a possible implementation, the screening of the set of candidate sub-array combinations to obtain the optimal sub-array partitioning result includes:

[0016] Calculate the phase center coordinates corresponding to each sub-array position combination in the set of sub-array position combinations, and obtain the corresponding first horizontal axis value set and first vertical axis value set according to the phase center coordinates;

[0017] Calculate the phase center coordinates corresponding to each candidate sub-array combination in the set of candidate sub-array combinations, and perform statistics according to the phase center coordinates to obtain the corresponding second horizontal axis value set and second vertical axis value set;

[0018] Traverse the elements in the first horizontal axis value set, and judge the number of times the jth element appears in the second horizontal axis value set, and take this number as the number of phase centers of the sub-arrays in the jth column;

[0019] Traverse the elements in the first vertical axis value set, and judge the number of times the ith element appears in the second vertical axis value set, and take this number as the number of phase centers of the sub-arrays in the ith column;

[0020] Calculate the variance corresponding to each candidate subarray combination based on the number of phase centers of the subarray in the j-th column and the number of phase centers of the subarray in the i-th row, and determine the candidate subarray combination corresponding to the minimum variance as the optimal subarray division result.

[0021] In a possible implementation manner, the irregular subarray division design model is expressed as:

[0022] Find X=[x1,x2,…,x R T

[0023]

[0024] s.t.XL=1;

[0025]

[0026] where X represents a binary selection vector; N represents the sum of the first abscissa X data value and the first ordinate Y data value; v n represents the row-column statistical feature splicing vector; F(v) represents the variance of the candidate subarray combination; L represents the dictionary matrix; p represents the maximum value of the number of rows of all possible positions of the phase centers corresponding to each subarray position combination in the subarray position combination set; q represents the maximum value of the number of columns of all possible positions of the phase centers corresponding to each subarray position combination in the subarray position combination set; represents the number of phase centers of the subarray in the i-th row; x r represents whether to select the r-th candidate subarray; represents the number of phase centers of the subarray in the j-th column; R represents the number of candidate subarray combinations; XL represents a full-one row vector.

[0027] In a possible implementation manner, using the optimal subarray division result, the Grey Wolf Optimization algorithm is used to optimize the excitation amplitude of the optimal subarray division result to reduce the sidelobe level of the radiation pattern, including:

[0028] Construct an optimization model; the optimization variable of the optimization model is the excitation amplitude of the optimal subarray division result, and the optimization objective of the optimization model is to minimize the maximum sidelobe level PSLL of the radiation pattern corresponding to the optimal subarray division result;

[0029] Use the Grey Wolf Optimization algorithm to solve the optimization model to obtain the excitation amplitude of the optimized optimal subarray division result; wherein, the Grey Wolf Optimization algorithm uses a non-linear convergence factor to adjust the search step size when solving the optimization model.

[0030] In a possible implementation manner, the radiation pattern is expressed as:

[0031] ​

[0032] Among them, I is the number of array elements in the array element set; K represents the set of rows of all possible positions of the phase center corresponding to the sub-array combination in the candidate sub-array combination set; x k represents the abscissa (X-axis coordinate) of the phase center position of the k-th candidate sub-array combination; y k represents the ordinate (Y-axis coordinate) of the phase center position of the k-th candidate sub-array combination; u represents the projection of the ray direction extending arbitrarily in space from the antenna location on the abscissa (X-axis); v represents the projection of the ray direction extending arbitrarily in space from the antenna location on the ordinate (Y-axis); u0 is the first parameter; v0 is the second parameter; α k represents the excitation amplitude of the k-th candidate sub-array combination; λ represents the wavelength; δ ip is the attribution factor; λ0 represents the resonant wavelength; xi represents the abscissa (X-axis coordinate) of the phase center position of the i-th candidate sub-array combination; yi represents the ordinate (Y-axis coordinate) of the phase center position of the i-th candidate sub-array combination; F(u, v) represents the radiation pattern when the parameters are u and v.

[0033] In a possible implementation, the optimization model is expressed as:

[0034]

[0035] Among them, Q represents the excitation amplitude vector; α P represents the excitation amplitude of the p-th candidate sub-array combination; α i represents the excitation amplitude of the i-th candidate sub-array combination; P represents the number of candidate sub-array combinations.

[0036] In a possible implementation, the shape of the sub-array position combination includes: 2-element rectangle, L-shaped or T-shaped, and the sub-array size is scalable.

[0037] One or more technical solutions provided in the present invention have at least the following technical effects or advantages: By adopting an irregular sub-array division design method for a low sidelobe wide-angle scanning array antenna, the physical array surface is abstracted into a discrete set, which is convenient for subsequent combinatorial optimization and the application of mathematical tools, supports arbitrary element arrangements, does not rely on regular grids, and adapts to complex antenna design requirements; An irregular sub-array division design model is constructed on the candidate sub-array combination set to screen the optimal division. Optimize the sidelobe and array complexity to avoid engineering infeasibility caused by a single objective; Only screen in the candidate set, significantly reduce the search space, improve efficiency, and make up for the sidelobe problems that may be left in the sub-array division stage. Optimize the excitation amplitude of the optimal sub-array division result through the Grey Wolf Optimization Algorithm; This method combines mathematical modeling and intelligent optimization to significantly improve the pattern performance while ensuring coverage completeness, and is applicable to the design of high-performance phased array systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a flowchart of the steps of the irregular sub-array division design method for the low sidelobe wide-angle scanning array antenna provided by the embodiment of the present invention;

[0039] Figure 2 It is a schematic diagram of the sub-array position combination set provided by the embodiment of the present invention;

[0040] Figure 3a It is a global optimal result diagram output by the abscissa X algorithm provided by the embodiment of the present invention;

[0041] Figure 3b It is a diagram of the array surface structure output by the method provided by the embodiment of the present invention;

[0042] Figure 4a It is a schematic diagram of the optimal irregular sub-array provided by the embodiment of the present invention;

[0043] Figure 4b It is a schematic diagram of the sub-optimal irregular sub-array provided by the embodiment of the present invention;

[0044] Figure 4c It is a schematic diagram of the regular sub-array provided by the embodiment of the present invention;

[0045] Figure 5a For the optimal irregular array provided by the embodiment of the present invention scanned to θ = 30°, the normalized power pattern;

[0046] Figure 5b For the sub-optimal irregular array provided by the embodiment of the present invention scanned to θ = 30°, the normalized power pattern;

[0047] Figure 5c For the regular array provided by the embodiment of the present invention scanned to θ = 30°, Normalized power pattern Specific implementation mode

[0048] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0049] The present invention provides a non-regular sub-array division design method for a low sidelobe wide-angle scanning array antenna. Refer to Figure 1 , this method includes the following steps S101 to S104.

[0050] S101: Discretize the array surface into an array element set, perform permutations and combinations on the array elements in the array element set to obtain a sub-array position combination set, and construct a dictionary matrix according to the array element set and the sub-array position combination set;

[0051] Specifically, the array elements corresponding to each sub-array position combination in the sub-array position combination set are physically adjacent on the array surface.

[0052] The dictionary matrix uniquely covers each array element in the array element set. The dictionary matrix is a binary matrix; among them, when the element L(m,n) = 1 in the dictionary matrix, it means that the nth array element belongs to the mth sub-array position combination; when the element L(m,n) = 0 in the dictionary matrix, it means that the nth array element does not belong to the mth sub-array position combination.

[0053] Here, the shape of the sub-array position combination includes but is not limited to a 2-element rectangle, an L shape, or a T shape, and the sub-array size can be extended.

[0054] Exemplarily, refer to Figure 2 , in Figure 2 In the shown structure, the array surface set is expressed as: A = {1, 2, 3, 4, 5, 6}. Taking dominoes (two-element sub-arrays) as an example, seven different sub-array position combinations can be obtained:

[0055]

[0056] Secondly, construct a dictionary matrix L, and L represents the relationship between all different sub-array position sets and the array surface set.

[0057] Among them, the dictionary matrix L is expressed as:

[0058] [[ID=4s]]

[0059] Each row of the dictionary matrix L represents a sub-array, and each column represents a unit position in the aperture of the array. Its internal elements are:

[0060]

[0061] S102. Transform the sub-array partitioning problem into a set covering problem. By solving the binary selection vector, a full row vector can be obtained from the dictionary matrix and the binary selection vector, and then a set of candidate sub-array combinations covering the array surface is obtained.

[0062] Exemplarily, the array surface sub-array partitioning problem can be transformed into a set covering problem, which can be described in mathematical terms as: several rows of the dictionary matrix L can be linearly superimposed to exactly obtain a full row vector, that is: x T L = 1.

[0063] Take Figure 2 as an example. There are three results for the selection vector x that meet the conditions, namely {1, 0, 1, 0, 0, 0, 1}, {0, 1, 0, 1, 1, 0, 0}, and {0, 0, 0, 0, 1, 1, 1}.

[0064] S103. Construct an irregular sub-array partitioning design model, screen the set of candidate sub-array combinations, and obtain the optimal sub-array partitioning result.

[0065] Specifically, in step S103, screening the set of candidate sub-array combinations to obtain the optimal sub-array partitioning result includes the following steps S1031 to S1035.

[0066] S1031. Calculate the phase center coordinates corresponding to each sub-array position combination in the set of sub-array position combinations, and obtain the corresponding first horizontal axis value set and first vertical axis value set according to the phase center coordinates.

[0067] S1032. Calculate the phase center coordinates corresponding to each candidate sub-array combination in the set of candidate sub-array combinations, and perform statistics according to the phase center coordinates to obtain the corresponding second horizontal axis value set and second vertical axis value set.

[0068] S1033. Traverse the elements in the first horizontal axis value set, and judge the number of times the j-th element appears in the second horizontal axis value set, and use this number as the number of phase centers of the sub-arrays in the j-th column.

[0069] S1034. Traverse the elements in the first vertical axis value set, and judge the number of times the i-th element appears in the second vertical axis value set, and use this number as the number of phase centers of the sub-arrays in the i-th column.

[0070] S1035. Calculate the variance corresponding to each candidate subarray combination based on the number of phase centers of the j-th column subarray and the number of phase centers of the i-th row subarray, and determine the candidate subarray combination corresponding to the minimum variance as the optimal subarray partitioning result.

[0071] Here, the irregular subarray partitioning design model is expressed as:

[0072] Find X=[x1,x2,…,x R T

[0073]

[0074] s.t.XL=1(1.4);

[0075]

[0076] where X represents a binary selection vector; N represents the sum of the first abscissa X data value and the first ordinate Y data value; v n represents the row-column statistical feature splicing vector; F(v) represents the variance of the candidate subarray combination; L represents the dictionary matrix; p represents the maximum value of the number of rows of all possible positions of the phase centers corresponding to each subarray position combination in the subarray position combination set; q represents the maximum value of the number of columns of all possible positions of the phase centers corresponding to each subarray position combination in the subarray position combination set; represents the number of phase centers of the i-th row subarray; x r represents whether to select the r-th candidate subarray; represents the number of phase centers of the j-th column subarray; R represents the number of candidate subarray combinations; XL represents a full one-row vector.

[0077] Exemplarily, taking S1 as an example, the position coordinates of array elements 1 and 2 are (1, 1) and (1, 2), so the phase center of this subarray is (1, 1.5). By analogy, the phase centers of the remaining six different-position subarrays are (1, 2.5), (2, 1.5), (2, 2.5), (1.5, 1), (1.5, 2), and (1.5, 3).

[0078] Therefore, the first abscissa X data value of all possible positions of the phase centers in the subarray position combination set is 3 (abscissa X = 1, 1.5, 2), and the first ordinate Y data value is 5 (ordinate Y = 1, 1.5, 2, 2.5, 3). For the first partitioning result, that is, the first value of the abscissa X of the binary selection vector, S1, S3, and S7 are selected. At this time, the total number of phase centers in each row and each column of the candidate subarray combination set is (1, 1, 1) and (0, 2, 0, 0, 1).

[0079] ​Calculate the total number of sub - array phase centers in each row and each column of each array - surface division scheme, and solve the variance of this set of data. For example, refer to Figure 4c , Figure 4c the regular sub - array shown. Since the sub - array of 1×2 is adopted, the sub - array phase centers are only distributed in the 1st, 3rd, 5th, 7th, 9th, and 11th columns, and there are no sub - array phase centers in the 2nd, 4th, 6th, 8th, and 10th columns. That is, the distribution of the number of sub - array phase centers in each column is [12 0 12 0 12 0 12 0 12 0 12 0], and its column variance is 39.2727.

[0080] The present invention takes the total variance as the optimization objective. An optimization model is established as shown in formula (1.4). Specifically, in formula (1.4), the variance corresponding to the number of sub - array phase centers arranged in rows is expressed as:

[0081]

[0082] The variance corresponding to the number of sub - array phase centers arranged in columns is expressed as:

[0083]

[0084] This optimization problem is a non - linear pure integer programming problem, which can be solved by the Gurobi solver.

[0085] S104. Utilize the optimal sub - array division result and adopt the grey - wolf optimization algorithm to optimize the excitation amplitude of the optimal sub - array division result to reduce the sidelobe level of the radiation pattern.

[0086] Specifically, in step S104, utilizing the optimal sub - array division result and adopting the grey - wolf optimization algorithm to optimize the excitation amplitude of the optimal sub - array division result to reduce the sidelobe level of the radiation pattern includes the following steps S1041 to S1042.

[0087] S1041. Construct an optimization model; the optimization variable of the optimization model is the excitation amplitude of the optimal sub - array division result, and the optimization objective of the optimization model is to minimize the maximum sidelobe level PSLL of the radiation pattern corresponding to the optimal sub - array division result;

[0088] Here, the optimization model is expressed as:

[0089] Find Q = [α1,α2,…,α P T

[0090] min PSLL(1.7);

[0091] s.t.α i ≥0.2i = 1,2,…,P

[0092] α i ​≤ 1 i = 1, 2, …, P

[0093] Among them, Q represents the excitation amplitude vector; α P represents the excitation amplitude of the p-th candidate subarray combination; α i represents the excitation amplitude of the i-th candidate subarray combination; P represents the number of candidate subarray combinations; PSLL represents the maximum sidelobe level.

[0094] S1042. Use the grey wolf optimization algorithm to solve the optimization model to obtain the excitation amplitude of the optimized optimal subarray division result; among them, the grey wolf optimization algorithm uses a non-linear convergence factor to adjust the search step size when solving the optimization model.

[0095] Here, the optimization model is expressed as:

[0096]

[0097] Among them, I is the number of array elements in the array element set; K represents the set of row numbers of all possible positions of the phase center corresponding to the subarray combination in the candidate subarray combination set; x k represents the abscissa (X-axis coordinate) of the phase center position of the k-th candidate subarray combination; y k represents the ordinate (Y-axis coordinate) of the phase center position of the k-th candidate subarray combination; u represents the projection of the ray direction extending arbitrarily in space from the antenna position on the abscissa (X-axis); v represents the projection of the ray direction extending arbitrarily in space from the antenna position on the ordinate (Y-axis); u0 is the first parameter; v0 is the second parameter; α k represents the excitation amplitude of the k-th candidate subarray combination; λ represents the wavelength; δ ip is the attribution factor; λ0 represents the resonant wavelength; xi represents the abscissa (X-axis coordinate) of the phase center position of the i-th candidate subarray combination; yi represents the ordinate (Y-axis coordinate) of the phase center position of the i-th candidate subarray combination; F(u, v) represents the radiation pattern when the parameters are u and v.

[0098] Exemplarily, for a planar phased array precisely covered by P subarrays, its radiation pattern can be expressed by formula (1.8). Based on the optimal subarray division result obtained in step S103 and the non-linear convergence factor use the grey wolf optimization algorithm to optimize the excitation amplitude of the optimal subarray division result to reduce the sidelobe level. As shown in formula (1.7). The value range of Y is [0.2, 1], and PSLL is the maximum sidelobe level.

[0099] It can be understood that the non-linear convergence factor is obtained with the help of existing papers. Among them, t max represents the maximum number of iterations; t represents the current number of iterations.

[0100] The method proposed by the present invention replaces the direct calculation of the sidelobe level, thereby improving the calculation efficiency. Through research, there is a certain correlation between the sidelobe level and the periodicity of the subarray phase center. For the periodically arranged subarrays, their phase centers will gather on the determined row (in the direction of the ordinate Y-axis) or column (in the direction of the abscissa X-axis), resulting in the number of phase centers in each row or column deviating from the uniform distribution. Therefore, the greater the variance of the subarray division structure of the array antenna, the more periodic it is. Vice versa. Thus, the variance of the total number of subarray phase centers in each row and column in the array surface distribution can be used to describe the irregularity of the subarray arrangement. The smaller the variance, the more irregular the subarray arrangement, and the lower the corresponding sidelobe level.

[0101] In a simulation experiment provided by the present invention, a rectangular array with 432 (M = 12, N = 36) elements and a half-wavelength spacing is used, and an L-shaped eight-element subarray is adopted.

[0102] In the prior art, it took about 1.296×10 6 seconds to find all 12,845,409 division schemes that meet the exact coverage by using the X algorithm, and it took about 8.896×10 6 seconds to select the optimal division scheme. The globally optimal result found is as Figure 3a shown. Under the same background, the present invention took 489.4 seconds to output the result. Figure 3b It is the array surface structure output by the minimum variance method.

[0103] SLL = min{SLL broadsie + SLL scan}(1.9);

[0104] where SLL represents the maximum sidelobe level of the radiation pattern, and SLL broadsie , SLL scan are the sidelobe levels of the static state and when scanned to [20°, 0°] respectively.

[0105] Table 1 gives the comparison of the electronic scanning performance of the exact coverage solution schemes obtained by the X algorithm and the minimum variance method. It can be seen from Table 1 that the electronic scanning performance of the structure output by the method of the present invention is basically the same as that of the optimal scheme obtained by the global search. Under the condition of equal amplitude, the difference in the highest sidelobe level between the two is about 0.5 dB; after optimizing the excitation amplitude, the difference in the highest sidelobe level between the two is only about 0.1 dB. Intuitively, the method of the present invention can effectively and quickly obtain the target solution.

[0106] Table 1 Comparison of the scanning performance of the two methods

[0107]

[0108] Simulation experiment 2:

[0109] (1) Simulation parameters

[0110] A rectangular planar array with 144 (M = N = 12) elements and a half-wavelength spacing is adopted, and a two-element subarray is used. Under the broadband wide-angle scanning structure, the broadband condition f / f0 = 1.2 is set.

[0111] (2) Simulation content and results

[0112] First, the optimal and sub-optimal non-regular subarray partitioning schemes are obtained through the minimum variance criterion, and compared with the variance of the regular subarray (the worst non-regular subarray partitioning scheme) (see Table 2.1). Specifically, see Figure 4a as the optimal non-regular subarray, see Figure 4b as the sub-optimal non-regular subarray, Figure 4c as the regular subarray; the total variances of the optimal non-regular subarray and the sub-optimal non-regular subarray are the same. At the same time, the row and column variances of the optimal non-regular subarray have the same numerical values, while the column variance of the sub-optimal non-regular subarray is smaller, even better than the row and column variances of the optimal non-regular subarray. The row variance of the regular subarray is 0, but the column variance is very large, resulting in the largest total variance.

[0113] Next, the excitation amplitudes of the optimal subarray partitioning results are optimized using the Grey Wolf Optimization algorithm to obtain three arrays and perform scans:

[0114]

[0115] The corresponding sidelobe levels (see Table 2.2). The optimal non-regular subarray has similar sidelobe levels in the and scanning directions, while the sub-optimal non-regular subarray has the lowest sidelobe level in the direction scan, which is better than the sidelobe level of the optimal non-regular subarray in this direction. The regular array has a relatively poor sidelobe level in the direction scan, but has the optimal sidelobe level in the direction scan. When scanned to , the sidelobe level of the regular array is about 8 dB higher than that of the non-regular array. When scanned to , it is more than 10 dB higher.

[0116] See Figure 5a , for the normalized power pattern of the optimal non-regular array scanned to θ = 30°, ; see Figure 5b , for the normalized power pattern of the sub-optimal non-regular array scanned to θ = 30°, ; see Figure 5c , for the normalized power pattern of the regular array scanned to θ = 30°, .

[0117] According to Table 2.1 and Table 2.2, it can be seen that the smaller the variance of the sub-array row (column), the better the scanning sidelobe level in the direction. At the same time, the irregular sub-array effectively broadens the scanning angle. Therefore, to judge the scanning ability of the irregular array, only the variance value needs to be calculated, reducing the complexity. The irregular sub-array division design method of the present invention can obtain better electrical performance at non-single scanning angles, and achieve high efficiency with an output structure meeting the good performance of low sidelobe level and wide-angle scanning.

[0118] Table 2.1 Variance calculation results of three arrays

[0119] Optimal irregular array Sub-optimal irregular array Regular array Total variance var(v) 0.6493 0.6493 18.7826 <![CDATA[Row variance var(v row )]]> 0.6640 0.7549 0 <![CDATA[Column variance var(v col )]]> 0.6640 0.5731 39.2727

[0120] Table 2.2 Scanning performance information of three arrays

[0121]

[0122]

[0123] The various embodiments in this specification are described in a progressive manner. For the same or similar parts between the various embodiments, reference can be made to each other. Each embodiment focuses on the differences from other embodiments. All or part of the present invention can be used in many general-purpose or special-purpose computer system environments or configurations. For example: personal computers, server computers, handheld devices or portable devices, tablet devices, mobile communication terminals, multi-processor systems, microprocessor-based systems, programmable electronic devices, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, and so on.

[0124] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than limiting the present invention; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the present invention.

Claims

1. A design method for irregular sub - array division of a low - sidelobe wide - angle scanning array antenna, characterized in that, Including: Discretize the array surface into an array element set, perform permutations and combinations on the array elements in the array element set to obtain a set of sub-array position combinations, and construct a dictionary matrix according to the array element set and the set of sub-array position combinations; Transform the sub-array partitioning problem into a set covering problem, and solve the binary selection vector to make the dictionary matrix and the binary selection vector obtain a full one-row vector, thereby obtaining a set of candidate sub-array combinations covering the array surface; Construct an irregular sub-array partitioning design model, screen the set of candidate sub-array combinations, and obtain the optimal sub-array partitioning result; Using the optimal sub-array partitioning result, adopt the grey wolf optimization algorithm to optimize the excitation amplitude of the optimal sub-array partitioning result to reduce the sidelobe level of the radiation pattern.

2. The irregular sub-array division design method of the low sidelobe wide-angle scanning array antenna according to claim 1, characterized in that The array elements corresponding to each sub-array position combination in the set of sub-array position combinations are physically adjacent in the array surface.

3. The non-regular sub-array division design method of the low sidelobe wide-angle scanning array antenna according to claim 1, characterized in that The dictionary matrix is a binary matrix; where, when the element L(m,n) in the dictionary matrix is 1, it means that the nth array element belongs to the mth sub-array position combination; when the element L(m,n) in the dictionary matrix is 0, it means that the nth array element does not belong to the mth sub-array position combination.

4. The irregular sub-array division design method of the low sidelobe wide-angle scanning array antenna according to claim 1, characterized in that The dictionary matrix uniquely covers each array element in the array element set.

5. The design method for irregular subarray division of the low sidelobe wide-angle scanning array antenna according to claim 1, characterized in that, The screening of the set of candidate sub-array combinations to obtain the optimal sub-array partitioning result includes: Calculate the phase center coordinates corresponding to each sub-array position combination in the set of sub-array position combinations, and obtain the corresponding first horizontal axis value set and first vertical axis value set according to the phase center coordinates; Calculate the phase center coordinates corresponding to each candidate sub-array combination in the set of candidate sub-array combinations, and perform statistics according to the phase center coordinates to obtain the corresponding second horizontal axis value set and second vertical axis value set; Traverse the elements in the first horizontal axis value set, and judge the number of times the jth element appears in the second horizontal axis value set, and use this number as the number of sub-array phase centers in the jth column; Traverse the elements in the first vertical axis value set, and judge the number of times the ith element appears in the second vertical axis value set, and use this number as the number of sub-array phase centers in the ith row; Calculate the variance corresponding to each candidate sub-array combination according to the number of sub-array phase centers in the jth column and the number of sub-array phase centers in the ith row, and determine the candidate sub-array combination corresponding to the minimum variance as the optimal sub-array partitioning result.

6. The non - regular sub - array division design method of the low - sidelobe wide - angle scanning array antenna according to claim 5, wherein, The irregular sub-array partitioning design model is expressed as: Wherein, X represents a binary selection vector; N represents the sum of the first abscissa X data value and the first ordinate Y data value; v n represents a row-column statistical feature splicing vector; F(v) represents the variance of the candidate sub-array combination; L represents a dictionary matrix; p represents the maximum value of the number of rows of all possible positions of the phase centers corresponding to each sub-array position combination in the sub-array position combination set; q represents the maximum value of the number of columns of all possible positions of the phase centers corresponding to each sub-array position combination in the sub-array position combination set; represents the number of phase centers of the sub-arrays in the i-th row; x r represents whether to select the r-th candidate sub-array; represents the number of phase centers of the sub-arrays in the j-th column; R represents the number of candidate sub-array combinations; XL represents a full row vector.

7. The non-regular subarray division design method of the low sidelobe wide-angle scanning array antenna according to claim 1, characterized in that The using the optimal sub-array partitioning result and adopting the grey wolf optimization algorithm to optimize the excitation amplitude of the optimal sub-array partitioning result to reduce the sidelobe level of the radiation pattern includes: Construct an optimization model; the optimization variable of the optimization model is the excitation amplitude of the optimal sub-array partitioning result, and the optimization objective of the optimization model is to minimize the maximum sidelobe level PSLL of the radiation pattern corresponding to the optimal sub-array partitioning result; Adopt the grey wolf optimization algorithm to solve the optimization model to obtain the optimized excitation amplitude of the optimal sub-array partitioning result; where, the grey wolf optimization algorithm uses a non-linear convergence factor to adjust the search step size when solving the optimization model.

8. The non-regular sub-array division design method of the low sidelobe wide-angle scanning array antenna according to claim 7, characterized in that The radiation pattern is expressed as: where I is the number of array elements in the array element set; K represents the set of row numbers of all possible positions of the phase centers corresponding to the sub-array combinations in the candidate sub-array combination set; x k represents the abscissa (X-axis coordinate) of the phase center position of the k-th candidate sub-array combination; y k represents the ordinate (Y-axis coordinate) of the phase center position of the k-th candidate sub-array combination; u represents the projection of the ray direction extending arbitrarily in space from the position where the antenna is located on the abscissa (X-axis); v represents the projection of the ray direction extending arbitrarily in space from the position where the antenna is located on the ordinate (Y-axis); u0 is the first parameter; v0 is the second parameter; α k represents the excitation amplitude of the k-th candidate sub-array combination; λ represents the wavelength; δ ip is the attribution factor; λ0 represents the resonant wavelength; xi represents the abscissa (X-axis coordinate) of the phase center position of the i-th candidate sub-array combination; yi represents the ordinate (Y-axis coordinate) of the phase center position of the i-th candidate sub-array combination; F(u, v) represents the radiation pattern when the parameters are u and v.

9. The irregular sub-array division design method of the low sidelobe wide-angle scanning array antenna according to claim 7, characterized in that The optimization model is expressed as: Among them, Q represents the excitation amplitude vector; α P represents the excitation amplitude of the P-th candidate subarray combination; α i represents the excitation amplitude of the i-th candidate subarray combination; P represents the number of candidate subarray combinations; PSLL represents the maximum sidelobe level.

10. The design method for irregular sub - array division of the low sidelobe wide - angle scanning array antenna according to claim 1, characterized in that, The shapes of the sub-array position combinations include: 2-element rectangles, L-shapes, or T-shapes, and the sub-array size is scalable.

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