A large aperture array antenna subarray structure adjustment method for electrical performance

Abstract

The application discloses a large-aperture array antenna subarray structure adjustment method facing electrical performance, and comprises the following steps: S1, determining maximum gain loss; S2, establishing sensitivity distribution matrix; S3, calculating position tolerance distribution weight; S4, giving initial installation tolerance standard; S5, calculating position tolerance distribution matrix; S6, generating position error random sample; S7, calculating antenna electrical performance; S8, judging whether the position error random sample meets the requirement; S9, calculating new position tolerance standard; and S10, calculating maximum allowed structure adjustment amount. The application can realize the target of taking antenna electrical performance as the target, quantitatively giving the subarray structure adjustment amount of different regions of a large-aperture array antenna, strictly requiring the structure precision of the subarray in the region with high electrical performance sensitivity, appropriately reducing the structure precision requirement in the region with low electrical performance sensitivity, reducing the processing and manufacturing difficulty of the large-aperture array surface, improving the adjustment efficiency of the large-aperture array antenna, and guaranteeing the high performance of the array antenna.

Description

Technical Field

[0001] This invention relates to the field of antenna technology, and more specifically to a method for adjusting the structure of a large-aperture array antenna subarray with regard to electrical performance. Background Technology

[0002] Compared to mechanically scanned antennas, array antennas offer numerous advantages, including flexible and agile beamforming, fast response, multifunctionality, and strong anti-interference capabilities. They are widely used in radar communication, aerospace, and other fields, becoming the mainstream of antenna technology development today. With the advancement of science and technology, array antenna equipment is required to have longer detection ranges and more refined target resolution, identification, and tracking capabilities. This drives the continuous development of array antennas towards larger sizes and digitalization. The application of large-aperture array antennas is becoming increasingly widespread, with the number of array elements reaching tens of thousands. The increasing scale of arrays has spurred the emergence, development, and application of subarray technology. Currently, in engineering, subarray structures are typically used to assemble large-aperture array antennas.

[0003] The array structure of a large-aperture antenna is both the carrier and the constraint on its electrical performance. As antenna operating frequencies and detection distances increase, structural design specifications become increasingly stringent. In practical engineering, random position errors inevitably occur in antenna elements due to manufacturing processes and assembly. For traditional low-frequency antennas, whose operating wavelengths are generally large, the positional variations caused by random errors in element placement are insufficient to affect the antenna's electrical performance compared to the operating wavelength. However, for high-frequency, high-gain array antennas, where the operating wavelength is on the millimeter scale, even minute random positional errors can be on the same order of magnitude as the operating wavelength, inevitably leading to significant fluctuations in antenna electrical performance. Therefore, adjusting the positional errors of antenna elements is essential. Especially for large-aperture array antennas, with numerous elements and array sizes reaching hundreds of meters, adjusting individual element positional errors requires substantial manpower and resources and is extremely inefficient. Researching subarray-level structural adjustment methods can effectively improve the efficiency of adjusting array structure errors in large-aperture array antennas, providing technical support for achieving high performance in large-aperture array antennas.

[0004] To reduce the impact of array element position errors, the antenna's electrical performance can be guaranteed by improving the positional accuracy of the array antenna elements. However, in practical engineering, considering manufacturing costs and efficiency, it is impossible to increase the processing and assembly accuracy of the array elements indefinitely. Traditional methods usually use structural tolerance design to give the positional adjustment amount of the antenna array elements. This method requires that the positional adjustment amount of all array elements be the same for the entire array antenna. For example, in Hsiao J K. Design of error tolerance of aphased array[J]. Electronics Letters,1985,21(19):834-836, he used probabilistic statistical methods to determine the error tolerance in the array antenna. Without considering the different array element arrangement areas, the critical error value obtained from the analysis was used as the positional tolerance of all array elements. However, in practice, the position errors of different array elements have different effects on the electrical performance of the array antenna. For example, the work of Lanne M. Design aspects and pattern prediction for phased arrays with subarray position errors[C].IEEE International Symposium on Phased Array Systems and Technology (ARRAY), 2010:440-446 shows that there is a correlation between the position errors of array elements in the antenna subarray and the antenna electrical performance. The position errors of different array elements have different effects on the array electrical performance. This shows that it is insufficient to apply the same tolerance design value to all array elements of the array antenna.

[0005] In view of the above-mentioned defects, the inventors of this invention have finally obtained this invention after a long period of research and practice. Summary of the Invention

[0006] To address the aforementioned technical deficiencies, this invention provides a method for adjusting the structure of a large-aperture array antenna subarray, focusing on electrical performance.

[0007] A method for adjusting the subarray structure of a large-aperture array antenna with consideration for electrical performance includes the following steps:

[0008] S1: Determine the maximum gain loss

[0009] Based on the electromagnetic performance requirements of large-aperture array antennas, determine the maximum gain loss ΔG of the large-aperture array antenna. max ;

[0010] S2: Establish the sensitivity distribution matrix

[0011] Based on the calculation formula for the electrical performance of a large-aperture triangular grating array antenna, the sensitivity distribution matrix of the antenna gain in the x, y, and z directions of the array elements in the subarray is established.

[0012] S3: Calculate the position tolerance allocation weight

[0013] Based on the sensitivity distribution matrix, calculate the position tolerance allocation weights of the array elements in the x, y, and z directions in the subarray;

[0014] S4: Given initial installation tolerance standards

[0015] Given different initial installation tolerance standards for large-aperture array antenna subarray elements;

[0016] S5: Calculate the positional tolerance distribution matrix

[0017] Based on the initial installation tolerance standard in step S4, and combined with the position tolerance allocation weights of the array elements in the x, y, and z directions in step S3, calculate the position tolerance distribution matrix of the array elements in the x, y, and z directions.

[0018] S6: Generate random samples of positional error

[0019] Based on the position tolerance distribution matrix in step S5, generate random samples of position errors in the x, y, and z directions of the array elements in the subarray;

[0020] S7: Calculate antenna electrical performance

[0021] A structure-electromagnetic coupling model of a large-aperture array antenna is used to calculate the antenna's electrical performance under random samples of position error.

[0022] S8: Determine whether the random sample of positional error meets the requirements.

[0023] Check whether the random sample of position errors of the subarray elements that meet the maximum gain loss requirement of the antenna reaches 98% in the x, y, and z directions; if the requirement is met, proceed to step S10; if the requirement is not met, proceed to step S9.

[0024] S9: Calculate the new positional tolerance standard

[0025] Calculate the average value of the maximum gain loss of the antenna under random samples of position error that meet the requirements under different tolerance standards, and use a polynomial to fit the relationship between the position tolerance standard of the subarray element and the gain loss. Combine the maximum gain loss to calculate the new position tolerance standard of the subarray element, and repeat steps S4 to S8.

[0026] S10: Calculate the maximum permissible structural adjustment amount

[0027] The maximum allowable structural adjustment amount of the subarray structure oriented towards electrical performance in the x, y, and z directions is obtained.

[0028] Furthermore, step S2 includes the following steps:

[0029] S21: A triangular grating array antenna in the Oxy plane, with array elements arranged in an M-row N-column triangular grating pattern, where the spacing between array elements along the x-axis is d. x The spacing along the y-axis is d. y That is, each triangular grid has a base of d. x The height is d y An isosceles triangle;

[0030] Assume the position vector of the antenna element in the m-th row and n-th column is r. mn =x mn i+y mn j+z mn k, where x and y are the x and y coordinates along the x and y axes, respectively. mn and y mn They are respectively represented as

[0031]

[0032] The position vector r of the (m, n)th antenna element mn The direction cosine r0 = cosα of the observation point in the far field x i+cosα y j+cosα z By combining k, the radiation pattern function E of the triangular grating array antenna can be obtained. a (θ, φ), the calculation formula is as follows:

[0033]

[0034] Among them, I mn , These represent the amplitude and phase of the excitation current for the (m, n)th element, respectively. Let λ be the space wave constant, λ be the operating wavelength of the array antenna, and cosσ be the x-direction cosine. x =sinθcosφ, y-direction cosα y =sinθsinφ, z-direction cosα z =cosθ, θ∈(0,π) and φ∈(0,2π) are the elevation angle and azimuth angle of the observation direction, respectively;

[0035] Based on the array factor pattern function E of the triangular grating array antenna a Given (θ, φ), the gain G(θ, φ) of the array antenna can be calculated using the following formula:

[0036]

[0037] Where η is the antenna radiation efficiency, η0 is the free-space wave impedance, and P r It is the radiated power of the array antenna;

[0038] S22: Calculate the sensitivity distribution matrix along the x, y, and z directions.

[0039] The array factor pattern function E of the triangular grating array antenna a (θ, φ) can be converted into the form of adding the real and imaginary parts, as shown in the following expression:

[0040]

[0041]

[0042] The array factor pattern function E of the triangular grating array antenna a Substituting (θ, φ) into the gain G(θ, φ) of the array antenna, the gain G(θ, φ) is obtained. The calculation formula is as follows:

[0043]

[0044] Based on the gain G(θ, φ), the gain-sensitivity matrix of the large-aperture triangular grating array antenna along the x-direction is calculated using the direct differentiation method. The calculation formula is as follows:

[0045]

[0046] in, and Calculate using the following formulas respectively:

[0047]

[0048]

[0049] Will and Combining the gain-sensitivity matrix of the large-aperture triangular grating array antenna along the x-direction, the gain-sensitivity of the subarray elements of the triangular grating array antenna along the x-direction can be obtained, and the calculation formula is as follows:

[0050]

[0051] Similarly, the gain of the triangular grating array antenna can be used to calculate the sensitivity of the subarray elements along the y and z directions, as follows:

[0052]

[0053] S23: Arrange the sensitivities of the array elements within the subarray along the x, y, and z directions from step S22 according to their corresponding distribution positions within each subarray. This forms the sensitivity matrix St of the triangular grating array antenna gain pair with the subarray element positions along the x, y, and z directions. Gx S Gy S Gz .

[0054] Furthermore, step S3 includes the following:

[0055] The sensitivity matrix S of the subarray elements along the x, y, and z directions is based on the gain of the triangular grating array antenna. Gx S Gy S Gz Calculate the position tolerance allocation weights of the subarray elements in each direction;

[0056] Since the positional tolerance of each subarray element is inversely proportional to its sensitivity, the sensitivity matrix S is calculated separately. Gx S Gy S Gz After taking the reciprocal and normalizing, the positional tolerance allocation weights of the array elements in the subarray along the x, y, and z directions are obtained. The calculation formula is as follows:

[0057]

[0058]

[0059]

[0060] in, These are the weights assigned to the positional tolerances of the subarray elements along the x, y, and z directions, respectively, and T is the total number of triangular grating array antennas.

[0061] Furthermore, step S4 includes the following:

[0062] Based on the basic structure of large-aperture array antennas, several different initial installation tolerance standards for array antenna subarray elements are given, namely σ std = [σ1, σ2, ..., σ h , …, σ H ] T H represents the number of installation tolerance standards.

[0063] Furthermore, step S5 includes the following specific details:

[0064] Based on the weighting of the positional tolerances of the subarray elements along the x, y, and z directions in step S3, and combined with the different initial installation tolerance standards σ of the subarray elements in step S4... hGiven that 1 ≤ h ≤ H, calculate the position tolerance distribution matrix of the subarray elements in the x, y, and z directions. The calculation formula is as follows:

[0065]

[0066]

[0067]

[0068] Where, σ x =[σ x1 , σ x2 , …, σ xL ], σ y =[σ y1 , σ y2 , …, σ yL ], σ z =[σ z1 , σ z2 , …, σ zL ] are the positional tolerance distribution matrices of the subarray elements in the x, y, and z directions, respectively, where L = T·H.

[0069] Furthermore, step S6 includes the following specific details:

[0070] Based on the position tolerance distribution matrix in step S5, generate random position error samples of the subarray elements along the x, y, and z directions, respectively, using the position tolerance distribution matrix σ. x σ y σ z The positional tolerance σ of each array element xi σ yi σ zi Let be the standard deviation, where 1 ≤ i ≤ L;

[0071] Based on the normal distribution, P groups of random samples containing the positional errors of the subarray elements in the x, y, and z directions are generated.

[0072] Furthermore, step S7 includes the following steps:

[0073] S71: For a planar array antenna with elements arranged in a triangular grid pattern, let the random error of the position of the (m, n)th element be (Δx) mn Δy mn Δz mn Therefore, the structure-electromagnetic coupling model of the triangular lattice array antenna is established as follows:

[0074]

[0075] Among them, E S(θ, φ) represents the electrical performance of the triangular grating array antenna under the influence of structural errors.

[0076] S72: Substitute the random samples containing the x, y, z direction position errors of the subarray elements in group P of step S6 into the structure-electromagnetic coupling model of the triangular grid array antenna.

[0077] By selecting the direction of the main antenna beam, the electrical performance, i.e., the gain loss, of the triangular grid array antenna under random samples of position error is calculated.

[0078] Furthermore, step S8 includes the following:

[0079] S81: In the random sample of subarray element position errors in group P, the gain loss obtained in step S7 is compared with the maximum gain loss ΔG. max By comparison, the number of samples that meet the maximum gain loss requirement is obtained, i.e., Q groups. It is then determined whether 98% of the random samples of position error meet the electrical performance requirements, i.e., Q / P≥98%.

[0080] S82: If the requirements are met, proceed to step S10;

[0081] If the requirements are not met, proceed to step S9.

[0082] Furthermore, step S9 includes the following specific steps:

[0083] S91: Arrange the array antenna gain loss values ​​calculated from the random samples of the position errors of the P group subarray elements in ascending order, and take the average value ΔG of the gain loss results that meet the maximum gain loss requirement. h_avg As the corresponding positional tolerance standard σ h The gain loss value is set below, and multiple sets of ΔG are used. h_avg With σ h The positional tolerance matrix and gain loss matrix are listed separately;

[0084] S92: Based on σ in the positional tolerance matrix and gain loss matrix h ΔG h_avg (1≤h≤H), a polynomial is used to fit the correlation polynomial between the positional tolerance standard and the gain loss:

[0085]

[0086] Where ΔG represents the gain loss variable of the triangular grating array antenna, a H-1 a H-2 ..., a0 are the coefficients of the polynomial. For positional tolerance variable σ hv H-1 power; For positional tolerance variable σhv H-2;

[0087] S93: Combining maximum gain loss ΔG max Let the gain loss variable of the triangular grating array antenna on the left side of the correlation polynomial in step S92 be ΔG = ΔG max Solving this polynomial yields the new tolerance standard σ. h_new Using this as the new positional tolerance, repeat steps S4 to S8, thus forming an iterative process.

[0088] Furthermore, step S10 includes the following:

[0089] By determining the maximum permissible tolerance of the subarray in the x, y, and z directions, the maximum permissible structural adjustment amount of the subarray structure in the x, y, and z directions for electrical performance is obtained.

[0090] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0091] 1. During the fabrication and installation of large-aperture array antennas, the actual positions of the array elements inevitably deviate from their ideal positions, resulting in structural errors and deterioration of the array antenna's electrical performance. While improving the fabrication accuracy of the array antenna elements can improve electrical performance, in practice, considering manufacturing costs and efficiency, it is impossible to increase the fabrication and assembly accuracy indefinitely. This invention clarifies the sensitivity information of the electrical performance of large-aperture array antennas to the positions of array elements in each subarray, achieving the goal of rationally allocating the position tolerances of array elements within the subarrays for antenna electrical performance, thus balancing the electrical performance and manufacturing costs of large-aperture array antennas.

[0092] 2. The ever-increasing demand for longer detection ranges and finer target resolution in array antennas is driving the development of larger antennas. The number of array elements in an antenna array can reach tens of thousands. The traditional method of adjusting the position of individual array elements would consume a great deal of manpower and resources. This invention proposes a subarray structure adjustment method oriented towards electrical performance. It can ensure that the array antenna meets the electrical performance requirements while controlling the array elements within the subarray to have the same adjustment amount, while the adjustment amounts between subarrays are different. For large-aperture array antennas, this can effectively improve the adjustment efficiency of their large-aperture array surfaces. Attached Figure Description

[0093] Figure 1 This is a flowchart of the method for adjusting the structure of a large-aperture array antenna subarray, which is oriented towards electrical performance, according to the present invention.

[0094] Figure 2 This is a schematic diagram of a triangular lattice array antenna arrangement;

[0095] Figure 3 This is a schematic diagram of the arrangement of subarray structures for a large-aperture array antenna;

[0096] Figure 4 This is a diagram showing the gain and sensitivity distribution of the antenna array subarray elements in the x-direction.

[0097] Figure 5 This is a diagram showing the gain and sensitivity distribution of the antenna array subarray elements in the y-direction.

[0098] Figure 6 This is a diagram showing the z-axis gain and sensitivity distribution of the subarray elements of the antenna array;

[0099] Figure 7 This is a gain-sensitivity distribution diagram of the antenna subarray in the x-direction;

[0100] Figure 8 This is a diagram showing the gain and sensitivity distribution of the antenna subarray in the y-direction.

[0101] Figure 9 This is a diagram showing the gain and sensitivity distribution of the antenna subarray in the z-direction.

[0102] Figure 10 It is the weighting of the positional tolerance of the antenna subarray along the x-direction;

[0103] Figure 11 It is the weighting of the positional tolerance of the antenna subarray along the y-direction;

[0104] Figure 12 It is the weighting of the position tolerance of the antenna subarray along the z-direction;

[0105] Figure 13 It is the amount of position adjustment of the antenna subarray along the x-direction;

[0106] Figure 14 It is the amount of position adjustment of the antenna subarray along the y-direction;

[0107] Figure 15 It is the amount of position adjustment of the antenna subarray along the z-direction;

[0108] Figure 16 This is the gain pattern of a triangular grating array antenna under ideal conditions;

[0109] Figure 17 This is the gain pattern of the triangular grating array antenna after the subarray structure was adjusted. Detailed Implementation

[0110] The above-mentioned and other technical features and advantages of the present invention will be described in more detail below with reference to the accompanying drawings.

[0111] This invention analyzes the sensitivity of the electrical performance of a large-aperture array antenna to the positional error of subarray elements, clarifies the quantitative impact of structural errors in different installation directions on the antenna's electrical performance, and establishes a structure-electromagnetic coupling model between the positional error of subarray elements and the electrical performance of a large-aperture triangular grating array antenna. Based on this model, the changes in electrical performance under the influence of subarray element positional errors are analyzed, and finally, the subarray structure adjustment amount that meets the antenna's electrical performance requirements is given, thus ensuring and improving the electrical performance of the large-aperture array antenna.

[0112] Example 1

[0113] like Figure 1 As shown, this embodiment provides a technical solution: a method for adjusting the structure of a large-aperture array antenna subarray oriented towards electrical performance, including the following specific steps:

[0114] S1: Determine the maximum gain loss

[0115] Based on the electromagnetic performance requirements of large-aperture array antennas, determine the maximum gain loss ΔG of the large-aperture array antenna. max ;

[0116] S2: Establish the sensitivity distribution matrix

[0117] Based on the calculation formula for the electrical performance of a large-aperture triangular grating array antenna, the sensitivity distribution matrix of the antenna gain in the x, y, and z directions of the array elements in the subarray is established.

[0118] S3: Calculate the position tolerance allocation weight

[0119] Based on the sensitivity distribution matrix, calculate the position tolerance allocation weights of the array elements in the x, y, and z directions in the subarray;

[0120] S4: Given initial installation tolerance standards

[0121] Given different initial installation tolerance standards for large-aperture array antenna subarray elements;

[0122] S5: Calculate the positional tolerance distribution matrix

[0123] Based on the initial installation tolerance standard in step S4, and combined with the position tolerance allocation weights of the array elements in the x, y, and z directions in step S3, calculate the position tolerance distribution matrix of the array elements in the x, y, and z directions.

[0124] S6: Generate random samples of positional error

[0125] Based on the position tolerance distribution matrix in step S5, generate random samples of position errors in the x, y, and z directions of the array elements in the subarray;

[0126] S7: Calculate antenna electrical performance

[0127] A structure-electromagnetic coupling model of a large-aperture array antenna is used to calculate the antenna's electrical performance under random samples of position error.

[0128] S8: Determine whether the random sample of positional error meets the requirements.

[0129] Check whether the random sample of position errors of the subarray elements that meet the maximum gain loss requirement of the antenna reaches 98% in the x, y, and z directions; if the requirement is met, proceed to step S10; if the requirement is not met, proceed to step S9.

[0130] S9: Calculate the new positional tolerance standard

[0131] Calculate the average value of the maximum gain loss of the antenna under random samples of position error that meet the requirements under different tolerance standards, and use a polynomial to fit the relationship between the position tolerance standard of the subarray element and the gain loss. Combine the maximum gain loss to calculate the new position tolerance standard of the subarray element, and repeat steps S4 to S8.

[0132] S10: Calculate the maximum permissible structural adjustment amount

[0133] The maximum allowable structural adjustment amount of the subarray structure oriented towards electrical performance in the x, y, and z directions is obtained.

[0134] Example 2

[0135] To evaluate the performance of this invention, the following simulation experiments were conducted:

[0136] I. Determining the parameters of a large-aperture array antenna

[0137] This embodiment takes a large-aperture array antenna with a triangular grating arrangement as an example, such as... Figure 2 As shown, the operating frequency band is the P-band, and the antenna array consists of 180 subarrays, arranged in 12 rows and 15 columns, as follows. Figure 3 As shown, the antenna elements in the subarray are arranged in a triangular grid, and the excitation current amplitude of the elements adopts equal amplitude and in phase.

[0138] The parameters of this large-aperture triangular grating array antenna are shown in Table 1:

[0139] Table 1. Parameters of Large-Aperture Array Antennas

[0140]

[0141] II. Calculation of Subarray Structure Adjustment for Electrical Performance

[0142] S1: Determine the maximum gain loss of the large-aperture array antenna.

[0143] Based on the electromagnetic performance requirements of large-aperture array antennas, engineering practice typically requires that the antenna gain loss be controlled within 0.5 dB. Therefore, the maximum gain loss ΔGdB of the large-aperture array antenna needs to be determined. max .

[0144] S2: Establish the sensitivity matrix of the antenna gain pairs in the x, y, and z directions of the array elements in the subarray.

[0145] S21: As Figure 2 As shown, in the Oxy plane, the triangular grating array antenna has its elements arranged in an M-row N-column triangular grating pattern, where the spacing between the elements along the x-axis is d. x The spacing along the y-axis is d. y That is, each triangular grid has a base of d. x The height is d y An isosceles triangle, assuming the position vector of the antenna element in the m-th row and n-th column is r. mn =x mn i+

[0146] y mn j+z mn k, where x and y are the x and y coordinates along the x and y axes, respectively. mn and y mn They are respectively represented as

[0147]

[0148] The position vector of the (m, n)th antenna element is intersected with the direction cosine r0 = cosα of the observation point in the far field. x i+cosα y j+cosα z By combining k, the radiation pattern function E of the triangular grating array antenna can be obtained. a (θ, φ), the calculation formula is as follows:

[0149]

[0150] Among them, I mn , These represent the amplitude and phase of the excitation current for the (m, n)th element, respectively. Let λ be the space wave constant, λ be the operating wavelength of the array antenna, and cosα be the wavelength of the antenna. x =sinθcosφ,cosα y =sinθsinφ,cosα z =cosθ, where θ∈(0,π) and φ∈(0,2π) are the elevation angle and azimuth angle of the observation direction, respectively.

[0151] According to equation (1), the array factor pattern function E of the triangular grating array antenna aGiven (θ, φ), the gain G(θ, φ) of the array antenna can be calculated, as shown in the following expression:

[0152]

[0153] Where η is the antenna radiation efficiency, η0 is the free-space wave impedance, and P r It is the radiated power of the array antenna.

[0154] S22: The array factor pattern function E of the triangular grating array antenna. a (θ, φ) can be expressed as the sum of its real and imaginary parts, as follows:

[0155]

[0156] Substituting formula (4) into formula (3), we get:

[0157]

[0158] The gain-sensitivity matrix of a large-aperture triangular lattice array antenna along the x-direction is calculated using the direct differentiation method, and the formula is as follows:

[0159]

[0160] In formula (6) and They can be calculated using the following formulas:

[0161]

[0162]

[0163] Substituting formulas (7) and (8) into formula (6), we can obtain the sensitivity of the triangular grating array antenna gain to the subarray element along the x-direction, calculated as follows:

[0164]

[0165] Similarly, the gain of the triangular grating array antenna can be obtained to correlate with the sensitivity of the subarray elements along the y and z directions.

[0166]

[0167]

[0168] S23: Arrange the sensitivity of the array elements in the subarray along the x, y, and z directions according to the corresponding distribution positions of the array elements in each subarray, as shown in formulas (9) to (11), to form the sensitivity matrix S of the triangular grating array antenna gain to the positions of the array elements along the x, y, and z directions. Gx SGy S Gz .

[0169] Selecting the main lobe regions θ∈(-0.2, 0.2) and φ∈(0, 2π) of the antenna far-field pattern, the sensitivity distribution of the antenna gain to the position error of the array elements is calculated using formulas (9), (10), and (11), respectively. Figures 4-6 As shown;

[0170] By selecting the maximum sensitivity of all elements in each subarray to represent the sensitivity of each subarray's location, the sensitivity information of the subarray structure can be obtained, such as... Figures 7-9 As shown;

[0171] in Figures 4-9 The vertical axes Sx, Sy, and Sz represent the antenna gain electrical performance and the sensitivity of the array elements and subarray structure in the x, y, and z directions, respectively.

[0172] S3: Calculate the position tolerance allocation weights of array elements in the x, y, and z directions in the subarray.

[0173] The sensitivity matrix S of the subarray elements along the x, y, and z directions is based on the gain of the triangular grating array antenna. Gx S Gy S Gz The positional tolerances of the subarray elements in each direction are weighted. Since the positional tolerance of each subarray element is inversely proportional to its sensitivity, the sensitivity matrix S is weighted accordingly. Gx S Gy S Gz After taking the reciprocal and normalizing, the weights for the positional tolerances of the array elements along the x, y, and z directions in the subarray are obtained. The calculation formula is as follows:

[0174]

[0175]

[0176]

[0177] in, These are the weights assigned to the positional tolerances of the subarray elements along the x, y, and z directions, respectively, and T is the total number of triangular grating array antennas.

[0178] according to Figures 7-9 The sensitivity matrix S of the subarray in the x, y, and z directions Gx S Gy S Gz Equations (12) to (14) are used to apply the sensitivity matrix S respectively. Gx S GyS Gz After taking the reciprocal and normalizing, the positional tolerance allocation weights of the submatrix in the x, y, and z directions can be obtained. Distribution map, such as Figures 10-12 As shown.

[0179] S4: Given multiple different initial installation tolerance standards for array antenna subarray elements

[0180] Based on the basic structure of large-aperture array antennas, several different initial installation tolerance standards for array antenna subarray elements are given, namely σ std = [σ1, σ2, ..., σ h , …, σ H ] T H represents the number of installation tolerance standards. Here, the initial installation tolerance standard is taken as σ. std =[λ / 30, λ / 25, λ / 20, λ / 15, λ / 10].

[0181] S5: Calculate the position tolerance distribution matrix of the subarray elements in the x, y, and z directions.

[0182] Based on the weighting of the positional tolerances of the array elements in the subarray along the x, y, and z directions according to equations (12) to (14), and combined with the different initial installation tolerance standards σ of the array elements in the subarray... h Given that 1 ≤ h ≤ H, calculate the positional tolerance distribution matrix of the subarray elements in the x, y, and z directions, as shown below.

[0183]

[0184]

[0185]

[0186] In the formula, σ x =[σ x1 , σ x2 , …, σ xL ], σ y =[σ y1 , σ y2 , …, σ yL ], σ z =[σ z1 , σ z2 , …, σ zL ] are the positional tolerance distribution matrices of the subarray elements in the x, y, and z directions, respectively, where L = T·H.

[0187] S6: Generate random error samples of the positions of array elements in the subarray along the x, y, and z directions.

[0188] Based on the position tolerance distribution matrix, random position error samples of the array elements in the subarray along the x, y, and z directions are generated, i.e., based on the position tolerance distribution matrix σ. x σ y σ z The positional tolerance σ of each array element xi σ yi σ zi Let 1 ≤ i ≤ L be the standard deviation. Based on the normal distribution, P groups of random samples containing the positional errors of the subarray elements in the x, y, and z directions are generated. Here, the Latin hypercube method is used to generate 100 groups of random samples each time.

[0189] S7: Using a structure-electromagnetic coupling model of a large-aperture array antenna, calculate the antenna's electrical performance under the influence of random samples of position error.

[0190] S71: For a planar array antenna with elements arranged in a triangular grid pattern, let the random error of the position of the (m, n)th element be (Δx) mn Δy mn Δz mn Therefore, the structure-electromagnetic coupling model of the triangular lattice array antenna is established as follows:

[0191]

[0192] In the formula, E S (θ, φ) represents the electrical performance of the triangular grating array antenna under the influence of structural errors.

[0193] S72: Substitute the random samples of the position errors of the subarray elements in the x, y, and z directions into equation (18), select the direction of the main beam of the antenna, and calculate the gain loss of the triangular grid array antenna under the random sample of position error.

[0194] S8: Determine whether 98% of the random samples of position error meet the electrical performance requirements.

[0195] In the random sample of position error of subarray elements in group P, count the number of samples that meet the maximum gain loss requirement, i.e., group Q. Determine whether 98% of the random sample of position error meets the electrical performance requirement, i.e., Q / P≥98%. If the requirement is met, proceed to step S10; otherwise, proceed to step S9.

[0196] S9: Calculate the average value of the maximum gain loss under random samples of position error that meet the requirements, and use a polynomial to fit the relationship between the subarray element position tolerance standard and the gain loss. Combine the maximum gain loss to calculate the new position tolerance standard of the subarray elements, and repeat steps (4) to (8).

[0197] S91: Arrange the array antenna gain loss values ​​calculated from the random samples of the position errors of the P group subarray elements in ascending order, and take the average value ΔG of the gain loss results that meet the maximum gain loss requirement. h_avg As the corresponding positional tolerance standard σ h The gain loss value is set below, and multiple sets of ΔG are used. h_avg With σ h The positional tolerance matrix and gain loss matrix are listed separately;

[0198] S92: Based on σ in the positional tolerance matrix and gain loss matrix h ΔG h_avg (1≤h≤H), a polynomial is used to fit the correlation polynomial between the positional tolerance standard and the gain loss:

[0199]

[0200] In the formula, ΔG represents the gain loss variable of the triangular grating array antenna, and a H-1 a H-2 ..., a0 are the coefficients of the polynomial. For positional tolerance variable σ hv H-1 power.

[0201] S93: Combining maximum gain loss ΔG max Let the gain loss variable of the triangular grating array antenna on the left side of formula (19) be ΔG=ΔG max Solving this polynomial yields the new tolerance standard σ. h_new Using this as the new positional tolerance, steps (4) to (8) are repeated, thus forming an iterative process.

[0202] S10: If the requirements are met, the maximum allowable structural adjustment of the subarray structure in the x, y, and z directions for electrical performance is obtained.

[0203] Based on the maximum permissible tolerance of the subarray in the x, y, and z directions, the maximum permissible structural adjustment amount of the subarray structure oriented towards electrical performance in the x, y, and z directions can be obtained.

[0204] After the above calculations, the requirements are met when the tolerance standard is λ / 30. Substituting this into formulas (15) to (17), the maximum allowable structural adjustment amounts in the x, y, and z directions of the subarray structure in the large-aperture array antenna can be obtained as follows: Figures 13-15 As shown.

[0205] Example 3

[0206] like Figures 4-9 The sensitivity distribution diagram of the large-aperture array antenna elements and subarrays shows that:

[0207] The gain of the triangular grating array antenna is more sensitive to the position of the subarray in the z-direction than to the position of the subarray in the x and y directions. This indicates that changes in the position of the subarray in the z-direction will have a greater impact on the electrical performance of the array antenna than changes in the x and y directions.

[0208] The maximum sensitivity distribution of the array antenna gain to the z-axis position of the subarrays appears at subarrays (6,8), (7,8), (6,9), and (7,9), all located in the center region of the array. The minimum sensitivity appears at the edge of the array, indicating that the structural error at different z-axis positions has different effects on the electrical performance.

[0209] from Figures 10-15 It can be seen from the tolerance allocation weights and adjustment amounts in different directions of the subarray structure that:

[0210] For the x, y, and z directions, the positional tolerance of the central region of the array is the smallest, meaning that the positional tolerance of the central region is the smallest, and its structural accuracy must be strictly controlled. Conversely, the positional tolerance of the elements at the edge regions is relatively large, indicating that these subarray regions have a weaker impact on the antenna's electrical performance, and their positional tolerance requirements can be appropriately relaxed.

[0211] For this large-aperture array antenna, the maximum allowable adjustment range of the subarray structure in the central region in the x, y, and z directions is the smallest, which is λ / 60, λ / 60, and λ / 100 respectively, while the maximum allowable adjustment range of the subarray structure in the four corner regions is the largest, with a maximum value of λ / 30 for each region.

[0212] The structural adjustments of the subarray in the x, y, and z directions calculated above are taken as the subarray position changes. Using the structure-electromagnetic coupling model of the triangular grating array antenna (18), the antenna electrical performance under ideal conditions and after structural adjustments is calculated respectively. The calculation results are shown in Table 2, and the antenna gain pattern is shown in Table 2. Figure 16 , Figure 17 .

[0213] Table 2 Antenna electrical performance and its variations

[0214]

[0215] contrast Figure 16 and Figure 17 It can be seen that for an ideal antenna, i.e., all array elements have no positional error, and for an antenna after structural adjustment, i.e., allowing for positional adjustments to the subarray structure, the gain loss of the antenna after structural adjustment is 0.02dB, which meets the requirement of less than 0.5dB for antenna gain loss in engineering. This proves that after allocating the maximum allowable structural adjustment amount to the subarray structure, the electrical performance of the large-aperture array antenna can still be guaranteed. At the same time, it can also provide a certain positional error capacity for the manufacturing and installation of the antenna array, thereby reducing the processing and assembly difficulty of the large-aperture array antenna. This has reference value for the installation and adjustment of large-aperture array antennas in engineering.

[0216] This invention enables quantitative adjustment of subarray structures in different regions of a large-aperture array antenna, with the antenna's electrical performance as the target. This allows for strict precision requirements on subarray structures in regions with high electrical performance sensitivity, while appropriately reducing precision requirements in regions with low electrical performance sensitivity. This reduces the manufacturing difficulty of large-aperture arrays, improves the adjustment efficiency of large-aperture array antennas, and ensures the high performance of the array antenna.

[0217] The above description is merely a preferred embodiment of the present invention and is illustrative rather than restrictive. Those skilled in the art will understand that many changes, modifications, and even equivalents can be made within the spirit and scope defined by the claims of the present invention, all of which will fall within the protection scope of the present invention.

Claims

1. A method for adjusting the subarray structure of a large-aperture array antenna oriented towards electrical performance, characterized in that, Includes the following steps: S1: Determine the maximum gain loss Based on the electromagnetic performance requirements of large-aperture array antennas, determine the maximum gain loss ΔG of the large-aperture array antenna. max ; S2: Establish the sensitivity distribution matrix Based on the calculation formula for the electrical performance of a large-aperture triangular grating array antenna, the sensitivity distribution matrix of the antenna gain in the x, y, and z directions of the array elements in the subarray is established. S3: Calculate the position tolerance allocation weight Based on the sensitivity distribution matrix in step S2, calculate the position tolerance allocation weights of the array elements in the x, y, and z directions in the subarray. S4: Given initial installation tolerance standards Given different initial installation tolerance standards for large-aperture array antenna subarray elements; S5: Calculate the positional tolerance distribution matrix Based on the initial installation tolerance standard in step S4, and combined with the position tolerance allocation weights of the array elements in the x, y, and z directions in step S3, calculate the position tolerance distribution matrix of the array elements in the x, y, and z directions. S6: Generate random samples of positional error Based on the position tolerance distribution matrix in step S5, generate random samples of position errors in the x, y, and z directions of the array elements in the subarray; S7: Calculate antenna electrical performance Using a structure-electromagnetic coupling model of a large-aperture array antenna, the antenna's electrical performance under random samples of position error is calculated. S8: Determine whether the random sample of positional error meets the requirements. Does the ratio of the subarray element that meets the maximum gain loss requirement of the antenna to the random sample of position errors in the x, y, and z directions reach 98%? If the requirements are met, proceed to step S10; if the requirements are not met, proceed to step S9. S9: Calculate the new positional tolerance standard Calculate the average value of the maximum gain loss of the antenna under random samples of position error that meet the requirements under different tolerance standards, and use a polynomial to fit the relationship between the position tolerance standard of the subarray element and the gain loss. Combine the maximum gain loss to calculate the new position tolerance standard of the subarray element, and repeat steps S4 to S8. S10: Calculate the maximum permissible structural adjustment amount The maximum allowable structural adjustment of the subarray structure in the x, y, and z directions is obtained for electrical performance. Step S2 includes the following steps: S21: A triangular grating array antenna in the Oxy plane, with array elements arranged in an M-row N-column triangular grating pattern, where the spacing between array elements along the x-axis is d. x The spacing along the y-axis is d. y That is, each triangular grid has a base of d. x The height is d y An isosceles triangle; Assume the position vector of the antenna element in the m-th row and n-th column is r. mn =x mn i+y mn j+z mn k, where x and y are the horizontal and vertical coordinates along the x and y axes, respectively. mn and y mn They are respectively represented as The position vector r of the (m,n)th antenna element mn The direction cosine r0 = cosα of the observation point in the far field x i+cosα y j+cosα z By combining k, the radiation pattern function E of the triangular grating array antenna can be obtained. a (θ,φ), the calculation formula is as follows: Among them, I mn , These represent the amplitude and phase of the excitation current for the (m,n)th element, respectively. Let λ be the space wave constant, λ be the operating wavelength of the array antenna, and cosα be the x-direction cosine. x =sinθcosφ, y-direction cosα y =sinθsinφ, z-direction cosα z =cosθ, θ∈(0,π) and v∈(0,2π) are the pitch angle and azimuth angle of the observation direction, respectively; Based on the array factor pattern function E of the triangular grating array antenna a Given (θ,φ), the gain G(θ,φ) of the antenna array can be calculated using the following formula: Where η is the antenna radiation efficiency, η0 is the free-space wave impedance, and P r It is the radiated power of the array antenna; S22: The array factor pattern function E of the triangular grating array antenna a (θ,φ) can be converted into the form of adding the real and imaginary parts, as shown in the following expression: The array factor pattern function E of the triangular grating array antenna a Substituting (θ,φ) into the gain G(θ,φ) of the array antenna, the gain G(θ,φ) is obtained. The calculation formula is as follows: Based on the gain G(θ,φ), the gain-sensitivity matrix of the large-aperture triangular lattice array antenna along the x-direction is calculated using the direct differentiation method. The calculation formula is as follows: in, and Calculate using the following formulas respectively: Will and Combining the gain-sensitivity matrix of the large-aperture triangular grating array antenna along the x-direction, the gain-sensitivity of the subarray elements of the triangular grating array antenna along the x-direction can be obtained, and the calculation formula is as follows: Similarly, the gain of the triangular grating array antenna can be used to calculate the sensitivity of the subarray elements along the y and z directions, as follows: S23: Arrange the sensitivities of the array elements within the subarray along the x, y, and z directions from step S22 according to their corresponding distribution positions within each subarray. This forms the sensitivity matrix St of the triangular grating array antenna gain pair with the subarray element positions along the x, y, and z directions. Gx S Gy S Gz .

2. The method for adjusting the subarray structure of a large-aperture array antenna oriented towards electrical performance as described in claim 1, characterized in that, Step S3 includes the following: The sensitivity matrix S of the subarray elements along the x, y, and z directions is based on the gain of the triangular grating array antenna. Gx S Gy S Gz Calculate the position tolerance allocation weights of the subarray elements in each direction; Since the positional tolerance of each subarray element is inversely proportional to its sensitivity, the sensitivity matrix S is calculated separately. Gx S Gy S Gz After taking the reciprocal and normalizing, the positional tolerance weights of the array elements in the subarray along the x, y, and z directions are obtained. The calculation formula is as follows: in, These are the weights assigned to the positional tolerances of the subarray elements along the x, y, and z directions, respectively, and T is the total number of triangular grating array antennas.

3. The method for adjusting the subarray structure of a large-aperture array antenna oriented towards electrical performance as described in claim 2, characterized in that, Step S4 includes the following: Based on the basic structure of large-aperture array antennas, several different initial installation tolerance standards for array antenna subarray elements are given, namely σ std =[σ1,σ2,…,σ h ,…,σ H ] T H represents the number of installation tolerance standards.

4. The method for adjusting the subarray structure of a large-aperture array antenna oriented towards electrical performance as described in claim 3, characterized in that, Step S5 includes the following specific steps: Based on the weighting of the positional tolerances of the subarray elements along the x, y, and z directions in step S3, and combined with the different initial installation tolerance standards σ of the subarray elements in step S4... h , 1≤h≤H, calculate the position tolerance distribution matrix of the subarray elements in the x, y, and z directions respectively. The calculation formula is as follows: Where, σ x =[σ x1 ,σ x2 ,…,σ xL ], σ y =[σ y1 ,σ y2 ,…,σ yL ], σ z =[σ z1 ,σ z2 ,…,σ zL ] are the positional tolerance distribution matrices of the subarray elements in the x, y, and z directions, respectively, where L = T·H.

5. The method for adjusting the subarray structure of a large-aperture array antenna oriented towards electrical performance as described in claim 4, characterized in that, Step S6 includes the following specific contents: Based on the position tolerance distribution matrix in step S5, generate random position error samples of the subarray elements along the x, y, and z directions, respectively, using the position tolerance distribution matrix σ. x σ y σ z The positional tolerance σ of each array element xi σ yi σ zi Let be the standard deviation, where 1 ≤ i ≤ L; Based on the normal distribution, P groups of random samples containing the positional errors of the subarray elements in the x, y, and z directions are generated.

6. The method for adjusting the subarray structure of a large-aperture array antenna oriented towards electrical performance as described in claim 5, characterized in that, Step S7 includes the following steps: S71: For a planar array antenna with elements arranged in a triangular grid pattern, let the random error of the position of the (m,n)th element be (Δx) mn ,Δy mn ,Δz mn Therefore, the structure-electromagnetic coupling model of the triangular lattice array antenna is established as follows: Among them, E S (θ,φ) represents the electrical performance of the triangular grating array antenna under the influence of structural errors; S72: Substitute the random samples containing the x, y, z direction position errors of the subarray elements in group P of step S6 into the structure-electromagnetic coupling model of the triangular grid array antenna. By selecting the direction of the main antenna beam, the electrical performance, i.e., the gain loss, of the triangular grid array antenna under random samples of position error is calculated.

7. The method for adjusting the subarray structure of a large-aperture array antenna oriented towards electrical performance as described in claim 6, characterized in that, Step S8 includes the following: S81: In the random sample of subarray element position errors in group P, the gain loss obtained in step S7 is compared with the maximum gain loss ΔG. max By comparison, the number of samples that meet the maximum gain loss requirement is obtained, i.e., Q groups. It is then determined whether 98% of the random samples of position error meet the electrical performance requirements, i.e., Q / P≥98%. S82: If the requirements are met, proceed to step S10; If the requirements are not met, proceed to step S9.

8. The method for adjusting the subarray structure of a large-aperture array antenna oriented towards electrical performance as described in claim 7, characterized in that, Step S9 includes the following specific steps: S91: Arrange the array antenna gain loss values ​​calculated from the random samples of the position errors of the P group subarray elements in ascending order, and take the average value ΔG of the gain loss results that meet the maximum gain loss requirement. h_avg As the corresponding positional tolerance standard σ h The gain loss value is set below, and multiple sets of ΔG are used. h_avg With σ h The positional tolerance matrix and gain loss matrix are listed separately; S92: Based on σ in the positional tolerance matrix and gain loss matrix h ΔG h_avg (1≤h≤H), a polynomial is used to fit the correlation polynomial between the positional tolerance standard and the gain loss: Where ΔG represents the gain loss variable of the triangular grating array antenna, a H-1 ,a H-2 ..., a0 are the coefficients of the polynomial. For positional tolerance variable σ hv H-1 power; For positional tolerance variable σ hv H-2; S93: Combining the maximum gain loss ΔG max Let the gain loss variable of the triangular grating array antenna on the left side of the correlation polynomial in step S92 be ΔG = ΔG max Solving this polynomial yields the new tolerance standard σ. h_new Using this as the new positional tolerance, repeat steps S4 to S8, thus forming an iterative process.

9. The method for adjusting the subarray structure of a large-aperture array antenna oriented towards electrical performance as described in claim 7, characterized in that, Step S10 includes the following: By determining the maximum permissible tolerance of the subarray in the x, y, and z directions, the maximum permissible structural adjustment amount of the subarray structure in the x, y, and z directions for electrical performance is obtained.

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