A multi-frequency common aperture array layout optimization method

Abstract

The present invention discloses a multi-frequency common aperture array layout optimization method. According to the array bandwidth, the working frequency band is divided into several sub-frequency bands; then according to the array aperture, the rectangular array surface is divided into several symmetrical sub-areas, the arrangement of the array elements is optimized in a single sub-area, and then the symmetry of the array surface is used to obtain the arrangement of the entire array; with the array working bandwidth, the spacing between array elements in different frequency bands and the array sidelobe level as the optimization targets, the CMA‑ES algorithm is used to optimize the spacing of array elements in the sub-area, wherein the spacing includes the spacing between array elements in the same frequency band and the spacing between array elements in different frequency bands. Under the premise of ensuring the array working bandwidth, non-overlapping array elements and sidelobe performance requirements, the unknown quantities to be optimized are reduced, the complexity of the calculation is reduced, and the efficiency of the solution is improved, providing a fast and efficient layout optimization method for solving multi-frequency common aperture array surfaces.

Description

Technical Field

[0001] The invention belongs to the field of array antenna optimization design, and in particular relates to a multi-frequency co-aperture array layout optimization method. Background Art

[0002] Modern wireless electronic communication systems are developing towards multi-function, high data transmission rate, large coverage, long-distance transmission and other directions. Traditionally, multiple antennas working in different frequency bands are used to achieve different functions and meet different needs. However, due to the limited space of the assembly platform, strong coupling is easily generated between different antennas, affecting the normal use of the system. Broadband antenna arrays can work in different frequency bands under the same radiation aperture to achieve different functions, so the use of broadband antenna arrays can greatly save assembly space; at the same time, advanced functions such as high-precision detection applications and high-resolution imaging applications of radar systems and high-speed transmission requirements of wireless communication systems have put forward higher and higher requirements on the hardware foundation of wireless electronic systems. As one of the key components of wireless electronic systems, phased array antennas are bound to develop towards wider working bandwidth and wider scanning range. It is not difficult to foresee that the future electronic platform will not only have better performance, but also more diverse functions. Its development direction should tend to the integrated development of electronic reconnaissance, electronic interference, radar detection, wireless communication and other multi-functions. The rise of common aperture array antennas is to solve the multi-function and integrated needs of radar systems. For example, microwave remote sensing, communication, mapping and imaging and other application fields require antenna systems to have multi-band, multi-polarization and multi-beam performance. By integrating different antenna arrays into the same aperture, a multi-channel or multi-functional subsystem is realized. In the face of tight space resources, integration and multi-functionality are the development trends of modern antenna systems. The development of multi-frequency common aperture array technology is particularly important for the development of radar and communication systems.

[0003] The optimization of multi-frequency co-aperture array technology faces the following challenges:

[0004] More operating frequency bands mean more antenna units and more complex array layouts. How to reduce the algorithm complexity, improve the calculation efficiency, and quickly obtain a reasonable array element layout while ensuring the array aperture, the array element spacing requirements of each frequency band, and the various frequency deviation performance indicators is a major difficulty of the present invention. Summary of the invention

[0005] The purpose of the present invention is to provide a multi-frequency common aperture array layout optimization method. According to the array bandwidth, the working frequency band is divided into several sub-bands; then according to the array aperture, the rectangular array surface is divided into several symmetrical sub-areas, the arrangement of the array elements is optimized in a single sub-area, and then the symmetry of the array surface is used to obtain the arrangement of the entire array; the array working bandwidth, the spacing between array elements in different frequency bands and the array sidelobe level are used as optimization targets, and the CMA-ES algorithm is used to optimize the spacing of array elements in the sub-area, wherein the spacing includes the spacing between array elements in the same frequency band and the spacing between array elements in different frequency bands. Under the premise of ensuring the array working bandwidth, non-overlapping array elements and sidelobe performance requirements, the unknown quantities required for optimization are reduced, the complexity of calculation is reduced, and the efficiency of solution is improved, providing a fast and efficient layout optimization method for solving multi-frequency common aperture arrays. The computer numerical simulation results show that the array optimized by this method has good performance in each frequency band and has the advantage of high computational efficiency, providing an effective and fast method for layout optimization of multi-frequency common aperture arrays.

[0006] The technical solution to achieve the purpose of the present invention is: a multi-frequency common aperture array layout optimization method, the steps are as follows:

[0007] The first step is to initialize the optimized frequency band. According to the desired working frequency band, the array working frequency band is divided into three sub-bands: high, medium and low, which correspond to the low-frequency array, medium-frequency array and high-frequency array respectively; then proceed to the second step.

[0008] The second step is to initialize the array optimization area, divide the array into sub-areas according to the array aperture and select the first sub-area as the array arrangement optimization area; then proceed to the third step.

[0009] The third step is to initialize the covariance matrix and step size of CMA-ES, initialize the array element spacing constraints, and the array element spacing includes six constraints, namely: minimum spacing of low-frequency array elements, minimum spacing of medium-frequency array elements, minimum spacing of high-frequency array elements, minimum spacing of low-medium-frequency array elements, minimum spacing of low-high-frequency array elements, and minimum spacing of medium-high-frequency array elements; then proceed to the fourth step.

[0010] The fourth step is to initialize the expected sidelobe level. There are three types of expected sidelobe levels, namely, the expected sidelobe level of the low-frequency array, the expected sidelobe level of the intermediate-frequency array, and the expected sidelobe level of the high-frequency array; then proceed to the fifth step.

[0011] In the fifth step, the CMA-ES algorithm is used to calculate the position of the array elements in the first sub-area, and the array elements in the first sub-area are translated to obtain the array layout of each frequency band on the entire array surface; then proceed to the sixth step.

[0012] Step 6: Determine whether the array element spacing meets the requirements. If so, proceed to step 7. If not, update the covariance matrix and step size and repeat step 5.

[0013] The seventh step is to calculate the fitness function value. When it is determined that the requirements are met, the optimization ends. If the requirements are not met, the covariance matrix and step size are updated, and the array layout of the array is updated back to the fifth step until the requirements are met.

[0014] Compared with the prior art, the present invention has the following significant advantages:

[0015] (1) By dividing the region into symmetrical regions, the unknown quantities for computational optimization are reduced, the efficiency of the solution is improved, and the optimization time is reduced.

[0016] (2) Through the layout of a multi-frequency array, the array can provide a wider bandwidth.

[0017] (3) The algorithm has a good effect and can effectively suppress the sidelobe level in the normal direction and during scanning while ensuring that the array elements are not blocked.

[0018] The present invention is further described in detail below in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a schematic diagram of dividing the rectangular array into sub-areas in the present invention.

[0020] Figure 2 It is a flow chart of the principle of the CMA-ES algorithm in the present invention.

[0021] Figure 3 It is a flow chart of the multi-frequency common aperture array layout optimization method of the present invention.

[0022] Figure 4 It is a schematic diagram of the layout of array elements in a single sub-region obtained by optimization in the present invention.

[0023] Figure 5 It is a schematic diagram of the array element layout in the entire area obtained in the present invention.

[0024] Figure 6 It is the normal direction of the common aperture array low frequency array in the present invention and the direction when the scanning range reaches 60° Figure 2 dimensional cross-sectional diagram, where (a) to (c) represent the directional diagrams at 0.8 GHz, 4 GHz, and 6 GHz frequencies, respectively.

[0025] Figure 7 It is the normal direction of the intermediate frequency array of the common aperture array of the present invention and the direction when the scanning range reaches 60° Figure 2 dimensional cross-sectional diagram, where (a) to (c) represent the directional diagrams at 6 GHz, 10 GHz, and 18 GHz frequencies, respectively.

[0026] Figure 8 It is the normal direction of the common aperture array high frequency array in the present invention and the direction when the scanning range reaches 60° Figure 2 dimensional cross-sectional diagram, where (a) to (c) represent the directional diagrams at 18 GHz, 32 GHz, and 40 GHz frequencies, respectively. DETAILED DESCRIPTION

[0027] Combination Figure 1 to Figure 5 The present invention proposes a multi-frequency common aperture array layout optimization method, the steps are as follows:

[0028] The first step is to initialize the optimized frequency band. According to the desired working frequency band, the array working frequency band is divided into three sub-bands: high, medium and low, which correspond to the low-frequency array, medium-frequency array and high-frequency array respectively.

[0029] According to the desired operating frequency band of the array [f l ,f h ], divided into three sub-bands: low, medium and high.

[0030]

[0031] Among them, f l is the minimum operating frequency required by the array, f h is the maximum operating frequency required by the array; F l 、F m 、F h The low, medium and high frequency bands are divided respectively; f ll is the lowest operating frequency corresponding to the low-frequency array, f lh is the highest operating frequency corresponding to the low-frequency array, f ml is the lowest operating frequency corresponding to the mid-frequency array, f mh is the highest operating frequency corresponding to the mid-frequency array, f hl is the lowest operating frequency corresponding to the high-frequency array, f hh is the highest operating frequency corresponding to the high-frequency band array; and the lowest frequency and the highest frequency between each frequency band should satisfy the following relationship

[0032]

[0033] To ensure that the sub-band covers the entire working frequency band.

[0034] The second step is to initialize the array optimization area and combine Figure 1 , divide the array surface into sub-areas according to the array aperture and select the first sub-area as the array arrangement optimization area.

[0035] The array surface is divided into N×N sub-areas according to the array aperture R, where the size of each sub-area is (R / N)×(R / N).

[0036] Optimize the arrangement of the sub-area arrays to obtain the layout of the entire array.

[0037] The array element distribution in the first sub-area is

[0038] [X 1，1 , Y 1，1 ]=[(x l1 , x m1 , x h1 ), (y l1 ,y m1 ,y h1 )] (3)

[0039] Where X 1，1 is the horizontal coordinate set of all frequency band array elements in the first sub-area, Y 1，1 is the horizontal coordinate set of all frequency band array elements in the first sub-area, x l1 ,y l1 are the horizontal and vertical coordinate sets corresponding to the low-frequency array elements in the first sub-area, respectively. m1 ,y m1 are the horizontal and vertical coordinate sets corresponding to the mid-frequency array elements in the first sub-area, respectively. h1 ,y h1 They are respectively the horizontal and vertical coordinate sets corresponding to the low-frequency band array elements in the first sub-area.

[0040] The third step is to initialize the covariance matrix and step size of CMA-ES; initialize the array element spacing constraints, which include six constraints: minimum spacing of low-frequency array elements, minimum spacing of medium-frequency array elements, minimum spacing of high-frequency array elements, minimum spacing of low-medium-frequency array elements, minimum spacing of low-high-frequency array elements, and minimum spacing of medium-high-frequency array elements.

[0041] The fourth step is to initialize the expected sidelobe level. There are three types of expected sidelobe levels, namely, the expected sidelobe level of the low-frequency array, the expected sidelobe level of the intermediate-frequency array, and the expected sidelobe level of the high-frequency array.

[0042] The fifth step is to use the CMA-ES algorithm to calculate the position of the array elements in the first sub-area, translate the array elements in the first sub-area, and obtain the array layout of each frequency band on the entire array surface.

[0043] The array layout of the entire array can be obtained by translating the array elements in the first sub-area. The entire array is divided into N rows and N columns of sub-arrays. The first sub-area is translated from left to right and from top to bottom in the order of l, 2, ..., N. 2sub-regions, then the position of the array element in the sub-region of the i-th row and the l-th column can be expressed as

[0044]

[0045] Where X i，j is the set of horizontal coordinates of all frequency band array elements in the sub-region of the i-th row and the l-th column, Y i，l is the set of horizontal coordinates of all frequency band array elements in the sub-region of the i-th row and the l-th column.

[0046] The sixth step is to determine whether the array element spacing meets the requirements. If so, proceed to the seventh step. If not, update the covariance matrix and step size and repeat the fifth step.

[0047] The seventh step is to calculate the fitness function value. When it is determined that the requirements are met, the optimization ends. If the requirements are not met, the covariance matrix and step size are updated, and the array layout of the array is updated back to the fifth step until the requirements are met.

[0048] The calculation formula of the two-dimensional planar array factor is expressed as

[0049]

[0050] Where AF represents the array factor, k is the corresponding frequency phase constant, (x h ,y h ) is the position coordinate corresponding to the hth array element, j represents the imaginary part, θ represents the azimuth angle, represents the pitch angle, I h is the excitation corresponding to the hth array element, in the following form

[0051] I h =I h exp(jψ h ) (6)

[0052]

[0053] Among them I h is the excitation amplitude corresponding to the hth array element, ψ h is the excitation phase corresponding to the hth array element, is the maximum beam pointing direction; when only the position is optimized and not the unit amplitude and phase, I h is a vector of all 1s;

[0054] Then the array factor of each frequency band array of the entire array after translation can be calculated by the following formula:

[0055]

[0056]

[0057]

[0058] AFL total 、AFM total , AFH total are the array factors corresponding to the low, medium and high frequency bands of the entire array, and ML, MM and MH represent the number of low, medium and high frequency band array elements in a single sub-area. i，l is the set of horizontal coordinates of all frequency band array elements in the sub-region of the i-th row and the l-th column, Y i，l is the set of horizontal coordinates of all frequency band array elements in the sub-region of the i-th row and the l-th column, and (i, l, m) represents the m-th array element in the sub-region of the i-th row and the l-th column. The array sidelobe level is defined as follows

[0059]

[0060]

[0061]

[0062] PSLL L 、PSLL M 、PSLL H They are the sidelobe levels corresponding to the low, medium and high frequency band arrays. Mainbeam represents the main beam area of ​​the pattern.

[0063] The present invention innovatively proposes the fitness function of the CMA-ES algorithm, which is expressed as

[0064]

[0065] where dmin L 、dmin M 、dmin H 、dmin LM 、dmin LH 、dmin MH They are the minimum spacing of low-frequency array elements, the minimum spacing of medium-frequency array elements, the minimum spacing of high-frequency array elements, the minimum spacing of low-medium-frequency array elements, the minimum spacing of low-high-frequency array elements, and the minimum spacing of medium-high-frequency array elements; dtarget L 、dtarget M 、dtarget H 、dtarget LM 、dtarget LH 、dtarget MHare the expected minimum spacing of low-frequency array elements, the minimum spacing of medium-frequency array elements, the minimum spacing of high-frequency array elements, the minimum spacing of low-medium-frequency array elements, the minimum spacing of low-high-frequency array elements, and the minimum spacing of medium-high-frequency array elements; c L 、c M 、c H , c0 is the weight coefficient, c L 、c M 、c H The value is le4 and the value of c0 is 1.

[0066] The CMA-ES algorithm principle flow chart is as follows Figure 2 As shown in the flowchart of the proposed multi-frequency common aperture array layout optimization method, Figure 3 shown.

[0067] The comprehensive parameter settings are as follows:

[0068] The array aperture is 1.5m×1.5m, the working bandwidth is 0.8GHz-40GHz, and the array is divided into 9 symmetrical areas. The low-frequency array works in the frequency band of 0.8GHz-6GHz, the mid-frequency array works in the frequency band of 6GHz-18GHz, and the high-frequency array works in the frequency band of 18GHz-40GHz. The number of low-frequency array elements is 20×9, the number of mid-frequency array elements is 45×9, and the number of high-frequency array elements is 75×9. The minimum spacing between low-frequency array elements is 0.266 times the wavelength corresponding to 0.8GHz, the minimum spacing between mid-frequency array elements is 0.266 times the wavelength corresponding to 6GHz, and the minimum spacing between high-frequency array elements is 0.4 times the wavelength corresponding to 18GHz.

[0069] Comprehensive example Figure 4 and Figure 5 As shown, Figure 4 This is a schematic diagram of the distribution of array elements in a single sub-area. Figure 5 This is a distribution diagram of the entire area. Figure 6 It is the two-dimensional cross-sectional pattern of the normal radiation at different frequencies in the low-frequency array working frequency band and the array factor scanning 60° in the common aperture array. Figure 7 It is the two-dimensional cross-sectional pattern of the normal radiation of different frequencies in the working frequency band of the intermediate frequency array in the common aperture array and the array factor of scanning 60°. Figure 8 It is the two-dimensional cross-sectional pattern of the normal radiation at different frequencies within the working frequency band of the high-frequency array in the common aperture array and the array factor scanning 60°.

Claims

1. A multi-frequency common aperture array layout optimization method, characterized in that: Here are the steps: Step 1, initialize the optimized frequency band, divide the array working frequency band into three sub-bands of high, medium and low according to the desired working frequency band, which correspond to the low frequency array, medium frequency array and high frequency array respectively; proceed to step 2; Step 2, initialize the array optimization area, divide the array into sub-areas according to the array aperture and select the first sub-area as the array arrangement optimization area; go to step 3; Step 3, initialize the covariance matrix and step size of CMA-ES, initialize the array element spacing constraints, the array element spacing includes six constraints: minimum spacing of low-frequency array elements, minimum spacing of medium-frequency array elements, minimum spacing of high-frequency array elements, minimum spacing of low-medium-frequency array elements, minimum spacing of low-high-frequency array elements, and minimum spacing of medium-high-frequency array elements; proceed to step 4; Step 4, initializing the expected sidelobe level, which includes three types, namely, the expected sidelobe level of the low-frequency array, the expected sidelobe level of the intermediate-frequency array, and the expected sidelobe level of the high-frequency array; proceeding to step 5; Step 5, using the CMA-ES algorithm to calculate the position of the array elements in the first sub-area, translate the array elements in the first sub-area, and obtain the array layout of each frequency band on the entire array surface; S5.1, the array element distribution in the first sub-area is [X 1,1 ,Y 1,1 ]=[(x l1 ,x m1 ,x h1 ),(y l1 ,y m1 ,y h1 )] (3) Where X 1,1 is the horizontal coordinate set of all frequency band array elements in the first sub-area, Y 1,1 is the ordinate set of all frequency band array elements in the first sub-area, x l1 ,y l1 are the horizontal and vertical coordinates of the low-frequency array elements in the first sub-area, respectively. m1 ,y m1 are the horizontal and vertical coordinates of the mid-frequency array elements in the first sub-area, respectively. h1 ,y h1 They are the horizontal and vertical coordinates corresponding to the low-frequency band array elements in the first sub-area respectively; S5.

2. Translate the array elements in the first sub-region to obtain the array layout of the entire array: Shift the first sub-region 1, 2, ..., N times from left to right and from top to bottom. 2 sub-regions, then the position of the array element in the sub-region of the i-th row and the l-th column is expressed as Among them, X i,l is the set of horizontal coordinates of all frequency band array elements in the sub-region of the i-th row and the l-th column, Y i,l is the set of ordinates of all frequency band array elements in the sub-region of the i-th row and the l-th column; Go to step 6; Step 6, determine whether the array element spacing meets the requirements. If so, proceed to step 7. If not, update the covariance matrix and step size, and repeat step 5. Step 7, calculate the fitness function value, and end the optimization when it is determined that the requirements are met; if the requirements are not met, update the covariance matrix and step size, and return to step 5 to update the array layout of the array until the requirements are met; Calculate the fitness function value as follows: The calculation formula of the array factor AF of a two-dimensional planar array is expressed as Where H represents the total number of array elements, k is the corresponding frequency phase constant, (x h ,y h ) is the position coordinate corresponding to the hth array element, j represents the imaginary part, θ represents the pitch angle, Indicates the azimuth, I h is the excitation corresponding to the hth array element, in the following form I h =I h exp(jψ h ) (6) Among them I h is the excitation amplitude corresponding to the hth array element, ψ h is the excitation phase corresponding to the hth array element, is the maximum beam pointing direction; when only the position is optimized and not the unit amplitude and phase, I h is a vector of all 1s; Then the array factor of each frequency band array of the entire array after translation is calculated by the following formula: AFL total 、AFM total , AFH total are the array factors corresponding to the low, medium and high frequency bands of the entire array, ML, MM and MH represent the number of low, medium and high frequency band array elements in a single sub-area, respectively; X i,l is the set of horizontal coordinates of all frequency band array elements in the sub-region of the i-th row and the l-th column, Y i,l is the ordinate set of all frequency band array elements in the sub-region of the i-th row and the l-th column, and (i, l, m) represents the m-th array element in the sub-region of the i-th row and the l-th column; The array sidelobe level is defined as follows PSLL L 、PSLL M 、PSLL H They are the sidelobe levels corresponding to the low, medium and high frequency band arrays respectively; Mainbeam represents the main beam area of ​​the pattern; The fitness function fitness is expressed as where dmin L 、dmin M 、dmin H 、dmin LM 、dmin LH 、dmin MH They correspond to the minimum spacing of low-frequency array elements, the minimum spacing of medium-frequency array elements, the minimum spacing of high-frequency array elements, the minimum spacing of low-medium-frequency array elements, the minimum spacing of low-high-frequency array elements, and the minimum spacing of medium-high-frequency array elements; dtarget L 、dtarget M 、dtarget H 、dtarget LM 、dtarget LH 、dtarget MH They correspond to the expected minimum spacing of low-frequency array elements, the minimum spacing of medium-frequency array elements, the minimum spacing of high-frequency array elements, the minimum spacing of low-medium-frequency array elements, the minimum spacing of low-high-frequency array elements, and the minimum spacing of medium-high-frequency array elements, respectively; c L 、c M 、c H , c0 are weight coefficients, c L 、c M 、c H The values ​​are all 1e4, and the c0 value is 1.

2. The multi-frequency common aperture array layout optimization method according to claim 1, characterized in that: The initialization optimization frequency band in step 1 is as follows: According to the desired operating frequency band of the array [f l ,f h ], divided into three sub-bands: low, medium and high. Among them, f l is the minimum operating frequency required by the array, f h is the maximum operating frequency required by the array; F l 、F m 、F h The low, medium and high frequency bands are divided respectively; f ll is the lowest operating frequency corresponding to the low-frequency array, f lh is the highest operating frequency corresponding to the low-frequency array, f ml is the lowest operating frequency corresponding to the mid-frequency array, f mh is the highest operating frequency corresponding to the mid-frequency array, f hl is the lowest operating frequency corresponding to the high-frequency array, f hh is the highest operating frequency corresponding to the high-frequency band array; and the lowest frequency and the highest frequency between each frequency band should satisfy the following relationship To ensure that the sub-band covers the entire working frequency band.

3. The multi-frequency common aperture array layout optimization method according to claim 1, characterized in that: The initialization array optimization area in step 2 is as follows: According to the array aperture R, the array surface is divided into N×N sub-areas, where the size of each sub-area is (R / N)×(R / N); and the first sub-area is selected as the array arrangement optimization area.

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