An efficient sparse array optimization method for large-scale multi-frequency co-boresight array based on interpolation theory

Abstract

The application discloses a large-scale ultra-wideband multi-frequency common aperture array high-efficiency sparse array optimization method based on interpolation theory, a mathematical model of common aperture array synthesis is established, the element position and constraint conditions of the common aperture array are uniformly described, a common aperture array position updating strategy based on interpolation theory is introduced, the element position is iteratively updated, and controllable movement of the element in a global and local range is realized; and in combination with an array optimization switching strategy, different array updates are adaptively selected in the iteration process, cooperative layout optimization between arrays is realized, and the synthesis performance can be improved with the target of reducing the peak side lobe level on the premise of meeting the array aperture, the element quantity and the minimum spacing and other constraints. Meanwhile, by combining a fast calculation method of a directional diagram, the calculation amount in the optimization iteration process is reduced, and the solution efficiency of the large-scale common aperture array synthesis is improved.

Description

Technical Field

[0001] This invention belongs to the field of array antenna optimization design, specifically involving an efficient sparse distribution optimization method for large-scale ultra-wideband multi-frequency common aperture arrays based on interpolation theory. Background Technology

[0002] As radar, communication, and electronic countermeasures systems continue to evolve towards multi-band, multi-functional, and highly integrated designs, achieving coordinated operation of multiple arrays within a limited physical aperture has become a significant challenge. Common-aperture arrays, by integrating multiple arrays operating in different frequency bands or performing different functions into a single physical aperture, improve aperture resource utilization efficiency while effectively controlling system size and weight. This is a crucial technological approach for achieving multi-functionality and high integration of array antennas and has become one of the important development directions for modern array antennas.

[0003] Rapid optimization of common-aperture array arrangements presents the following challenges:

[0004] In practical co-aperture design, as the array size and number of elements increase, different arrays face mutual constraints in spatial layout, minimum element spacing, and electromagnetic coupling, leading to a complex array synthesis problem characterized by high dimensionality and multiple constraints. Traditional array design and synthesis methods often suffer from low computational efficiency, difficulty in optimization convergence, and limited engineering feasibility when addressing these complex constraints, making it difficult to simultaneously meet the dual requirements of performance and efficiency in large-scale co-aperture array synthesis. Therefore, conducting systematic research on efficient synthesis of large-scale co-aperture arrays, aiming to achieve reasonable arrangement and collaborative optimization of multiple arrays within the same physical aperture, fully utilize limited aperture resources, improve overall radiation performance and system integration, and reduce array design complexity and engineering implementation costs, remains a pressing issue in the field of array antennas. Summary of the Invention

[0005] The purpose of this invention is to provide an efficient sparse distribution optimization method for large-scale ultra-wideband multi-frequency common aperture arrays based on interpolation theory.

[0006] The technical solution to achieve the purpose of this invention is as follows: an efficient sparse distribution optimization method for large-scale ultra-wideband multi-frequency common-aperture arrays based on interpolation theory, comprising the following steps:

[0007] Step 1: Set the maximum number of iterations, the radiation pattern evaluation weight, the grid discretization density, and the minimum spacing constraint between different arrays;

[0008] Step 2: Based on the given array aperture size and the number of array elements corresponding to array A and array B, and under the premise of satisfying various minimum array element spacing constraints, randomly generate a common aperture array layout as the initial solution.

[0009] Step 3: Based on the radiation pattern of the initial common aperture array layout, obtain the sidelobe levels of array A and array B respectively, and use them as fitness values;

[0010] Step 4: Calculate and determine the array to be updated in this iteration based on the proportional rotation strategy;

[0011] Step 5: In the selected array, randomly select a single array element as the update object, and calculate the position adjustment based on the selection coefficient to determine whether to use a common aperture exploration strategy or a common aperture development strategy in this iteration, so as to obtain a new array layout.

[0012] Step 6: Calculate the radiation pattern and update the fitness value based on the new array layout;

[0013] Step 7: If the fitness value of the new array is better than that of the array before the iteration, then retain the layout of the new array; otherwise, retain the original array layout.

[0014] Step 8: When the maximum number of iterations is met or the preset optimization target is reached, the iteration terminates and the optimal array layout is output; otherwise, return to step 4 to continue the next iteration.

[0015] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps of the method described above.

[0016] A computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the steps of the above-described method.

[0017] A computer program product includes a computer program that, when executed by a processor, implements the steps of the above-described method.

[0018] Compared with the prior art, the significant advantages of this invention are:

[0019] (1) This invention introduces interpolation theory into co-aperture sparse distribution synthesis, and realizes the controllable movement of array elements in the global and local ranges through two different position update strategies, thereby improving the efficiency of feasible layout generation and search effectiveness. (2) By introducing a proportional rotation strategy, collaborative layout optimization and constraint coordination between different arrays are realized in the iterative optimization process, thereby improving convergence stability and synthesis effect. (3) The algorithm has good performance and can effectively reduce the sidelobe level of the array within the desired frequency band, thereby improving array performance.

[0020] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0021] Figure 1This is a schematic diagram of the initial array layout in this invention.

[0022] Figure 2 This is a schematic diagram of the CCP's caliber exploration strategy in this invention.

[0023] Figure 3 This is a schematic diagram of the local optimization region construction of the CCP caliber development strategy of this invention.

[0024] Figure 4 The operation flow of the efficient sparse distribution synthesis method for large-scale ultra-wideband multi-frequency common aperture array based on interpolation theory in this invention is shown in the figure.

[0025] Figure 5 This is a diagram of the sparse array layout of the common aperture in this invention.

[0026] Figure 6 (a), (b), (c), (d), (e), and (f) in this invention represent the low-frequency band array of the common aperture array in the present invention, respectively. , , At that time , Side views of the normalized radiation pattern under two scanning angles.

[0027] Figure 7 (a), (b), (c), (d), (e), and (f) in this invention represent the low-frequency band array of the common aperture array in the present invention, respectively. , , At that time , Direction pattern results of two cross-sections

[0028] Figure 8 (a), (b), (c), (d), (e), and (f) in this invention represent the high-frequency band array of the common aperture array in the present invention, respectively. , , At that time , Side views of the normalized radiation pattern under two scanning angles.

[0029] Figure 9 (a), (b), (c), (d), (e), and (f) in this invention represent the high-frequency band array of the common aperture array in the present invention, respectively. , , At that time , The direction pattern results of the two cross-sections. Detailed Implementation

[0030] This invention proposes an efficient sparse array method for large-scale ultra-wideband multi-frequency co-aperture arrays based on interpolation theory. The basic idea is to optimize the array element arrangement to minimize sidelobe levels and improve overall computational efficiency while simultaneously satisfying the minimum spacing constraints for elements of the same and different frequencies, thereby shortening the solution time. However, traditional methods typically require individual determination of the spacing between all element pairs to ensure the distance constraints are met, leading to high computational overhead and low efficiency. For co-aperture arrays, multiple types of spacing constraints between multi-frequency arrays must also be considered, further increasing the burden of constraint determination and iterative computation, making the overall optimization process even more time-consuming. Therefore, it is necessary to propose an array element arrangement optimization algorithm that can satisfy multiple minimum spacing constraints while maintaining both high efficiency and high performance.

[0031] To achieve rapid synthesis of array element arrangements, this invention proposes a novel optimization method. By establishing a mathematical model for common-aperture array synthesis, the positions and constraints of the array elements are uniformly described. This leads to the introduction of a common-aperture array position update strategy based on interpolation theory, iteratively updating the element positions to achieve controllable movement of elements within both global and local ranges. Furthermore, combined with an array optimization switching strategy, different arrays are adaptively selected for updating during the iteration process, achieving collaborative layout optimization among the arrays. This improves synthesis performance by reducing peak sidelobe levels while meeting constraints such as array aperture, number of elements, and minimum spacing. Simultaneously, by incorporating a fast radiation pattern calculation method, the computational load during the optimization iteration process is reduced, improving the solution efficiency for large-scale common-aperture array synthesis. Simulation results show that the array synthesized using this method has lower sidelobe levels across the entire operating frequency band and saves significant computation time, providing an effective method for the rapid synthesis of large-scale ultra-wideband multi-frequency common-aperture arrays.

[0032] An efficient sparse distribution optimization method for large-scale ultra-wideband multi-frequency co-aperture arrays based on interpolation theory is proposed, with the following specific steps:

[0033] The first step is to set the maximum number of iterations, the radiation pattern evaluation weights, the grid discretization density, and the minimum spacing constraints between different arrays;

[0034] The second step involves randomly generating a common-aperture array layout as an initial solution, based on the given array aperture size and the number of array elements corresponding to arrays A and B, while satisfying various minimum element spacing constraints. Figure 1 As shown;

[0035] Initializing the common aperture array layout involves randomly placing elements within the array aperture. The array elements of array A and The array elements of array element B satisfy the minimum element spacing constraints within and between arrays under the Chebyshev distance form.

[0036] The third step is to obtain the sidelobe levels of array A and array B respectively based on the radiation pattern of the initial common aperture array layout, and use them as fitness values.

[0037] The fourth step is to calculate and determine the array to be updated in this iteration based on the proportional rotation strategy;

[0038] The proportional rotation strategy allocates update probabilities based on the number of array elements in each array, ensuring that each array can achieve a level of participation commensurate with its size throughout the optimization process. This effectively avoids imbalances such as a single array dominating or some arrays being ignored.

[0039] Suppose that the sparsely distributed array with a common aperture consists of two arrays, array A and array B, with the number of array elements respectively. and To ensure that both arrays have update probabilities commensurate with their size during optimization, the proportional rotation strategy stipulates that the probabilities of selecting array A or array B for updating in t iterations are respectively:

[0040] , (1)

[0041] in and These represent the probabilities of choosing to update the positions of array A and array B, respectively.

[0042] In the specific implementation, random sampling is used to determine the array to be updated in this iteration, that is, a random number is generated in each iteration. ,when If the position is not specified, select an element in array A for updating; otherwise, select an element in array B for position updating.

[0043] By adopting a proportional rotation strategy, larger arrays gain more update opportunities and are thus fully optimized; at the same time, smaller arrays are not neglected in the long term. This strategy effectively avoids bias towards any particular array in the optimization process by adaptively balancing the update probabilities among arrays of different sizes.

[0044] To further illustrate the rationality and effectiveness of the proportional recurrence strategy, the following analysis examines the probability of array element updates from a statistical expectation perspective. Let the maximum number of iterations be... When using a proportional rotation strategy, the expected number of optimizations for arrays A and B are respectively:

[0045] , (2)

[0046] Furthermore, we can obtain:

[0047] (3)

[0048] The fifth step is to randomly select a single array element as the update target in the selected array, and calculate the position adjustment based on the selection coefficient to determine whether to use a common aperture exploration strategy or a common aperture development strategy in this iteration, so as to obtain a new array layout.

[0049] (1) Common caliber exploration strategy

[0050] In the sparse synthesis optimization of co-aperture arrays, the element position search space is often constrained by multiple constraints, such as array boundaries and minimum element spacing. Since arrays A and B share the same physical aperture, elements from different arrays are not allowed to overlap in actual structure. Simultaneously, to reduce coupling effects between elements and suppress sidelobe levels, elements in the same frequency band must meet a minimum element spacing requirement. Furthermore, all elements must be strictly located within the array aperture boundaries, and no out-of-bounds operations are permitted. Based on these requirements, during array synthesis, element position adjustments are not freely performed across the entire aperture region but are restricted to a series of feasible regions that satisfy the constraints.

[0051] The common-aperture exploration strategy updates only a single element of array A or array B in each iteration, while keeping the positions of the remaining elements unchanged. It first discretizes the array aperture into a set of candidate points formed by a regular grid. Then, under the premise of satisfying the minimum element spacing constraint, it selects a new position for that point from the candidate points and moves it. In the common-aperture exploration strategy, each iteration only needs to adjust the position of a single element in array A or array B, while the positions of the remaining elements remain unchanged. First, the array aperture region is discretized, dividing the continuous physical aperture into a set of candidate positions composed of regular grid vertices. Based on this, when updating the position, the element can select a new position from the grid vertices and move it while satisfying the minimum element spacing constraint.

[0052] First, we need to... The array aperture is discretized, dividing it into a set of discrete points composed of a regular grid. The side length d of the grid is... s Determined by equation (4), where the parameter w is used to adjust the mesh density. ω is the minimum spacing between array elements. Considering that in a co-aperture structure, the array elements of array A and array B may differ in physical size and minimum element spacing constraints, w can be set to w for different arrays. A and w B This allows for the construction of discrete grids with varying densities to better suit the characteristics of each array.

[0053] (4)

[0054] After the mesh is generated, the set of all mesh vertices is defined as the candidate solution space for the element positions. This is represented as:

[0055] (5)

[0056] in, and They represent the first The y-coordinates of the q-th grid point and the q-th grid point It is a function that rounds down. It is the number of vertices along the x-axis. It represents the number of vertices along the y-axis.

[0057] After constructing the candidate solution space, the positions of the array elements that need updating are updated, denoted as P. The goal of the common-aperture exploration strategy is to... Find a feasible mesh vertex that satisfies the minimum spacing constraint as the new position of the array element. The specific steps are as follows:

[0058] First, from the set Randomly select a grid vertex as the current candidate position, with coordinates as follows: Random selection can enhance the global nature of the search and reduce the probability of the search getting stuck in local dense areas.

[0059] Next, calculate the Chebyshev distance between the candidate position and the positions of all other array elements except P in the array. Let the coordinates of the i-th element in array A be... The coordinates of the j-th element in array B are... , This represents the Chebyshev distance between the candidate position and the i-th element in array A. Let Chebyshev distance represent the distance between a candidate position and the j-th element in array B. The corresponding expression is:

[0060] (6)

[0061] (7)

[0062] If P is an element in array A, check the minimum spacing constraints within the same array and between different arrays in turn. This represents the minimum spacing constraint between arrays A. The minimum spacing constraint between array A and array B is shown.

[0063] , (8)

[0064] If the candidate solution satisfies the minimum spacing constraint, then update the position of the array element and end the position search for this common aperture exploration strategy; otherwise, start from... The process continues, selecting the next candidate grid vertex and re-evaluating until a point that meets the requirements is found.

[0065] Similarly, if P is an element in array B, it must also satisfy the corresponding minimum spacing constraint. If any condition is not met, the corresponding operation is repeated. A schematic diagram of the common aperture exploration strategy is shown below. Figure 2 As shown.

[0066] (2) Common caliber development strategy

[0067] The basic idea of ​​the common aperture development strategy is to construct a local optimization range around a single array element that satisfies the minimum spacing constraint and aperture boundary constraint. This ensures that the position of the candidate solution is always feasible, avoids the sudden changes in the radiation pattern caused by jump position updates, and thus improves the convergence accuracy in the later stages of iteration.

[0068] For sparsely distributed array structures with the same aperture, the elements of different arrays may vary significantly in size, number, and arrangement density, resulting in varying degrees of constraints on their optimization space. Traditional position update methods often struggle to simultaneously account for the minimum spacing constraints of elements from different arrays within a single array, significantly increasing the overall optimization complexity.

[0069] To address the aforementioned issues, the common-aperture development strategy constructs separate local optimization regions for arrays A and B to coordinate their constraints. Since the two arrays differ in size and spacing constraints, their corresponding local optimization regions also differ in shape. By constructing the intersection of the local optimization regions of arrays A and B, it can be ensured that the movement of array elements in array A will not intrude into the minimum spacing range of array B, while the movement of array elements in array B will not disrupt the layout structure of array A.

[0070] First, for any array element in array A or array B, its local optimization region is constrained by the minimum spacing constraints of neighboring array elements in the same array, the minimum spacing constraints of neighboring array elements in different arrays, and the aperture boundary. For array element P in array A, its candidate solution set with other array elements in array A is determined by equations (9) to (12). , , , and the candidate solution set of array B , , , ,Right now:

[0071] (9)

[0072] (10)

[0073] (11)

[0074] (12)

[0075] in, , , , Let represent the set of feasible solutions for the positions of the matrix elements in the four directions. It represents the set consisting of all array elements in the current array. Represents a set The coordinates of the nth element in the array are represented as follows: .

[0076] If any of the above sets is not empty, then select the array element that is closest to array element P from it, and its mathematical expression is as follows:

[0077] 1) If ,but:

[0078] (13)

[0079] 2) If ,but:

[0080] (14)

[0081] 3) If ,but:

[0082] (15)

[0083] 4) If ,but:

[0084] (16)

[0085] Candidates , , , Next, it is necessary to further verify whether the following constraints are met:

[0086] for It needs to meet the following requirements:

[0087] (17)

[0088] for It needs to meet the following requirements:

[0089] (18)

[0090] for It needs to meet the following requirements:

[0091] (19)

[0092] for It needs to meet the following requirements:

[0093] (20)

[0094] For the array element P to be moved, its position is denoted as... The nearest array element searched in its four directions (up, down, left, and right) is denoted as follows: , , , The corresponding coordinates are represented as , , , .

[0095] Further combining equations (13) and (20) yields the final result. , , , as well as , , , .

[0096] Based on this, according to the minimum spacing and This allows us to obtain the local optimization regions associated with the array elements in the same array. Local optimization regions associated with different array elements For any point within the local search region Its location is , means as follows:

[0097] (twenty one)

[0098] (twenty two)

[0099] When an array element is located at the edge of the array and there is no feasible solution satisfying the distance constraint in its neighboring directions, the boundary of the local optimization region needs to be further constrained by the array aperture boundary. The region that can be effectively optimized while satisfying the minimum spacing constraints of arrays A and B serves as a feasible solution region for element position updates, such as... Figure 3 As shown.

[0100] To further enhance the search capability of the common-caliber development strategy in the local optimization stage, the local optimization region is expanded according to the development strategy. The specific expression for the expansion condition is as follows:

[0101] 1) Array A expansion conditions:

[0102] (twenty three)

[0103] or

[0104] (twenty four)

[0105] Among them, the expansion condition of array A Can be taken separately , , , Combinatorial form. If any one of the above intervals satisfies the condition, it can be considered that a feasible extended optimization region exists in the horizontal direction. Correspondingly, let... Can be taken separately , , , Combinatorial form. As long as one of the above intervals satisfies the conditions, it can be considered that there is a feasible extended optimization region in the vertical direction.

[0106] 2) Array B expansion conditions:

[0107] (25)

[0108] or

[0109] (26)

[0110] Among them, the array B expansion condition Can be taken separately , , , Combinatorial form. If any one of the above intervals satisfies the condition, it can be considered that a feasible extended optimization region exists in the horizontal direction. Accordingly, let... Can be taken separately , , , Combinatorial form. As long as one of the above intervals satisfies the conditions, it can be considered that there is a feasible extended optimization region in the vertical direction.

[0111] Based on the expansion conditions of array A and array B, 0 to 8 local optimization regions for array A and 0 to 8 local optimization regions for array B can be derived, denoted as . .

[0112] In summary, in the common-aperture development strategy, the element positions are updated through... A region is randomly selected from the public area as the local optimization region and its position is interpolated to ensure the position of the newly generated array elements. All constraints are satisfied.

[0113] The flowchart of the proposed efficient optimization method for large-scale ultra-wideband multi-frequency common-aperture arrays based on interpolation theory is shown below. Figure 4 As shown.

[0114] The sixth step is to calculate the radiation pattern and update the fitness value based on the new array layout.

[0115] Let the array layout before iteration be The new array layout is Comparing the array layout before and after the iteration, only the i-th element moved. The formula for calculating the radiation pattern can be expressed as:

[0116] (27)

[0117] in, It is an array Direction map, It is a new array layout Direction map, and This represents the contribution of element i to the array pattern before and after its position is updated. By replacing the contribution of element i to the array pattern, the pattern of the new array layout can be obtained quickly without having to repeatedly accumulate and calculate for all elements.

[0118] In the synthesis of common-aperture arrays, to take into account the radiation performance of arrays in different frequency bands, a weighted fitness function can be constructed, which takes the following form:

[0119] (28)

[0120] in, and The weighting coefficients are non-negative. and These are the peak sidelobe levels of arrays A and B, respectively.

[0121] Step 7: If the fitness value of the new array is better than that of the array before the iteration, then retain the layout of the new array; otherwise, retain the original array layout.

[0122] Step 8: When the maximum number of iterations is met or the preset optimization target is reached, the iteration terminates and the optimal array layout is output; otherwise, return to step 4 to continue the next iteration.

[0123] Comprehensive examples Figure 5 As shown, a dual-band, co-aperture sparsely distributed array is constructed. The array adopts a planar co-aperture structure, simultaneously placing low-frequency and high-frequency arrays within this aperture. The low-frequency array has 300 elements, and the high-frequency array has 900 elements. Both share the physical aperture but are independent in the frequency domain. The operating frequency bands are set as follows: the operating frequency band of the low-frequency array covers... The operating frequency band of the high-frequency array covers , and The corresponding frequencies are respectively and The wavelength at that time. The frequency relationship satisfies... , To meet broadband communication requirements. The array aperture is set to... In the synthesis of sparsely distributed arrays with the same aperture, minimum element spacing was set for two types of arrays: the minimum element spacing for the low-frequency array was... The minimum element spacing of the high-frequency array is Meanwhile, to accommodate the staggered arrangement of array elements from different frequency bands in a common-aperture structure, the minimum element spacing between array elements of different frequency bands needs to be limited. The minimum spacing is [missing information]. The scan angle of the array It also requires good sidelobe suppression performance throughout the entire scanning range. Figure 6 Figures (a)-(f) show the low-frequency array in [the following diagrams]. , , At that time , Side view of the normalized radiation pattern under two scanning angles. Figure 7 Figures (a)-(f) show the low-frequency array in [the following diagrams]. , , At that time , The direction pattern results of the two cross-sections. Figure 8 Figures (a)-(f) show the high-frequency arrays in [the image / image / image]. , , At that time , Side view of the normalized directional pattern under two scanning angles. Figure 9 Figures (a)-(f) show the high-frequency arrays in [the image / image / image]. , , At that time , The direction pattern results of the two cross-sections.

Claims

1. A highly efficient sparse distribution optimization method for large-scale ultra-wideband multi-frequency common-aperture arrays based on interpolation theory, characterized in that, Includes the following steps: Step 1: Set the maximum number of iterations, the radiation pattern evaluation weight, the grid discretization density, and the minimum spacing constraint between different arrays; Step 2: Based on the given array aperture size and the number of array elements corresponding to array A and array B, and under the premise of satisfying various minimum array element spacing constraints, randomly generate a common aperture array layout as the initial solution. Step 3: Based on the radiation pattern of the initial common aperture array layout, obtain the sidelobe levels of array A and array B respectively, and use them as fitness values; Step 4: Calculate and determine the array to be updated in this iteration based on the proportional rotation strategy; Step 5: In the selected array, randomly select a single array element as the update object, and calculate the position adjustment based on the selection coefficient to determine whether to use a common aperture exploration strategy or a common aperture development strategy in this iteration, so as to obtain a new array layout. Step 6: Calculate the radiation pattern and update the fitness value based on the new array layout; Step 7: If the fitness value of the new array is better than that of the array before the iteration, then retain the layout of the new array; otherwise, retain the original array layout. Step 8: When the maximum number of iterations is met or the preset optimization target is reached, the iteration terminates and the optimal array layout is output. Otherwise, return to step 4 and continue to the next iteration.

2. The efficient sparse distribution optimization method for large-scale ultra-wideband multi-frequency common-aperture arrays based on interpolation theory according to claim 1, characterized in that, In step 2, initializing the common aperture array layout involves randomly placing elements within the array aperture. The array elements of array A and The array elements of array element B satisfy the minimum element spacing constraints within and between arrays under the Chebyshev distance form.

3. The efficient sparse distribution optimization method for large-scale ultra-wideband multi-frequency common-aperture arrays based on interpolation theory according to claim 1, characterized in that, The proportional rotation strategy described in step 4 is as follows: The proportional rotation strategy allocates update probabilities based on the number of array elements in each array, so that each array can obtain a level of participation commensurate with its size throughout the optimization process. Suppose that the sparsely distributed array with a common aperture consists of two arrays, array A and array B, with the number of array elements respectively. and To ensure that both arrays have update probabilities commensurate with their size during optimization, the proportional rotation strategy stipulates that the probabilities of selecting array A or array B for updating in t iterations are respectively: ， (1) in and These represent the probabilities of choosing to update the position in array A and array B, respectively. The array to be updated in this iteration is determined by random sampling, that is, a random number is generated in each iteration. ,when If the position is not specified, select an element in array A for updating; otherwise, select an element in array B for position updating. By adopting a proportional rotation strategy, larger arrays get more update opportunities. This strategy effectively avoids the optimization process from favoring any particular array by adaptively balancing the update probabilities among arrays of different sizes. Let the maximum number of iterations be When using a proportional rotation strategy, the expected number of optimizations for arrays A and B are respectively: ， (2) We can obtain: (3)。 4. The efficient sparse distribution optimization method for large-scale ultra-wideband multi-frequency common-aperture arrays based on interpolation theory according to claim 1, characterized in that, The two common aperture position update strategies in step 5 are as follows: (1) Common caliber exploration strategy The common aperture exploration strategy updates only a single element of array A or array B in each iteration, while keeping the other elements unchanged. First, the array aperture is discretized into a set of candidate points of a regular grid. Then, under the premise of satisfying the minimum spacing constraint, a new position is selected for the point from the candidate points and moved. First, we need to... The array aperture is discretized, dividing it into a set of discrete points composed of a regular grid; the side length d of the grid is... s Determined by equation (4), where the parameter w is used to adjust the mesh density. The minimum spacing between array elements; w is set to w according to different arrays. A and w B This allows for the construction of discrete meshes with varying densities. (4) After the mesh is generated, the set of all mesh vertices is defined as the candidate solution space for the element positions. This is represented as: (5) in, and They represent the first The y-coordinates of the q-th grid point and the q-th grid point It is a function that rounds down. It is the number of vertices along the x-axis. It represents the number of vertices along the y-axis. After constructing the candidate solution space, the positions of the array elements that need updating are updated, denoted as P; the goal of the common-aperture exploration strategy is to... Find a feasible mesh vertex that satisfies the minimum spacing constraint as the new position of the array element; the specific steps are as follows: First, from the set A grid vertex is randomly selected as the current candidate position, and its coordinates are: ; Secondly, calculate the Chebyshev distance between the candidate position and the positions of all other array elements except P; let the coordinates of the i-th element in array A be... The coordinates of the j-th element in array B are... , This represents the Chebyshev distance between the candidate position and the i-th element in array A. Let Chebyshev distance represent the distance between a candidate position and the j-th element in array B. The corresponding expression is: (6) (7) If P is an element in array A, check the minimum spacing constraints within the same array and between different arrays in turn. This represents the minimum spacing constraint between arrays A. The minimum spacing constraint between array A and array B is shown. ， (8) If the candidate solution satisfies the minimum spacing constraint, then update the position of the array element and end the position search for this common aperture exploration strategy; otherwise, start from... The process continues by selecting the next candidate grid vertex and re-evaluating it until a point that meets the requirements is found. Similarly, if P is an element in array B, it must also satisfy the corresponding minimum spacing constraint; if any condition is not met, the corresponding operation is repeated. (2) Common caliber development strategy The common aperture development strategy coordinates the constraints between arrays A and B by constructing their own local optimization regions. By constructing the intersection of the local optimization regions of arrays A and B, it ensures that the movement of array elements of array A will not intrude into the minimum spacing range of array B, while the movement of array elements of array B will not disrupt the layout structure of array A. First, for any array element in array A or array B, its local optimization region is constrained by the minimum spacing constraints of neighboring array elements in the same array, the minimum spacing constraints of neighboring array elements in different arrays, and the aperture boundary. For array element P in array A, its candidate solution set with other array elements in array A is determined by equations (9) to (12). , , , and the candidate solution set of array B , , , ,Right now: (9) (10) (11) (12) in, , , , Let represent the set of feasible solutions for the positions of the matrix elements in the four directions. It represents the set consisting of all array elements in the current array. Represents a set The coordinates of the nth element in the array are represented as follows: ; If any of the above sets is not empty, then select the array element that is closest to array element P from it, and its mathematical expression is as follows: 1) If ,but: (13) 2) If ,but: (14) 3) If ,but: (15) 4) If ,but: (16) Candidates , , , Next, it is necessary to further verify whether the following constraints are met: for It needs to meet the following requirements: (17) for It needs to meet the following requirements: (18) for It needs to meet the following requirements: (19) for It needs to meet the following requirements: (20) For the array element P to be moved, its position is denoted as... The nearest array element searched in its four directions (up, down, left, and right) is denoted as follows: , , , The corresponding coordinates are represented as , , , ; Combining equations (13) and (20), we get , , , as well as , , , ; Based on this, according to the minimum spacing and The local optimization regions associated with the array elements in the same array are obtained respectively. Local optimization regions associated with different array elements For any point within the local search region Its location is , means as follows: (21) (22) When an array element is located at the edge of the array and there is no feasible solution satisfying the distance constraint in its neighboring directions, the boundary of the local optimization region needs to be further constrained by the array aperture boundary. It can obtain an effective optimization range and simultaneously meet the minimum spacing constraint requirements of arrays A and B, serving as a feasible solution region for element position updates; The local optimization region is expanded, and the specific expression for the expansion condition is as follows: 1) Array A expansion conditions: (23) or (24) Among them, the expansion condition of array A Can be taken separately , , , Combinatorial form; as long as one of the above intervals satisfies the condition, it can be considered that there is a feasible extended optimization region in the horizontal direction; correspondingly, let Can be taken separately , , , Combination form; as long as one of the above intervals satisfies the conditions, it can be considered that there is a feasible extended optimization region in the vertical direction; 2) Array B expansion conditions: (25) or (26) Among them, the array B expansion condition Can be taken separately , , , Combinatorial form; as long as one of the above intervals satisfies the condition, it can be considered that there is a feasible extended optimization region in the horizontal direction; accordingly, let Can be taken separately , , , Combination form; as long as one of the above intervals satisfies the conditions, it can be considered that there is a feasible extended optimization region in the vertical direction; Based on the expansion conditions of array A and array B, 0 to 8 local optimization regions for array A and 0 to 8 local optimization regions for array B can be derived, denoted as . ; In the common-aperture development strategy, the element positions are updated by... A region is randomly selected from the public area as the local optimization region and its position is interpolated to ensure the position of the newly generated array elements. All constraints are satisfied.

5. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method according to any one of claims 1-4.

6. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method described in any one of claims 1-4.

7. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the steps of the method described in any one of claims 1-4.

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