Spherical subarray dissection and full airspace coverage multi-beam subarray dynamic cooperative allocation method

Abstract

The application discloses a spherical subarray profiling and full-space coverage multi-beam subarray dynamic cooperative distribution method, and belongs to the technical field of antenna engineering. The method first completes array profiling by adapting the geometric characteristics of a spherical carrier to system operation indexes, realizes subarray profiling of different array requirements, then constructs an integer programming model based on the spatial similarity of array normal and beam pointing, realizes optimal matching of the array and the beam, and finally synthesizes the full polarization domain directional diagram of each beam by using a convex optimization algorithm, so that full utilization of array resources and optimization of beam performance are realized. The application effectively solves the technical problems of low resource utilization, insufficient spatial matching and difficult suppression of beam interference faced by existing conformal phased arrays in a full-space coverage scene, and provides an efficient and robust solution for full-space multi-target cooperative detection and communication in the fields of communication, radar and satellite navigation.

Description

Technical Field

[0001] This invention belongs to the field of antenna engineering technology, specifically a method for spherical subarray partitioning and dynamic collaborative allocation of multi-beam subarrays covering the entire airspace. Background Technology

[0002] With the rapid development of fields such as communications, radar, and satellite navigation, the demand for rapid and seamless full-space coverage is becoming increasingly urgent. Traditional single-beam or limited-space coverage systems struggle to simultaneously meet the requirements of multi-target tracking, multi-user communication, and high-gain coverage across the entire airspace. To address this, multi-beam, multi-array phased array systems have emerged. By arranging multiple antenna arrays on a conformal carrier, each array can independently or collaboratively form multiple beams, thereby achieving efficient full-space coverage. Therefore, dynamic collaborative allocation methods for multi-beam, multi-array coverage for full-space coverage have significant research value.

[0003] For example, the paper "Shi Pengcheng. Research on Intelligent Scheduling Algorithm for Multi-Beam Resources in the Entire Airspace [D]. China Electronics Technology Group Corporation Electronic Science Research Institute, 2024" proposes a method for scheduling beam resources of ellipsoidal conformal phased arrays based on a hybrid genetic algorithm. By modeling the satellite task allocation problem as a multi-knapsack problem, it achieves intelligent scheduling of array beams using matrix encoding and a greedy correction strategy. However, this method aims to minimize the total transmit power of the array, and its allocation decision relies on satellite visibility pre-screening and iterative optimization using the genetic algorithm, resulting in slow convergence and a tendency to get trapped in local optima. Furthermore, this method only considers task allocation under power constraints, failing to fully consider the spatial matching degree between the array normal and the beam pointing, making it difficult to guarantee that all beams in the multi-beam system achieve optimal gain performance and that all arrays participate in beamforming, thus limiting the system efficiency for full airspace coverage. To address this issue, how to fully utilize array resources while achieving simultaneous multi-beam scanning is a key point that needs careful consideration.

[0004] In the literature “Chen Tianfu, Liu Yazhao, Duan Zhen, et al. A design of a four-beam full-space S-band phased array antenna [J]. Marine Electronics Technology, 2025, 45(8): 50-54”, the authors proposed a design based on three tilting This phased array antenna scheme achieves full-space four-beam coverage through a three-array configuration. However, this scheme employs a static binding strategy for array array and beam allocation, and each array array faces the challenge of simultaneously transmitting multiple beams, which can easily lead to crosstalk during scanning. Therefore, avoiding simultaneous participation of all array arrays in the synthesis of multiple beams during array array scheduling is also a factor that needs to be considered.

[0005] It can be observed that the key to the dynamic collaborative allocation method of spherical subarray partitioning and multi-beam subarrays with full spatial coverage lies in solving the problem of dynamic and spatial matching between array partitioning and array resources and beam scanning requirements, so as to maximize the utilization of full array resources. Existing design schemes generally achieve this through non-convex optimization and full array participation in multi-beamforming. However, based on the above research status, the dynamic collaborative allocation of multi-beam multi-arrays with full spatial coverage still faces some challenges. First, existing methods cannot simultaneously consider spatial matching optimization and resource utilization maximization. Second, the optimization process has too many iterative steps and lacks a mathematical mechanism to converge to the global optimum. Furthermore, when multiple beams work in parallel, there is a lack of systematic collaborative mechanisms for beam crosstalk suppression and phase consistency calibration between arrays. Traditional methods either use hard switching strategies that lead to beam interruption or ignore coupling interference between multiple beams, making it difficult to ensure the signal quality and service continuity of each beam under full spatial large-angle scanning conditions. Summary of the Invention

[0006] To address the problems of insufficient spatial matching between array resources and beam pointing in existing full-space multi-beam multi-array phased array systems, low array utilization, and difficulty in avoiding inter-beam interference, this invention proposes a spherical subarray partitioning method and a dynamic collaborative allocation method for multi-beam multi-array based on maximizing spatial similarity and array resource utilization. This method first completes array partitioning by adapting to the geometric characteristics of the spherical carrier and system performance indicators, achieving subarray partitioning for different array requirements. Then, it achieves optimal matching between arrays and beams through integer programming. Finally, it uses a convex optimization algorithm to synthesize the full polarization domain radiation pattern of each beam, thereby achieving full utilization of all array resources and optimization of beam performance.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A method for spherical subarray partitioning and dynamic collaborative allocation of multi-beam subarrays covering the entire spatial domain includes the following steps:

[0009] S1. The spherical carrier is divided into array surfaces to obtain a set of conformal array surfaces composed of multiple antenna subarrays;

[0010] Based on the system's performance indicators and the geometric constraints of the conformal carrier, different spherical meshing methods are selected to discretize the spherical surface. Optimization principles are used to maximize spherical surface coverage uniformity and minimize inter-array radiative coupling. The mesh density and boundary orientation are adjusted to ensure that each antenna subarray meets the array coordinate constraints, size constraints, and element arrangement requirements. After meshing, the conformal carrier surface forms N independent antenna subarrays, each containing M antenna elements. The total number of antenna elements in all antenna subarrays is... .

[0011] The performance indicators include: consistency of antenna subarray quantity allocation, antenna element size and boundary conditions, antenna subarray layout (e.g., rectangular grid array, triangular grid array, ring array, etc.), maximum allowable size of antenna subarray, and size consistency.

[0012] The array surface partitioning methods include triangular partitioning, quadrilateral partitioning, and Gothenburg spherical partitioning. Triangular partitioning has the strongest geometric adaptability and is suitable for any irregular curved surface. Quadrilateral partitioning is easy to be compatible with rectangular grid antenna element layout. Gothenburg spherical partitioning can achieve a high degree of uniformity in array surface distribution on the sphere while ensuring that the array surface area is approximately equal.

[0013] Specifically, methods for discretizing the spherical surface include:

[0014] S11. Select the spherical meshing method to perform frontal meshing on the spherical carrier and obtain the initial meshing model;

[0015] When the antenna subarray adopts a triangular grid array or needs to be adapted to a conformal layout of curved surfaces, triangular grid partitioning is selected to improve the fitting accuracy of local curvature changes of the carrier; when the antenna subarray adopts a rectangular grid array, quadrilateral grid partitioning is selected; when the system requires that the effective radiation area of ​​each antenna subarray be equal and the uniformity of spherical coverage is the primary indicator, Goldberg spherical grid partitioning is selected, and a grid structure combining regular hexagons and regular pentagons is used to achieve a globally uniform spherical distribution.

[0016] S12. Based on the optimization principle of maximizing the uniformity of spherical coverage and minimizing the radiative mutual coupling between frontal surfaces, adjust the density and boundary orientation of the mesh.

[0017] Specifically, based on the spatial correspondence between the normal of each antenna subarray and the main coverage area of ​​the spherical surface, the grid density is increased in the expected high scanning angle region, and the grid is merged in the low utilization region to balance the effective isotropic radiation power of each array. Taking the center normal of each antenna subarray as the reference, the edge diffraction coupling coefficient between adjacent antenna subarrays is calculated. By translating or rotating the grid boundary nodes, the discontinuity of the tangential electric field component of the boundary of adjacent antenna subarrays is reduced, thereby suppressing the mutual coupling caused by surface wave coupling and edge diffraction. After each adjustment, it is checked whether the size of each antenna subarray meets the maximum allowable size constraint of the antenna subarray and whether the antenna subarray can accommodate a complete periodic arrangement of antenna elements. If not, the adjustment is rolled back and iterated again.

[0018] S2. Determine the full-space beam scanning mode;

[0019] Based on the system's mission requirements of full-space scanning and uniform discrete beam coverage, the number of beams K operating simultaneously is determined; the entire airspace is then divided into elevation angle ranges. Divide evenly into K parts, azimuth range It is also evenly divided into K parts; let the desired pointing range of the first beam be: elevation angle Azimuth Then the desired pointing (elevation and azimuth) of the k-th beam is determined by the following formula:

[0020] ;

[0021] ;

[0022] This scanning method ensures uniform discrete coverage of the beam in both elevation and azimuth dimensions, providing a clear pointing reference for subsequent array allocation and beam synthesis.

[0023] S3. Establish the conformal array model and beam pointing set;

[0024] Let the normal unit vectors corresponding to the N antenna subarrays on the conformal carrier be respectively R is the real number field, and all the normal vectors of the array face form a matrix. ;

[0025] Based on the desired beam pointing direction determined in step 2, the desired pointing unit vector of the k-th beam is defined as:

[0026] ;

[0027] The expected pointing unit vectors of all beams form a matrix. .

[0028] S4. Construct the array-beam space similarity matrix;

[0029] Define the similarity matrix When the element in the i-th row and k-th column of matrix S When the direction of the antenna subarray is perpendicular to or opposite to the beam direction, the antenna subarray will not participate in the current beam synthesis and will be assigned a preset negative penalty value, which is usually no greater than [value missing]. This combination is excluded in subsequent optimizations; after penalty assignment, the optimized array-beam space similarity matrix is ​​obtained.

[0030] S5. Optimal array-beam allocation based on integer programming;

[0031] An integer programming model is constructed with the objective of maximizing the sum of spatial similarities of all array-beam assignment pairs. The model satisfies the following constraints: each beam is assigned a fixed number of antenna subarrays, and each antenna subarray is uniquely assigned to one beam. The constructed integer programming model is as follows:

[0032] ;

[0033] Among them, decision variables The value is either 1 or 0. A value of 1 indicates that the i-th antenna subarray is assigned to the k-th beam, and a value of 0 indicates otherwise. A linear integer programming model is solved to obtain the optimal allocation matrix X* composed of decision variables, thereby determining the set of antenna subarray indices corresponding to each beam. .

[0034] S6. Calculate the local polarization basis of each beam;

[0035] Based on the system's preset primary polarization and cross-polarization type indices, the polarization mode of the spherical array is determined; based on the polarization mode of the spherical array, polarization base coordinate transformation is performed to obtain the steering vector of the entire polarization domain, and then the primary polarization component and cross-polarization component are selected according to the system's working requirements.

[0036] When the polarization mode is linear polarization, the linear polarization steering vector matrix corresponding to each antenna element in the Ludwig third type coordinate system is obtained according to the following formula:

[0037] ;

[0038] in, and These are the vertical polarization steering vector and the horizontal polarization steering vector corresponding to each antenna element in the Ludwig third-type coordinate system, respectively. and These are the elevation components corresponding to each antenna element in the global spherical coordinate system. and azimuth components The guide vector below;

[0039] When the polarization mode is circular polarization, the circular polarization steering vector matrix corresponding to each antenna element in the global spherical coordinate system is obtained through coordinate transformation:

[0040] ;

[0041] in, and These are the right-hand circular polarization steering vector and the left-hand circular polarization steering vector corresponding to each antenna element in the global spherical coordinate system.

[0042] S7. Full polarization domain and beam synthesis based on convex optimization algorithm;

[0043] Based on the antenna subarray index set corresponding to each beam The corresponding antenna subarray is activated, and then the convex optimization algorithm is used to suppress the main polarization sidelobe level and cross-polarization component to obtain the full polarization domain and beam pattern that satisfy low sidelobe and low cross-polarization ratio.

[0044] In summary, the beneficial effects of this invention are as follows:

[0045] 1. This invention proposes a method for spherical subarray partitioning and dynamic collaborative allocation of multi-beam subarrays covering the entire spatial domain. By introducing various spherical mesh discretization techniques, including triangular partitioning, quadrilateral partitioning, and Goldberg spherical partitioning, it solves the problems of large differences in array area and insufficient spatial coverage uniformity in traditional conformal array partitioning. During the array partitioning stage, optimized design is performed based on system performance indicators and carrier geometry, effectively balancing the effective radiation aperture of each array. This avoids inter-beam crosstalk and phase calibration pressure caused by multiple tasks on a single array at the system architecture level, laying a solid foundation for subsequent balanced resource allocation and mutual coupling suppression of multiple beams.

[0046] 2. This invention constructs an integer programming model with the goal of maximizing the spatial similarity between the array surface normal and the beam pointing direction. At the same time, it constrains each beam to be assigned the same number of array surfaces and each array surface to be uniquely assigned to one beam. Thus, under the premise of ensuring uniform coverage of the entire airspace, it achieves the optimal spatial matching between array surface resources and beam pointing direction, avoids array surface idleness or overload, and significantly improves the utilization rate of the entire array surface resources.

[0047] 3. This invention has the capability of beamforming in the full polarization domain with low sidelobes and low cross-polarization ratio, and provides a complete mathematical framework for crosstalk suppression between multiple beams in the frequency, spatial and polarization domains when system resources allow. Attached Figure Description

[0048] Figure 1 This is a schematic diagram of the subarray based on triangular partitioning in this invention;

[0049] Figure 2 This is a schematic diagram of the subarray based on quadrilateral partitioning in this invention;

[0050] Figure 3 This is a schematic diagram of the subarray based on the Gothenburg spherical partitioning of the present invention;

[0051] Figure 4 This is a schematic diagram of the multi-faceted conformal phased array antenna of the present invention;

[0052] Figure 5 This is a schematic diagram of the activated array corresponding to beam 1 of the present invention;

[0053] Figure 6 This is a schematic diagram of the activated array corresponding to beam 2 of the present invention;

[0054] Figure 7 This is a schematic diagram of the activated array corresponding to beam 3 of the present invention;

[0055] Figure 8 This is a schematic diagram of the activated array corresponding to beam 4 of the present invention;

[0056] Figure 9 This is the main polarization and cross-polarization pattern of beam 1 of the present invention;

[0057] Figure 10 This is the main polarization and cross-polarization pattern of beam 2 of the present invention;

[0058] Figure 11 This is the main polarization and cross-polarization pattern of beam 3 of the present invention. Detailed Implementation

[0059] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings and examples.

[0060] This embodiment provides a method for spherical subarray partitioning and dynamic collaborative allocation of multi-beam subarrays covering the entire spatial domain. Through Goldberg conformal array partitioning of 40 subarrays, dynamic 4-beam array allocation based on an integer programming model, and a convex optimization beam synthesis algorithm, it achieves fast and uniform scanning radiation patterns with low sidelobes and low cross-polarization ratios across the entire spatial and polarization domains. The method includes the following steps:

[0061] S1. The spherical carrier is divided into array surfaces to obtain a set of conformal array surfaces composed of multiple antenna subarrays;

[0062] Based on the system's performance indicators and the geometric constraints of the conformal carrier, different spherical meshing methods are selected to discretize the spherical surface.

[0063] Figure 1 , Figure 2 , Figure 3 The diagrams shown are subarrays based on triangular partitioning, quadrilateral partitioning, and Goldberg spherical partitioning, respectively.

[0064] In this embodiment, the system performance indicators are as follows: the system must have full spatial coverage capability; the antenna subarrays adopt a rectangular grid array; the maximum allowable physical size of a single antenna subarray is limited by the radius of curvature of the sphere and the spacing between the elements; each subarray contains an equal number of antenna elements to ensure the consistency of the radiation aperture and radiation pattern characteristics of each subarray; based on the principle of maximizing full spatial beam coverage and spherical coverage uniformity, and minimizing radiation mutual coupling between array surfaces, each subarray after subdivision needs to have a high degree of topological consistency.

[0065] Based on the above indicators, this embodiment selects the Gothenburg spherical subdivision, such as... Figure 4 As shown, a multi-array conformal phased array antenna is constructed based on the Gothenburg GP(2,0) spherical mesh, consisting of N=40 hexagonal antenna subarrays. Each subarray contains 64 antenna elements, for a total of 2560 antenna elements across all subarrays. During the meshing process, the mesh boundaries were fine-tuned based on the spherical curvature distribution and the consistency of the antenna subarrays to balance the radiating aperture of each subarray.

[0066] S2. Determine the full spatial scanning method;

[0067] Based on the system's requirements for rapid full-space scanning and uniform beam distribution coverage, this embodiment sets the total number of beams operating simultaneously to K=4. The core of this invention lies in using a dynamic collaborative allocation mechanism to intelligently divide these 40 arrays into subarray sets corresponding to the currently required number of beams, thereby achieving full-space coverage with optimal spatial matching.

[0068] To determine the desired pointing of each beam in three-dimensional space, the elevation angle range [0°, 90°] and azimuth angle range [0°, 360°] are first uniformly discretized according to the number of beams. Here, the initial desired pointing of the first beam is set to 0° elevation and 0° azimuth. The desired pointing of the k-th beam is then determined by the following formula:

[0069] ;

[0070] ;

[0071] The calculated expected pointing unit vectors for the four beams are as follows: beam 1 points to (0°, 0°), beam 2 points to (90°, 22.5°), beam 3 points to (0°, -45°), and beam 4 points to (90°, -67.5°). These four beams form a mutually separated, uniform coverage configuration in the spatial domain. It is important to note that this expected beam pointing is an instantaneous pointing; the scanning method utilizes several such instantaneous pointings to achieve dynamic subarray allocation and dynamic scanning across the entire spatial and polarimetric domain.

[0072] S3. Establish the conformal array model and beam pointing set;

[0073] Let the normal unit vectors corresponding to the 40 antenna subarrays on the conformal carrier be respectively R is the real number field, and all the normal vectors of the array face form a matrix. ;

[0074] Based on the desired beam pointing direction determined in step 2, the desired pointing unit vector of the k-th beam is defined as:

[0075] ;

[0076] The expected pointing unit vectors of all beams form a matrix. .

[0077] S4. Construct the array-beam space similarity matrix;

[0078] The normal unit vectors of all 40 array faces on the conformal carrier in the three-dimensional coordinate system are extracted and compared with the spatial similarity of the four beam pointing unit vectors calculated above. This process quantifies the degree of matching by calculating the dot product between the array face normal and the beam pointing.

[0079] Specifically, define the similarity matrix. When the element in the i-th row and k-th column of matrix S When the orientation of the antenna subarray is perpendicular to or opposite to the beam pointing direction, it indicates that the antenna subarray will not participate in the synthesis of the current suitable beam and will be assigned a value. As a negative penalty term, the possibility of the array surface serving the beam is excluded; after the penalty assignment, the optimized array surface-beam space similarity matrix is ​​obtained.

[0080] S5. Optimal array-beam allocation based on integer programming;

[0081] After completing the spatial similarity assessment, an integer programming model is introduced to solve for the globally optimal array allocation scheme. The optimization objective of this model is very clear: to maximize the sum of spatial similarities of all selected "array-beam" combinations. Under this objective, the model simultaneously enforces two rigid constraints: First, each beam must be allocated exactly 10 antenna subarrays (i.e., the total number of arrays, 40, divided by the number of beams, 4) to ensure a balanced coverage capability of each beam; second, each antenna subarray can and must serve only one beam in the current scheduling cycle, and the same array is not allowed to participate in the synthesis of multiple beams simultaneously.

[0082] The constructed integer programming model is as follows:

[0083] ;

[0084] Among them, decision variables The value is either 1 or 0. A value of 1 indicates that the i-th antenna subarray is assigned to the k-th beam, and a value of 0 indicates otherwise. After calculating this model, the optimal allocation matrix X* composed of decision variables is obtained, which in turn determines the set of antenna subarray indices corresponding to each beam. .

[0085] Reference Figure 5 , Figure 6 , Figure 7 , Figure 8 This allocation matrix specifically indicates the affiliation of the 40 array faces. For example... Figure 5 As shown, 10 arrays are grouped into subarray set P1, specifically responsible for synthesizing beam 1 pointing to (0°, 0°); as Figure 6As shown, another 10 arrays are grouped into subarray set P2, responsible for synthesizing beam 2 pointing to (90°, 22.5°); as Figure 7 As shown, another 10 arrays are grouped into subarray set P3, responsible for synthesizing beam 3 pointing to (0°, -45°); as Figure 8 As shown in the figure, another 10 arrays are grouped into a subarray set P4, which is responsible for synthesizing beam 4 pointing to (90°, -67.5°). As can be seen from the attached figure, the physical orientation of each array in the activated subarray set has good spatial compliance with the beam it is responsible for. This allocation strategy eliminates the phenomenon of array idleness or overload at the physical architecture level.

[0086] S6. Calculate the local polarization basis for each beam;

[0087] The polarization mode of the spherical array is determined based on the system's preset main polarization and cross polarization type indices. In this embodiment, the main polarization is vertical polarization. After transformation, the steering vector of the full polarization domain is obtained, and then the main polarization component and cross polarization component are selected according to the system's working requirements.

[0088] S7. Full polarization domain and beam synthesis based on convex optimization algorithm;

[0089] After the array configuration is determined, the system enters the beamforming execution phase. This is based on the antenna subarray index set corresponding to each beam. The corresponding 10 antenna subarrays are activated; then, a convex optimization algorithm is used to iteratively solve the excitation weights of the activated array surfaces. During the optimization process, the algorithm uses reducing sidelobe levels and suppressing cross-polarization components as strong constraints, ultimately calculating the full polarization domain and beam pattern that satisfy low sidelobes and low cross-polarization ratio, as shown below. Figure 9 , Figure 10 , Figure 11 As shown in the figure, each beam not only points precisely, but also achieves excellent radiation characteristics with sidelobe levels below -18dB and cross-polarization ratios above 25dB within a wide-angle scanning range.

[0090] Thus, the entire system has completed a closed-loop process from subarray partitioning, spatial domain division, spatial matching decision-making to final beamforming implementation. This implementation fully demonstrates the outstanding advantages of the present invention in maximizing array resource utilization, avoiding inter-beam interference, and achieving high-performance coverage across the entire polarization domain.

[0091] The above description is only one specific embodiment of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention should be considered equivalent substitutions and are included within the protection scope of the present invention.

Claims

1. A method for spherical subarray partitioning and dynamic collaborative allocation of multi-beam subarrays covering the entire spatial domain, characterized in that, Includes the following steps: S1. The spherical carrier is divided into array surfaces to obtain a set of conformal array surfaces composed of multiple antenna subarrays; Based on the system's performance indicators and the geometric constraints of the conformal carrier, different spherical meshing methods are selected to discretize the spherical surface. Optimization principles are used to maximize spherical surface coverage uniformity and minimize inter-array radiative coupling. The mesh density and boundary orientation are adjusted to ensure that each antenna subarray meets the array coordinate constraints, size constraints, and element arrangement requirements. After meshing, the conformal carrier surface forms N independent antenna subarrays, each containing M antenna elements. The total number of antenna elements in all antenna subarrays is... ; S2. Determine the full-space beam scanning mode; Based on the system's mission requirements of full-space scanning and uniform discrete beam coverage, the number of beams K operating simultaneously is determined; the entire airspace is then divided into elevation angle ranges. Divide evenly into K parts, azimuth range It is also evenly divided into K parts; let the desired pointing range of the first beam be: elevation angle Azimuth The desired pointing direction of the k-th beam is determined by the following formula: ； ； S3. Establish the conformal array model and beam pointing set; Let the normal unit vectors corresponding to the N antenna subarrays on the conformal carrier be respectively R is the real number field, and all the normal vectors of the array face form a matrix. ; Based on the desired beam pointing direction determined in step 2, the desired pointing unit vector of the k-th beam is defined as: ； The expected pointing unit vectors of all beams form a matrix. ; S4. Construct the array-beam space similarity matrix; Define the similarity matrix When the element in the i-th row and k-th column of matrix S If the value is negative, it is assigned a preset negative penalty value to exclude the combination in subsequent optimization; after penalty assignment, the optimized array-beam space similarity matrix is ​​obtained. S5. Optimal array-beam allocation based on integer programming; An integer programming model is constructed with the goal of maximizing the sum of spatial similarities of all array-beam assignment pairs. The model satisfies the following constraints: each beam is assigned a fixed number of antenna subarrays, and each antenna subarray is uniquely assigned to one beam. Solving the linear integer programming model yields the optimal allocation matrix X* composed of decision variables, which in turn determines the set of antenna subarray indices corresponding to each beam. . S6. Calculate the local polarization basis of each beam; Based on the system's preset primary polarization and cross-polarization type indices, the polarization mode of the spherical array is determined; based on the polarization mode of the spherical array, polarization base coordinate transformation is performed to obtain the steering vector of the entire polarization domain; and then, according to the system's operational requirements, the primary polarization component and cross-polarization component are selected. S7. Full polarization domain and beam synthesis based on convex optimization algorithm; Based on the antenna subarray index set corresponding to each beam The corresponding antenna subarray is activated, and then the convex optimization algorithm is used to suppress the main polarization sidelobe level and cross-polarization component to obtain the full polarization domain and beam pattern that satisfy low sidelobe and low cross-polarization ratio.

2. The method for spherical subarray partitioning and dynamic collaborative allocation of multi-beam subarrays covering the entire spatial domain as described in claim 1, characterized in that, The performance indicators include: consistency of antenna subarray quantity allocation, antenna element size and boundary conditions, antenna subarray layout, maximum allowable size of antenna subarray, and size consistency.

3. The method for spherical subarray partitioning and dynamic collaborative allocation of multi-beam subarrays covering the entire spatial domain as described in claim 2, characterized in that, The array surface partitioning methods include triangular mesh partitioning, quadrilateral mesh partitioning, and Gothenburg spherical mesh partitioning.

4. The method for spherical subarray partitioning and dynamic collaborative allocation of multi-beam subarrays covering the entire spatial domain as described in claim 3, characterized in that, In step S1, the methods for dividing the spherical surface into frontal sections include: S11. Select the spherical meshing method to perform frontal meshing on the spherical carrier and obtain the initial meshing model; When the antenna subarray adopts a triangular grid array or needs to be adapted to a curved surface conformal layout, triangular grid partitioning is selected; when the antenna subarray adopts a rectangular grid array, quadrilateral grid partitioning is selected; when the system requires that the effective radiation area of ​​each antenna subarray is equal and the spherical coverage uniformity is the primary indicator, Gothenburg spherical grid partitioning is selected. S12. Based on the optimization principle of maximizing the uniformity of spherical coverage and minimizing the radiative mutual coupling between frontal surfaces, adjust the density and boundary orientation of the mesh. Specifically, based on the spatial correspondence between the normal of each antenna subarray and the main coverage area of ​​the spherical surface, the grid density is increased in the expected high scanning angle region, and the grid is merged in the low utilization region to balance the effective isotropic radiation power of each array. Taking the center normal of each antenna subarray as the reference, the edge diffraction coupling coefficient between adjacent antenna subarrays is calculated. By translating or rotating the grid boundary nodes, the discontinuity of the tangential electric field component of the boundary of adjacent antenna subarrays is reduced, thereby suppressing the mutual coupling caused by surface wave coupling and edge diffraction. After each adjustment, it is checked whether the size of each antenna subarray meets the maximum allowable size constraint of the antenna subarray and whether the antenna subarray can accommodate a complete periodic arrangement of antenna elements. If not, the adjustment is rolled back and iterated again.

5. A method for spherical subarray partitioning and dynamic collaborative allocation of multi-beam subarrays covering the entire spatial domain, as described in any one of claims 2-4, characterized in that, In step S5, the constructed integer programming model is as follows: ； Among them, decision variables The value is either 1 or 0. When the value is 1, it means that the i-th antenna subarray is assigned to the k-th beam; otherwise, it is 0.

6. A method for spherical subarray partitioning and dynamic collaborative allocation of multi-beam subarrays covering the entire spatial domain, as described in any one of claims 2-4, characterized in that, In step S6, when the polarization mode is linear polarization, the linear polarization steering vector matrix corresponding to each antenna element in the Ludwig third type coordinate system is obtained according to the following formula: in, and These are the vertical polarization steering vector and the horizontal polarization steering vector corresponding to each antenna element in the Ludwig third-type coordinate system, respectively. and These are the elevation components corresponding to each antenna element in the global spherical coordinate system. and azimuth components The guide vector below; When the polarization mode is circular polarization, the circular polarization steering vector matrix corresponding to each antenna element in the global spherical coordinate system is obtained through coordinate transformation: in, and These are the right-hand circular polarization steering vector and the left-hand circular polarization steering vector corresponding to each antenna element in the global spherical coordinate system.

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