Phased array antenna co-sited electromagnetic interference coupling prediction method based on subarray decomposition

Abstract

The application discloses a phased array antenna co-sited electromagnetic interference coupling prediction method based on subarray decomposition, which comprises the following steps: step 1, analyzing the radiation characteristics in the phased array antenna element array through a multilayer fast multipole method; step 2, solving by using a consistent geometric diffraction theory, analyzing the direct path, reflection path and diffraction path effects of the platform structure, the solving process comprising path tracking and field value tracking, and obtaining electromagnetic interference field analysis results under the influence of the complex platform structure; and step 3, performing vector synthesis on the electromagnetic interference coupling fields of the direct path, reflection path and diffraction path from the phased array antenna transmitting antenna element to the receiving antenna, obtaining a total electric field vector, and then calculating the electromagnetic interference energy coupled by the receiving antenna. The application takes into account the advantages of high precision of a full-wave solving method and fast speed of a high-frequency method, guarantees the solving precision, obtains a fast solving speed, and has low requirements on the computing hardware resources.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic compatibility simulation design technology, and in particular to a method for predicting electromagnetic interference coupling of co-located phased array antennas based on subarray decomposition. Background Technology

[0002] Phased array antennas have advantages such as multiple functions, strong anti-interference ability, and easy integration into conformal systems, and are increasingly widely used in platforms such as ships and aircraft. However, these platforms integrate a large number of frequency-using equipment antennas in a limited space, which can cause serious electromagnetic interference problems. Therefore, it is necessary to accurately predict the electromagnetic interference coupling of phased array antennas to support the design of phased array antenna optimization layout and electromagnetic interference control.

[0003] Currently, the solution to electromagnetic interference (EMI) coupling problems of phased array antennas within platforms is mainly divided into full-wave methods and high-frequency methods. The multilayer fast multipole method (MLFMM) within the full-wave method uses a surface mesh to discretize the computational object and then uses integral equations to solve the electromagnetic problem of the object. This makes it particularly suitable for solving EMI coupling problems of electrically large platforms, and it offers high accuracy. However, as the solution frequency increases, the EMI coupling problem of phased array antennas on platforms such as ships and aircraft becomes an ultra-electrically large problem, rapidly increasing the solution complexity and memory requirements, ultimately rendering it unsolvable. The Unified Geometric Diffraction (UTD) method in high-frequency methods is based on geometric optics and can consider the direct field, reflected field, and diffracted field. It solves the problem of zero field value in the shadow region of the geometric optics method, improves the accuracy of the solution, and has a fast solution speed. However, this method cannot consider the near-field effect of phased array antennas, resulting in poor accuracy in solving near-field problems. The phased array antennas in the platform are compactly arranged, and their mutual electromagnetic interference is a near-field effect. Therefore, the accuracy of using UTD to solve the co-located electromagnetic interference problem of phased array antennas is poor.

[0004] A review of domestic and international literature reveals a lack of methods for predicting electromagnetic interference coupling in co-located phased array antennas based on a combination of subarray decomposition and high-low frequency hybrid approaches. This invention fully leverages the advantages of high accuracy in full-wave solutions and high speed in high-frequency methods, achieving both high accuracy and fast solution speed, making it highly suitable for solving electromagnetic interference coupling problems of phased array antennas within a platform. Summary of the Invention

[0005] The technical problem to be solved by this invention is to provide a method for predicting electromagnetic interference coupling of co-located phased array antennas based on subarray decomposition, thereby addressing the deficiencies in the prior art and solving the problem of predicting electromagnetic interference coupling of co-located phased array antennas within a platform.

[0006] The technical solution adopted by this invention to solve its technical problem is:

[0007] This invention provides a method for predicting co-located electromagnetic interference coupling of phased array antennas based on subarray decomposition, used to predict co-located electromagnetic interference coupling between phased array antennas and receiving antennas on a platform structure. The method includes the following steps:

[0008] Step 1: Using the multi-level fast multipole method, calculations are performed in a multi-level grouping manner, including two processes: uplink and downlink. In the uplink process, the outward plane wave expansion function of the non-empty group in all layers is calculated. In the downlink process, starting from the second layer, the inward wave function of each of the remaining layers is obtained by recursively deriving through translation and inverse interpolation operations until the highest layer is reached, thus obtaining the radiation characteristic analysis results of the phased array antenna array elements.

[0009] Step 2: Based on the analysis results of the radiation characteristics in the phased array antenna array elements, the uniform geometric diffraction theory is used to solve the problem and analyze the effects of the direct path, reflection path and diffraction path of the platform structure. The solution process includes path tracing and field value tracing to obtain the electromagnetic interference field analysis results under the influence of the complex structure of the platform, including the electromagnetic interference coupling field of the direct path, reflection path and diffraction path.

[0010] Step 3: Perform vector synthesis of the electromagnetic interference coupling fields of the phased array antenna transmitting antenna element to the receiving antenna along the direct path, reflection path, and diffraction path to obtain the total electric field vector of the phased array antenna transmitting antenna element at the receiving antenna, and then calculate the electromagnetic interference energy coupled to the receiving antenna.

[0011] Furthermore, the method in step 1 of the present invention specifically comprises:

[0012] The computational process of the Multilevel Fast Multipole Method (MLFMA) is divided into two processes: up and down. The up process includes multi-level sub-expansion of the highest level and the layer-by-layer aggregation process from sub-layers to parent layers. When going up to the second level, each distant relative group is transferred and calculated. During the up process, the outward plane wave expansion function of all non-empty groups in all layers l = 2, ..., L is calculated, where L represents the total number of levels in MLFMA.

[0013] The downlink process then begins, which includes multi-level configuration from parent to child layers, transfer calculations between distant relatives in the same layer, and field expansion operations after reaching the highest layer. Starting from the second layer, the inward wave functions of the remaining layers are obtained by recursion through translation and inverse interpolation operations until the highest layer is reached, thus completing the downlink process of MLFMA. The calculation in the downlink process is to calculate the expansion function of the inward wave.

[0014] Furthermore, the path tracing method in step 2 of the present invention is specifically as follows:

[0015] First, based on the panoramic bounding box of the target or scene, determine the size of the virtual aperture surface for the incident plane wave. Then, construct the virtual aperture surface at a certain distance from the target and divide it to build a ray tube matrix. Rays start from the virtual aperture surface and enter the scene. Track each ray, traversing all surface elements in the scene to determine the intersection position of the ray with the object, and save the intersection information and path. Then, generate new reflected and diffracted rays, continue to track them, and if they intersect with the object, find the intersection again; otherwise, discard the ray. Recursively track all rays in this way, guiding all rays to leave the scene or decay their energy to a certain threshold, thus completing the path tracking of all rays.

[0016] Furthermore, the field tracking method in step 2 of the present invention is specifically as follows:

[0017] Based on the path tracing algorithm, the direct path, reflection path, and diffraction path of the phased array antenna from the transmitting antenna to the receiving antenna under the influence of the platform structure are obtained, and the electromagnetic interference coupling field at the receiving antenna is calculated.

[0018] Furthermore, the method for solving the straight path according to the present invention is specifically as follows:

[0019] For solving the electromagnetic interference coupled field tracing problem along a direct path, a single ray represents an astigmatic wave. According to the law of conservation of energy, when the source point is at point S and the field point is at point R, with a distance d between the two points, the magnitude of the field strength after the ray travels a path of length d is:

[0020]

[0021] Where E(R) is the electric field intensity at field point R, E(S) is the electric field intensity at source point S, the two principal radii of curvature of the incident wavefront are ρ1 and ρ2, k is the propagation constant, and e -jkd This represents the phase factor.

[0022] Furthermore, the method for solving the reflection path of the present invention is specifically as follows:

[0023] For solving the electromagnetic interference coupled field tracing problem along the reflection path, according to the principles of geometric optics, the reflecting plane and the incident plane lie in the same plane, and the reflection angle is equal to the incident angle. Based on the boundary condition of continuous tangential electric field on the metal surface, let W be the reflection point on the object surface, the source point be at point S, the field point be at point R, the two principal radii of curvature of the reflecting wavefront be ρ1 and ρ2, and d be the path length between the reflection point W and the field point R. The reflected field at the field point R can be expressed in the following form:

[0024]

[0025] Among them, E r(R) represents the reflected electric field intensity at point R, E i (S) represents the incident electric field intensity at the source point S, and k is the propagation constant. is the diatonic reflection coefficient.

[0026] Furthermore, the method for solving the diffraction path of the present invention is specifically as follows:

[0027] For solving the electromagnetic interference coupled field tracing along the diffraction path, the Uniform Diffraction Theory (UTD) is used to analyze the diffraction field. According to the UTD theory, the diffraction field formula is:

[0028]

[0029] in, and Project D onto the diffraction field vector at the diffraction point in directions parallel to and perpendicular to the diffraction plane. / / and D ⊥ These are the diffraction coefficients parallel to and perpendicular to the diffraction plane, respectively. and Let A(s) be the projections of the incident field vector at the diffraction point onto the directions parallel to and perpendicular to the incident plane, respectively. Let A(s) be the spatial attenuation factor, and e be the projections of the incident field vector onto the directions parallel to and perpendicular to the incident plane. -jβs This represents the phase factor.

[0030] Furthermore, the method for calculating the electromagnetic interference energy coupled by the receiving antenna in step 3 of the present invention is specifically as follows:

[0031] By solving the electromagnetic interference coupled field tracing problem, the electromagnetic interference coupled fields of the phased array antenna transmitting antenna element to the receiving antenna along the direct path, reflection path, and diffraction path under the influence of the platform structure are obtained. Then, these path fields are vector synthesized to obtain the total electric field vector E of the phased array antenna transmitting antenna element at the receiving antenna. i_total ;

[0032] Calculate the received electromagnetic interference coupling energy P based on the antenna aperture of the receiving antenna. i for:

[0033]

[0034] Among them, E i_total Let G be the total electric field vector of the i-th element of the phased array antenna at the receiving antenna, and let G be the total electric field vector of the receiving antenna at the receiving antenna. i_total The antenna gain corresponding to the direction, η is the wave impedance constant, and λ is the wavelength corresponding to the calculated frequency;

[0035] For a phased array antenna with N elements, the electromagnetic interference energy P coupled to the receiving antenna is expressed by the following formula:

[0036]

[0037] Among them, P i Let be the electromagnetic interference coupling energy of the i-th phased array antenna transmitting element to the receiving antenna; Let be the phase of the transmitting antenna of the i-th phased array antenna.

[0038] The beneficial effects of this invention are: the prediction method for co-located electromagnetic interference coupling of phased array antennas based on subarray decomposition of this invention (1) has high accuracy and fast speed in solving co-located electromagnetic interference coupling of phased array antennas. This invention takes into account the advantages of high accuracy of full-wave solution method and fast speed of high frequency method. While ensuring the accuracy of solution, it obtains a faster solution speed; (2) has strong applicability. According to the characteristics of phased array antenna, this invention adopts a solution method based on subarray decomposition and high and low frequency hybrid method, which is particularly suitable for solving the problem of co-located electromagnetic interference coupling of phased array antennas of ultra-large electric platforms. Moreover, it does not require high computing hardware resources. Attached Figure Description

[0039] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0040] Figure 1 This is a schematic diagram of the current element interaction in the multilayer fast multipole method according to an embodiment of the present invention;

[0041] Figure 2 This is a schematic diagram of the interaction between current elements in the method of moments according to an embodiment of the present invention;

[0042] Figure 3 This is a schematic diagram of ray path tracing of the cavity geometry in an embodiment of the present invention;

[0043] Figure 4 This is a diagram showing the arrangement of the phased array antenna and receiving antenna on the platform according to an embodiment of the present invention;

[0044] Figure 5 These are the radiation patterns of the phased array antenna elements in this embodiment of the invention; (a) E-plane radiation pattern; (a) H-plane radiation pattern;

[0045] Figure 6 This is the electromagnetic interference propagation path between the phased array antenna transmitting array antenna and the receiving antenna in an embodiment of the present invention;

[0046] Figure 7 This is a curve showing the change of electromagnetic interference energy with the elevation scanning angle of the phased array antenna according to an embodiment of the present invention. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0048] The present invention provides a method for predicting co-located electromagnetic interference coupling of phased array antennas based on subarray decomposition. This method is used to predict co-located electromagnetic interference coupling between phased array antennas and receiving antennas on a platform structure. The method includes the following steps:

[0049] Step 1: Using the multi-level fast multipole method, calculations are performed in a multi-level grouping manner, including two processes: uplink and downlink. In the uplink process, the outward plane wave expansion function of the non-empty group in all layers is calculated. In the downlink process, starting from the second layer, the inward wave function of each of the remaining layers is obtained by recursively deriving through translation and inverse interpolation operations until the highest layer is reached, thus obtaining the radiation characteristic analysis results of the phased array antenna array elements.

[0050] Step 2: Based on the analysis results of the radiation characteristics in the phased array antenna array elements, the uniform geometric diffraction theory is used to solve the problem and analyze the effects of the direct path, reflection path and diffraction path of the platform structure. The solution process includes path tracing and field value tracing to obtain the electromagnetic interference field analysis results under the influence of the complex structure of the platform, including the electromagnetic interference coupling field of the direct path, reflection path and diffraction path.

[0051] Step 3: Perform vector synthesis of the electromagnetic interference coupling fields of the phased array antenna transmitting antenna element to the receiving antenna along the direct path, reflection path, and diffraction path to obtain the total electric field vector of the phased array antenna transmitting antenna element at the receiving antenna, and then calculate the electromagnetic interference energy coupled to the receiving antenna.

[0052] In another specific embodiment of the present invention, the following technical solution is adopted:

[0053] (1) Analysis of radiation characteristics in phased array antenna elements

[0054] The Multilevel Fast Multipole Method (MLFMA) employs a multilevel grouping approach for computation, dividing the interactions between groups into near-field interactions and far-field interactions, such as... Figure 1 As shown; compared to the matrix-vector product of the method of moments (MoM), it can be considered as the direct interaction between N current elements, such as Figure 2 As shown, compared to MoM, MLFMA reduces storage complexity from O(N²) to O(NlogN) and time complexity from O(N³) to O(NlogN), making it particularly suitable for accurately analyzing the radiation characteristics of phased array antenna elements.

[0055] The entire computational process of MLFMA is divided into two processes: uplink and downlink. The uplink process includes multi-level sub-expansion at the highest level and layer-by-layer aggregation from the child layer to the parent layer. When the process reaches the second level, each distant relative group performs transfer calculations. Then the downlink process begins, which includes multi-level configuration from the parent layer to the child layer, transfer calculations between distant relative groups at the same level, and finally, field expansion operation after reaching the highest level.

[0056] During the uplink process, MLFMA calculates the outward plane wave expansion function for all non-empty groups in layers l = 2, ..., L, where L represents the total number of layers in the MLFMA. After the uplink process is completed, MLFMA transitions to the downlink process, starting from the second layer and recursively obtaining the inward wave function for each of the remaining layers through translation and inverse interpolation operations until the highest layer is reached, thus completing the downlink process of MLFMA. The computation during the downlink process mainly involves calculating the inward wave expansion function. Through the above calculation strategy, the storage and computational complexity of MLFMA are greatly improved, enabling accurate analysis of the radiation characteristics in finely structured phased array antenna elements.

[0057] (2) Electromagnetic interference field analysis under the influence of complex platform structure

[0058] Due to the complex structure of the platform, the electromagnetic interference coupling propagation path of the co-located phased array antennas becomes complex and variable. Using Uniform Geometric Diffraction (UTD) theory for solution can fully consider the direct, reflection, and diffraction effects of the platform structure, improving the accuracy of the calculation. The main solution steps of this method are path tracing and field value tracing.

[0059] 1) Path tracing: First, based on the panoramic bounding box of the target or scene, determine the size of the virtual aperture surface of the incident plane wave; then, divide the virtual aperture surface and construct a two-dimensional matrix composed of ray tubes. To ensure calculation accuracy, the density of the tracing rays must be guaranteed. For example... Figure 3 As shown, taking a typical cavity structure as an example, a virtual aperture surface is constructed at a certain distance from the target, and it is divided to construct a ray tube matrix. Rays originate from the virtual aperture surface and enter the scene. Each ray is tracked, traversing all facets in the scene to determine the intersection points between the ray and the object, and the intersection information and path are saved. New reflected and diffracted rays are then generated, and they are continued to be tracked. If they intersect with the object, the intersection is calculated again; otherwise, the ray is discarded. This process is recursively repeated to track all rays, guiding them to leave the scene or until their energy decays to a certain threshold. This completes the path tracking of all rays.

[0060] 2) Field value tracing solution: Based on the path tracing algorithm, the direct path, reflection path and diffraction path of the phased array antenna transmitting antenna to the receiving antenna under the influence of the platform structure are obtained, and the electromagnetic interference coupling field at the receiving antenna is calculated.

[0061] ① For solving the electromagnetic interference coupled field tracing problem along a direct path, taking a single ray as an example, a single ray represents an astigmatic wave. According to the law of conservation of energy, when the source point is at point S and the field point is at point R, with a distance d between the two points, the magnitude of the field strength after the ray has traveled a path of length d can be derived as follows:

[0062]

[0063] In the above formula, E(R) is the electric field intensity at the field point R, E(S) is the electric field intensity at the source point S, the two principal radii of curvature of the incident wavefront are ρ1 and ρ2, and k is the propagation constant.

[0064] ② For solving the electromagnetic interference coupled field tracing problem along the reflection path, according to the principles of geometric optics, the reflecting plane and the incident plane lie in the same plane, and the reflection angle is equal to the incident angle. Based on the boundary condition of continuous tangential electric field on the metal surface, let W be the reflection point on the object surface, the source point be at point S, the field point be at point R, the two principal radii of curvature of the reflecting wavefront be ρ1 and ρ2, and d be the path length between the reflection point W and the field point R. Therefore, the reflected field at the field point R can be expressed as follows:

[0065]

[0066] Among them, E r (R) represents the reflected electric field intensity at point R, E i (S) represents the incident electric field intensity at the source point S, and k is the propagation constant. is the diatonic reflection coefficient.

[0067] ③ For the electromagnetic interference coupled field tracing solution of the diffraction path, the Uniform Diffraction Theory (UTD) is used to analyze the solution of the diffraction field. According to UTD theory, the diffraction field formula is:

[0068]

[0069] in, and Project D onto the diffraction field vector at the diffraction point in directions parallel to and perpendicular to the diffraction plane. / / and D ⊥ These are the diffraction coefficients parallel to and perpendicular to the diffraction plane, respectively. and Let A(s) be the projections of the incident field vector at the diffraction point onto the directions parallel to and perpendicular to the incident plane, respectively. Let A(s) be the spatial attenuation factor, and e be the projections of the incident field vector onto the directions parallel to and perpendicular to the incident plane. -jβs This represents the phase factor.

[0070] (3) Electromagnetic interference coupling vector synthesis based on phased array excitation

[0071] By solving the electromagnetic interference coupling field tracing problem, the electromagnetic interference coupling fields along the direct path, reflection path, and diffraction path of the phased array antenna transmitting antenna element to the receiving antenna can be obtained under the influence of the platform structure. Then, these path fields are vector synthesized to obtain the total electric field vector E of the phased array antenna transmitting antenna element at the receiving antenna. i_total Based on the antenna aperture of the receiving antenna, the received electromagnetic interference coupling energy P can be calculated. i for:

[0072]

[0073] Among them, E i_total Let G be the total electric field vector of the i-th element of the phased array antenna at the receiving antenna, and let G be the total electric field vector of the receiving antenna at the receiving antenna. i_total The antenna gain corresponding to the direction, η is the wave impedance constant, and λ is the wavelength corresponding to the calculated frequency.

[0074] Based on the above solution process, the electromagnetic interference coupling energy P of each phased array antenna transmitting antenna element to the receiving antenna can be obtained. i For a phased array antenna with N elements, the electromagnetic interference energy P coupled by the receiving antenna can be expressed by the following formula:

[0075]

[0076] Among them, P i φ represents the electromagnetic interference coupling energy between the i-th phased array antenna transmitting element and the receiving antenna; i Let be the phase of the transmitting antenna of the i-th phased array antenna.

[0077] (4) Case Study on Electromagnetic Interference Coupling Prediction for Co-located Phased Array Antennas

[0078] Following the steps outlined above, the electromagnetic interference coupling of a phased array antenna on a large platform is predicted. This phased array antenna has 2304 elements, selected as broadband printed symmetrical elements. The receiving antenna is also a broadband printed symmetrical element antenna. The platform's dimensions are 130m × 20m × 8m (length × width × height). The phased array antenna operates at 6GHz with a total radiated power of 1W. The antenna beam azimuth plane points towards the receiving antenna. The electromagnetic interference energy coupled to the receiving antenna is calculated when the elevation plane scans within the range of 0° to 60° (0° horizontally, with positive angles above the horizontal plane). Figure 4 A 3D model of a phased array antenna and a receiving antenna mounted on a large platform. Figure 5 This is the radiation pattern of the antenna elements in the phased array antenna transmitting array. Figure 6This represents the propagation paths of the direct, reflected, and diffracted fields from the transmitting array antenna of a phased array antenna to the receiving antenna. Figure 7 The curve shows the electromagnetic interference coupling energy between the phased array antenna and the receiving antenna as a function of the phased array antenna beam scanning.

[0079] It should be understood that those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

Claims

1. A method for predicting electromagnetic interference coupling in co-located phased array antennas based on subarray decomposition, characterized in that, The method for predicting co-located electromagnetic interference coupling between a phased array antenna and a receiving antenna on a platform structure includes the following steps: Step 1: Using the multi-level fast multipole method, calculations are performed in a multi-level grouping manner, including two processes: uplink and downlink. In the uplink process, the outward plane wave expansion function of the non-empty group in all layers is calculated. In the downlink process, starting from the second layer, the inward wave function of each of the remaining layers is obtained by recursively deriving through translation and inverse interpolation operations until the highest layer is reached, thus obtaining the radiation characteristic analysis results of the phased array antenna array elements. Step 2: Based on the analysis results of the radiation characteristics in the phased array antenna array elements, the uniform geometric diffraction theory is used to solve the problem and analyze the effects of the direct path, reflection path and diffraction path of the platform structure. The solution process includes path tracing and field value tracing to obtain the electromagnetic interference field analysis results under the influence of the complex structure of the platform, including the electromagnetic interference coupling field of the direct path, reflection path and diffraction path. Step 3: Perform vector synthesis of the electromagnetic interference coupling fields of the phased array antenna transmitting antenna element to the receiving antenna along the direct path, reflection path, and diffraction path to obtain the total electric field vector of the phased array antenna transmitting antenna element at the receiving antenna, and then calculate the electromagnetic interference energy coupled to the receiving antenna.

2. The method for predicting co-located electromagnetic interference coupling of phased array antennas based on subarray decomposition according to claim 1, characterized in that, The method in step 1 is specifically as follows: The computational process of the Multilevel Fast Multipole Method (MLFMA) is divided into two processes: up and down. The up process includes multi-level sub-expansion of the highest level and the layer-by-layer aggregation process from sub-layers to parent layers. When going up to the second level, each distant relative group is transferred and calculated. During the up process, the outward plane wave expansion function of all non-empty groups in all layers l = 2, ..., L is calculated, where L represents the total number of levels in MLFMA. Then the downlink process begins, which includes multi-level configuration from parent to child layers, transfer calculations between distant relatives in the same layer, and field unfolding operations after reaching the highest layer. Starting from the second layer, the inward wave function of each of the remaining layers is obtained by recursion through translation and inverse interpolation operations until the highest layer is reached, thus completing the downlink process of MLFMA; the operation in the downlink process is to calculate the expansion function of the inward wave.

3. The method for predicting co-located electromagnetic interference coupling of phased array antennas based on subarray decomposition according to claim 1, characterized in that, The path tracing method in step 2 is as follows: First, determine the size of the virtual aperture surface of the incident plane wave based on the panoramic bounding box of the target or scene; then, construct the virtual aperture surface at a certain distance from the target and divide it to construct the ray tube matrix. A ray originates from a virtual aperture surface and enters the scene. Each ray is tracked, traversing all surfaces in the scene to determine the intersection point between the ray and the object, and the intersection information and path are saved. Then, new reflected and diffracted rays are generated, and they are tracked again. If they intersect with an object, the intersection is calculated again; otherwise, the ray is discarded. This process is repeated to track all rays, guiding them to leave the scene or for their energy to decay to a certain threshold, thus completing the path tracking of all rays.

4. The method for predicting co-located electromagnetic interference coupling of phased array antennas based on subarray decomposition according to claim 1, characterized in that, The specific method for field tracking in step 2 is as follows: Based on the path tracing algorithm, the direct path, reflection path, and diffraction path of the phased array antenna from the transmitting antenna to the receiving antenna under the influence of the platform structure are obtained, and the electromagnetic interference coupling field at the receiving antenna is calculated.

5. The method for predicting co-located electromagnetic interference coupling of phased array antennas based on subarray decomposition according to claim 4, characterized in that, The specific method for solving the direct path is as follows: For solving the electromagnetic interference coupled field tracing problem along a direct path, a single ray represents an astigmatic wave. According to the law of conservation of energy, when the source point is at point S and the field point is at point R, with a distance d between the two points, the magnitude of the field strength after the ray travels a path of length d is: Where E(R) is the electric field intensity at field point R, E(S) is the electric field intensity at source point S, the two principal radii of curvature of the incident wavefront are ρ1 and ρ2, k is the propagation constant, and e -jkd This represents the phase factor.

6. The method for predicting co-located electromagnetic interference coupling of phased array antennas based on subarray decomposition according to claim 4, characterized in that, The specific method for solving the reflection path is as follows: For solving the electromagnetic interference coupled field tracing problem along the reflection path, according to the principles of geometric optics, the reflecting plane and the incident plane lie in the same plane, and the reflection angle is equal to the incident angle. Based on the boundary condition of continuous tangential electric field on the metal surface, let W be the reflection point on the object surface, the source point be at point S, the field point be at point R, the two principal radii of curvature of the reflecting wavefront be ρ1 and ρ2, and d be the path length between the reflection point W and the field point R. The reflected field at the field point R can be expressed in the following form: Among them, E r (R) represents the reflected electric field intensity at point R, E i (S) represents the incident electric field intensity at the source point S, and k is the propagation constant. is the diatonic reflection coefficient.

7. The method for predicting co-located electromagnetic interference coupling of phased array antennas based on subarray decomposition according to claim 4, characterized in that, The specific method for solving the diffraction path is as follows: For solving the electromagnetic interference coupled field tracing along the diffraction path, the Uniform Diffraction Theory (UTD) is used to analyze the diffraction field. According to the UTD theory, the diffraction field formula is: in, and Project D onto the diffraction field vector at the diffraction point in directions parallel to and perpendicular to the diffraction plane. / / and D ⊥ These are the diffraction coefficients parallel to and perpendicular to the diffraction plane, respectively. and Let A(s) be the projections of the incident field vector at the diffraction point onto the directions parallel to and perpendicular to the incident plane, respectively. Let A(s) be the spatial attenuation factor, and e be the projections of the incident field vector onto the directions parallel to and perpendicular to the incident plane. -jβs This represents the phase factor.

8. The method for predicting co-located electromagnetic interference coupling of phased array antennas based on subarray decomposition according to claim 1, characterized in that, The method for calculating the electromagnetic interference energy coupled by the receiving antenna in step 3 is as follows: By solving the electromagnetic interference coupled field tracing problem, the electromagnetic interference coupled fields of the phased array antenna transmitting antenna element to the receiving antenna along the direct path, reflection path, and diffraction path under the influence of the platform structure are obtained. Then, these path fields are vector synthesized to obtain the total electric field vector E of the phased array antenna transmitting antenna element at the receiving antenna. i_total ; Calculate the received electromagnetic interference coupling energy P based on the antenna aperture of the receiving antenna. i for: Among them, E i_total Let G be the total electric field vector of the i-th element of the phased array antenna at the receiving antenna, and let G be the total electric field vector of the receiving antenna at the receiving antenna. i_total The antenna gain corresponding to the direction, η is the wave impedance constant, and λ is the wavelength corresponding to the calculated frequency; For a phased array antenna with N elements, the electromagnetic interference energy P coupled to the receiving antenna is expressed by the following formula: Among them, P i Let be the electromagnetic interference coupling energy of the i-th phased array antenna transmitting element to the receiving antenna; Let be the phase of the transmitting antenna of the i-th phased array antenna.

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