Common-caliber electromagnetic window aperiodic decoupling metasurface design method based on non-uniform Green function

Abstract

The invention discloses a common-caliber electromagnetic window aperiodic decoupling metasurface design method based on a non-uniform Green function, which is used for improving the electromagnetic radiation capability of a system and accelerating the design of a decoupling metasurface. The method is divided into an offline storage part and an online optimization part, through an offline accelerated storage method, a non-uniform Green function and other offline data which can truly reflect electromagnetic wave propagation of a common-caliber electromagnetic window system are obtained, and rapid gain solving of the whole electromagnetic window is achieved; and through an online optimization method, rapid optimization of the gain directional diagrams of different frequencies is realized. According to the method, the aperiodic metasurface with high degree of freedom is introduced into the decoupling design in the common-caliber electromagnetic window and radiation system for the first time, and the non-uniform Green function is introduced, so that the efficiency and high reliability of the electromagnetic window level optimization of the base station are improved. The cost of the forward model in high-degree-of-freedom decoupling metasurface iterative optimization can be effectively reduced, the computing resource demand and the time cost are remarkably reduced, and the optimization efficiency is improved.

Description

Technical Field

[0001] The present invention belongs to the field of radio frequency system design, and relates to a non-uniform metasurface method in a portable complex system, and specifically to a co-aperture electromagnetic window non-periodic decoupling metasurface design method based on a non-uniform Green's function. Background Art

[0002] In mobile communication systems, as the integration density and operating frequency of transmitting and receiving antennas increase, electromagnetic coupling between antenna radiating elements increases. Metasurface-based antenna decoupling technology is a viable solution. Due to the large overall size of the co-aperture antenna-decoupling metasurface system and the subwavelength features of many metal patterns, full-wave electromagnetic simulation can be extremely time-consuming and memory-intensive, not to mention traditional metasurface structure optimization based on full-wave electromagnetic simulation.

[0003] Furthermore, aperiodic decoupled metasurfaces break the limitations of traditional periodic designs. By loading different units into the metasurface array, they achieve the integration of performance across multiple control domains and frequency bands based on multifunctional mixing and optimization strategies. Due to their high degree of design and control freedom, aperiodic metasurface structures have important application value in the design of antenna base stations that require broadband, wide-angle, and multifunctional applications.

[0004] Based on electromagnetic principles, researchers have established proxy models for various forward design processes. The relationship between aperiodic metasurfaces and observation surfaces can be established using methods such as the Huygens-Fresnel principle. However, these forward models are based on the free-space assumption. In actual base station antennas, the densely packed interiors of various conductor and dielectric transceiver components create complex electromagnetic wave propagation processes, making it difficult to accurately describe the far-field electromagnetic radiation system. Summary of the Invention

[0005] In view of the defects in the prior art, the purpose of the present invention is to provide a method for designing a non-periodic decoupling metasurface of a common-aperture electromagnetic window based on non-uniform Green's function, so as to realize the rapid solution of the antenna radiation source gain of the common-aperture electromagnetic window and the optimal design of the non-periodic decoupling metasurface.

[0006] The technical solution adopted in the present invention is as follows:

[0007] A design method for a co-aperture electromagnetic window non-periodic decoupling metasurface based on non-uniform Green's function is used to efficiently and confidently optimize the gain of the electromagnetic window under the decoupling metasurface, including an offline storage process and an online optimization process.

[0008] The offline process includes the parallel calculation and storage of data such as the unit response function, incident field, and non-uniform Green's function, which together constitute the forward solver; the online process is an iterative optimization process that includes the verification of the forward solver, which is implemented using the conjugate gradient optimization method.

[0009] The principle of the forward solver is to divide the system using a spatial partitioning strategy to simplify the original problem. Specifically, the following steps are included:

[0010] Step 1: Use the antenna decoupling metasurface to segment the areas where antenna arrays of different frequency bands in the base station system are located to reduce the coupling between different frequency bands.

[0011] Step 2: Add an equivalent source plane in the near-field region of the decoupling metasurface to divide the common-aperture electromagnetic window into an inner region and a far-field region.

[0012] Step 3: Under the excitation of the antenna array, based on the unit response function and incident field stored in the offline process, the initial incident field is used as the unit's real incident field to solve the near-field equivalent source of the decoupled metasurface unit according to the Born approximation;

[0013] Step 4: Based on the equivalent principle and the non-uniform background Green's function stored in the offline process, the far field of the antenna array system is calculated according to the solved near-field equivalent source, that is,

[0014]

[0015] in, represents the incident field stored offline, represents the non-uniform Green's function from the equivalent source corresponding to the i-th unit to the observation point. Both are related to the background and there is no analytical solution. R(s i ) represents the unit response function, and β represents the normalization parameter.

[0016] Step 5: Calculate the far-field gain based on the far-field of the antenna array, that is,

[0017]

[0018] Among them, P a is the effective power of the antenna (array), U is the received radiation intensity in the specified direction, |E| is the amplitude of the far-field radiation field, η0 = 376.7Ω; R is the distance from the observation position to the antenna (array).

[0019] Based on the above, a parallel offline process is needed to store each element in the forward solver, including:

[0020] (1) Discretely sample the structural parameters of the designed decoupling unit and perform full-wave electromagnetic simulation of the unit structure using numerical simulation methods under the assumption of local periodicity and unit incident field. Then, organize the simulation results and use analytical expressions for fitting to obtain the unit response function, that is, the response of the unit under unit incident field;

[0021] (2) Under different electromagnetic radiation (antenna array) excitations, the field at the decoupling metasurface position is solved. Considering the near-field effect of the transmitting antenna, it is necessary to add actual radiation (antenna) excitation in the numerical calculation;

[0022] (3) For the Green's function under non-uniform conditions, the Rayleigh-Casson reciprocity theorem is applied to calculate the field generated by a point source in the far field on the near-field equivalent source plane through simulation software; when running the electromagnetic solver based on FEM or MoM, the LU decomposition preprocessing technology is used. During the first numerical calculation, the LU decomposition result is stored and loaded in subsequent calculations, which greatly reduces the calculation time at the expense of storage memory;

[0023] (4) A full-wave calculation is performed, in which a periodic metasurface of the initial unit is placed at the decoupling metasurface, and the obtained true far field is compared with the value calculated by the forward solver to obtain the normalized parameters.

[0024] Furthermore, during the online optimization process, the vertical beam gain of the antenna at each frequency point is maximized while the effective power of the radiation source array remains unchanged.

[0025] Furthermore, the online optimization is divided into ideal equivalent source distribution optimization and structural parameter optimization, both of which use the conjugate gradient descent method. Two unit structures are used: one is a unit structure with a metal pattern, and the other is a pure metal structure. The optimization steps are as follows:

[0026] In the first step, the objective function is first determined. Assuming that the amplitude of the equivalent source in each unit is consistent and continuously adjustable, and the phase difference of the equivalent source is constant, the conjugate gradient algorithm is used to optimize the ideal equivalent source amplitude and phase distribution.

[0027] Step 2: Determine the type and spatial distribution of decoupling units based on the ideal amplitude distribution;

[0028] In the third step, the conjugate gradient algorithm is used to optimize the metasurface structure parameters, output the results and conduct experimental verification.

[0029] Furthermore, the online optimization specifically includes:

[0030] First, define the initial design and obtain the far-field gain through the forward solver to further evaluate the objective function. Second, calculate the gradient of the far-field gain with respect to the structure and use it to obtain the adjoint gradient of the objective function. Furthermore, the conjugate gradient method is used to optimize the structural parameters: First, the optimization direction is determined according to the accompanying gradient of the objective function. Secondly, according to the optimization direction, determine the optimal optimization step size α k ; Finally, the parameters are updated, so k=k+1, simulate the updated structural design and evaluate the objective function, repeat the above steps until the indicators are met and obtain the final design And perform simulation verification.

[0031] The beneficial effects of the present invention are:

[0032] The present invention uses an offline accelerated storage method to obtain non-uniform Green's functions and other offline data that can truly reflect the propagation of electromagnetic waves in a co-aperture electromagnetic window system, thereby achieving rapid solution of the overall gain of the electromagnetic window. Through an online optimization method, rapid optimization of gain patterns at different frequencies is achieved. For the first time, the present invention introduces a non-periodic metasurface with a high degree of freedom into the decoupling design of a co-aperture electromagnetic window and radiation system, and introduces non-uniform Green's functions, thereby improving the efficiency and reliability of base station electromagnetic window-level optimization. This can effectively reduce the cost of the forward model in the iterative optimization of high-degree-of-freedom decoupling metasurfaces, significantly reducing computing resource requirements and time costs, and improving optimization efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is the specific process of the design method of the common-aperture electromagnetic window non-periodic decoupling metasurface described in the present invention;

[0034] Figure 2 3D schematic diagram of a common aperture electromagnetic window according to an example of the present invention;

[0035] Figure 3 is the gain pattern of the antenna at direct common aperture at f = 1.7 GHz;

[0036] Figure 4 yes Figure 2 Schematic diagram of a co-aperture electromagnetic radiation source (antenna);

[0037] Figure 5 It is an equivalent source plane region division based on the method of the present invention;

[0038] Figure 6 is the initial structure of the decoupling unit and its S-parameters;

[0039] Figure 7 This is a comparison of the simulation gain and forward acceleration algorithm results when the radiation source array antenna array is tilted for radiation. The left side is 0.825 GHz and the right side is 2.2 GHz.

[0040] Figure 8is the optimized ideal amplitude distribution of the equivalent source;

[0041] Figure 9 It is the optimization result of the aperiodic decoupled metasurface containing metal units and metasurface units;

[0042] Figure 10 is the gain comparison between the designed metasurface and the initial uniform metasurface at f = 0.825 GHz;

[0043] Figure 11 is the gain comparison between the designed metasurface and the initial uniform metasurface at f = 2.2 GHz;

[0044] Figure 12 is the gain comparison between the designed metasurface and the initial uniform metasurface at f = 1.7 GHz;

[0045] Figure 13 is the initial structure of the example non-periodic metasurface unit and its S-parameters;

[0046] Figure 14 It is an optimized and processed non-periodic metasurface structure;

[0047] Figure 15 This is the test performance of the designed non-periodic metasurface at f = 10 GHz. DETAILED DESCRIPTION

[0048] The technical solution of the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0049] In order to deal with the design problem of decoupling metasurface under base station antenna, Figure 1 This is the detailed process for the design method of the common-aperture electromagnetic window aperiodic decoupling metasurface described in this invention. It includes an offline storage process and an online optimization process. The offline process involves the parallel calculation and storage of data such as the unit response function, incident field, and non-uniform Green's function, which together constitute the forward solver. The online process is an iterative optimization process that includes forward solver verification and is implemented using the conjugate gradient optimization method.

[0050] Figure 2A three-dimensional schematic diagram of a common-aperture electromagnetic window is given as an example. It consists of two groups of antenna arrays with different frequency bands and both apertures facing upward. Among them, the relatively large electromagnetic radiation source (antenna array) is located above and is a 0.69-0.96GHz low-frequency antenna array. The relatively small antenna array is a 1.7-2.7GHz high-frequency antenna array. To reduce losses and ensure the quality of high-frequency signals, its ground wire is connected to the metal floor below. By adjusting the excitation phase and amplitude of different radiation sources in the antenna array, the gain beam can be deflected. In this system, different operating frequency bands are isolated by non-periodic metasurfaces, and the metasurface is closer to the low-frequency radiation source. When the upper radiation source is excited, the metasurface exhibits reflective characteristics, acting as its floor and enhancing the directionality of the radiation source; when the lower radiation source is excited, the metasurface is transparent to the high-frequency signal, reducing losses.

[0051] Let the distance between the radiation source array elements be dx1 = dy1 = 250mm, dx2 = 120mm, dy2 = 75mm, and the vertical distance between the high-frequency radiation source (antenna) floor and the low-frequency radiation source (antenna) bottom be dz1 = 120mm. When the antennas are directly co-apertured, that is, when there is no decoupling metasurface, the radiation source simulated gain pattern at f = 1.7GHz is as follows Figure 3 As shown, a clear depression appears. Therefore, without changing the structure and arrangement of the radiation source array, the radiation source pattern is improved by optimizing the metasurface. The distance dz2 between the metasurface and the bottom of the low-frequency radiation source array is set to 5 mm, the metasurface thickness is 1 mm, and the overall size is 300 mm × 300 mm.

[0052] The forward process is divided into the following steps:

[0053] (1) In the first step, the radiation source decoupling metasurface is used to divide the area where the radiation source arrays of different frequency bands in the base station system are located to reduce the coupling between different frequency bands: Figure 5 As shown in the figure, when a low-frequency radiation source radiates, part of the energy radiates upward, considered the original radiation field, while the other part of the energy radiates upward after being scattered by the metasurface, considered the scattered field. In this case, the total radiation field of the radiation source is the sum of the original radiation field and the scattered field. When a high-frequency radiation source radiates, assuming the metasurface is large enough to cover the high-frequency radiation source, the original radiation field all passes through the metasurface, forming the total radiation field.

[0054] (2) In the second step, an equivalent source plane is added to the near-field region of the decoupling metasurface to divide the common aperture electromagnetic window into an inner region and a far-field region: Figure 6 , an equivalent source plane is added between the decoupling metasurface and the low-frequency radiation source array, i.e., the near-field region of the decoupling metasurface. The problem is equivalent to the case where the equivalent source on the plane radiates upward. The upper half of the equivalent source plane is defined as the far-field region, and the lower half is Figure 6 The hidden area is the interior area.

[0055] (3) Step 3: Under the excitation of the radiation source array, based on the unit response function and incident field stored in the offline process, according to the Born approximation, the initial incident field is used as the unit's real incident field to solve the near-field equivalent source of the decoupled metasurface unit;

[0056] (4) Step 4: Based on the equivalent principle and the non-uniform background Green's function stored in the offline process, the electromagnetic window and the far field of the radiation source array system are calculated according to the solved near-field equivalent source;

[0057] (5) In step 5, the far-field gain is calculated based on the far-field of the radiation source array.

[0058] Among them, during the offline storage process of steps 3 and 4:

[0059] (1) When there are only low-frequency radiation sources in space, the Green's function is stored. In particular, the equivalent source plane is sampled at a spacing of 5mm, with a total of 3600 near-field points. For the far-field beam, on a spherical surface with a radius of 2m, an azimuth scan from -60 degrees to 60 degrees is performed at intervals of 15 degrees, and an elevation scan from -15 degrees to 15 degrees is performed at intervals of 1 degree, with a total of 279 far-field points. The field generated by the point source in the far field on the equivalent source is calculated by simulation software, that is, the Green's function. For a far-field point, a point source of unit intensity (1A*m) is set in the x, y, and z directions at the far-field point, and the field value of the near-field point is calculated.

[0060] (2) Regarding the storage of the incident field, the low-frequency incident field is the field generated by the radiation source on the upper surface of the metasurface when the space only contains the upper radiation source. The high-frequency incident field is the field generated by the radiation source on the lower surface of the metasurface when the space only contains the high-frequency radiation source and its floor.

[0061] (3) For the unit response, full-wave electromagnetic simulation can be performed on the decoupled unit structure using numerical simulation under the assumption of local periodicity. Then, after sorting the simulation results, the analytical expression is used for fitting. When considering the low-frequency case, the normalized plane wave is incident on the structural unit, and the average scattered electric field of FSS in the x / y / z direction at z=z0 is calculated. At high frequencies, the total field is averaged below the FSS element at z = -z0. Finally, the response function is fitted in the form of a polynomial using the sampled structural parameters as input.

[0062] Select the appropriate decoupling unit for step 5 to verify the forward algorithm: Figure 6is the initial structure of the decoupling unit and its S-parameters; the structural parameters are defined as: P = 20mm, l1 = 14mm, l2 = 10mm, l3 = 6mm, l4 = 10mm, l5 = 7.35mm, w1 = 2.5mm, w2 = 0.5mm, w3 = 0.7mm, w4 = 0.3mm, g1=3.5mm. Change the phase and amplitude of the radiation source excitation to achieve tilted beam and verify the forward algorithm. For the sake of convenience, the three-dimensional gain map with elevation angles from -15° to 15° is sliced at different azimuth angles. Figure 7 As shown in Figure 2, the simulation gain and forward acceleration algorithm results at the low-frequency and high-frequency center frequencies (0.825 GHz and 2.2 GHz) are in good agreement.

[0063] During the online optimization process, the vertical beam gain of the antenna at each frequency point is the maximum radiation field energy in the vertical direction under the condition that the effective power of the radiation source array remains unchanged. In order to improve the control diversity, two unit structures are adopted. One is Figure 6 The decoupled metasurface unit structure is divided into two parts: ideal equivalent source distribution optimization and structural parameter optimization, both of which use the conjugate gradient descent method:

[0064] First, define the initial design and obtain the far-field gain through the forward model to further evaluate the objective function. Secondly, calculate the gradient of the far-field gain with respect to the structure and use it to obtain the accompanying gradient of the objective function. Furthermore, the conjugate gradient method is used to optimize the structural parameters: First, the optimization direction is determined according to the accompanying gradient of the objective function. Secondly, according to the optimization direction, determine the optimal optimization step size α k ; Finally, the parameters are updated, so k=k+1. Simulate the updated structural design and evaluate the objective function, repeat the above steps until the indicators are met and obtain the final design And perform simulation verification.

[0065] According to a specific embodiment of the present invention, the specific optimization steps are:

[0066] (1) In the first step, in the optimization of the ideal equivalent source distribution, Figure 6 The phase and amplitude of the unit response shown in the figure vary smoothly within a small range. Assuming that the amplitude of the unit equivalent source at each high frequency point is consistent and continuously adjustable, and the phase difference of the equivalent source is constant, the near-field equivalent source of the unit at different frequencies is:

[0067]

[0068] Among them, x1 represents the uniform amplitude of the high-frequency equivalent source, ranging from [0,1], x2 represents the phase of the unit equivalent source when f = 1.7 GHz, ranging from [0,π], Δθ represents the phase difference, E in Represents the incident field at each frequency point. The conjugate gradient algorithm is used to optimize the distribution of x1 and x2 in the metasurface, and the values of x1 less than 0.5 are set to 0, and those greater than or equal to 0.5 are set to 1. The results are as follows: Figure 8 shown.

[0069] (2) The second step is to determine the type and spatial distribution of the decoupling unit according to the ideal amplitude distribution. Figure 8 The "0" unit in the figure is a pure metal unit, and the "1" unit is a metasurface unit. The l2 and l5 parameters in each metasurface unit are independently adjustable. To prevent the metal wires within the unit from contacting each other and changing their electromagnetic properties, l4 = 0.8 * l2 and l5 = ra1 * l4 - 0.5 mm. The adjustable range of l2 is [5, 15.5], and the adjustable range of ra1 is [0.7, 0.9]. Therefore, the relationship between the equivalent source and the structural parameters in the unit can be expressed as:

[0070]

[0071] Among them, E in,f represents the incident field at the corresponding frequency f, R 金属,f represents the scattered field response of the metal unit at the corresponding frequency, R f (l2,ra1) represents the response function of the decoupling unit at the corresponding frequency.

[0072] (3) The third step is to use the conjugate gradient algorithm to optimize the metasurface structure parameters, output the results and conduct experimental verification. Figure 9 is the optimization result of the non-periodic decoupled metasurface containing metal units and metasurface units. The optimization results are simulated and verified, such as Figure 10 and Figure 11 As shown in the figure, the gain comparison of the initial uniform structure and the designed metasurface at the low-frequency and high-frequency center frequency points when the azimuth angle is 0° is given; at f = 0.825GHz, the maximum gain of the design result is about 13.6dB, which is 0.74dB higher than the initial structure. At f = 2.2GHz, the maximum gain of the design result is about 14.6dB, which is 0.70dB higher than the initial structure and 1.33dB higher than the direct common aperture case, that is, when there is no metasurface. In particular, considering the optimization of the radiation source array gain at f = 1.7GHz, as shown in the figure, Figure 12As shown, the design achieves a maximum gain of approximately 10.54 dB, a 2.95 dB improvement over the initial structure's maximum gain of 7.6 dB. This improvement is 8.24 dB higher than the 2.31 dB vertical gain of the direct co-aperture approach, achieving a transition from a concave beam to normal, vertical upward radiation. The following table shows the time and memory consumption for the offline and online optimization processes, respectively.

[0073] In summary, Figure 6 There are two optimizable variables in the structural unit of Figure 8 and Figure 9 The non-periodic decoupled metasurface shown has 30*30=900 independent optimization units, so the total number of optimizable variables is 900-1800.

[0074] The above describes the specific embodiments of the present invention. It should be understood that the present invention is not limited to the above-mentioned specific embodiments, and those skilled in the art can make various changes or modifications within the scope of the claims, such as the co-aperture electromagnetic window scenario (such as the number and arrangement of antennas), unit structure, array size, number of optimizable variables and specific performance requirements in the specific embodiments, which do not affect the essence of the present invention. In the absence of conflict, the embodiments of this application and the features in the embodiments can be arbitrarily combined with each other. For example, through the above invention, it is achieved as follows Figure 13 The non-periodic metasurface unit shown is designed and processed as follows Figure 14 The structure shown has an array size of 25*25 and the number of independently optimizable variables is 625. The optimization target is its scattering performance. The performance achieved is as follows Figure 15 The above hardware achieves the following: operating frequency bands include at least three bands among the L-band, S-band, C-band, X-band, and Ku-band; co-polarization wave transmission band -3dB bandwidth ≥ ±10%; wave absorption -10dB bandwidth ≥ ±30%; and scattering angle deviation ≥ 30°.

[0075]

Claims

1. A method for designing a co-aperture electromagnetic window aperiodic decoupling metasurface based on non-uniform Green's function, characterized by: It includes an offline storage process and an online optimization process; the offline process includes parallel calculation and storage of unit response function, incident field, and non-uniform Green's function data, which together constitute the forward solver; the online process is an iterative optimization process that includes forward solver verification, which is implemented using the conjugate gradient optimization method.

2. The method for designing a co-aperture electromagnetic window aperiodic decoupling metasurface based on non-uniform Green's function according to claim 1 is characterized in that: The forward solver uses a space partitioning strategy to partition the system, which specifically includes the following steps: Step 1: Use the electromagnetic radiation system decoupling metasurface to divide the areas where antenna radiation sources of different frequency bands are located in the radiation system to reduce the coupling between different frequency bands. Step 2: Add an equivalent source plane in the near-field region of the decoupling metasurface to divide the common-aperture electromagnetic window into an inner region and a far-field region. Step 3: Under the excitation of the antenna array, based on the unit response function and incident field stored in the offline process, the initial incident field is used as the unit's real incident field to solve the near-field equivalent source of the decoupled metasurface unit according to the Born approximation; Step 4: Based on the equivalent principle and the non-uniform background Green's function stored in the offline process, the far field of the antenna array system is calculated according to the solved near-field equivalent source; Step 5: Calculate the far-field gain based on the far-field of the antenna array system.

3. The method for designing a co-aperture electromagnetic window aperiodic decoupling metasurface based on non-uniform Green's function according to claim 2 is characterized in that: The far field of the antenna array system in step 4 is: in, represents the incident field stored offline, represents the non-uniform Green's function from the equivalent source corresponding to the i-th unit to the observation point. Both are related to the background and there is no analytical solution. R(s i ) represents the unit response function, β represents the normalization parameter, and M is the number of radiation source array elements.

4. The method for designing a co-aperture electromagnetic window aperiodic decoupling metasurface based on non-uniform Green's function according to claim 2, characterized in that: The far-field gain in step 5 is: Among them, P a is the effective power of the antenna array, U is the received radiation intensity in the specified direction, and |E| is the far-field radiation field The amplitude of η0 is 376.7Ω; R is the distance between the observation position and the antenna array.

5. The method for designing a co-aperture electromagnetic window aperiodic decoupling metasurface based on non-uniform Green's function according to claim 1 is characterized in that: Parallel calculation and storage of unit response functions, incident fields, and non-uniform Green's functions, including the following: (1) Discrete sampling of the structural parameters of the designed decoupling unit is performed. Under the assumption of local periodicity and unit incident field, full-wave electromagnetic simulation of the unit structure is performed using numerical simulation methods. Then, the simulation results are sorted and fitted using analytical expressions to obtain the unit response function, that is, the response of the unit under unit incident field. (2) Under different antenna array excitations, the field at the decoupling metasurface position is solved, considering the near-field effect of the transmitting antenna and adding additional actual antennas for excitation in the numerical calculation; (3) For the Green's function under non-uniform conditions, the Rayleigh-Casson reciprocity theorem is applied to calculate the field generated by a point source in the far field on the near-field equivalent source plane through simulation software; when running the electromagnetic solver based on FEM or MoM, the LU decomposition preprocessing technology is used. During the first numerical calculation, the LU decomposition result is stored and loaded in the subsequent calculation; (4) A full-wave calculation is performed, in which a periodic structure of the initial unit is placed at the decoupling metasurface, and the obtained true far field is compared with the value calculated by the forward solver to obtain the normalized parameters.

6. The method for designing a co-aperture electromagnetic window aperiodic decoupling metasurface based on non-uniform Green's function according to claim 1, characterized in that: During the online optimization process, the vertical beam gain of the antenna at each frequency point is optimized to maximize the radiation field energy in the vertical direction while keeping the effective power of the radiation source array unchanged.

7. The method for designing a co-aperture electromagnetic window aperiodic decoupling metasurface based on non-uniform Green's function according to claim 1 is characterized in that: The online optimization is divided into ideal equivalent source distribution optimization and structural parameter optimization, both of which use the conjugate gradient descent method. Two unit structures are used: one with a metal pattern and the other with a pure metal structure. The optimization steps are as follows: In the first step, the objective function is first determined. Assuming that the amplitude of the equivalent source in each unit is consistent and continuously adjustable, and the phase difference of the equivalent source is constant, the conjugate gradient algorithm is used to optimize the ideal equivalent source amplitude and phase distribution. Step 2: Determine the type and spatial distribution of decoupling units based on the ideal amplitude distribution; In the third step, the conjugate gradient algorithm is used to optimize the metasurface structure parameters, output the results and conduct experimental verification.

8. The method for designing a co-aperture electromagnetic window aperiodic decoupling metasurface based on non-uniform Green's function according to claim 7 is characterized in that: The online optimization specifically includes: First, define the initial design and obtain the far-field gain through the forward solver to further evaluate the objective function. Second, calculate the gradient of the far-field gain with respect to the structure and use it to obtain the adjoint gradient of the objective function. Furthermore, the conjugate gradient method is used to optimize the structural parameters: First, the optimization direction is determined according to the accompanying gradient of the objective function. Afterwards, the optimal optimization step length α is determined according to the optimization direction k ; Finally, the parameters are updated, so k=k+1, simulate the updated structural design and evaluate the objective function, repeat the above steps until the indicators are met and obtain the final design

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