Method and apparatus for determining subarray size of reconfigurable intelligent metasurface combined array

Abstract

The application relates to a subarray size determination method of a reconfigurable intelligent metasurface combined array, and solves the subarray division problem of a large array under a deformation condition. The method comprises the following steps: determining the total size of the array and a beam control target, establishing a deformation geometric model; calculating an ideal phase distribution under a flat state; combining the deformation model and the ideal phase to calculate the beam amplitude of different size subarrays; calculating the total beam amplitude of each division scheme based on the beam superposition principle; finally, selecting a scheme with a total beam amplitude higher than a performance threshold and a subarray number lower than a complexity threshold. The application also contains a device corresponding to the method. The application quantifies the phase error caused by deformation, quickly predicts the radiation performance under different divisions, and provides an efficient design means for the engineering application of a large metasurface array.

Description

Technical Field

[0001] This application relates to the field of intelligent manufacturing technology, and in particular to a method and apparatus for determining the subarray size of a reconfigurable intelligent metasurface combined array. Background Technology

[0002] Reconfigurable smart metasurfaces (RIS) are a key technology in next-generation wireless communication, often requiring increased physical size to improve coverage and controllability. However, due to limitations in current PCB manufacturing processes, large-area RIS typically require the assembly of multiple smaller subarrays.

[0003] However, the design of this large combined array faces two major technical challenges:

[0004] First, deformation (such as bending and warping) is inevitable during the fabrication and installation of the subarray. According to the generalized Snell's law, this deformation introduces an additional phase difference, leading to a significant degradation in its electromagnetic beam control performance (such as the beam amplitude in the target direction). Currently, there is a lack of methods for scientifically determining the optimal size of the subarray to balance the effects of deformation and fabrication complexity under known deformation conditions.

[0005] Secondly, the radiation performance evaluation of large-scale combined arrays is highly dependent on full-wave electromagnetic simulation software such as CST. However, its computational complexity increases exponentially with scale, resulting in extremely low efficiency and making it difficult to quickly and cost-effectively predict and iteratively optimize the performance of various subarray partitioning schemes.

[0006] Currently, although some studies have proposed wavefront control theories for curved metasurfaces to actively design phases on curved surfaces to achieve beam modulation, these studies have not further solved the core problem of this application: that is, systematically analyzing how "deformation" destroys the performance of the "original planar design", nor have they provided a rapid prediction method to solve the performance degradation and design optimization problems of large combined arrays under deformation conditions. Summary of the Invention

[0007] This application proposes a method and apparatus for determining the subarray size of a reconfigurable smart metasurface composite array, which solves the problem that existing technologies cannot quickly and accurately determine the optimal subarray size under the premise of deformation in large-size reconfigurable smart metasurface composite arrays.

[0008] In a first aspect, embodiments of this application provide a method for determining the subarray size of a reconfigurable smart metasurface combined array, comprising the following steps:

[0009] The overall size and beam control target of the combined array are determined, and a geometric model of the pre-deformed combined array is established; the beam control target includes the incident wave direction and the desired outgoing wave direction;

[0010] Calculate the ideal phase distribution of the combined array under flat conditions based on the beam control target;

[0011] The beam amplitude of subarrays of different sizes in the desired output wave direction is calculated based on the geometric model and ideal phase distribution.

[0012] Calculate the total beam amplitude in the direction of the desired emitted wave for different subarray sizes;

[0013] Determine a scheme where the total beam amplitude is higher than a preset performance threshold and the number of subarrays is lower than a preset complexity threshold.

[0014] In one embodiment, the method for establishing the geometric model includes:

[0015] The deformation type and degree are determined based on one or more of the following: the shape of the support structure of the combined array, the coefficient of thermal expansion of the material, or the processing and assembly parameters.

[0016] In one embodiment, when calculating the beam amplitude, the additional phase delay caused by the vertical distance between the metasurface unit and the reference plane is taken into account.

[0017] In one embodiment, the preset performance threshold is a relative value determined based on the total beam amplitude of the combined array in the desired output wave direction under flat conditions.

[0018] In one embodiment, the preset complexity threshold is determined based on the maximum number of assembleable subarrays of the combined array or the minimum processable size of the subarray.

[0019] In one embodiment, the total beam amplitude is calculated by multiplying the number of subarrays by the beam amplitude of a single deformable subarray.

[0020] In one embodiment, the subarray size is selected with the optimization objective of maximizing the total beam amplitude and minimizing the number of subarrays.

[0021] Secondly, embodiments of this application also provide a subarray size determination device for a reconfigurable smart metasurface combined array, used to implement the subarray size determination method for a reconfigurable smart metasurface combined array as described in any embodiment of the first aspect, comprising: an acquisition module, used to acquire the total size and beam control target of the combined array, and establish a geometric model of the combined array with a preset deformation; the beam control target includes an incident wave direction and a desired outgoing wave direction. A calculation module, used to calculate the ideal phase distribution of the combined array in a flat state according to the beam control target; also used to calculate the beam amplitude of subarrays of different sizes in the desired outgoing wave direction according to the geometric model and the ideal phase distribution; also used to calculate the total beam amplitude of subarrays of different sizes in the desired outgoing wave direction. A determination module, used to determine schemes where the total beam amplitude is higher than a preset performance threshold and the number of subarrays is lower than a preset complexity threshold.

[0022] Thirdly, embodiments of this application also provide a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method described in any one of the embodiments of the first aspect.

[0023] Fourthly, embodiments of this application also provide an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method as described in any embodiment of the first aspect.

[0024] The above-described technical solutions adopted in the embodiments of this application can achieve the following beneficial effects:

[0025] This application systematically solves for the first time the problem of scientifically determining the optimal size of the subarray under the premise of knowing the processing deformation. By establishing a deformation geometric model and quantifying the phase error caused by it, the far-field radiation performance under different subarray partitioning schemes can be predicted quickly and accurately. Thus, while ensuring beam modulation performance and suppressing gain attenuation caused by deformation, it effectively reduces the processing and assembly complexity caused by excessively large or small subarray size, providing an efficient and low-cost digital design tool for the engineering application of large metasurface arrays. Attached Figure Description

[0026] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings:

[0027] Figure 1 A flowchart illustrating a method for determining the subarray size of a reconfigurable smart metasurface combined array, as provided in an embodiment of this application;

[0028] Figure 2-1This is a schematic diagram of the structure of the spherical array, conformal sphere, and reference plane provided in the embodiments of this application;

[0029] Figure 2-2 This is a schematic diagram of the simulation array model provided in the embodiments of this application;

[0030] Figure 2-3 This is a diagram of the metasurface structure of Unit "1" in Embodiment "1" of this application;

[0031] Figure 2-4 This is a diagram of the metasurface structure of unit "0" in an embodiment of this application;

[0032] Figure 2-5 This is a reflection amplitude diagram of the metasurface unit in an embodiment of this application;

[0033] Figure 2-6 This is a reflection phase diagram of a metasurface unit in an embodiment of this application;

[0034] Figure 3 A phase arrangement diagram of a spherical array provided in an embodiment of this application;

[0035] Figure 4 Normalized beam amplitude theoretical prediction curves for flat subarrays and quasi-spherical subarrays (r = 1000 mm) of different sizes provided in the embodiments of this application under normal incidence conditions;

[0036] Figure 5 A comparison of normalized beam amplitude theoretical and simulation curves for flat subarrays and quasi-spherical subarrays (r = 1000 mm) of different sizes provided in the embodiments of this application;

[0037] Figure 6 Theoretical beam amplitude prediction curves of a 20×20 element flat subarray and a quasi-spherical subarray with different degrees of deformation provided in the embodiments of this application under normal incidence conditions;

[0038] Figure 7 The simulation results of normalized beam amplitude of a 20×20 element flat subarray and a quasi-spherical subarray with different degrees of deformation provided in the embodiments of this application under normal incidence conditions are shown in the figure.

[0039] Figure 8 The theoretical prediction curves of the total beam amplitude of a combined array with a total size of 144 elements × 144 elements under different numbers of subarray divisions provided in the embodiments of this application.

[0040] Figure 9 This application provides a structural diagram of a subarray size determination device for a reconfigurable smart metasurface combined array, as shown in the embodiments of this application.

[0041] Figure 10 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0042] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0043] Reconfigurable smart metasurfaces (RIS), also known as smart reflectors (IRS), are a key technology in next-generation wireless communication systems. They enable adaptive channel adjustment in complex environments and have broad application prospects, attracting significant attention in the industry. RIS are typically fabricated using PCB technology. In many applications, larger sizes of smart metasurfaces are required to cover a wider area and achieve more flexible channel adjustment. However, current PCB fabrication technology can only produce 50cm x 50cm RIS arrays. While arrays around 60cm x 120cm can be fabricated, the cost is high, making practical application difficult. Therefore, directly fabricating larger arrays is technically challenging. In most cases, smaller RIS arrays (50cm x 50cm subarrays) that are technically easier to implement are used to assemble larger RIS arrays.

[0044] A reconfigurable intelligent surface (RIS) is an artificial electromagnetic surface structure capable of dynamically controlling electromagnetic waves, typically composed of a large number of subwavelength units. By integrating tunable devices (such as diodes, varactors, and liquid crystals), the RIS can adjust the amplitude, phase, polarization, and other characteristics of electromagnetic waves in real time, thereby achieving flexible manipulation of electromagnetic waves. Its core working principle is to control the tunable elements on each metasurface unit, changing the unit's local electromagnetic response to electromagnetic waves, and thus achieving precise control of macroscopic electromagnetic waves.

[0045] Currently, the design of metasurface arrays largely relies on full-wave simulation software (such as CST Studio Suite). This approach is highly applicable and efficient for small-scale arrays, but its applicability significantly decreases when dealing with large-scale arrays due to the sharp increase in computational complexity and resource requirements. If the deformation characteristics of large arrays are further considered, the computational complexity increases even more significantly. Specifically, CST Studio Suite, as an electromagnetic simulation tool based on the Finite Integral Method (FIT) and the Finite-Difference Time Method (FDTD), has the following significant shortcomings when handling large-scale arrays:

[0046] First, the complexity and computational cost of mesh generation increase exponentially. The simulation accuracy of CST Studio Suite is highly dependent on the fineness of the mesh, especially when dealing with arrays with deformation characteristics (such as curved surface arrays or non-uniformly distributed arrays), where more detailed mesh generation is required to capture changes in the local electromagnetic field. However, as the array size increases, the number of meshes increases dramatically, leading to a significant increase in computational cost. For example, an array containing hundreds of elements may require millions or even hundreds of millions of mesh elements, which not only significantly extends the simulation time but also places extremely high demands on the computer's memory and processor performance.

[0047] Secondly, the efficiency and applicability of the solvers are limited. CST Studio Suite provides a variety of solvers (such as time-domain solvers and frequency-domain solvers), but their efficiency is often unsatisfactory when dealing with large arrays. Time-domain solvers have advantages in handling broadband problems, but their computational efficiency is low in large-scale array simulations due to time step limitations. While frequency-domain solvers are more efficient in specific scenarios, they may face convergence difficulties when dealing with complex deformed arrays, especially in high-frequency bands or scenarios with strong coupling effects.

[0048] Furthermore, hardware resource bottlenecks limit the scale of simulations. The simulation performance of CST Studio Suite depends on the computer's hardware configuration, including the number of processor cores, memory capacity, and storage speed. However, for simulations of very large-scale arrays, even high-performance workstations may not be able to meet the computational demands, leading to simulation interruptions or insufficient accuracy of results. Although this problem can be mitigated through distributed computing or high-performance computing clusters, this requires additional hardware investment and technical support, increasing implementation difficulty and cost.

[0049] Finally, the verification and optimization of simulation results are inefficient. For simulations of large arrays, the long computation time makes it difficult for users to quickly verify the accuracy of simulation results or optimize parameters. Especially in the early stages of design, when performance predictions for multiple subarray configurations are required, the low simulation efficiency significantly slows down the design process and affects overall development efficiency. This inefficient design process severely restricts the rapid iteration and engineering application of large RIS arrays.

[0050] Existing research on curved (conformal) metasurfaces largely focuses on the phase arrangement design of curved metasurfaces, that is, achieving specific functions such as beam focusing, electromagnetic stealth, and radar cross-section reduction by optimizing the phase distribution on curved metasurfaces. However, it also lacks a systematic analysis of how deformation affects the beam control performance of coded metasurfaces under ideal planar arrangements. In other words, current technology focuses on active conformal design while neglecting the key engineering problem of how processing deformation damages the original design performance.

[0051] The coding metasurface is an important branch of metasurface technology. It simplifies the design process and significantly improves design flexibility and reconfigurability by quantizing the phase response of metasurface units into finite discrete states (such as "0" and "1"). According to the generalized Snell's law, electromagnetic wave beam deflection can be achieved by designing the phase distribution (arrangement of "0" and "1" units) of the coding metasurface.

[0052] The Generalized Snell's Law describes the reflection and refraction of electromagnetic waves at interfaces with phase gradients (such as metasurfaces). Unlike the traditional Snell's Law, the Generalized Snell's Law considers phase abrupt changes or phase gradients at the interface, thus explaining the anomalous reflection and refraction phenomena of electromagnetic waves on metasurfaces.

[0053] The phase gradient method is a technique for precisely controlling electromagnetic waves by designing the phase distribution of metasurface units. Following the generalized Snell's law, the core idea of ​​the phase gradient method is to introduce a phase gradient onto the metasurface, causing a specific phase change in electromagnetic waves as they pass through it, thereby enabling flexible control over the reflection, refraction, and focusing of electromagnetic waves.

[0054] It should be noted that the phase gradient method is a specific implementation of the generalized Snell's theorem, used to construct the phase gradient dΦ / dx required by the generalized Snell's theorem on a subwavelength scale plane. For the coded metasurface in this embodiment, the phase response of the metasurface units is quantized into finite discrete states and arranged in a specific manner to form a "phase gradient," thereby achieving electromagnetic beam deflection.

[0055] The prior art proposes a wavefront control theory for two-dimensional curved coded metasurfaces, and the proposed far-field radiation formula for curved metasurfaces is as follows:

[0056]

[0057] Where Φ(n,m) represents the discontinuous phase change introduced at element (n,m). (θ,φ), (θ i ,φ i ) represent the outgoing and incoming directions, respectively, ΔΦ' p ,ΔΦ' i These represent the phase responses caused by the incident and emitted waves, respectively. ΔΦ h The phase difference between the surface and the reference plane is h(n,m), where h(n,m) represents the vertical distance between the surface where the element (n,m) is located and the reference plane, and is related to the deformation mode and degree.

[0058] Existing technologies, based on a newly proposed far-field radiation formula for curved metasurfaces, derive the phase distribution of curved metasurfaces and experimentally verify their effectiveness in achieving beam control under arbitrary incident and exit directions. However, this research does not further explore the impact of deformation on the beam control performance of coded metasurfaces under ideal planar arrangement, especially the phase error caused by deformation and its influence on the beam amplitude in the target direction. Furthermore, it lacks in-depth research on the subarray size optimization selection method under deformation conditions, which is precisely the core technical problem that this application aims to solve.

[0059] The technical solutions provided by the various embodiments of this application are described in detail below with reference to the accompanying drawings.

[0060] Figure 1 A flowchart illustrating a method for determining the subarray size of a reconfigurable smart metasurface combined array, provided in this application embodiment, includes the following steps:

[0061] Step 110: Determine the overall size and beam control target of the combined array, and establish a geometric model of the preset deformation of the combined array; the beam control target includes the incident wave direction and the desired outgoing wave direction.

[0062] The total array size is determined to be n elements × n elements, and the incident direction (θ) is determined. i ,φ i ) and the desired exit direction (θ,φ).

[0063] The preset deformation includes the deformation that may occur in the combined array.

[0064] For example, common deformation patterns in the actual processing of metasurfaces include cylindrical deformation and spherical deformation.

[0065] For example, a representative spherical deformation is selected as the analysis object. In CST Studio Suite, a spherical conformal array model is constructed by aligning the array center with the spherical vertex. The modeling result is as follows. Figure 2-1 As shown, the degree of deformation can be quantitatively characterized by the conformal sphere radius r, where the smaller the value of r, the more significant the array deformation; the larger the value of r, the closer the array is to an ideal planar array.

[0066] It should be noted that this application uses a spherical shape as an example, but this application applies to all deformation methods in metasurface processing or use.

[0067] In one embodiment, the method for establishing the geometric model includes:

[0068] The deformation type and degree are determined based on one or more of the following: the shape of the support structure of the combined array, the coefficient of thermal expansion of the material, or the processing and assembly parameters.

[0069] By analyzing various mechanical and technological factors that affect the physical morphology of metasurface arrays, we can pre-determine and define their possible structural deformation modes and their quantitative characterization in a digital manner, providing accurate geometric input for subsequent electromagnetic performance calculations.

[0070] Metasurface arrays are not perfectly planar; their final shape is constrained by various physical factors. By systematically considering these factors, a virtual model (i.e., a geometric model) reflecting the actual processing results can be constructed in advance in digital space. This model not only defines the type of deformation (such as bending, twisting, etc.) but also precisely describes the magnitude of the deformation (such as the curvature and warp height). This step is fundamental to all subsequent precise calculations; if the deformation model is inaccurate, subsequent electromagnetic performance predictions will be meaningless.

[0071] For example, if a large RIS array is planned to be installed on the surface of a curved aircraft wing (with a cylindrical support structure), its deformation type can be determined as cylindrical bending, and the degree of deformation is quantified by the radius of curvature of the wing (e.g., R = 5m).

[0072] If the RIS array is made of silicon and its supporting frame is made of metal, their coefficients of thermal expansion are mismatched. After undergoing a high-temperature soldering process, the silicon shrinks more than the metal frame, causing the array center to be stretched and potentially resulting in spherical protrusion deformation. The degree of deformation can be quantified by calculating the maximum warpage height (e.g., h = 2 mm) based on the process temperature difference and the difference in the material's coefficient of thermal expansion.

[0073] When mounting an array onto a planar base using vacuum adsorption, uneven vacuum pressure (e.g., strong adsorption around the edges and weak adsorption in the center) may cause the array to be flattened around the edges while the center bulges, resulting in a saddle-shaped deformation. The degree of deformation can be characterized by the hypercurvature (e.g., K1 = 0.001, K2 = -0.001) calculated from process parameters (e.g., pressure distribution diagram).

[0074] By integrating one or more of the above factors, a high-fidelity geometric model capable of predicting actual morphology can be established, thereby significantly improving the accuracy of subsequent performance predictions. The method described in this application, through multi-source parameter fusion modeling, significantly improves the accuracy of deformation prediction, laying a solid foundation for subsequent performance optimization.

[0075] Step 120: Calculate the ideal phase distribution of the combined array under flat conditions based on the beam control target.

[0076] The combined array in the flat state serves as a reference plane, which is the plane where the array lies in its ideal, deformation-free state. It is worth noting that the position of the reference plane can be arbitrarily chosen in principle. In practice, for any deformation mode, the reference plane can be flexibly selected according to its deformation characteristics to facilitate subsequent calculations. Taking a quasi-spherical deformation with radius r as an example, the reference plane can be selected as the horizontal cross-section at the vertex of the conformal sphere, as shown in the schematic diagram below. Figure 2-1 As shown.

[0077] The ideal phase distribution is calculated based on an ideal flat array. The phase arrangement at cell (m,n) is calculated using the following formula:

[0078] φ m,n =k0(x m,n sinθ i cosφ i +y m,n sinθ i sinφ i )-

[0079] k0(x m,n sinθcosφ+y m,n sinθsinφ) formula 2

[0080] Where, φ m,n ∈(0°, 360°). Different phase distributions can be obtained for different subarray sizes and incident / exit angles.

[0081] Figure 2-2 This is a schematic diagram of a simulation array model provided in an embodiment of this application. A metasurface unit is disposed thereon. For example, the metasurface unit (3.85mm × 3.85mm × 1.176mm) consists of a three-layer structure. The bottom ground plane and the upper patch material are made of metallic copper with a thickness of 0.018mm. The intermediate dielectric material is FR-4 (dielectric constant 2.5, loss factor 0.025) with a thickness of 1.14mm.

[0082] like Figure 2-3 and Figure 2-4 As shown, the metasurface unit comprises "0" units and "1" units.

[0083] In the embodiments of this application, the metasurface unit, as a key physical structure for realizing beamforming, modulates the electromagnetic wave response characteristics through the coding combination of two basic units, "0" unit and "1" unit.

[0084] The "0" and "1" units, based on the same three-layer physical structure (copper-FR4 dielectric-copper), achieve different electromagnetic properties through differences in the geometry of the upper layer patch, such as... Figure 2-3 and Figure 2-4As shown.

[0085] For example, at the target frequency of 26 GHz, the reflection amplitudes of both "0" and "1" units are higher than 0.9, and the phase difference between the reflections of the two units is around 180°, which meets the requirements of 1-bit encoded metasurface units.

[0086] The “0” unit generates a reference reflection phase at the target frequency of 26GHz through a specific patch shape design.

[0087] The "1" unit, through a differentiated patch design, generates a reflected phase approximately 180° different from the "0" unit at the same frequency. Figure 2-5 As shown in Figure 2-6. Both also maintain a reflection amplitude higher than 0.9.

[0088] This design enables both units to have binary phase control capabilities: when the metasurface is arranged with “0” and “1” units in a specific sequence, its overall reflected wavefront can be precisely shaped, thereby achieving electronic control of the beam direction.

[0089] The combination of this metasurface array with the aforementioned beamforming method is manifested in the following way: by dynamically configuring the spatial distribution pattern of "0" and "1" cells, the beamforming effect required for zero spatial constraints can be physically realized at the hardware level, i.e., generating a radiation pattern that meets specific directional requirements. This allows the information user beam to form an equivalent zero field strength in the energy user direction, while ensuring the signal strength in the information user direction. This metasurface-based implementation provides a reconfigurable physical carrier for beamforming algorithms, avoiding the high complexity and high cost problems of traditional phased arrays.

[0090] Figure 3 This demonstrates a flat array with a size of 20×20 elements at an incident angle (θ). i ,φ i The phase distribution under the conditions of (θ, φ) = (0°, 0°) and (θ, φ) = (30°, 30°) is used. This phase distribution is the basis for realizing functions such as beam deflection. Its calculation follows the generalized Snell's law, and the electromagnetic wavefront is controlled by introducing a phase gradient.

[0091] Step 130: Calculate the beam amplitude of subarrays of different sizes in the desired outgoing wave direction based on the geometric model and ideal phase distribution.

[0092] The formula for far-field radiation of an ideal flat array is known:

[0093]

[0094] The calculated phase distribution φ m,n Substituting, we get:

[0095] F1(θ,φ)=(2×s+1)2=q2 Formula 4

[0096] Where q = 2 × s + 1 represents the number of units contained on one side of the subarray, which can be used as a quantitative indicator of the subarray size. As can be seen from formula (3), under ideal phase distribution, the far-field radiation intensity in the target direction is positively correlated with the array size. The larger the array size, the stronger the far-field radiation intensity in the target direction.

[0097] In one embodiment, when calculating the beam amplitude, the additional phase delay caused by the vertical distance between the metasurface unit and the reference plane is taken into account.

[0098] Theoretically, once the array deformation mode and degree are determined, the distance h(m,n) between the metasurface element (m,n) and the reference plane is also determined. h(m,n) is closely related to the specific deformation mode and degree. Theoretically, for any deformation mode, h(m,n) is uniquely determined once the aforementioned reference plane is defined. For regular deformations (such as quasi-spherical deformations), they can be quickly calculated using geometric formulas; however, for other complex deformations, it may be necessary to perform element-level partitioning calculations based on the deformation mode, or even element-by-element calculations. Taking a quasi-spherical deformation with radius r as an example, as shown in Figure 2, its geometric relationship can be clearly characterized.

[0099]

[0100] The additional phase delay introduced by deformation is a key factor leading to performance degradation. Its magnitude is proportional to the product of the vertical distance from the element to the reference plane and the wavenumber. Accurately calculating this value is the core of evaluating the effect of deformation.

[0101] Step 140: Calculate the total beam amplitude in the desired outgoing wave direction for different subarray sizes.

[0102] Compared to the far-field radiation formula for a flat array, the radiation formula for a deformed array adds a phase response term caused by deformation -(cosθ). i +cosθ)·h(m,n), the formula is as follows:

[0103]

[0104] This formula applies to all metasurface deformation modes. In practice, for a specific deformation mode, substituting h(m,n) yields the array radiation formula for that deformation mode. Similarly, taking a quasi-spherical deformation with radius r as an example, substituting h(m,n) for a quasi-spherical deformation with a conformal sphere radius r, we obtain the following expression:

[0105]

[0106] Based on formulas 4 and 6, the beam amplitude distribution characteristics of the flat subarray and the deformable subarray can be obtained by iterating through the subarray size parameter s.

[0107] For example, Figure 4 The normalized beam amplitude theoretical prediction curves for flat subarrays and quasi-spherical subarrays (r = 1000 mm) of different sizes are presented, with the beam amplitude normalized to a unit of 1 for the flat subarray. Analysis results show that under specific deformation conditions, the normalized beam amplitude of the quasi-spherical subarray significantly decreases with increasing subarray size, indicating that the larger the subarray size, the more pronounced the beam amplitude attenuation compared to the flat array. This phenomenon further verifies the necessity of using a segmented combination method for large arrays. Furthermore, under normal incidence conditions, the deformation array curves differ for different exit directions, mainly due to the influence of the exit elevation angle on the phase response term caused by deformation. CST simulations verify this. Figure 5 As shown, the theoretical predictions and simulation data exhibit good agreement under both normal and oblique incidence conditions. This indicates that the theoretical model proposed in this application has high accuracy and can be used to quickly predict the performance of deformable arrays.

[0108] To further explore the influence of deformation degree on beam amplitude, this paper fixes the subarray size (parameter s) and analyzes the beam amplitude characteristics of quasi-spherical subarrays with different deformation degrees (conformal sphere radius r).

[0109] For example, Figure 6 The theoretically predicted beam amplitude curves for a 20×20 element flat subarray and quasi-spherical subarrays with varying degrees of deformation are presented. The results show that, for a specific subarray size, the larger the conformal sphere radius *r*, the smaller the array curvature, and the closer its beam amplitude is to that of a flat array, which is consistent with theoretical expectations. Furthermore, under normal incidence conditions, the differences in the deformation array curves for different exit directions are also due to the influence of the exit elevation angle *θ* on the phase response term. CST simulation verification results are shown below. Figure 7 As shown, this further confirms the consistency between theoretical predictions and simulation data.

[0110] Under the equal division method, based on the total area n of the combined array 2 With subarray area q 2 The number of subarrays can be derived as follows:

[0111]

[0112] According to the principle of beam superposition, the total beam amplitude of the combined array can be represented by the product of the number of subarrays and the beam amplitude of each subarray. Combining Equations 4 and 8, the total beam amplitude of the planar combined array can be expressed as:

[0113] Ftotal1 (θ,φ)=t×F1(θ,φ=n 2 Formula 9

[0114] Similarly, the total beam amplitude of the deformation combined array can be obtained:

[0115]

[0116] In Matlab, by iterating through the subarray quantity parameter t, the combined array beam amplitude corresponding to different subarray quantities under a fixed deformation condition can be calculated, and corresponding images can be generated. Since Equation 6 is universally applicable to all deformation methods, Equation 10 is also applicable to any deformation method. Referring to the combined array beam amplitude corresponding to different subarray quantities under a fixed deformation condition and the flat combined array beam amplitude, subsequent subarray size decisions can be made. For ease of analysis, taking quasi-spherical deformation as an example, the total size of the combined array is set to 144 elements × 144 elements. Figure 8 The normalized theoretical curves of the total beam amplitude of a flat combined array and a quasi-spherical combined array under normal incidence conditions are presented. Analysis results show that the greater the array deformation (i.e., the smaller the r-value), the more subarrays are needed to achieve a higher total beam amplitude level. Furthermore, at the same r-value, the deformation array curves differ for different exit directions, mainly due to the influence of the exit elevation angle θ on the phase response term caused by deformation.

[0117] Step 150: Determine a scheme where the total beam amplitude is higher than a preset performance threshold and the number of subarrays is lower than a preset complexity threshold.

[0118] Based on the above analysis, the radiation characteristics of the combined array can be predicted as follows: Under specific deformation conditions, when the number of subarrays is t, the percentage of the total beam amplitude of the combined array relative to the flat combined array can be calculated by the following formula:

[0119]

[0120] Similarly, since it does not involve specific deformation methods, Equation 11 is applicable to the prediction of radiation characteristics of combined arrays with all deformation methods. For ease of analysis, let's take... Figure 8 For example, for a combined array with a total size of 144 units × 144 units, under spherical deformation (r = 1000 mm), when the number of subarrays reaches 36 (6 × 6), the total beam amplitude of the combined array is expected to reach about 90% of that of the flat combined array. At this time, the size of the subarray is 24 units × 24 units.

[0121] When the number of subarrays is too small, the subarray size is large and significantly affected by deformation, resulting in a low total beam amplitude of the combined array. However, when the number of subarrays is too large, two problems may arise: first, the complexity of subsequent processing and splicing processes increases significantly; second, due to the small size of the subarrays, their phase gradient may not be obvious enough, thus affecting the overall performance of the subarrays and the combined array. Therefore, the selection of the number of subarrays needs to be optimized by balancing deformation effects, processing complexity, and phase gradient. It should be noted that the optimized selection of the number (or size) of subarrays needs to comprehensively consider multiple factors such as deformation effects, processing complexity, and phase gradient, and be determined based on the actual application requirements. However, this problem is not the core research content of this invention, and therefore will not be discussed in detail. The embodiments of this application cleverly transform the complex multi-objective optimization problem into an operable engineering decision problem by introducing a dual threshold constraint mechanism.

[0122] In one embodiment, the preset performance threshold is a relative value determined based on the total beam amplitude of the combined array in the desired output wave direction under flat conditions.

[0123] The preset performance threshold is a relative performance benchmark, defined as the percentage by which the total beam amplitude of the deformable array must reach the total beam amplitude of the ideal flat array under the same beam control target.

[0124] The preset performance threshold transforms the absolute performance problem into a relative performance retention problem, aiming to ensure that the performance degradation of the array after deformation is within an acceptable range.

[0125] For example, if the total beam amplitude of an ideal flat array deflected by 30 degrees north is calculated to be 100 dBμV / m, then setting the preset performance threshold to 90% (i.e., 90 dBμV / m) means that the estimated performance of all candidate subarray partitioning schemes must be no less than 90% of the ideal value, thus ensuring that the system performance after deformation does not decrease significantly. This relative index allows arrays of different sizes to be evaluated using a unified performance standard.

[0126] In one embodiment, the preset complexity threshold is determined based on the maximum number of assembleable subarrays of the combined array or the minimum processable size of the subarray.

[0127] The preset complexity threshold is an objective upper limit based on manufacturing and assembly capability constraints. It is defined as the upper limit of the number of subarrays that the system can support or the lower limit of the size of the subarrays that can be stably processed under a specific production process level.

[0128] Setting a pre-defined complexity threshold quantifies the abstract concept of "complexity" into measurable engineering metrics, aiming to ensure that the design solution is engineering-feasible.

[0129] For example, based on the mounting accuracy and splicing process of the production line, the maximum number of subarrays that can be reliably assembled is determined to be 100; or based on the minimum reliable wiring spacing and unit size of the PCB board, the minimum processable size of a single subarray is determined to be 8cm × 8cm. Any subarray partitioning scheme must satisfy the requirement that the number of subarrays is ≤100 or the subarray size is ≥8cm, otherwise it will be judged as an infeasible scheme.

[0130] In one embodiment, the total beam amplitude is calculated by multiplying the number of subarrays by the beam amplitude of a single deformable subarray.

[0131] The total beam amplitude calculation method is based on the beam superposition principle, which is defined as simplifying the total radiation performance of the entire deformable array in the far-field target direction to the linear superposition of the radiation contributions of all subarrays. That is, the total beam amplitude is equal to the product of the number of subarrays and the beam amplitude of a single deformable subarray in that direction.

[0132] The embodiments of this application transform the complex electromagnetic calculation problem of large-scale arrays into efficient algebraic operations. The core assumption is that the mutual coupling effect between subarrays can be ignored or is already implicit in the calculation of subarray amplitude.

[0133] For example, when a deformable array is divided into 16 sub-arrays of 4×4, and the beam amplitude of a single sub-array in the desired output direction is obtained through simulation calculation, the total beam amplitude of the array can be quickly estimated as 16X dBμV / m, thus avoiding the time-consuming full-wave simulation of the entire array.

[0134] In one embodiment, the subarray size is selected with the optimization objective of maximizing the total beam amplitude and minimizing the number of subarrays.

[0135] The principle for selecting the optimization objective is a dual-objective trade-off strategy, which is defined as the need to simultaneously pursue two mutually constraining objectives when selecting the final solution: optimal system electromagnetic performance (maximum total beam amplitude) and minimum engineering complexity (minimum number of subarrays).

[0136] The embodiments of this application clarify the value orientation of design decisions, namely, to select the partitioning scheme with the simplest structure and the fewest number of subarrays as much as possible while ensuring that the performance meets the standards.

[0137] For example, during the design process, we might find Scheme A: 36 subarrays with a total beamwidth of 92% of the ideal value; and Scheme B: 64 subarrays with a total beamwidth of 95% of the ideal value. Although Scheme B has slightly better performance, its number of subarrays is significantly increased, leading to higher manufacturing and splicing complexity. Based on this optimization principle, Scheme A, while meeting performance requirements (e.g., >90%), becomes the superior choice due to its significantly lower complexity.

[0138] Figure 9 This application provides a structural diagram of a subarray size determination device for a reconfigurable smart metasurface combined array, used to implement the subarray size determination method for a reconfigurable smart metasurface combined array as described in any embodiment of the first aspect, characterized in that it includes:

[0139] The acquisition module 910 is used to acquire the total size of the combined array and the beam control target, and to establish a geometric model of the preset deformation of the combined array; the beam control target includes the incident wave direction and the desired outgoing wave direction.

[0140] The calculation module 920 is used to calculate the ideal phase distribution of the combined array under flat conditions according to the beam control target; it is also used to calculate the beam amplitude of subarrays of different sizes in the desired output wave direction according to the geometric model and the ideal phase distribution; and it is also used to calculate the total beam amplitude in the desired output wave direction by different subarray division methods.

[0141] The determination module 930 is used to determine schemes where the total beam amplitude is higher than a preset performance threshold and the number of subarrays is lower than a preset complexity threshold.

[0142] Furthermore, the acquisition module includes a first acquisition unit, used to acquire the total size of the combined array and the beam control target, and to establish a geometric model of the preset deformation of the combined array; the beam control target includes the incident wave direction and the desired outgoing wave direction.

[0143] The calculation module includes a first calculation unit, which is used to calculate the ideal phase distribution of the combined array under flat conditions according to the beam control target; it is also used to calculate the beam amplitude of subarrays of different sizes in the desired output wave direction according to the geometric model and the ideal phase distribution; and it is also used to calculate the total beam amplitude in the desired output wave direction by different subarray division methods.

[0144] The determining module includes a first determining unit, used to determine a scheme in which the total beam amplitude is higher than a preset performance threshold and the number of subarrays is lower than a preset complexity threshold.

[0145] In one embodiment, the acquisition module further includes:

[0146] The second acquisition unit is used to determine the deformation type and degree of the combined array based on one or more of the following: the shape of the support structure, the coefficient of thermal expansion of the material, or the processing and assembly parameters.

[0147] The embodiments of this application are used to implement the technical solution of establishing a deformation geometric model based on multi-source parameters as described in the specification.

[0148] In one embodiment, the computing module further includes:

[0149] The second calculation unit is used to take into account the additional phase delay caused by the vertical distance between the metasurface unit and the reference plane due to deformation when calculating the beam amplitude.

[0150] The embodiments of this application are used to implement the technical solution for phase error caused by quantization deformation in the specification.

[0151] In one embodiment, the determining module further includes:

[0152] The second determining unit is used to set the preset performance threshold as a relative value determined based on the total beam amplitude of the combined array in the desired output wave direction under flat conditions.

[0153] The embodiments of this application are used to implement the technical solution in the specification that uses relative performance indicators as the evaluation benchmark.

[0154] In one embodiment, the determining module further includes:

[0155] The third determining unit is used to determine the preset complexity threshold based on the maximum number of assembleable subarrays of the combined array or the minimum processable size of the subarray.

[0156] The embodiments of this application are used to implement the technique described in the specification that defines a complexity threshold based on manufacturing capability constraints.

[0157] Technical solution.

[0158] In one embodiment, the computing module further includes:

[0159] The third calculation unit is used to calculate the total beam amplitude by multiplying the number of subarrays by the beam amplitude of a single deformable subarray.

[0160] The embodiments of this application are used to implement the technical solution for system performance prediction based on the beam superposition principle in the specification.

[0161] In one embodiment, the determining module further includes:

[0162] The fourth determining unit is used to select the final subarray size scheme with the optimization objectives of maximizing the total beam amplitude and minimizing the number of subarrays.

[0163] The embodiments of this application are used to implement the technical solution for multi-objective optimization decision-making in the specification.

[0164] In one embodiment, the device further includes:

[0165] The output module is used to output the selected subarray size and division number scheme to guide the processing and assembly production of the reconfigurable smart metasurface combination array.

[0166] The embodiments of this application are used to implement the technical solution for linking the design results output in the specification with downstream applications.

[0167] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0168] Therefore, this application also proposes a computer-readable storage medium having a computer program stored thereon that, when executed by a processor, implements the methods described in any embodiment of this application.

[0169] Furthermore, this application also proposes an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method described in any embodiment of this application.

[0170] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0171] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0172] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0173] In a typical configuration, a computing device includes one or more processors (CPUs), input / output interfaces, a network interface, and memory. Memory may include non-persistent storage in computer-readable media, such as random access memory (RAM) and / or non-volatile memory, such as read-only memory (ROM) or flash RAM. Memory is an example of computer-readable media.

[0174] Figure 10 This is a schematic diagram of an electronic device provided in an embodiment of this application. The electronic device 1000 shown is merely an example and should not be construed as limiting the functionality or scope of use of the embodiments of this application. It includes: one or more processors 1020; and a storage device 1010 for storing one or more programs. When the one or more programs are executed by the one or more processors 1020, the one or more processors 1020 implement the subarray size determination method for a reconfigurable smart metasurface combined array provided in an embodiment of this application. The method includes:

[0175] The overall size and beam control target of the combined array are determined, and a geometric model of the pre-deformed combined array is established; the beam control target includes the incident wave direction and the desired outgoing wave direction;

[0176] Calculate the ideal phase distribution of the combined array under flat conditions based on the beam control target;

[0177] The beam amplitude of subarrays of different sizes in the desired output wave direction is calculated based on the geometric model and ideal phase distribution.

[0178] Calculate the total beam amplitude in the direction of the desired emitted wave for different subarray sizes;

[0179] Determine a scheme where the total beam amplitude is higher than a preset performance threshold and the number of subarrays is lower than a preset complexity threshold.

[0180] The electronic device 1000 also includes an input device 1030 and an output device 1040; the processor 1020, storage device 1010, input device 1030 and output device 1040 in the electronic device can be connected by a bus or other means, as shown in the figure, which is connected by a bus 1050.

[0181] Storage device 1010, as a computer-readable storage medium, can be used to store software programs, computer-executable programs, and module units, such as the program instructions corresponding to the subarray size determination method of the reconfigurable smart metasurface combined array in the embodiments of this application. Storage device 1010 may mainly include a program storage area and a data storage area. The program storage area may store the operating system and at least one application program required for a function; the data storage area may store data created based on terminal usage, etc. Furthermore, storage device 1010 may include high-speed random access memory and may also include non-volatile memory, such as at least one disk storage device, flash memory device, or other non-volatile solid-state storage device. In some instances, storage device 1010 may further include memory remotely located relative to processor 1020, and these remote memories can be connected via a network. Examples of such networks include, but are not limited to, the Internet, enterprise intranets, local area networks, mobile communication networks, and combinations thereof.

[0182] Input device 1030 can be used to receive input digital, character, or voice information, and to generate key signal inputs related to user settings and function control of the electronic device. Output device 1040 may include electronic devices such as a display screen and a speaker.

[0183] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0184] Those skilled in the art will understand that, unless otherwise stated, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be understood that when a device or component is “connected” to another device or component, it may be directly connected to the other device or component, or there may be an intermediary device or component. Furthermore, the term “connection” as used herein may include partially wireless connections as well as partially wired connections.

[0185] In the description of this application, it should be understood that the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance. Those skilled in the art can understand the specific meaning of the above terms in this application based on the specific circumstances. Furthermore, in the description of this application, unless otherwise stated, "multiple" refers to two or more. "And / or" describes the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship.

[0186] The above description is merely an embodiment of this application and is not intended to limit the scope of this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of the claims of this application.

Claims

1. A method for determining the subarray size of a reconfigurable smart metasurface composite array, characterized in that, Includes the following steps: The overall size and beam control target of the combined array are determined, and a geometric model of the pre-deformed combined array is established. The deformation type and degree are determined according to one or more of the following: the shape of the supporting structure of the combined array, the coefficient of thermal expansion of the material, or the processing and assembly parameters. The beam control target includes the incident wave direction and the desired outgoing wave direction. Calculate the ideal phase distribution of the combined array under flat conditions based on the beam control target; The beam amplitude of subarrays of different sizes in the desired output wave direction is calculated based on the geometric model and ideal phase distribution; when calculating the beam amplitude, the additional phase delay caused by the vertical distance between the metasurface unit and the reference plane is taken into account. The total beam amplitude in the desired outgoing wave direction is calculated by multiplying the number of subarrays by the beam amplitude of a single deformable subarray. Determine a scheme where the total beam amplitude is higher than a preset performance threshold and the number of subarrays is lower than a preset complexity threshold.

2. The method for determining the subarray size of a reconfigurable intelligent metasurface combined array according to claim 1, characterized in that, The preset performance threshold is a relative value determined based on the total beam amplitude of the combined array in the desired output wave direction under flat conditions.

3. The method for determining the subarray size of the reconfigurable intelligent metasurface combined array according to claim 1, characterized in that, The preset complexity threshold is determined based on the maximum number of assembleable subarrays of the combined array or the minimum processable size of the subarray.

4. The method for determining the subarray size of the reconfigurable intelligent metasurface combined array according to claim 1, characterized in that, The subarray size is selected with the optimization objective of maximizing the total beam amplitude and minimizing the number of subarrays.

5. A subarray size determination device for a reconfigurable intelligent metasurface composite array, used to implement the subarray size determination method for a reconfigurable intelligent metasurface composite array according to any one of claims 1-4, characterized in that, include: The acquisition module is used to acquire the total size of the combined array and the beam control target, and to establish a geometric model of the preset deformation of the combined array; the beam control target includes the incident wave direction and the desired outgoing wave direction; The calculation module is used to calculate the ideal phase distribution of the combined array under flat conditions according to the beam control target; it is also used to calculate the beam amplitude of subarrays of different sizes in the desired output wave direction according to the geometric model and the ideal phase distribution; and it is also used to calculate the total beam amplitude in the desired output wave direction of subarrays of different sizes. The determination module is used to determine schemes where the total beam amplitude is higher than a preset performance threshold and the number of subarrays is lower than a preset complexity threshold.

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

7. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method as described in any one of claims 1-4.

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