A multi-state simulation method for reconfigurable intelligent surfaces

Abstract

The present invention belongs to the field of computational electromagnetics and provides a multi-state simulation method for a reconfigurable intelligent surface to achieve the purpose of shortening the calculation time and reducing the memory consumption. First, obtain the unit model of the reconfigurable intelligent surface, expand the unit model to form a 3×3 characteristic sub-unit basic array, and regard it as an invariant geometric structure item, and regard the two-dimensional equivalent circuit model as a variable state description item. Then, extract the characteristics of the invariant geometric structure item and the variable state description item to obtain the system matrix of the reconfigurable intelligent surface and construct a system equation. Finally, solve the system equation to obtain the unknown electromagnetic field quantities to be solved, so as to calculate the electromagnetic characteristics of the reconfigurable intelligent surface and complete the multi-state simulation of the reconfigurable intelligent surface. The present invention effectively optimizes the repeated calculation part in the multi-state simulation process of the reconfigurable intelligent surface, significantly reduces the memory consumption, and greatly shortens the simulation time under the condition of ensuring the solution accuracy.

Description

Technical Field

[0001] The present invention belongs to the field of computational electromagnetics, and specifically provides a multi-state simulation method for reconfigurable intelligent surfaces. Background Art

[0002] Reconfigurable intelligent surfaces can be flexibly configured according to different communication requirements. By applying electrically controlled components, amplitude and phase regulation of electromagnetic waves can be achieved to adapt to different wireless communication scenarios. They have the characteristics of small volume, light weight, and easy installation, and are widely used in the field of wireless communication. When performing multi-state simulation on reconfigurable intelligent surfaces, traditional simulation methods cannot identify the commonalities of reconfigurable intelligent surfaces in different states, resulting in repeated calculations, increasing computing time and memory overhead. On this basis, how to shorten the simulation time has become an important issue of concern in the industrial community. Summary of the Invention

[0003] The purpose of the present invention is to provide a multi-state simulation method for reconfigurable intelligent surfaces, which is used to optimize the repeated calculation parts in different states, so as to achieve the purpose of shortening the calculation time and reducing memory consumption, thereby accelerating the simulation design of reconfigurable intelligent surfaces.

[0004] To achieve the above purpose, the technical solution adopted by the present invention is as follows:

[0005] A multi-state simulation method for reconfigurable intelligent surfaces includes the following steps:

[0006] Step 1: Obtain the unit model of the reconfigurable intelligent surface, expand the unit model of the reconfigurable intelligent surface to form a 3×3 basic array of characteristic sub-units, and perform mesh division on the basic array of characteristic sub-units to obtain an invariant geometric structure item mesh file; Equivalent the loaded lumped element to a two-dimensional equivalent circuit model and conformally load it onto the basic array of characteristic sub-units; Extract the two-dimensional mesh surface corresponding to the two-dimensional equivalent circuit model from the invariant geometric structure item mesh file and assign an attribute label to obtain a variable state description item mesh file;

[0007] Step 2: According to the invariant geometric structure item mesh file, use the finite element boundary element domain decomposition method to calculate the system matrix of the invariant geometric structure item;

[0008] Step 3: According to the variable state description item mesh file, calculate the additional loading value of the variable state description item;

[0009] Step 4: Load the additional loading value of the variable state description item into the self-coupling matrix of the system matrix of the invariant geometric structure item in the way of indexing and loading according to the basis function number, update to obtain a self-coupling matrix library, and further obtain a system matrix library of the reconfigurable intelligent surface;

[0010] Step 5: For each state loading of the reconfigurable intelligent surface, call the system matrix from the system matrix library according to the array state loading information file to form a system equation;

[0011] Step 6: Use the GMRES iterative method to solve the system equation to obtain the unknown electromagnetic field to be solved, thereby calculating the electromagnetic characteristics of the reconfigurable intelligent surface and completing the multi-state simulation of the reconfigurable intelligent surface.

[0012] Further, in Step 1, the two-dimensional equivalent circuit model uses an RLC circuit, including series and parallel types.

[0013] Further, in Step 2, the system equation constructed by the finite element boundary element domain decomposition method is:

[0014] ,

[0015] ,

[0016] where, represents the system matrix, represents the unknown electromagnetic field to be solved, represents the excitation term; represents the self-coupling matrix of the i-th sub-region, represents the mutual coupling matrix between the i-th sub-region and the j-th sub-region, represents the mutual coupling matrix between the i-th sub-region and the boundary element region, represents the mutual coupling matrix between the boundary element region and the i-th sub-region, is the boundary element self-coupling matrix; , represents the array dimension.

[0017] Further, in Step 3, the additional loading value of the variable state description term is expressed as:

[0018] ,

[0019] where, represents the additional loading value of the conformal of the invariant geometric structure term in the i-th sub-region and the k-th type of variable state description term in the m-th state loading, represents the imaginary unit, represents the wave vector in free space, represents the impedance in free space; represents the imaginary unit, represents the wave vector in free space, represents the impedance in free space; and respectively represent the length and width of the two-dimensional rectangular surface of the variable state description term;

[0020] Indicates the th state loading, the th sub-region loading, and the equivalent admittance value of the variable state description item of the type; ; represents the total number of state loadings of the reconfigurable intelligent surface, represents the total number of types of variable state description items in the reconfigurable intelligent surface;

[0021] And respectively represent the Whitney basis functions with the basis function numbers in the th sub-region of the invariant geometric structure item and ; represents the and where the triangular mesh cells are located.

[0022] Furthermore, for a series RLC circuit, the equivalent admittance value is expressed as: ; for a parallel RLC circuit, the equivalent admittance value is expressed as: ; where represents the angular frequency, represents the complex frequency, represents the admittance value of the resistor, , , respectively represent the equivalent resistance value, equivalent inductance value and equivalent capacitance value of the variable state description item.

[0023] Further, in step 5, the array state loading information file is prior information. In the mth state loading, according to the array state loading information file, the boundary conditions and lumped element loading information of each array element are obtained. For any array element, according to the boundary conditions, the sub-region information i of the corresponding invariant geometric structure item is determined, and according to the lumped element loading information, the type information s of the corresponding variable state description item is determined. The self-coupling matrix is selected from the self-coupling matrix library and filled into the system matrix of the reconfigurable intelligent surface, and then the system matrix of the reconfigurable intelligent surface is obtained by combining the mutual coupling matrix and the boundary element self-coupling matrix.

[0024] Based on the above technical solutions, the beneficial effects of the present invention are as follows:

[0025] The present invention provides a multi-state simulation method for reconfigurable intelligent surfaces. By using the characteristic sub-region method and the feature extraction method, first, for the invariant geometric structure items, the characteristic sub-region method is adopted. A 3×3 matrix index library is established according to the relative positions of the units in the original array. On this basis, for the variable state description items, the feature extraction method is used to separately export the admittance of the variable state items in the form of a product, so as to significantly reduce the memory overhead and time overhead during the system matrix filling process, matrix inversion process, and iteration. The present invention can greatly reduce the electromagnetic simulation time and simulation memory consumption under the condition of ensuring the unchanged solution accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 It is a schematic diagram of the principle of the multi-state simulation method for reconfigurable intelligent surfaces in the present invention.

[0027] Figure 2 It is a schematic diagram of the target self-coupling matrix of the reconfigurable intelligent surface in the embodiment of the present invention.

[0028] Figure 3 It is a schematic diagram of the self-coupling matrix library of the reconfigurable intelligent surface in the embodiment of the present invention.

[0029] Figure 4 It is a loading schematic diagram of the additional loading value of the variable state description item of the self-coupling matrix library in the embodiment of the present invention.

[0030] Figure 5 It is a three-dimensional schematic diagram of the unit structure of the reconfigurable intelligent surface in the embodiment of the present invention.

[0031] Figure 6 It is a top view schematic diagram of the unit structure of the reconfigurable intelligent surface in the embodiment of the present invention.

[0032] Figure 7 It is a schematic diagram of the array structure of the first state loading of the reconfigurable intelligent surface in the embodiment of the present invention.

[0033] Figure 8 It is a schematic diagram of the array structure of the second state loading of the reconfigurable intelligent surface in the embodiment of the present invention.

[0034] Figure 9 It is a bistatic scattering result diagram of the first state loading of the reconfigurable intelligent surface in the embodiment of the present invention.

[0035] Figure 10 It is a bistatic scattering result diagram of the second state loading of the reconfigurable intelligent surface in the embodiment of the present invention.

[0036] Figure 11 It is a bistatic scattering result diagram of the third state loading of the reconfigurable intelligent surface in the embodiment of the present invention.

[0037] Figure 12 This is the time consumption result graph of the reconfigurable intelligent surface with the total number of states loaded in the embodiment of the present invention.

[0038] Figure 13 This is the memory consumption result graph of the reconfigurable intelligent surface with the array scale in the embodiment of the present invention.

[0039] Figure 14 This is the time consumption result graph of the reconfigurable intelligent surface with the array scale in the embodiment of the present invention. Detailed implementation manners

[0040] To make the objectives, technical solutions and beneficial effects of the present invention clearer and more understandable, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0041] This embodiment provides a multi-state simulation method for a reconfigurable intelligent surface, which specifically includes the following steps:

[0042] Step 1: Obtain the unit model of the reconfigurable intelligent surface, expand the unit model of the reconfigurable intelligent surface to form a 3×3 basic array of characteristic sub-units, and perform mesh division on the basic array of characteristic sub-units to obtain an invariant geometric structure item mesh file; Equivalently load the lumped element as a two-dimensional equivalent circuit model and conformally load it onto the basic array of characteristic sub-units; Extract the two-dimensional mesh surface corresponding to the two-dimensional equivalent circuit model from the invariant geometric structure item mesh file and assign attribute labels to obtain a variable state description item mesh file; The two-dimensional equivalent circuit model adopts an RLC circuit, including series type and parallel type.

[0043] Step 2: According to the invariant geometric structure item mesh file, calculate the system matrix of the invariant geometric structure item by using the finite element boundary element domain decomposition method; The system equation constructed by the finite element boundary element domain decomposition method is:

[0044] ,

[0045] ,

[0046] wherein, represents the system matrix, represents the unknown electromagnetic field quantity to be solved, represents the excitation term; represents the self-coupling matrix of the i-th sub-region, represents the mutual coupling matrix between the i-th sub-region and the j-th sub-region, represents the mutual coupling matrix between the i-th sub-region and the boundary element region (BEM region), represents the mutual coupling matrix between the boundary element region and the i-th sub-region, is the boundary element self-coupling matrix; , Indicates the array dimension. For invariant geometric structure terms, ;

[0047] Step 3: Calculate the additional loading value of the variable state description term according to the variable state description term grid file;

[0048] The additional loading value of the variable state description term is expressed as:

[0049] ,

[0050] where, Indicates the additional loading value of the th state loading, where the th sub-region of the invariant geometric structure term is conformal to the th type of variable state description term, Indicates the imaginary unit, Indicates the free space wave vector, Indicates the free space impedance; and respectively represent the length and width of the two-dimensional rectangular surface of the variable state description term;

[0051] Indicates the equivalent admittance value of the th state loading, where the th sub-region is loaded with the th type of variable state description term, , , Indicates the total number of state loadings of the reconfigurable intelligent surface, Indicates the total number of types of variable state description terms in the reconfigurable intelligent surface;

[0052] For a series RLC circuit, its equivalent admittance value is expressed as: ; For a parallel RLC circuit, its equivalent admittance value is expressed as: ; where, Indicates the angular frequency, Indicates the complex frequency, , Indicates the admittance value of the resistance, , , , respectively represent the equivalent resistance value, equivalent inductance value, and equivalent capacitance value of the variable state description term;

[0053] and respectively represent the th sub-region of the invariant geometric structure term, where the basis function serial number is and Whitney basis functions represent the triangular mesh element where

[0054] Step 4: Load the additional loading values of the variable state description terms into the self-coupling matrix of the system matrix of the invariant geometric structure terms in the way of indexing by the basis function number, update to obtain the self-coupling matrix library, and further obtain the system matrix library of the reconfigurable intelligent surface;

[0055] Specifically, the additional loading values of the variable state description terms are correspondingly superimposed on the elements in the self-coupling matrix of the nth sub-region of the invariant geometric structure terms where the basis function numbers are and to obtain the self-coupling matrix of the nth sub-region conformally loaded with the kth state loading of the mth type of variable state description terms, denoted as , and further form the self-coupling matrix library;

[0056] Step 5: For each state loading of the reconfigurable intelligent surface, call the system matrix from the system matrix library according to the array state loading information file to form a system equation;

[0057] The array state loading information file is prior information. In the mth state loading, according to the array state loading information file, obtain the boundary conditions and lumped element loading information of each array unit. For any array unit, determine the sub-region information i of the corresponding invariant geometric structure term according to the boundary conditions, and determine the type information s of the corresponding variable state description term according to the lumped element loading information. Select the self-coupling matrix from the self-coupling matrix library and fill it into the system matrix of the reconfigurable intelligent surface; then combine the mutual coupling matrix , , and the boundary element self-coupling matrix to obtain the system matrix of the reconfigurable intelligent surface;

[0058] Step 6: Solve the system equation using the GMRES iterative method and accelerate the convergence process by combining the preconditioning technique to obtain the unknown electromagnetic field quantities to be solved, thereby calculating the electromagnetic characteristics of the reconfigurable intelligent surface, specifically the RCS (scattering) or the far-field pattern (radiation), and complete the multi-state simulation of the reconfigurable intelligent surface.

[0059] In terms of the working principle:

[0060] For a reconfigurable intelligent surface, when no lumped elements are loaded, it can be regarded as a quasi-periodic array. Therefore, in the present invention, a unit model is obtained from the quasi-periodic array, and thus a 3×3 characteristic sub-unit basic array is expanded and formed. The characteristic sub-unit basic array is regarded as an invariant geometric structure term, and the two-dimensional equivalent circuit model is regarded as a variable state description term. Thus, the system matrix of the reconfigurable intelligent surface is obtained through feature extraction of the invariant geometric structure term and the variable state description term, and then the electromagnetic characteristics of the reconfigurable intelligent surface are solved to complete multi-state simulation, such as Figure 1 shown;

[0061] For an N×N reconfigurable intelligent surface, the system matrix of its quasi-periodic array can be filled according to the system matrix of the 3×3 characteristic sub-unit basic array, thereby simplifying the calculation process of the system matrix of the quasi-periodic array. Specifically, the characteristic sub-region method can be referred to; and in the process of loading the additional load value of the variable state description term into the self-coupling matrix of the invariant geometric structure term, since the variable state description term is conformally loaded on the Whitney basis function of the invariant geometric structure term, combined with the characteristic sub-region method, the M×N×N loading process is simplified to S×3×3 times; and, the present invention can store the equivalent admittance value separately, further reducing the repeated calculation cost of the equivalent admittance value .

[0062] An embodiment with 4 types of variable state description terms is exemplarily given below, such as Figure 2 shown as the target self-coupling matrix of the reconfigurable intelligent surface in the m-th state loading, sorted in sequence as , , ; such as Figure 3 shown as the self-coupling matrix library obtained by the multi-state simulation method of the present invention, such as Figure 4 shown as the additional load value of the variable state description term obtained by the multi-state simulation method of the present invention. Taking the self-coupling matrix as an example, according to the boundary condition determination, the sub-region information i = 1 of the corresponding invariant geometric structure term is obtained, and according to the lumped element loading information, the type information s = 3 of the corresponding variable state description term is determined, then the corresponding additional load value is , then the additional load value of the variable state description term is loaded into the of the system matrix of the invariant geometric structure term according to the basis function serial number index; in addition, for the mutual coupling matrices , , , since the lumped element and the boundary surface basis function are not conformal, the mutual coupling matrix only needs to be calculated and stored using the characteristic sub-region method, and then indexed and filled into the system matrix; similarly, for the boundary element matrix The storage can be calculated according to the traditional boundary integral method.

[0063] Furthermore, as Figure 5 shown is the schematic diagram of the unit structure of the reconfigurable intelligent surface in this embodiment. Among them, the medium height H = 3.3 mm, the relative permittivity of the medium ε = 2.65. The bottom of the unit structure is coated with a PEC metal plate, and the upper surface of the unit structure is two PEC surfaces, and lumped elements are loaded between the two PEC surfaces; as Figure 6 shown is the top view of the unit structure of the reconfigurable intelligent surface in this embodiment. Among them, the dimension parameters L1 - L9 are 27.2 mm, 19.9 mm, 8.8 mm, 4.2 mm, 25.4 mm, 18.5 mm, 18.1 mm, 4.3 mm, and 3.5 mm respectively. The length h and width w of the two-dimensional rectangular surface at the lumped element loading position are 1.3 mm and 0.25 mm respectively. The loaded load is a series load, and the series load value has four states of loading, which are sequentially marked as s = 1, 2, 3, 4. The resistance values are all 0.3 ohm, the inductance values are all 0.7 nH, and the capacitance loading values are 2.6 pF, 1.25 pF, 1.14 pF, and 1 pF respectively; as Figure 7 , Figure 8 shown are the schematic diagrams of the array structures of the first state loading and the second state loading of the reconfigurable intelligent surface in this embodiment. Among them, the array element dimension of the reconfigurable intelligent surface is 16, and the numbers in each array element respectively correspond to the type information s of the variable state description item. In addition, the third state loading is set to not load any lumped elements.

[0064] The above reconfigurable intelligent surface is simulated by using the multi-state simulation method in this embodiment to calculate the RCS (scattering) or the far-field pattern (radiation); the bistatic scattering results of the three state loadings are successively as Figures 9 to 11 shown, where the 3.15 GHz electromagnetic wave is incident from the +z direction; it can be seen from the figure that the simulation results of this embodiment are in good agreement with the reference values, demonstrating the accuracy of the present invention.

[0065] Furthermore, taking the 4×4 reconfigurable intelligent surface in this embodiment as an example, a comparative test is carried out on the total number of state loadings M from two aspects of memory consumption and time consumption. The results are shown in Table 1, where the visualization result of the time consumption is as Figure 12 shown. It can be seen from the chart that as the total number of state loadings M increases, the advantages of the present invention gradually increase.

[0066] Table 1

[0067]

[0068] In addition, in this embodiment, a comparative test of the array scale is carried out from two aspects of memory consumption and time consumption, and the results are shown in Table 2. Among them, the visualization results of memory consumption and time consumption are as follows in sequence Figure 13 and Figure 14 shown. It can be seen from the chart that as the array scale gradually increases, the advantages of the present invention gradually increase.

[0069] Table 2

[0070]

[0071] To sum up, the present invention can perform multi-state loading simulation on the reconfigurable intelligent surface, and under the variable state descriptions of a limited type, with the increase of the state loading times and the array scale, it can greatly reduce the memory consumption and time consumption.

[0072] The above is only the specific implementation manner of the present invention. Any feature disclosed in this specification, unless specifically described, can be replaced by other equivalent or alternative features with similar purposes; all the features disclosed, or all the steps in any method or process, except for mutually exclusive features and / or steps, can be combined in any way.

Claims

1. A multi-state simulation method for reconfigurable intelligent surfaces, characterized in that, It includes the following steps: Step 1: Obtain the unit model of the reconfigurable intelligent surface, expand the unit model of the reconfigurable intelligent surface to form a 3×3 basic array of characteristic sub-units, and perform mesh division on the basic array of characteristic sub-units to obtain an invariant geometric structure item mesh file; Equivalent the loaded lumped element to a two-dimensional equivalent circuit model and conformally load it onto the basic array of characteristic sub-units; Extract the two-dimensional mesh surface corresponding to the two-dimensional equivalent circuit model from the invariant geometric structure item mesh file and assign attribute labels to obtain a variable state description item mesh file; Step 2: According to the invariant geometric structure item mesh file, use the finite element boundary element domain decomposition method to calculate the system matrix of the invariant geometric structure item; Step 3: According to the variable state description item mesh file, calculate the additional loading value of the variable state description item; The additional loading value of the variable state description item is expressed as: wherein, represents the additional loading value of the i-th sub-region of the invariant geometric structure term being conformal to the s-th type of variable state description term in the m-th state loading, j represents the imaginary unit, k represents the free space wave vector, and η0 represents the free space impedance; h and w respectively represent the length and width of the two-dimensional rectangular surface of the variable state description term; Denote the equivalent admittance value of the s-th type of variable state descriptor loaded in the i-th sub-region during the m-th state loading, where m = 1, 2, …, M, s = 1, 2, …, S, M represents the total number of state loadings of the reconfigurable intelligent surface, and S represents the total number of types of variable state descriptors in the reconfigurable intelligent surface; and respectively represent the Whitney basis functions with the basis function numbers p and q in the i-th sub-region of the invariant geometric structure term, and Γ represents and the triangular mesh element where they are located; Step 4: Load the additional loading value of the variable state description item into the self-coupling matrix of the system matrix of the invariant geometric structure item in the way of indexing the loading by the basis function number, update to obtain the self-coupling matrix library, and further obtain the system matrix library of the reconfigurable intelligent surface; Step 5: For each state loading of the reconfigurable intelligent surface, call the system matrix from the system matrix library according to the array state loading information file to form a system equation; Step 6: Iteratively solve the system equation to obtain the unknown electromagnetic field to be solved, so as to calculate the electromagnetic characteristics of the reconfigurable intelligent surface and complete the multi-state simulation of the reconfigurable intelligent surface.

2. The multi-state simulation method for a reconfigurable intelligent surface according to claim 1, characterized in that In Step 1, the two-dimensional equivalent circuit model adopts an RLC circuit, including series type and parallel type.

3. The multi-state simulation method for a reconfigurable intelligent surface according to claim 1, wherein In Step 2, the system equation constructed by the finite element boundary element domain decomposition method is: Ax = b, Among them, A represents the system matrix, x represents the unknown electromagnetic field to be solved, and b represents the excitation term; K i represents the self-coupling matrix of the i-th sub-region, and C i,j represents the mutual-coupling matrix between the i-th sub-region and the j-th sub-region, and C i,B represents the mutual-coupling matrix between the i-th sub-region and the boundary element region, and C B,i represents the mutual-coupling matrix between the boundary element region and the i-th sub-region, and B is the boundary element self-coupling matrix; i, j = 1, 2, …, N×N, where N represents the array dimension.

4. The multi-state simulation method for a reconfigurable intelligent surface according to claim 1, characterized in that For a series RLC circuit, the equivalent admittance value is expressed as: For a parallel RLC circuit, the equivalent admittance value is expressed as: Where ω represents the angular frequency, f(ω) represents the complex frequency, G represents the admittance value of the resistor, and R, L, and C represent the equivalent resistance value, equivalent inductance value, and equivalent capacitance value of the variable state description term, respectively.

5. The multi-state simulation method for a reconfigurable intelligent surface according to claim 1, characterized in that In step 5, the array state loading information file is prior information. In the m-th state loading, the boundary conditions and lumped element loading information of each array element are obtained according to the array state loading information file. For any array element, the sub-region information i of the corresponding invariant geometric structure item is determined according to the boundary conditions, and the type information s of the corresponding variable state description item is determined according to the lumped element loading information. The self-coupling matrix is selected from the self-coupling matrix library. It is filled into the system matrix of the reconfigurable intelligent surface, and then the system matrix of the reconfigurable intelligent surface is obtained by combining the mutual coupling matrix and the boundary element self-coupling matrix.

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