Multi-state simulation method for reconfigurable intelligent surface

Abstract

The invention belongs to the field of computational electromagnetism, and provides a multi-state simulation method for a reconfigurable intelligent surface, which is used for achieving the purposes of shortening calculation time and reducing memory consumption. The method comprises the steps that firstly, a unit model of the reconfigurable intelligent surface is obtained, the unit model is expanded to form a 3 * 3 feature subunit basic array, the basic array is regarded as an invariant geometric structure item, and a two-dimensional equivalent circuit model is regarded as a variable state description item; then, obtaining a system matrix of the reconfigurable intelligent surface through feature extraction of an invariant geometric structure item and a variable state description item, and constructing a system equation; and finally, solving the system equation to obtain the unknown quantity of the 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. According to the method, the repeated calculation part is effectively optimized in the multi-state simulation process of the reconfigurable intelligent surface, the memory consumption is remarkably reduced, and the simulation time is greatly shortened under the condition that the solving precision is guaranteed.

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, and the amplitude and phase of electromagnetic waves can be regulated by applying electrical control elements 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 calculation 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 characteristic sub-unit basic array, and perform mesh division on the characteristic sub-unit basic array to obtain an invariant geometric structure item mesh file; load the lumped element equivalent as a two-dimensional equivalent circuit model and conformally load it onto the characteristic sub-unit basic array; 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 imaginary unit, represents the wave vector in free space, represents the wave vector in free space, represents the impedance of free space; represents the impedance of 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 th type of variable state description item. , , Indicates the total number of state loadings of the reconfigurable intelligent surface. Indicates 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. The indicates 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 unit are obtained. For any array unit, according to the boundary conditions, the sub-region information i of its corresponding invariant geometric structure item is determined, and according to the lumped element loading information, the type information s of its 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, which adopts the feature sub-region method and the feature extraction method. First, for the invariant geometric structure items, the feature sub-region method is used to establish a 3×3 matrix index library 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 adopted to separately derive 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 into 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; 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, use the finite element boundary element domain decomposition method to calculate the system matrix of the invariant geometric structure item; The system equation constructed by the finite element boundary element domain decomposition method is:

[0044] ,

[0045] ,

[0046] where, 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 of the invariant geometric structure term for the th sub-region 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 of the th sub-region 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 with the basis function serial number and Whitney basis functions denote and the triangular mesh element where it is located;

[0054] Step 4: Load the additional loading values of the variable state descriptors into the self - coupling matrix of the system matrix of the invariant geometric structure items in the way of indexing by the basis function numbers, 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 descriptors are correspondingly superimposed on the elements in the self - coupling matrix of the sub - region of the invariant geometric structure item with the basis function numbers and to obtain the self - coupling matrix of the type of variable state descriptors conformally loaded in the th state loading and the sub - region, denoted as , and further constitute 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 m - th 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 item according to the boundary conditions, and determine the type information s of the corresponding variable state descriptor 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 with the mutual - coupling matrix , , and the boundary - element self - coupling matrix to obtain the system matrix of the reconfigurable intelligent surface;

[0058] Step 6: Use the GMRES iterative method to solve the system equation, and combine with the pre - conditioning technique to accelerate the convergence process to obtain the unknown electromagnetic field quantities to be solved, so as to calculate 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 then 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 by 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 as 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] The following exemplarily gives an embodiment where the number of types of variable state description terms is 4. As Figure 2 shown is the target self-coupling matrix of the reconfigurable intelligent surface in the m-th state loading, which is sorted in sequence as , , ; as Figure 3 shown is the self-coupling matrix library obtained by the multi-state simulation method of the present invention. As Figure 4 shown is 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 a 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 dielectric constant 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 a 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 marked as s = 1, 2, 3, 4 in sequence. 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 schematic diagrams of the array structure of the 1st state loading and the 2nd state loading of the reconfigurable intelligent surface in this embodiment. Among them, the element dimension of the reconfigurable intelligent surface is 16, and the numbers in each element respectively correspond to the type information s of the variable state description item. In addition, the 3rd 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 far-field pattern (radiation); the bistatic scattering results of the three state loadings are as shown in Figures 9 - 11 sequence. Among them, 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 in terms of memory consumption and time consumption. The results are shown in Table 1. Among them, the visualization result of the time consumption is as shown in Figure 12 sequence. 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 on 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] In summary, the present invention can perform multi-state loading simulation on reconfigurable intelligent surfaces, and under a limited type of variable state description, with the increase of the number of state loadings and the array scale, it can greatly reduce 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 similar-purpose alternative features; 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 smart surfaces, characterized in that: The following steps are involved: Step 1, obtain the unit model of the reconfigurable smart surface, expand the unit model of the reconfigurable smart surface to form a 3×3 characteristic sub-unit basic array, and mesh the characteristic sub-unit basic array to obtain a grid file of the invariant geometric structure item; load the lumped element equivalent to a two-dimensional equivalent circuit model, and conformally load it onto the characteristic sub-unit basic array; Extract the two-dimensional mesh surface corresponding to the two-dimensional equivalent circuit model from the invariant geometry structure item mesh file and assign attribute labels to obtain the variable state description item mesh file; Step 2: According to the grid file of the invariant geometry item, the system matrix of the invariant geometry item is calculated by using the finite element boundary element domain decomposition method; Step 3, according to the variable state description item grid file, calculate the additional loading value of the variable state description item; 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 a manner of loading by the basis function serial number index, update the self-coupling matrix library, and further obtain the system matrix library of the reconfigurable smart surface; Step 5: For each state loading of the reconfigurable smart surface, the system matrix is ​​called from the system matrix library according to the array state loading information file to form a system equation; Step 6: Iteratively solve the system equations to obtain the unknown quantities of the electromagnetic field to be solved, thereby calculating the electromagnetic characteristics of the reconfigurable smart surface and completing the multi-state simulation of the reconfigurable smart surface.

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

3. The multi-state simulation method for reconfigurable smart surfaces according to claim 1, characterized in that: In step 2, the system equation constructed by the finite element boundary element domain decomposition method is: ， ， in, represents the system matrix, represents the unknown quantity of electromagnetic field to be solved, Indicates incentive item; represents the self-coupling matrix of the ith sub-region, represents the mutual coupling matrix between the ith sub-region and the jth sub-region, represents the mutual coupling matrix between the ith 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; , Indicates the array dimensions.

4. The multi-state simulation method for reconfigurable smart surfaces according to claim 1, characterized in that: In step 3, the additional loaded value of the variable state description item is expressed as: ， in, Indicated in The first item of the unchanged geometry structure in the sub-state loading Sub-regions and Class mutable state describes additional load values ​​conformally to the item, represents the imaginary unit, represents the free space wave vector, represents the free space impedance; and Respectively represent the length and width of the two-dimensional rectangular surface of the variable state description item; Indicated in Second state loading Sub-region loaded The equivalent admittance value of the class variable state description item, , , represents the total number of states loaded on the reconfigurable smart surface, Represents the total number of types of variable state description items in the reconfigurable smart surface; and They represent the invariant geometric structure terms The basis function numbers in the sub-regions are and The Whitney basis function, express and The triangular mesh unit where the 5. The multi-state simulation method for reconfigurable smart surfaces according to claim 4, 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: ;in, represents the angular frequency, represents the complex frequency, Represents the admittance value of the resistor, , , They respectively represent the equivalent resistance value, equivalent inductance value and equivalent capacitance value of the variable state description item.

6. The multi-state simulation method for reconfigurable smart surfaces according to claim 1, characterized in that: In step 5, the array state loading information file is a priori information. In the mth state loading, the boundary conditions and lumped element loading information of each array unit are obtained according to the array state loading information file. For any array unit, 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. Fill it into the system matrix of the reconfigurable smart surface, and then combine the mutual coupling matrix and the boundary element self-coupling matrix to obtain the system matrix of the reconfigurable smart surface.

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