CN113991304B - An Antenna Beamforming Method Based on Metasurface Array - Google Patents

Abstract

In order to meet the design requirements of high gain, wide frequency band and wide angle of an antenna, the embodiment of the application provides a method for carrying out beam forming on the antenna, which comprises the following steps: determining the side length and the relative dielectric constant of the super-surface unit according to the antenna center frequency point; simulation is carried out to obtain a corresponding table of transmission phase and patch geometric parameters of the super-surface unit under the condition that the transmittance requirement is met; calculating to obtain an equivalent phase center of the antenna so as to determine the distance between the antenna and the super-surface array; calculating to obtain the number N multiplied by M of units of the super-surface array; grouping the individual super surface units according to their geometric positions; calculating phase differences at geometric positions of each super-surface unit according to the Fermat principle; determining the patch geometric parameters of each group of super-surface units according to the phase difference selection; and performing simulation optimization within a certain range to realize the beam forming target.

Description

An Antenna Beamforming Method Based on Metasurface Array

technical field

The present application relates to the field of electronic information, in particular to an antenna beamforming method based on a metasurface array.

Background technique

Electromagnetic metamaterials refer to artificial structures formed by arranging subwavelength units in a periodic or non-periodic manner. Through the design of the metasurface unit and its arrangement, it is possible to realize the metamaterial parameters such as negative dielectric constant and negative refractive index that cannot be realized by materials in nature and traditional technologies.

At present, there are two problems that need to be solved urgently in the phased array antenna of through-the-wall radar: first, when the size of the phased array antenna is fixed, the characteristic of the limited aperture size of the antenna unit limits its gain, thus limiting the performance of the through-wall radar system. detection distance, it is urgent to find a wavefront control method and array miniaturization technology, and design a relatively compact phased array antenna that meets the high gain requirements; second, the beam direction of the antenna unit in the phased array antenna is generally It is relatively fixed for the antenna unit. This characteristic causes the larger the beam scanning angle, the lower the gain, which leads to the low tangential resolution of the through-wall radar. It is urgent to propose a beam control technology for the antenna unit to solve the problem of wide angle and high Contradictions between gains.

Contents of the invention

In view of this, the present application provides an antenna beamforming method based on a metasurface array, which can improve antenna gain or realize phase control through antenna beamforming.

In a first aspect, the present application provides a metasurface array structure, the metasurface unit adopts a sandwich resonant cavity structure, and the metasurface array is generally arranged in an N×M rectangle. Among them, the metasurface unit has a three-layer structure, including a bilaterally symmetrical patch layer composed of a square patch and a circular patch, and a dielectric substrate in the middle of the patch layer. In this design, the geometric parameters of the square patch Mainly affects the transmittance of the metasurface unit, and the geometric parameters of the circular patch mainly affect the transmission phase distribution of the metasurface unit. Through the comprehensive optimization of calculation and simulation, the geometric parameter range of the patch that meets the transmittance requirements is obtained, and the corresponding table of the transmission phase and the geometric parameter of the patch is obtained through simulation within this range.

In a possible implementation manner, the metasurface array can increase antenna gain. In order to realize this function, the phase difference of each group of metasurface units selected in the metasurface array design should satisfy the principle of phase compensation, so that the electromagnetic wave emitted by the antenna is as close as possible to a plane wave after passing through the metasurface array.

In a possible implementation manner, the metasurface array can realize polarization switching. The resonator model of the sandwich structure will go through three stages when the electromagnetic wave is incident, the energy is absorbed by the metal patch, the energy is stored by the dielectric plate, and the energy is emitted by the metal patch, so as to realize the control of the polarization mode of the electromagnetic wave.

In a possible implementation manner, the metasurface array can realize phase control. Based on the correspondence table between the transmission phase of the metasurface unit and the geometric parameters, arbitrary control of the phase of the incident electromagnetic wave can be realized, and any desired function can be designed and realized.

In a second aspect, the present application provides a metasurface array design optimization method. For a specific antenna, by adjusting the geometric parameters and relative permittivity of the metasurface element, the metasurface element with the same center frequency point can be obtained; by calculating the expression of its far-field electric field, the equivalent of the antenna can be determined Phase center coordinates. After determining the absolute coordinates of the equivalent phase center of the antenna, the metasurface array should be placed within the range between λ/2 and λ/4 from the absolute coordinates, which can be adjusted according to actual needs. The number of units N×M of the metasurface array should be determined by the maximum scanning angle of the antenna, and the optimal selection criterion is that the metasurface array should cover the area where the antenna gain is greater than -3dB and is located at the position of the metasurface array. After determining the number of units N×M of the metasurface array, it is necessary to group them according to the difference in optical path difference between different metasurface units and the equivalent phase center, so as to meet the different phase differences produced by different optical path differences. According to the calculated phase difference and the correspondence table between transmission phase and geometric parameters, the patch geometric parameters of each group of metasurface units are determined. The performance requirements of the completed metasurface array are simulated and verified, and optimized within a certain dynamic range to achieve the design goal.

Step 200, changing the central frequency point of the rectangular dielectric substrate of the metasurface unit by adjusting the geometric parameters and relative permittivity. The central frequency point of the metasurface unit is proportional to the side length of the rectangular dielectric substrate and inversely proportional to the relative permittivity, which can be expressed as

f ₀ = kL/ε _r (1)

Among them, f ₀ is the operating frequency point of the metasurface unit, L is the side length of the rectangular dielectric substrate, ε _r is the relative permittivity of the rectangular dielectric substrate, and k is the proportionality coefficient.

Step 210, a method of determining the equivalent phase center of the antenna by combining calculation and simulation. The phase center of the antenna is an equivalent concept. After the electromagnetic wave radiated by the antenna leaves a certain distance from the antenna, its equi-phase surface will approximately appear as a sphere, because it can be considered that the electromagnetic wave radiates outward from the equivalent phase center of the antenna. When determining the equivalent phase center of the antenna, first use the far-field Green's function to obtain the expression of the magnetic vector potential

Integrating this equation in the entire solution space, the expression of the far-field electric field can be obtained as

The equivalent phase center coordinates of the antenna can be determined by solving r ₀ among them. Add three far-field integrals to the antenna in the HFSS software, which are used to calculate the three-dimensional coordinates (x, y, z) of the antenna phase center. It is worth noting that when calculating the three-dimensional coordinates (x, y, z), different geometric ranges should be selected for different coordinates. In addition, since the derivation process assumes that the distance between any point on the far-field integral surface and the equivalent phase center is less than λ/2, it should be ensured that the distance between the corresponding geometric range of the solution space and the antenna equivalent phase center is less than λ /2 to ensure the accuracy of the solution process.

Step 220, a method for determining the position of the metasurface array and the number N×M of array units. According to the equivalent phase center of the antenna, the metasurface array is generally placed at a distance of λ/2 to λ/4 from its absolute coordinates. Considering the size of the antenna and other factors in the actual system, the array position of the metasurface can be adjusted to a certain extent. After determining the position of the metasurface array, the size of the metasurface array 2dθ _max required at this position can be obtained by calculation according to the maximum scanning angle of the antenna, where d is the distance between the equivalent phase center of the antenna and the geometric center of the metasurface array, θ _max is the maximum scan angle of the antenna. After determining the size of the metasurface array, according to the geometric parameters of the metasurface unit, the number of units N×M of the metasurface array can be determined.

Step 230, a method for determining geometric parameters of metasurface unit patches at different positions. Fermat's principle expresses the process of electromagnetic wave propagation between two points A and B as

According to this principle, the optical path difference of the electromagnetic waves emitted by the antenna at different metasurface units can be calculated

where A is the absolute coordinate of the equivalent phase center of the antenna, B and C are the geometric centers of different metasurface elements respectively, and the relationship between the optical path difference and the phase difference is generally expressed as

where λ is the wavelength of the electromagnetic wave.

According to the above principles, the patch geometry parameters of each metasurface are determined one by one by the phase elements in the supplementary matrix. In this process, for the convenience of calculation, the metasurface units with the same optical path difference can be divided into the same group, Choose the same patch geometry parameters.

Step 240, using the Matlab interface to control the HFSS software to model the metasurface array, and verifying whether its performance meets the requirements through simulation, and finally adjusting the parameters within a certain range. Based on the vbs script file function of the HFSS software, the mapping between the high-level language Matlab and the assembly language vbs is realized by using the Matlab package function, so as to realize the automatic modeling of the periodic structure of the metasurface array. At the same time, the HFSS software is controlled to optimize within a certain range through the Matlab interface, and the geometric parameters in the design are adjusted by using the optimization function of the HFSS software to meet the overall design requirements.

Beneficial effect

Utilizing the dynamic control capability of electromagnetic waves possessed by the artificial structure of electromagnetic metamaterials, the present invention proposes a super Antenna beamforming method of surface array, this method proposes a feasible metasurface unit structure, and proposes a corresponding optimal design method of metasurface array. Through the application of this metasurface unit structure and optimization method, the functions of gain enhancement, polarization conversion and phase control for different antennas can be effectively realized. Taking increasing the antenna gain as an example, comparing the gain changes of the rectangular microstrip patch antenna before and after loading the metasurface array, the gain diagram of the microstrip patch antenna without the metasurface array shows that its maximum gain is 6.57dB, and the gain of the microstrip patch antenna loaded with the metasurface array is 6.57dB. The gain graph of the microstrip patch antenna shows that its maximum gain is 8.7dB, and the maximum gain increases by 2.23dB before and after loading the metasurface array.

Description of drawings

Fig. 1 is a flow chart of a metasurface array optimal design method for realizing antenna beamforming;

Figure 2, Figure 3, and Figure 4 are three views of the HFSS simulation design of the metasurface unit structure with a center frequency of 6.5 GHz. The main parameters are: the side length L of the metasurface is 25 mm, the height H of the metasurface is 1.5 mm, and the square The width W of the patch is 1mm, the radius of the circular patch is 5mm and the number of layers N of the metasurface unit is 1;

Figure 5, Figure 6, and Figure 7 are three views of the HFSS simulation of the metasurface array designed for the microstrip patch antenna with a center frequency of 6.5 GHz, where the distance between the metasurface array and the equivalent phase center of the antenna is 25 mm, The number of metasurface array units is 5×5. Its main design parameters are: the side length L of the metasurface is 25mm, the height H of the metasurface is 1.5mm, the width W of the square patch is 1mm, and the radius Radius of each group of circular patches is 10.58mm from large to small. , 9.6mm, 9.06mm, 7.06mm, 6.56mm, 6.26mm, the number of layers N of the metasurface unit is 1;

Fig. 8 is a corresponding diagram of the geometric parameters of the 6.5GHz metasurface unit, the transmittance, and the transmittance phase.

Detailed ways

Embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings.

Fig. 1 is a flowchart of an optimal design method for metasurface arrays for antenna beamforming. For a specific known antenna, the optimal design method of metasurface array mainly includes: determining the geometric parameters and relative permittivity of the metasurface element, determining the equivalent phase center of the antenna, determining the position of the metasurface array, and determining the metasurface array element Number N×M, group the metasurface units, determine the patch geometry parameters of each group of metasurface units, and use the Matlab interface to control the HFSS software for simulation verification and local optimization.

Step 300, changing the central frequency point of the rectangular dielectric substrate of the metasurface unit by adjusting the geometric parameters and relative permittivity. The central frequency point of the metasurface unit is proportional to the side length of the rectangular dielectric substrate and inversely proportional to the relative permittivity function, which can be expressed as

f ₀ =kL/g(ε _r ) (7)

Among them, f ₀ is the operating frequency point of the metasurface unit, L is the side length of the rectangular dielectric substrate, g(ε _r ) is a function of the relative permittivity of the rectangular dielectric substrate, which is uniquely determined by it, and k is the proportionality coefficient.

Step 310, the basic principle and method of determining the equivalent phase center of the antenna. Using far-field Green's function to get the expression of magnetic vector potential

Integrating this equation in the entire solution space, the expression of the far-field electric field can be obtained as

Theoretically, by solving r ₀ in the above formula, the equivalent phase center of a specific antenna can be obtained.

The specific steps of using HFSS software to calculate its equivalent phase center through simulation include: setting the geometric range of coordinate calculation, where

Set the expression for coordinate calculation according to the above geometric range, where

x=integ(cang(deg(rETheta)*c0/(pi ² *4.5E9)*cos(Theta))) (13)

y=integ(cang(deg(rETheta)*c0/(pi ² *4.5E9)*cos(Phi))) (14)

z=integ(cang(deg(rETheta)*c0/(pi ² *4.5E9)*sin(Phi))) (15)

It should be noted that the above expressions are given in the form of function expressions in HFSS.

Figure 2, Figure 3, and Figure 4 are HFSS simulation design diagrams of the metasurface unit structure with a center frequency point of 6.5 GHz. For a known specific antenna, it is first necessary to adjust the length and relative permittivity of the metasurface unit to make it have the same center frequency as the antenna. Greater than 0.8. Due to the periodic characteristics of the metasurface unit, periodic boundary conditions can be set for the metasurface unit, thereby simulating the electromagnetic properties of the infinite periodic metasurface array. Specifically, the surface surrounding the metasurface unit is set as two pairs of master-slave connection boundaries, Master_Boundary and Slave_Boundary, respectively, and the upper and lower surfaces are respectively located at a wavelength away from the metasurface unit, and Floquet excitation is applied respectively, wherein the Floquet ports located on the upper surface Set to 1 port, the transmit power is 1W, as the transmit port, and the lower Floquet port is set to 2 port, the transmit power is 0W, as the receive port. Set the operating frequency of the simulation analysis to 6.5GHz, and set a linear step sweep within a certain frequency range to obtain its transmittance and transmittance phase.

Step 320, a method for determining the position of the metasurface array and the number N×M of array units. According to the equivalent phase center of the antenna, the metasurface array is generally placed at a distance of λ/2 to λ/4 from its absolute coordinates. Considering the size of the antenna and other factors in the actual system, the array position of the metasurface can be adjusted to a certain extent. After determining the position of the metasurface array, the size of the metasurface array 2dθ _max required at this position can be obtained by calculation according to the maximum scanning angle of the antenna, where d is the distance between the equivalent phase center of the antenna and the geometric center of the metasurface array, θ _max is the maximum scan angle of the antenna. After determining the size of the metasurface array, according to the geometric parameters of the metasurface unit, the number of units N×M of the metasurface array can be determined.

Figure 5, Figure 6, and Figure 7 are the HFSS simulation design diagrams of the metasurface array designed for the microstrip patch antenna with a center frequency of 6.5 GHz. Firstly, it is determined that the geometric center of the metasurface array should be located at λ/2 to λ/4 from the equivalent phase center of the antenna. In this example, 25mm is selected; further, using the maximum scanning angle of the microstrip patch antenna and the metasurface center The distance calculation between the equivalent phase center of the antenna and the element number of the metasurface array should be 5×5. For the metasurface array whose position and number of units are determined, the metasurface units in it need to be grouped. According to the distance between each metasurface unit and the equivalent phase center of the antenna, the above 5×5 metasurface array can be divided into 6 groups , each group should correspond to different patch geometry parameters.

Fig. 8 is a corresponding diagram of the geometric parameters of the 6.5GHz metasurface unit, the transmittance, and the transmittance phase. By setting the optimization method, the transmittance and transmittance phase of the metasurface unit at any frequency point can be solved by using HFSS software. Similarly, the surfaces surrounding the metasurface unit are respectively set as two pairs of master-slave connection boundaries Master_Boundary and Slave_Boundary, the upper and lower surfaces are respectively located at a wavelength away from the metasurface unit, and Floquet excitation is applied respectively, wherein the Floquet port on the upper surface is set as 1 port, the transmit power is 1W, as the transmit port, the Floquet port located below is set as 2 port, the transmit power is 0W, as the receive port. Set the operating frequency of the simulation analysis to 6.5GHz, and set the linear step sweep within a certain frequency range, and set the optimization range of the circular patch and the square patch at the same time, where the geometric parameters of the circular patch determine the metasurface unit. The transmission phase, the geometric parameter of the square patch determines the transmission of the metasurface unit. Generally speaking, the step of selecting geometric parameters is 0.01mm or 0.02mm, and this parameter is jointly determined by the computing power of the computer and the fine-grained requirements for the optimization goal. The results of the simulation are stored in table form. On the premise that the transmittance is greater than 0.8, the corresponding table between the transmission phase and the geometric parameters of the patch is obtained, thereby simplifying the design process.

Step 330, a method for determining geometric parameters of metasurface unit patches at different positions. Fermat's principle expresses the process of electromagnetic wave propagation between two points A and B as

According to this principle, the optical path difference of the electromagnetic waves emitted by the antenna at different metasurface units can be calculated

where A is the absolute coordinate of the equivalent phase center of the antenna, B and C are the geometric centers of different metasurface elements respectively, and the relationship between the optical path difference and the phase difference is generally expressed as

Where λ is the wavelength of the electromagnetic wave;

According to the number of units N×M of the metasurface array, the N×M dimensional target matrix A, error matrix B and supplementary matrix S are constructed, where the elements a _ij in the target matrix represent the designed target value of the outgoing wave phase, and the element b in the error matrix _ij represents the error value introduced by the non-plane wave emission characteristic of the antenna, and the element s _ij in the supplementary matrix represents the supplementary value of the metasurface unit at each position for the phase of the electromagnetic wave. The relationship between the above three should satisfy

a _ij =b _ij +s _ij (19)

According to the above principles, the patch geometry parameters of each metasurface are determined one by one by the phase elements in the supplementary matrix. In this process, for the convenience of calculation, the metasurface units with the same optical path difference can be divided into the same group, Choose the same patch geometry parameters.

Step 340, using the Matlab interface to control the HFSS software to model the metasurface array, and verifying whether its performance meets the requirements through simulation, and finally adjusting the parameters within a certain range. After completing the determination of the geometric parameters of the metasurface array and each metasurface unit, Matlab should be used to control the HFSS software for modeling and simulation optimization of the metasurface array, and the encapsulation functions involved in the code implementation for modeling the metasurface unit include: Draw a cuboid hfssBox, select the material hfssAssignMaterial, draw a rectangle hfssRectangle, draw a circle hfssCircle, subtract hfssSubtract multiple objects, add hfssUnite multiple objects, copy hfssDuplicateAlongLine objects, move hfssMove objects, and select the boundary material as the ideal electric surface hfssAssignPE.

The parameters that need to be passed in during the process of modeling the metasurface array include: the radius Radius of the circular patch of the metasurface unit, the width W of the square patch, and the coordinates of the geometric center of the metasurface unit on the xoy plane (Xposition, Yposition ) and the number num of the metasurface unit. It is worth noting that in the actual design, the function needs to be modified according to the results of the metasurface element design.

Those of ordinary skill in the art should recognize that the above embodiments are only used to illustrate the present invention, rather than as a limitation to the present invention, as long as within the scope of the present invention, changes and modifications to the above embodiments will fall In the protection scope of the present invention.

Claims (3)

1. The ultra-surface array optimization design method for realizing antenna beam forming is characterized by comprising the following steps of: determining geometric parameters and relative dielectric constants of the super-surface units aiming at a known central frequency point of a specific antenna, determining geometric coordinates of an antenna equivalent phase center, determining a super-surface array position, determining the number N multiplied by M of the super-surface array units, grouping the super-surface units, determining patch geometric parameters of each group of super-surface units, and controlling HFSS software by using a Matlab interface to perform simulation verification and local optimization;

the method for determining the geometric coordinates of the equivalent phase center of the antenna comprises the following steps: obtaining an expression of magnetic vector potential by using a far-field Green function, and integrating the expression in the whole solving space to obtain an expression of a far-field electric field

Setting the range of the solution of the antenna equivalent phase center of the antenna meeting the physical requirement, and calculating the coordinates of the antenna equivalent phase center by using HFSS, wherein the calculation method is (x, y, z) =

(integ(cang(deg(rETheta)*c0/(pi ² *4.5E9)*cos(Theta))),

integ(cang(deg(rETheta)*c0/(pi ² *4.5E9)*cos(Phi))),

integ(cang(deg(rETheta)*c0/(pi ² *4.5E9)*sin(Phi))))；

The method for determining the geometrical parameters of the super-surface single patch comprises the following steps: the optical path difference of electromagnetic waves emitted by the antenna at different super-surface units can be calculated according to the Fermat principle, and the phase difference can be further expressed as

Wherein A is the absolute coordinate of the antenna equivalent phase center, B and C are the geometric centers of different super-surface units respectively, lambda is the wavelength of electromagnetic waves, and an N x M-dimensional target matrix A, an error matrix B and a supplementary matrix S are constructed according to the number N x M of units of the super-surface array, wherein the target matrix comprisesElement a of (2) _ij Representing the designed outgoing wave phase target value, element b in the error matrix _ij Representing an error value introduced by the characteristic of the antenna of transmitting electromagnetic waves other than plane waves, supplementing the element s in the matrix _ij The complementary value of each position super-surface unit to electromagnetic wave phase is expressed, and the relation among the three should be satisfied

a _ij ＝b _ij +s _ij ,

According to the principle, the patch geometric parameters of each super-surface are determined by the phase elements in the supplementary matrix one by one, in the process, super-surface units with the same optical path difference can be divided into the same group for simple calculation, and the same patch geometric parameters are selected.

2. The method for optimizing design of a hypersurface array for antenna beam forming according to claim 1, wherein the method for changing the center frequency point of the hypersurface unit by adjusting the geometric parameters and the relative dielectric constant of the hypersurface unit rectangular dielectric substrate is characterized in that the center frequency point of the hypersurface unit is in direct proportion to the side length of the rectangular dielectric substrate and in inverse proportion to the function of the relative dielectric constant, and can be expressed as

f ₀ ＝kL/g(ε _r )

Wherein f ₀ Is the working frequency point of the super-surface unit, L is the side length of the rectangular dielectric substrate, g (epsilon) _r ) Is a function of the relative permittivity of the rectangular dielectric substrate, and is uniquely determined by the relative permittivity, and k is a proportionality coefficient.

3. The super-surface array designed by the super-surface array optimization design method for realizing antenna beam forming according to claim 1, wherein the super-surface unit adopts a sandwich type resonant cavity structure, the super-surface array adopts rectangular arrangement, the super-surface unit has a three-layer structure, the first layer and the third layer have symmetrical structures, the reflective layer is composed of square annular patches and circular patches, and the second layer is a rectangular dielectric substrate with a certain relative dielectric constant.