Pure amplitude modulation beamforming method based on sub-wavelength periodic electromagnetic surface

Abstract

The invention discloses a pure amplitude modulation beamforming method based on a sub-wavelength periodic electromagnetic surface, and belongs to the technical field of wireless communication beamforming. The method is applied to a sub-wavelength periodic two-dimensional array formed by metasurface units with the same geometric structure, the polarization direction of each unit is fixed, and the array topology meets specific rotation and translation conditions. According to the method, through the steps of mathematical modeling, initial state calculation, target state calculation, full modulation factor calculation, target state adjustment and the like, beam forming is simply and effectively achieved only by adjusting the coupling strength (amplitude modulation) of the metasurface unit and the excitation field. The method is suitable for metasurface antenna beam forming application, the requirement for the reconfigurable performance of the metasurface is lowered, real-time beam pointing change and multi-beam generation are supported, and the method has important value for achieving metasurface antenna dynamic beam forming.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication beamforming technology, specifically relating to a pure amplitude modulation beamforming method based on a subwavelength periodic electromagnetic surface, which can be used to realize flexible beamforming of metasurface antennas. Background Technology

[0002] With the development of modern wireless communication technology, the demand for precise control of electromagnetic beams is increasing. Existing beamforming technology typically uses array antennas, employing complex feeding networks, beamforming algorithms, and multiple feed sources to achieve beam control, which suffers from problems such as complex structure, large size, and high cost.

[0003] Metasurface antennas, as a novel antenna structure, enable flexible manipulation of electromagnetic waves through subwavelength-scale unit modulation, offering advantages such as low profile, light weight, and easy integration. However, traditional beamforming methods are difficult to apply directly to the electromagnetic manipulation of subwavelength periodic structures. In recent years, researchers have proposed several solutions for metasurface antenna beamforming. The existing technology "Flat Optics for Leaky-Waves on Modulated Metasurfaces: Adiabatic Floquet-Wave Analysis, IEEE Trans. Antennas Propagat., vol.64, no.9, pp.3896-3906, Sep.2016" addresses a class of metasurface antennas that generate radiating beams through interaction with surface waves. It establishes a boundary value problem using continuous non-uniform anisotropic boundary conditions and discloses a planar optical theory suitable for leakage wave analysis based on the adiabatic Floquet wave expansion of current. The local dispersion equation obtained by boundary condition matching provides an analytical solution for the radiation field and offers a closed-form expression for the leakage parameter. The existing technology "Synthesis of Modulated-Metasurface Antennas With Amplitude, Phase, and Polarization Control, IEEE Trans. Antennas Propagat., vol. 64, no. 9, pp. 3907-3919, Sep. 2016" discloses a systematic method that synthesizes the aperture field through analytical formulas and achieves beamforming based on aperture field modulation. Specifically, aperture field polarization control is based on local values ​​of anisotropy, phase modulation depends on the shape and periodicity of the modulation, and amplitude control is achieved by designing the local distribution of the leakage wave. However, on the one hand, the geometry and electromagnetic properties of existing metasurfaces are often non-reconfigurable, so there is no requirement for the complexity of the design method. The aforementioned aperture field synthesis method is suitable for this situation and has high accuracy, but its high complexity and computational cost will cause serious limitations in the future design of reconfigurable metasurface structures, making it difficult to meet the real-time requirements of dynamic beamforming. On the other hand, in the above-mentioned technologies, the geometry of the metasurface unit must have a certain degree of design freedom to match the corresponding impedance tensor. To a certain extent, this restricts its application range structurally and also limits the reconfigurability of the structure.

[0004] The existing technology "Analysis of a Waveguide-Fed Metasurface Antenna, Phys. Rev. Applied, vol. 8, no. 5, p. 054048, Nov. 2017" discloses a closed-form analytical expression describing the radiation characteristics of a waveguide-fed metasurface antenna. Waveguide-fed metasurface antennas offer design flexibility, similar to leaky-wave or traveling-wave antennas, and avoid phase-shifting networks by utilizing the phase-lead characteristic of waveguide modes. However, this technology, under conditions of limited phase control, partially compensates for the aperture field by combining holographic design methods with aperture field sampling coupling. It is only applicable to one-dimensional arrays and simple single-beam cases, and does not discuss beamforming for two-dimensional arrays and arbitrary radiation fields. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a pure amplitude modulation beamforming method based on a subwavelength periodic electromagnetic surface. This method only requires adjusting the coupling strength between the radiating element and the excitation field, and can achieve flexible beamforming under the condition that the metasurface geometry or electromagnetic parameters have limited reconfigurability. This is of great significance to the reconfigurability of metasurfaces.

[0006] The technical problem addressed by this invention is solved as follows:

[0007] A pure amplitude modulation beamforming method based on a subwavelength periodic electromagnetic surface is applied to a subwavelength periodic two-dimensional array composed of subwavelength radiating units with the same geometry but different directions. The radiation fields coupled from the excitation field by each subwavelength radiating unit together form the radiation field of the subwavelength periodic two-dimensional array, and the coupling strength can be changed.

[0008] Includes the following steps:

[0009] Step 1. Mathematical modeling and state definition;

[0010] Establish a Cartesian coordinate system. The array plane lies within the XOY plane and contains N×N subwavelength radiating elements, where N is an odd number. The geometric centers of each subwavelength radiating element form a uniformly distributed grid. The element spacing is d, with rows parallel to the x-axis and columns parallel to the y-axis. The geometric center of the metasurface element in the m-th row and n-th column is located at... Each subwavelength radiative unit is modeled as a short electric dipole or a time-harmonic surface current density vector (referred to as an oscillator) on a lattice point;

[0011] Define a reference oscillator array; compare each subwavelength radiating element with the reference oscillator at the corresponding position, and combine the amplitude scaling and phase difference into a complex number; traverse all subwavelength radiating elements to obtain a complex matrix used to characterize the state of the oscillator array, or simply array state.

[0012] Step 2. Initial state calculation;

[0013] Will be located at r mn The initial state of the oscillator is represented as Among them, A mn and Ψ nm They represent the locations at r respectively mn The amplitude and phase of the oscillator relative to the reference oscillator, A mn >0, j is the imaginary unit;

[0014] Step 3. Calculate the target state;

[0015] Define a unit direction vector associated with a single beam, and give the target state corresponding to the single beam; based on the principle of electromagnetic field superposition, synthesize the desired radiation beam by superimposing multiple single beams, and give the target state s corresponding to the desired radiation beam based on the target state corresponding to the single beam. ob (r mn );

[0016] Step 4. Calculate the full modulation factor;

[0017] Calculate the modulation factor m(r) that modulates the initial state to the target state corresponding to the desired radiation beam. mn ):

[0018]

[0019] The superscript * indicates conjugate;

[0020] Step 5. Target state adjustment;

[0021] The target state corresponding to the desired radiation beam is superimposed with the initial state to obtain the adjusted target state s. ob '(r mn );

[0022] Step 6. Modulation factor calculation;

[0023] Adjusted full modulation factor m'(r) mn )for:

[0024] m'(r mn )=m(r mn )+1

[0025] Amplitude modulation factor m A (r mn )for:

[0026]

[0027] Where Re represents the real part;

[0028] The amplitude modulation factor distributions corresponding to all subwavelength radiating elements form the final modulation map. Based on the modulation map, amplitude modulation is performed on each subwavelength radiating element to generate the desired radiating beam.

[0029] Furthermore, in a subwavelength periodic two-dimensional array, the polarization direction of each subwavelength radiating element is fixed, and can be characterized by the polarization direction, amplitude, and phase of the time-harmonic current induced on it. For example, when the excitation field is in a planar waveguide, the metasurface element is coupled to the excitation field in the waveguide by a slot with a certain orientation. The radiation field is generated by the induced time-harmonic current of a square, circular, or elliptical metal patch whose principal axis is aligned with the slot. The intensity, direction, and phase of the induced time-harmonic current density vector can be extracted to describe the surface current distribution. The two-dimensional array can be modeled as a periodically arranged subwavelength spacing equivalent short dipole array, with the short dipole vibration direction along the array plane.

[0030] Furthermore, in a subwavelength periodic two-dimensional array, the periodically arranged array topology satisfies the following: each subwavelength radiating element is rotated 90° around a straight line passing through its geometric center and perpendicular to the array plane, and the new array formed can be obtained by translating the original array in a certain direction within the array plane by no more than one subwavelength radiating element interval.

[0031] Furthermore, in step 1, a reference oscillator array is defined, consisting of elements located at r. mn It consists of N×N oscillators with an amplitude of 1 that vibrate simultaneously. The vibration direction of each oscillator is the same as the polarization direction of the corresponding subwavelength radiating element, and the angle between the vibration direction and the positive x-axis is ∠p. mn .

[0032] Furthermore, the specific process of step 3 is as follows:

[0033] Define the unit direction vector associated with a single beam as: in, θ represents the angle between the projection of the single beam pointing direction onto the XOY plane and the positive x-axis, and θ represents the angle between the single beam pointing direction and the positive z-axis.

[0034] Target state s corresponding to a single beam ob (r mn )for:

[0035]

[0036] Where k0 represents the electromagnetic wave number in a vacuum;

[0037] Let W be the number of sub-beams, and let the beam direction of the w-th sub-beam be... 1≤w≤W, θ represents the angle between the projection of the w-th sub-beam pointing direction onto the XOY plane and the positive x-axis.w The angle between the pointing direction of the w-th sub-beam and the positive z-axis is given by the following formula:

[0038] The target state s corresponding to the desired radiation beam ob (r mn )for:

[0039]

[0040] Where α is the radiation energy factor, expressed as:

[0041]

[0042] Furthermore, in step 5, the adjusted target state s ob '(r mn )for:

[0043]

[0044] The beneficial effects of this invention are:

[0045] The beamforming method described in this invention supports flexible beamforming of reconfigurable subwavelength periodic two-dimensional arrays. It can simply and efficiently calculate the modulation factor distribution to generate multiple beams with different beam directions and numbers. The method of this invention achieves beamforming only by modulating the radiation intensity of the metasurface unit, reducing the requirements for the reconfigurability of the subwavelength periodic two-dimensional array, thereby greatly reducing the difficulty of implementing reconfigurable technology and alleviating the design pressure of subwavelength periodic two-dimensional array antennas. Using the method of this invention, when the subwavelength periodic two-dimensional array has certain electromagnetic characteristic reconfigurability through feasible technologies such as variable capacitors or liquid crystal technology, dynamic beamforming can be realized, which is of great significance to the development of reconfigurable technology for subwavelength periodic two-dimensional arrays. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of the subwavelength periodic two-dimensional array structure in the method described in the embodiment;

[0047] Figure 2 This is a schematic diagram of the operation interface in the method described in the embodiment;

[0048] Figure 3 This is a schematic diagram of the initial radiation array state in the method described in the embodiment;

[0049] Figure 4In the method described in the embodiment, when N=31 and the unit spacing is 1 / 5 of the working wavelength, under the condition that the modulation factor has three degrees of freedom of polarization direction, amplitude and phase, the array distribution of the modulation generated dual beams and the normalized three-dimensional radiation pattern of its far-field radiation (in dBi) are generated.

[0050] Figure 5 In the method described in the embodiment, when N=31 and the unit spacing is 1 / 5 of the working wavelength, under the condition that the modulation factor has two degrees of freedom in amplitude and phase, the array distribution of the modulation generated dual beams and the normalized three-dimensional radiation pattern of its far-field radiation (in dBi) are obtained.

[0051] Figure 6 The modulation factor distribution, array distribution, and normalized three-dimensional radiation pattern (in dBi) of the dual beams generated by amplitude modulation are shown in the embodiment when N=31 and the unit spacing is 1 / 5 of the working wavelength.

[0052] Figure 7 In the method described in the embodiment, when N=51 and the unit spacing is 1 / 8 of the working wavelength, under the condition that the modulation factor has three degrees of freedom of polarization direction, amplitude and phase, the array distribution of flat-top beam and single beam and the normalized three-dimensional radiation pattern of far-field radiation are simultaneously generated by modulation.

[0053] Figure 8 In the method described in the embodiment, when N=51 and the unit spacing is 1 / 8 of the working wavelength, under the condition that the modulation factor has two degrees of freedom in amplitude and phase, the array distribution of the flat-top beam and the single beam and the normalized three-dimensional radiation pattern of the far-field radiation are simultaneously modulated to generate the array distribution and the far-field radiation (in dBi).

[0054] Figure 9 In the method described in the embodiment, when N=51 and the unit spacing is 1 / 8 of the working wavelength, the modulation factor distribution map, array distribution and normalized three-dimensional radiation pattern of the far-field radiation of the flat-top beam and the single beam are generated simultaneously by amplitude modulation (in dBi). Detailed Implementation

[0055] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0056] This embodiment provides a pure amplitude modulation beamforming method based on a subwavelength periodic electromagnetic surface. The application is a subwavelength periodic two-dimensional array composed of metasurface units with identical geometry but different orientations. The radiation fields coupled from the excitation field by each metasurface unit together form the array's radiation field, where the coupling strength can be varied. The beamforming method requires the periodically arranged array topology to satisfy the following condition: each metasurface unit is rotated 90° about a straight line passing through its geometric center and perpendicular to the array plane. The resulting new array can be obtained by translating the original array along a certain direction within the array plane by no more than one metasurface unit interval.

[0057] The structural schematic diagram of the subwavelength periodic two-dimensional array described in this embodiment is as follows: Figure 1 As shown, the structure includes a lower planar slotted waveguide and an upper metasurface, possessing the ability to reconfigure electromagnetic parameters based on liquid crystal properties. The waveguide is a cuboid cavity structure with square upper and lower surfaces. A monopole at the center of the cavity excites a guided wave on a cylindrical wavefront. A Cartesian coordinate system is established with the geometric center of the cavity as the origin, and the upper and lower surfaces of the waveguide are parallel to the XOY plane. The upper surface of the waveguide has densely distributed short slots. The upper metasurface is composed of rectangular plates corresponding one-to-one with the slots, with the rectangular plates oriented in the same direction as the slots. A rectangular plate and its corresponding slot form a resonant structure, called a resonant unit. The slots are excited by the electromagnetic field below to generate electromagnetic radiation. The radiation from these structures is superimposed to form the total radiation field of the metasurface. Liquid crystal is filled between the rectangular plates and the slots. By changing the bias voltage, the dielectric constant of the liquid crystal is adjusted, thereby changing the resonant frequency of the unit and thus adjusting the weight of the coupled radiation intensity of each resonant unit in the total radiation. By configuring the "weights" of each resonant unit, the desired radiation field is obtained. This weight distribution is called a modulation map. In this embodiment, the final modulation pattern is a distribution pattern composed of the dielectric constants of the resonant units at each position.

[0058] In this embodiment, the resonant unit couples electromagnetic energy from the electromagnetic field in the lower waveguide through waveguide slots. The rectangular plate above the resonant unit induces a time-harmonic current, generating electromagnetic radiation. The polarization direction of the current density is consistent with the orientation of the slots. In this embodiment, the angle between each slot and the line connecting its midpoint and the antenna center is ±45°, and they are alternately distributed. A resonant unit is characterized by the intensity direction and phase of the time-harmonic current density vector. Therefore, this model can be equivalent to a periodically arranged subwavelength-spaced equivalent short dipole array, where the short dipole vibration direction is along the array plane. The short dipoles are called oscillators, and in this embodiment, oscillators are used to describe the resonant unit.

[0059] For the aforementioned subwavelength periodic two-dimensional array, the method described in this embodiment specifically includes the following steps:

[0060] Step 1. Mathematical modeling and state definition;

[0061] Establish a Cartesian coordinate system. The array plane lies within the XOY plane and contains N×N resonant elements, where N is an odd number. The geometric centers of each resonant element form a uniformly distributed grid. The element spacing is d, with rows parallel to the x-axis and columns parallel to the y-axis. The geometric center of the metasurface element in the m-th row and n-th column is located at... 1≤n≤N, 1≤m≤N. Each resonant unit is modeled as an oscillator on a lattice point.

[0062] Define a reference oscillator array, consisting of elements located at r mn It consists of N×N oscillators with an amplitude of 1 that vibrate simultaneously. The vibration direction of each oscillator is the same as the polarization direction of the corresponding subwavelength radiating element, and the angle between the vibration direction and the positive x-axis is ∠p. mn When m+n is even, ∠p mn =φ mn +π / 4; when m+n is odd, ∠p mn =φ mn -π / 4. Where φ mn It points from (0,0) to r mn The angle between the direction vector and the positive x-axis ranges from 0 to 2π. This reference oscillator array is set up because the oscillator at each position actually vibrates one-dimensionally along a certain direction, and the direction is different at different positions. With the reference oscillator array, it is easier to express the various oscillator array states.

[0063] Each metasurface element is compared with the reference oscillator at the corresponding position, and the amplitude scaling and phase difference are combined into a complex number; by traversing all metasurface elements, a complex matrix is ​​obtained to characterize the state of the oscillator array, or simply array state.

[0064] Various oscillator array states, such as the initial state (the array state under initial uncontrolled conditions) and the target state (the array state that generates the target radiation beam), are all composed of N×N complex numbers s(r mn ) expression. For example, located at r mn The complex number corresponding to the oscillator in the target state is It indicates that it is related to r mn The reference oscillators at each point have opposite oscillation directions and lead the phase by π / 3, or have the same oscillation direction and lead the phase by 4π / 3. A spherical coordinate system is established with the center of the array as the origin to describe the radiation field associated with the array state.

[0065] Step 2. Initial state calculation;

[0066] Depending on the specific excitation field, the area located at r mn The initial state of the oscillator is represented as Among them, A mn and Ψ mn They represent the locations at r respectively mn The amplitude and phase of the oscillator relative to the reference oscillator, Amn >0, j is the imaginary unit.

[0067] In this embodiment, k0 is the electromagnetic wave number in vacuum, and || denotes modulus. This formula characterizes r mn The equivalent oscillator in the radiation state of the resonant unit, when unmodulated, has the same starting direction as the reference oscillator at that location, but lags behind by k in phase. g |r mn |

[0068] Step 3. Calculate the target state;

[0069] Define the unit direction vector as in, θ represents the angle between the projection of the single beam pointing direction onto the XOY plane and the positive x-axis, while θ represents the angle between the single beam pointing direction and the positive z-axis.

[0070] Target state s corresponding to a single beam ob (r mn )for:

[0071]

[0072] Where k0 represents the electromagnetic wave number in a vacuum.

[0073] Based on the superposition principle of electromagnetic fields, the desired radiation beam is synthesized by superimposing multiple single beams; then, due to the linearity from the array state to the radiation field, the corresponding array state of the desired radiation beam is the superposition of the target states of the sub-beams (i.e., single beams).

[0074] Let W be the number of sub-beams, and let the beam direction of the w-th sub-beam be... 1≤w≤W, θ represents the angle between the projection of the w-th sub-beam pointing direction onto the XOY plane and the positive x-axis. w The angle between the pointing direction of the w-th sub-beam and the positive z-axis is given by the following formula:

[0075] The target state s corresponding to the desired radiation beam ob (r mn )for:

[0076]

[0077] Here, α is used to maintain the same radiated energy regardless of the number of sub-beams.

[0078]

[0079] Step 4. Calculate the full modulation factor;

[0080] The modulated state (the modulated state of the oscillator array) is obtained by modulating the amplitude and phase of each oscillator in the initial state. The modulation factor is used to describe the modulation process. The modulation factor that modulates the initial state to the target state is called the full modulation factor.

[0081] Full modulation factor m(r) mn ) satisfies s ob (r mn )=m(r mn )s0(r mn ),Right now:

[0082]

[0083] Step 5. Target state adjustment;

[0084] Since amplitude modulation can only change the magnitude and not the sign, the amplitude modulation factor needs to be restricted to a positive number. Therefore, utilizing the linear relationship between the oscillator array and the radiation field, a non-directional array state of the radiation field can be superimposed on the target state. Here, for ease of calculation, an initial state is chosen to be superimposed again, resulting in the adjusted target state s. ob '(r mn ):

[0085]

[0086] Step 6. Modulation factor calculation;

[0087] By s ob '(r mn )=m'(r mn )s0(r mn The adjusted full modulation factor is:

[0088] m'(r mn )=m(r mn )+1

[0089] Amplitude modulation factor m A (r mn )for:

[0090]

[0091] Where Re represents the real part;

[0092] The amplitude modulation factor distributions corresponding to all resonant units form the final modulation map. Based on the modulation map, amplitude modulation is performed on each resonant unit to generate the desired radiation beam.

[0093] In this embodiment, the target state s ob (r mn The target radiation field obtained Represented as:

[0094]

[0095] in, Indicates the azimuth angle. The unit direction vector of the pitch angle θ.

[0096] In this embodiment, the amplitude modulation factor m A (r mn The resulting modulation state is:

[0097]

[0098] Its corresponding radiation field is expressed as:

[0099]

[0100] Figure 2 The interface of the beamforming method described in this embodiment is shown, which can intuitively present the relationship between modulation parameters and radiation field distribution.

[0101] Figure 3 This is a schematic diagram of the initial radiation array state when N=31 and the unit spacing is 1 / 5 of the working wavelength in the method described in this embodiment. The normalized arrow length quantifies the radiation intensity of the unit, the color level represents the phase distribution relative to the reference unit, and the arrow direction intuitively presents the oscillation direction of the time harmonic current of each unit, which completely depicts the electromagnetic state of the array before modulation.

[0102] Figure 4 In the method described in this embodiment, when N=31, the element spacing is 1 / 5 of the working wavelength, and the modulation factor has three degrees of freedom (polarization direction, amplitude, and phase), a dual-beam array and radiation pattern are generated. Under the same configuration, after constraining the vibration direction of each oscillator, the modulation factor loses its polarization direction degree of freedom. By adjusting the amplitude and phase of the initial state, the modulated array and generated radiation pattern are as follows. Figure 5 As shown. Simulation results show that, under the array topology used in this embodiment, the radiation pattern generated by the target state calculated through the geometric projection method in step 3 is consistent with... Figure 4 The results displayed are consistent. Figure 6 This paper demonstrates the amplitude modulation pattern, modulated array state, and resulting upper half-space far-field radiation pattern generated by the pure amplitude modulation beamforming method described in this embodiment, under further constraints on the phase of each element. Compared to the amplitude-phase modulation case, although the sidelobes increase, the desired beamforming effect is achieved.

[0103] Figure 7In the method described in this embodiment, when N=51, the unit spacing is 1 / 8 of the working wavelength, and the modulation factor has three degrees of freedom: polarization direction, amplitude, and phase, a flat-top beam and a single beam array and radiation pattern are generated. Figure 8 With the same configuration, under the array topology used in this embodiment, when the modulation factor has two degrees of freedom, amplitude and phase, the modulated array state and the corresponding radiation pattern are as follows. Figure 9 The results of pure amplitude modulation for the same beamforming task include amplitude modulation pattern, modulated array state, and far-field radiation pattern.

[0104] When the modulation degrees of freedom include three dimensions: oscillator direction, amplitude, and phase, an oscillator array is obtained by mapping the target radiation field, characterized by a set of complex vector distributions. Then, each complex vector in this distribution is geometrically projected onto the line where the oscillator actually vibrates. The resulting distribution is described by the target state expression in step 3. For array topologies that satisfy the conditions described in this embodiment, the radiation field generated by the array state obtained in this way is consistent with the target radiation field. The method described in this embodiment creatively extends the projection process of the geometric space to the complex space. Analogous to the case where the line where the oscillator vibrates cannot change in the geometric plane, the case where the phase of each oscillator does not support active modulation is described as: the direction of the complex vector representing the oscillator cannot change in the complex plane. Projection calculation in the geometric plane can compensate for the reduced modulation degree of freedom in the oscillator direction dimension, achieving beamforming through amplitude-phase modulation. Similarly, projection calculation in the complex plane (amplitude modulation reflected in complex space is projection calculation) compensates for the reduced modulation degree of freedom in the phase dimension, achieving beamforming only through amplitude modulation on an array where the phase of each radiation element is determined. In summary, simulation results demonstrate that the method proposed in this invention can achieve flexible beamforming simply through amplitude modulation.

Claims

1. A pure amplitude modulation beamforming method based on a subwavelength periodic electromagnetic surface, characterized in that, It is applied to a subwavelength periodic two-dimensional array composed of subwavelength radiating units with the same geometry but different orientations. The radiating fields coupled from the excitation field by each subwavelength radiating unit together form the radiating field of the subwavelength periodic two-dimensional array, and the coupling strength can be changed. Step 1. Mathematical modeling and state definition; Establish a Cartesian coordinate system. The array plane lies within the XOY plane and contains N×N subwavelength radiating elements, where N is an odd number. The geometric centers of each subwavelength radiating element form a uniformly distributed grid. The element spacing is d, with rows parallel to the x-axis and columns parallel to the y-axis. The geometric center of the metasurface element in the m-th row and n-th column is located at... Each subwavelength radiative unit is modeled as an oscillator on a lattice point; Define a reference oscillator, compare each subwavelength radiating element with the reference oscillator at the corresponding position, and combine the amplitude scaling and phase difference into a complex number; traverse all subwavelength radiating elements to obtain a complex matrix to characterize the oscillator array state, i.e., the array state; Step 2. Initial state calculation; Will be located at r mn The initial state of the oscillator is represented as Among them, A mn and Ψ mn They represent the locations at r respectively mn The amplitude and phase of the oscillator relative to the reference oscillator, A mn >0, j is the imaginary unit; Step 3. Calculate the target state; Define the unit direction vector corresponding to the pointing direction of a single beam, and give the target state corresponding to the single beam; based on the principle of electromagnetic field superposition, synthesize the desired radiation beam by superimposing multiple single beams, and give the target state s corresponding to the desired radiation beam based on the target state corresponding to the single beam. ob (r mn ); Step 4. Calculate the full modulation factor; Calculate the modulation factor m(r) that modulates the initial state to the target state corresponding to the desired radiation beam. mn ): The superscript * indicates conjugate; Step 5. Target state adjustment; The target state corresponding to the desired radiation beam is superimposed with the initial state to obtain the adjusted target state s. ob '(r mn ); Step 6. Modulation factor calculation; Adjusted full modulation factor m'(r) mn )for: m'(r mn )=m(r mn )+1 Amplitude modulation factor m A (r mn )for: Where Re represents the real part; The amplitude modulation factor distributions corresponding to all subwavelength radiating elements form the final modulation map. Based on the modulation map, amplitude modulation is performed on each subwavelength radiating element to generate the desired radiating beam.

2. The pure amplitude modulation beamforming method based on a subwavelength periodic electromagnetic surface according to claim 1, characterized in that, In a subwavelength periodic two-dimensional array, the polarization direction of each subwavelength radiating unit is fixed, and a metasurface unit can be characterized by the polarization direction, amplitude, and phase of the induced time-harmonic current.

3. The pure amplitude modulation beamforming method based on a subwavelength periodic electromagnetic surface according to claim 1, characterized in that, In a subwavelength periodic two-dimensional array, the periodically arranged array topology satisfies the following: each subwavelength radiating element is rotated 90° around a straight line passing through its geometric center and perpendicular to the array plane, and the new array formed can be obtained by translating the original array in a certain direction within the array plane by no more than one subwavelength radiating element interval.

4. The pure amplitude modulation beamforming method based on a subwavelength periodic electromagnetic surface according to claim 1, characterized in that, In step 1, a reference oscillator array is defined, consisting of elements located at r. mn It consists of N×N oscillators with an amplitude of 1 that vibrate simultaneously. The vibration direction of each oscillator is the same as the polarization direction of the corresponding subwavelength radiating element, and the angle between the vibration direction and the positive x-axis is ∠p. mn .

5. The pure amplitude modulation beamforming method based on a subwavelength periodic electromagnetic surface according to claim 4, characterized in that, The specific process of step 3 is as follows: Define the unit direction vector associated with a single beam as: in, θ represents the angle between the projection of the single beam pointing direction onto the XOY plane and the positive x-axis, and θ represents the angle between the single beam pointing direction and the positive z-axis. Target state s corresponding to a single beam ob (r mn )for: Where k0 represents the electromagnetic wave number in a vacuum; Let W be the number of sub-beams, and let the beam direction of the w-th sub-beam be... 1≤w≤W, θ represents the angle between the projection of the w-th sub-beam pointing direction onto the XOY plane and the positive x-axis. w The angle between the pointing direction of the w-th sub-beam and the positive z-axis is given by the following formula: The target state s corresponding to the desired radiation beam ob (r mn )for: Where α is the radiation energy factor, expressed as:

6. The pure amplitude modulation beamforming method based on a subwavelength periodic electromagnetic surface according to claim 5, characterized in that, In step 5, the adjusted target state s ob '(r mn )for:

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