Two-dimensional antenna array multi-beam scanning method based on holographic amplitude weighting

Abstract

The application relates to the field of wireless communication and sensing technology, and particularly discloses a two-dimensional antenna array multi-beam scanning method based on holographic amplitude weighting, which comprises the following steps: determining the position information of each radiation unit in the two-dimensional antenna array, including calculating the unit spacing and arrangement mode; generating the amplitude weighting value of each radiation unit according to the target wave direction; using the two-dimensional multi-beam holographic amplitude weighting technology, the amplitude weighting value of the radiation unit is determined through the two-dimensional multi-beam holographic amplitude weighting technology; generating the corresponding binary discretization coding sequence based on the amplitude weighting value to control the excitation amplitude of each radiation unit; designing a Ka-band two-dimensional holographic beam scanning leaky-wave antenna square array based on liquid crystals, and the radiation pattern of the two-dimensional antenna array is regulated and controlled through the coding sequence to realize multi-beam scanning.

Description

Technical Field

[0001] This invention relates to the field of wireless communication and sensing technology, specifically to a multi-beam scanning method for a two-dimensional antenna array based on holographic amplitude weighting. Background Technology

[0002] Currently, the demand for wireless communication and sensing technologies is growing rapidly, especially in fields such as 5G / 6G millimeter-wave communication, satellite communication, high-precision radar, and the Internet of Things (IoT). These application scenarios place higher demands on antenna systems, including the ability to achieve high gain, narrow beamwidth, simultaneous operation of multiple beams, fast beam scanning, and compact integration. As a key component for realizing these functions, the beam scanning capability of the antenna array is crucial. Traditional beam scanning methods, such as phase control via phase shifters (analog beamforming) or complex digital signal processing (digital beamforming), often face problems such as high cost, system complexity, high power consumption, or limited scanning speed.

[0003] In recent years, antenna design based on holographic principles has provided a novel and promising approach to beam scanning. Holographic antennas form a desired radiation pattern in the far field by precisely controlling the distribution of the electromagnetic field across the antenna aperture. Holographic amplitude weighting, as an important holographic technique, aims to synthesize the desired hologram by adjusting the radiation amplitude of the antenna array elements, thereby forming a specific beam. This technique exhibits unique advantages in leaky-wave antenna design due to its ability to achieve continuous beam scanning and more flexible beamforming capabilities.

[0004] Leaky wave antennas are a type of traveling wave antenna. Compared to traditional mechanically scanned and electrically controlled scanned antennas, leaky wave antennas offer advantages such as high gain, low profile, simple feeding system, and good beam scanning. Traditional leaky wave antennas are frequency-scanning antennas, meaning the main beam changes with frequency. However, due to increasingly scarce spectrum resources, this frequency-scanning characteristic limits the antenna's application range. Therefore, designing fixed-frequency beam-scanning leaky wave antennas has become an important research topic.

[0005] Currently, loading active devices such as PIN diodes or varactor diodes is a common method for achieving fixed-frequency beam scanning in leaky-wave antennas. However, its main drawback is that it cannot be effectively used in the millimeter-wave band or even higher frequencies, limiting its application range. Adding tunable materials such as graphene and ferrite to the antenna element can also achieve fixed-frequency beam scanning, but this suffers from increased loss as the frequency increases. In recent years, liquid crystal materials, with their excellent low-loss performance at high frequencies, have been applied in the field of reconfigurable antennas. Compared with active devices and other tunable materials, liquid crystal materials have a wider application frequency range, from 10 GHz to the optical band, and their insertion loss decreases as the frequency increases, making them well-suited for high-frequency antenna design. Therefore, liquid crystal materials have broad application prospects in fixed-frequency beam scanning leaky-wave antenna design.

[0006] Holographic amplitude weighting is a key technology for realizing fixed-frequency beam-scanning leaky antennas. The variable dielectric constant of liquid crystal materials can be well combined with holographic amplitude weighting to complete beam scanning tasks. Therefore, research on the design of liquid crystal-based holographic beam-scanning leaky antennas is of significant value. Furthermore, existing research has demonstrated the theoretical feasibility of holographic amplitude weighting in single-beam and multi-beam scanning of one-dimensional leaky antenna arrays, as well as single-beam scanning of two-dimensional leaky antenna arrays. In other words, most research on beam-scanning leaky antennas has only achieved single-beam scanning, with limited research on multi-beam scanning, especially lacking methods for multi-beam scanning of two-dimensional leaky antennas.

[0007] Therefore, in order to better meet the needs of millimeter-wave satellite communication, and addressing the problems of limited multi-beam scanning methods for two-dimensional antenna arrays, insufficient beam control flexibility, and high high-frequency loss in existing technologies, this invention proposes a two-dimensional multi-beam scanning method based on holographic amplitude weighting for leaky-wave antennas, and designs a two-dimensional leaky-wave antenna array based on liquid crystal metamaterials. The effectiveness and feasibility of the proposed method have been verified. Summary of the Invention

[0008] To achieve the objective of this invention, this application provides a multi-beam scanning method for a two-dimensional antenna array based on holographic amplitude weighting, comprising:

[0009] Step S1: Determine the position information of each radiating element in the two-dimensional antenna array, including the element spacing and arrangement;

[0010] Step S2: Generate the amplitude weighting value of each radiating element according to the target wave direction, and use two-dimensional multibeam holographic amplitude weighting technology to determine the amplitude weighting value of the radiating element.

[0011] Step S3: Generate a corresponding binary discretized encoding sequence based on the amplitude weighting value to control the excitation amplitude of each radiating unit;

[0012] Step S4: Design a Ka-band two-dimensional holographic beam scanning leaky antenna array based on liquid crystal, and control the radiation pattern of the two-dimensional antenna array through the coding sequence to achieve multi-beam scanning.

[0013] In some specific embodiments, in step S1, the two-dimensional antenna array includes:

[0014] Multiple periodically arranged radiating units, each radiating unit including a complementary open resonant ring slot structure and a liquid crystal layer;

[0015] A center-fed structure is used to provide a reference wave to the radiating element;

[0016] The control module is used to generate an encoding sequence and adjust the excitation amplitude of each radiating unit through the encoding sequence.

[0017] In some specific embodiments, in step S2, the magnitude weighting value is determined by the following method:

[0018] Holographic patterns are generated based on the interference effect between the reference wave and the target wave;

[0019] By addressing the beam center concavity problem present in two-dimensional arrays, the phase of the holographic pattern is corrected;

[0020] The contribution rate of each radiating element to the target beam direction is determined by the holographic pattern.

[0021] The contribution rate is discretized to obtain a binary discretized encoding sequence.

[0022] In some specific embodiments, the reference wave is determined according to the center-fed structure, and the target wave is determined according to the expected beam direction.

[0023] In some specific embodiments, the target wave, holographic pattern, and amplitude weighting function are determined according to the following formula:

[0024]

[0025] In the formula, y n The x-coordinate represents the ordinate of the nth radiating element relative to the excitation source. m Let k represent the x-coordinate of the m-th radiating element and the excitation source. ref Let k0 represent the propagation constant of the reference wave in the transmission medium, k0 represent the propagation constant in free space at the same frequency, and θ0 represent the direction of the target beam's elevation angle. Indicates the horizontal angle of the target beam.

[0026] In some specific embodiments, the target wave and amplitude weighting function are determined according to the following formula:

[0027]

[0028] In the formula, y n The x-coordinate represents the ordinate of the nth radiating element relative to the excitation source. m Let θ represent the x-coordinate of the m-th radiating element and the excitation source, k0 represent the propagation constant in free space at the same frequency, and θ represent the x-coordinate of the m-th radiating element and the excitation source. g This indicates the beam pointing at the g-th elevation angle. Let G represent the beam pointing at the t-th horizontal angle, G represent the number of target beam elevation angles, T represent the number of target beam horizontal angles, g represent the g-th target elevation angle, and t represent the t-th target horizontal angle.

[0029] In some specific embodiments, in step S3, the beam scanning function of the two-dimensional leaky antenna array is realized by combining the holographic antenna principle and amplitude weighting technology and weighting the excitation amplitude of each unit.

[0030] In some specific embodiments, in step S3, the two-dimensional leaky antenna array adopts a continuous amplitude weighted excitation amplitude function and a discrete amplitude weighted excitation amplitude function, respectively.

[0031] In some specific embodiments, the continuously amplitude-weighted excitation amplitude function, after addressing the beam center concavity problem, is determined according to the following formula:

[0032]

[0033] In the formula, k ref Let θ represent the propagation constant of the reference wave in the transmission medium, k0 represent the propagation constant in free space at the same frequency, and θ represent the propagation constant of the reference wave in the transmission medium. g This indicates the beam pointing at the g-th elevation angle. Let G represent the beam pointing at the t-th horizontal angle, G represent the number of target beam elevation angles, T represent the number of target beam horizontal angles, g represent the g-th target elevation angle, and t represent the t-th target horizontal angle.

[0034] In some specific embodiments, the discrete amplitude-weighted excitation amplitude function is determined according to the following formula:

[0035]

[0036] In the formula, θ g This indicates the beam pointing at the g-th elevation angle. This indicates the beam direction at the t-th horizontal angle.

[0037] The beneficial effects of the above technical solution are as follows:

[0038] Compared with existing technologies, the holographic amplitude-weighted two-dimensional antenna array multi-beam scanning method and the designed liquid crystal-based two-dimensional beam scanning leaky antenna array proposed in this invention have the following significant technical and beneficial effects:

[0039] 1. Improved beam scanning capability:

[0040] This invention proposes a multi-beam scanning method for a two-dimensional leaky wave antenna array based on holographic amplitude weighting. The two-dimensional array can generate multiple beams simultaneously, and these beams can be controlled to scan in two-dimensional space through coding switching, thus expanding the application range of antenna arrays.

[0041] 2. Performance advantages:

[0042] Antenna miniaturization, wide beam scanning range, and high gain: The designed antenna elements and array have the advantages of low profile and small size. Simulation results show that the Ka-band two-dimensional holographic leaky wave antenna array designed in this invention can achieve azimuth angle... Single-beam scanning from -36° to 40°, and from -60° to 38° elevation angle, can also achieve... Dual-beam / triple-beam scanning from -30° to 30° and θ from -60° to 30°, with a gain exceeding 12dB. Compared to two-dimensional leaky-wave antennas that can only achieve single-beam scanning, this invention has significant advantages in both scanning range and number of beams.

[0043] Application Expansion: This two-dimensional multi-beam scanning capability enables antenna arrays to simultaneously cover multiple targets or perform more flexible signal processing in complex environments, making it suitable for various applications such as radar, communication, and remote sensing. Furthermore, considering that leaky-wave antenna elements or arrays can serve as unit antennas for synthetic aperture arrays in the future, small, compact planar structures (such as rectangular slot waveguides or microstrip patch arrays) can be directly embedded in sparse arrays of synthetic aperture arrays, replacing traditional horn or dipole elements.

[0044] 3. Efficiency Improvement:

[0045] This invention employs a Python-HFSS(PH) control coding method in the simulation design of a two-dimensional leaky wave antenna array, which greatly improves coding efficiency. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 A leakage antenna radiation pattern provided for one embodiment of the present invention;

[0048] Figure 2 A schematic diagram of a holographic antenna beam control method based on binary weighting provided for an embodiment of the present invention;

[0049] Figure 3 A schematic diagram of a two-dimensional array structure provided for one embodiment of the present invention;

[0050] Figure 4 N provided as an embodiment of the present invention x ×N y Schematic diagram of a planar antenna array;

[0051] Figure 5 (a) Front view; (b) Top view; (c) Side view of an antenna element structure provided for an embodiment of the present invention;

[0052] Figure 6 A simulation diagram of the performance of a two-dimensional leaky antenna element provided for one embodiment of the present invention;

[0053] Figure 7 The distribution diagrams of electric field energy (a) and magnetic field energy (b) at the CSRR gap are provided for an embodiment of the present invention;

[0054] Figure 8(a) is a top view of a two-dimensional holographic leaky wave antenna structure provided in an embodiment of the present invention;

[0055] Figure 8(b) is a side view of a two-dimensional holographic leaky wave antenna structure provided in an embodiment of the present invention;

[0056] Figure 9 Provided as an embodiment of the present invention Holographic distribution at θ = 0°;

[0057] Figure 10 Provided as an embodiment of the present invention Far-field beam pattern at θ = 0°;

[0058] Figure 11 Modified phase provided as an embodiment of the present invention Holographic distribution at θ = 0°;

[0059] Figure 12 Modified phase provided as an embodiment of the present invention Far-field beam pattern at θ = 0°;

[0060] Figure 13 Provided as an embodiment of the present invention Holographic distribution diagrams of antenna arrays corresponding to different beam directions; (a) θ = 0°; (b) θ = -30°; (c) θ = 30°; (d) θ = -60°; (e) θ = 40°;

[0061] Figure 14 Provided as an embodiment of the present invention Beam gain diagrams corresponding to different beam directions;

[0062] Figure 15 Provided as an embodiment of the present invention S11 parameter diagrams corresponding to different beam directions;

[0063] Figure 16 Antenna gain diagrams corresponding to different beam directions are provided for one embodiment of the present invention, (a) (b) (c) (d)

[0064] Figure 17 Provided as an embodiment of the present invention Holographic distribution diagrams of antenna arrays with different multi-beam pointing at different times: (a) θ = -10° / 10°; (b) θ = -20° / 20°; (c) θ = -30° / 30°; (d) θ = -60° / 0°; (e) θ = -30° / 0° / 30°; (f) θ = -60° / -30° / 0°;

[0065] Figure 18 Provided as an embodiment of the present invention Beam gain diagrams corresponding to different beam directions at different times;

[0066] Figure 19 Provided as an embodiment of the present invention S11 parameter diagrams corresponding to different multi-beam pointing times;

[0067] Figure 20 Antenna gain diagrams corresponding to different multi-beam pointing directions are provided for one embodiment of the present invention, (a) (b) (c) (d)

[0068] Figure 21 This is a flowchart illustrating an embodiment of the present invention. Detailed Implementation

[0069] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0070] Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar symbols denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0071] Example 1

[0072] One embodiment of the present invention provides a multi-beam scanning method for a two-dimensional antenna array based on holographic amplitude weighting, referring to... Figure 21 As shown, it includes:

[0073] Step S1: Determine the position information of each radiating element in the two-dimensional antenna array, including calculating the element spacing and arrangement;

[0074] In a specific embodiment of the present invention, step S1 includes the two-dimensional antenna array comprising:

[0075] Multiple periodically arranged radiating units, each radiating unit including a complementary open resonant ring slot structure and a liquid crystal layer;

[0076] A center-fed structure is used to provide a reference wave to the radiating element;

[0077] The control module is used to generate an encoding sequence and adjust the excitation amplitude of each radiating unit through the encoding sequence.

[0078] Step S2: Generate the amplitude weighting value of each radiating element according to the target wave direction, and use two-dimensional multibeam holographic amplitude weighting technology to determine the amplitude weighting value of the radiating element.

[0079] In a specific embodiment of the present invention, in step S2, the magnitude weighting value is determined by the following method:

[0080] Based on existing one-dimensional leaky antenna single / multi-beam scanning methods and two-dimensional leaky antenna single-beam scanning methods based on holographic amplitude weighting, a two-dimensional array multi-beam scanning holographic amplitude weighting technique is proposed.

[0081] Holographic patterns are generated based on the interference effect between the reference wave and the target wave;

[0082] To solve the beam center concavity problem in two-dimensional arrays and correct the phase of holographic patterns;

[0083] The contribution rate of each radiating element to the target beam direction is determined by the holographic pattern.

[0084] The contribution rate is discretized to obtain a binary discretized encoding sequence.

[0085] In one specific embodiment of the present invention, the reference wave is determined according to the center-fed structure, and the target wave is determined according to the expected beam direction.

[0086] In one specific embodiment of the present invention, the target wave, the holographic pattern, and the amplitude weighting function are determined according to the following formula:

[0087]

[0088] In the formula, y n The x-coordinate represents the ordinate of the nth radiating element relative to the excitation source. m Let k represent the x-coordinate of the m-th radiating element and the excitation source. ref Let k0 represent the propagation constant of the reference wave in the transmission medium, k0 represent the propagation constant in free space at the same frequency, and θ0 represent the direction of the target beam's elevation angle. Indicates the horizontal angle of the target beam.

[0089] In a specific embodiment of the present invention, the target wave and the amplitude weighting function are determined according to the following formula:

[0090]

[0091]

[0092] In the formula, y n The x-coordinate represents the ordinate of the nth radiating element relative to the excitation source. m Let θ represent the x-coordinate of the m-th radiating element and the excitation source, k0 represent the propagation constant in free space at the same frequency, and θ represent the x-coordinate of the m-th radiating element and the excitation source. g This indicates the beam pointing at the g-th elevation angle. Let G represent the beam pointing at the t-th horizontal angle, G represent the number of target beam elevation angles, T represent the number of target beam horizontal angles, g represent the g-th target elevation angle, and t represent the t-th target horizontal angle.

[0093] Step S3: Generate a corresponding binary discretized encoding sequence based on the amplitude weighting value to control the excitation amplitude of each radiating unit;

[0094] In a specific embodiment of the present invention, in step S3, by combining the principle of holographic antenna and amplitude weighting technology, the beam scanning function of the two-dimensional leaky antenna array is realized by weighting and adjusting the excitation amplitude of each unit.

[0095] In a specific embodiment of the present invention, in step S3, the two-dimensional leaky antenna array adopts a continuous amplitude weighted excitation amplitude function and a discrete amplitude weighted excitation amplitude function, respectively.

[0096] In a specific embodiment of the present invention, the continuous amplitude-weighted excitation amplitude function, after solving the beam center concavity problem, is determined according to the following formula:

[0097]

[0098] In the formula, k ref Let θ represent the propagation constant of the reference wave in the transmission medium, k0 represent the propagation constant in free space at the same frequency, and θ represent the propagation constant of the reference wave in the transmission medium. g This indicates the beam pointing at the g-th elevation angle. Let G represent the beam pointing at the t-th horizontal angle, G represent the number of target beam elevation angles, T represent the number of target beam horizontal angles, g represent the g-th target elevation angle, and t represent the t-th target horizontal angle.

[0099] In a specific embodiment of the present invention, the discrete amplitude weighted excitation amplitude function is determined according to the following formula:

[0100]

[0101] In the formula, θ g This indicates the beam pointing at the g-th elevation angle. This indicates the beam direction at the t-th horizontal angle.

[0102] Step S4: Design a Ka-band two-dimensional holographic beam scanning leaky antenna array based on liquid crystal, and control the radiation pattern of the two-dimensional antenna array through the coding sequence to achieve multi-beam scanning.

[0103] Example 2

[0104] In one embodiment of the present invention, a holographic antenna can achieve desired beam scanning by adjusting the amplitude or phase of the unit to form a holographic pattern. Currently, there are two main methods for forming holographic patterns: one is joint amplitude and phase adjustment, using a phase shifter to control the phase and adjust the unit excitation amplitude to achieve spatial beam switching, but this method is complex and costly. The other is a fixed phase distribution, controlling beam formation and switching solely by adjusting the unit excitation amplitude; this method is simple, low-cost, and easy to integrate. Therefore, to achieve the beam scanning function of a leaky wave antenna, an amplitude weighting method is adopted. This method is based on the principle of holographic antennas and is a holographic antenna technology that only adjusts the unit excitation amplitude; therefore, it is also called holographic amplitude weighting technology or amplitude weighting technology based on the holographic principle. A holographic antenna mainly includes a source antenna and a holographic structure. The source antenna outputs a reference wave, and the desired beam is the target wave. The function of the holographic antenna is to generate a holographic image to record the information of the target wave. The target wave can be reconstructed by irradiating the holographic image with the reference wave. For a one-dimensional leaky wave antenna structure, the equations for the reference wave and the target wave are expressed as:

[0105] ψ ref (y n ) = exp(-jk ref y n (1)

[0106] ψ obj (y n ,θ0)=exp(-jk0sin(θ0)y n (2)

[0107] Among them, y n k represents the distance between the nth radiating element and the excitation source. ref θ represents the propagation constant of the reference wave in the transmission medium, k0 represents the propagation constant in free space at the same frequency, and θ0 represents the expected beam direction.

[0108] The interference pattern ψ(y) can be obtained from the principle of interference. n ,θ0) is:

[0109]

[0110] When the reference wave source ψ ref (y n When the holographic image is illuminated, the last term in equation (3) can be used to reproduce the target wave:

[0111]

[0112] ψ obj (y n ,θ0)=ψ inf (y n,θ0)ψ ref (y n ) / |ψ ref (y n )| 2 (5)

[0113] Holographic amplitude-weighted technology is a technique that uses an amplitude function to adjust the excitation amplitude at each unit, thereby forming a holographic pattern. This amplitude function can be expressed as:

[0114]

[0115] The contribution rate m(y) of each antenna element to the desired beam pointing θ0 can be obtained using formula (6). n The contribution rate is a number between 0 and 1; the larger the value, the stronger the contribution of y. n The closer the phase shift value at a given location is to the target phase shift value, the better. n The more energy radiated from a given element, the greater its contribution to the desired beam direction; conversely, the less energy radiated, the smaller its contribution. The amplitude function is discretized: when m(y n When m(y,θ0) is greater than 0.5, set it to "1"; when m(y n When θ0) is less than or equal to 0.5, it is set to "0". The processed element excitation amplitude can be expressed as:

[0116]

[0117] The binary discretized coding sequence corresponding to the expected beam direction can be obtained through formula (7). This holographic antenna beam control method based on binary weighting can be used... Figure 2 To express.

[0118] Beam modulation is achieved by constructing a holographic structure through weighted element amplitudes. This holographic amplitude weighting technique can be explained by the far-field pattern theory of array antennas. Consider a one-dimensional array antenna composed of N elements spaced by d, where the phase of each element changes by a fixed value ξ. The far-field region of the nth element is:

[0119]

[0120] For the radiation pattern function of the antenna element, I n and ξ n Let be the amplitude and phase of the nth unit. Applying the far-field approximation to equation (8), we obtain: 1 / r n ≈1 / r. The expression for the far-field total field of the array antenna is:

[0121]

[0122] Where, Δr=rr n =ndsinφ, where φ represents the expected beam direction. The far-field radiation pattern of the array antenna is:

[0123]

[0124] The expression for the matrix factor is:

[0125]

[0126] Given that the radiation characteristics of the antenna elements are known, the study of the antenna pattern can be reduced to the study of the antenna array factor. The phase of a holographic antenna element is determined by the distance between the element and the excitation source and the propagation constant of the reference wave in the medium, i.e., -k ref Therefore, the array factor of a holographic antenna can be expressed as:

[0127]

[0128] According to equation (12), the target beam can be obtained as long as the amplitude weighting value m(nd,φ) at each unit is determined by using holographic amplitude weighting technology.

[0129] The following section introduces a method for implementing one-dimensional array multi-beam scanning based on holographic amplitude weighting:

[0130] Multi-beam antennas can communicate simultaneously in multiple directions, thereby achieving more efficient data transmission and more stable signal reception. Beam scanning methods based on the principle of holographic antennas can control a single beam and also achieve one-dimensional or two-dimensional spatial multi-beam scanning. When the target beam points to two or more targets, one-dimensional multi-beam scanning based on holographic amplitude weighting requires modification of equations (2) and (6). The modified target wave equation and amplitude function are expressed as follows:

[0131]

[0132] Where, θ g The g-th beam direction is indicated. Formula (14) represents the amplitude function for continuous amplitude weighting, which can be further binarized to obtain the amplitude function for discrete amplitude weighting, as shown in Formula (15).

[0133]

[0134] For a two-dimensional holographic beam scanning leaky wave antenna, the design adopts a bottom surface feeding method, that is, a feed source is added at a specific position on the lower surface of the two-dimensional array. Figure 3A schematic diagram of a two-dimensional array is shown, in which each grid node represents an independent radiating element. A reference wave propagates from the bottom feed to all sides of the antenna, and as it passes through the elements, each element radiates energy into free space according to the weighting value specified by the target beam.

[0135] To achieve beam scanning functionality for a two-dimensional leaky wave antenna array, combining the principles of holographic antennas and amplitude weighting techniques, it is necessary to weight and adjust the excitation amplitude of each element. Constructing different two-dimensional planar holographic structures can record different holographic patterns; exciting these holographic structures with a reference wave yields different antenna radiation patterns. This two-dimensional spatial beam scanning method based on holographic amplitude weighting can be explained by the theory of radiation pattern synthesis for two-dimensional planar array antennas.

[0136] Specifically, the radiation pattern of a rectangular planar antenna array, which contains N x ×N y Each element is placed on the xy plane, and a coordinate system is established as follows: Figure 4 .

[0137] Let the row spacing between adjacent matrix grids be d. x The column spacing is d y The mn-th unit P mn The coordinates and position vectors are shown in formulas (16) and (17):

[0138]

[0139] Let r be the distance from the origin to a point in the far field, and let the unit vector be:

[0140]

[0141] Let the excitation current of the mn-th unit be... Its far-field region can be represented as:

[0142]

[0143] In the formula, This represents the radiation pattern function of the radiating element. In far-field radiation, the amplitude in equation (19) can be approximated as 1 / R. mn ≈1 / r.

[0144] Figure 4 It can be calculated from Then the far field of the mn-th element is:

[0145]

[0146] The total far-field of the entire array and its array factors are shown in equations (21) and (22):

[0147]

[0148] Assume the excitation current is distributed in columns as follows Distributed by row but

[0149]

[0150] In equation (23), I xm and I yn The amplitude distributions of the linear arrays in the x and y directions are respectively; ξ x and ξ y These represent the progressive phases of the linear arrays in the x and y directions, respectively. The amplitude expression is M((md) x ,nd y (θ,φ)) represents I xm I yn Therefore, the array factor expression for the far-field radiation field of a two-dimensional planar antenna array is:

[0151]

[0152] In a two-dimensional antenna array, a reference wave propagates from the center feed point along the transmission medium to the surrounding areas. As the wave passes through the periodically arranged elements on the two-dimensional plane, it radiates energy into free space. To construct a holographic pattern, amplitude weighting techniques can be used to weight each element at each location (md). x ,nd y Determine the appropriate weighting magnitude value M((md) for the cell at position ) x ,nd y ),(θ,φ)).

[0153] Based on the one-dimensional beam scanning formula, a two-dimensional beam scanning formula is derived. The reference wave (Equation (1)) is changed to the form of Equation (25), and the target wave (Equation (2)) is changed to the form of Equation (26). Where x m y n This represents the position information of the recording point on the holographic structure, where m represents the m-th column in the x-axis direction, n represents the n-th column in the y-axis direction, and θ0, This indicates the direction of a certain angle in two-dimensional space. The two-dimensional holographic distribution pattern can be represented by (27):

[0154]

[0155] According to formulas (25), (26), and (27), the unit excitation amplitude functions of the two-dimensional leaky antenna array when using continuous amplitude weighting and discrete amplitude weighting are obtained respectively. The amplitude function for continuous amplitude weighting is shown in formula (28), and the amplitude function for discrete amplitude weighting is shown in formula (29).

[0156]

[0157] In the design of two-dimensional antenna arrays, if a center-fed method is used, the forward and backward waves will be out of phase, resulting in different far-field radiation of the front and rear waves, which will cause beam center depression. Therefore, the above-mentioned single-beam scanning theory of two-dimensional holographic leaky wave antenna needs to be modified to address the beam depression problem caused by center feeding. Assuming that the antenna is y-polarized, the forward and backward waves of the antenna propagate along the positive and negative y axes in the three-dimensional coordinate system. Then, the xoz plane is used as the boundary to divide the surface of the antenna into two parts, namely xoy (left) and xoy (right). When the phase difference between the two planes reaches 180°, the beam center depression problem can be solved. For the two-dimensional holographic distribution formulas (27)(28)(29), after setting a 180° phase difference between the two planes, the new holographic distribution formulas are as shown in (30)(31)(32):

[0158]

[0159] The above discussion focused on one-dimensional antenna arrays, explaining single-beam and multi-beam scanning theories for leaky antennas based on holographic amplitude weighting. It also extended this approach to two-dimensional arrays, elucidating a single-beam scanning method for two-dimensional leaky antenna arrays based on holographic amplitude weighting. This application, building upon existing beam scanning theories based on holographic amplitude weighting, proposes a multi-beam scanning method for two-dimensional leaky antennas based on holographic amplitude weighting.

[0160] For the multi-beam implementation of a two-dimensional leaky wave antenna, referring to the multi-beam formula of a one-dimensional array, combining formulas (13)(14)(27)(28)(29) yields the target wave function and amplitude function for the multi-beam implementation of the two-dimensional leaky wave antenna as follows:

[0161]

[0162] Where, θ g This indicates the beam direction at the g-th elevation angle (Theta). This indicates the beam direction at the t-th horizontal angle (Phi).

[0163] According to formula (34), further binarization processing is performed to transform the continuous amplitude weighting into discrete amplitude weighting, as shown in formula (35).

[0164]

[0165] Here, referring to two-dimensional single-beam scanning, the above two-dimensional multi-beam method is modified to consider the beam center concavity problem, and formula (34) is modified to formula (36), as shown below.

[0166]

[0167] According to formula (36), further binarization is performed to transform the continuous amplitude weighting into discrete amplitude weighting, as shown in formula (37).

[0168]

[0169] The design and simulation of a Ka-band two-dimensional holographic leaky-wave antenna array based on liquid crystals includes: unit structure design and simulation. The antenna unit adopts a microstrip line model based on complementary split resonant ring (CSRR) slot units. CSRR is a complementary form of SRR. The SRR structure originated from the development of artificial electromagnetic metamaterials, and this structure consists of two concentric metal split rings. In leaky-wave antennas, frequency selectivity can be achieved by embedding the SRR structure into the antenna leaky-wave slot structure. The device design combined with the SRR structure not only has the advantages of simple structure and miniaturization, but also has good high-frequency resonance characteristics. In this way, CSRR also has the characteristic of negative permeability. Moreover, unlike the SRR structure, the CSRR slot unit has more adjustable size variables and a more complex slot structure, which is beneficial for optimizing the design of the structural unit and can more flexibly control the electromagnetic field radiation efficiency and the energy leaked into free space. Figure 5 This is a two-dimensional leaky wave antenna array element structure, comprising a copper ground plane, a transmission medium, a microstrip line based on CSRR slot elements, and a liquid crystal layer. The transmission medium is Rogers 4003 material with a relative permittivity of 3.55 and a loss tangent of 0.0027. A 0.035mm thick copper plate is placed at the bottom of the transmission medium as a ground plane. The microstrip line based on CSRR slot elements is made of 2µm thick copper metal, topped with a 0.2mm thick liquid crystal layer. The liquid crystal material used is GT3-23001, which has a wide tuning range, with a relative permittivity that can switch from 2.5 to 3.3 and a corresponding loss tangent that can switch from 0.0143 to 0.0038. Detailed dimensions of the antenna element are shown in Table 1.

[0170] Table 1 Antenna Size Parameters

[0171]

[0172] Simulations were performed on a two-dimensional leaky wave antenna element based on CSRR slot elements to obtain the S11 and S21 parameters of the antenna element. Changing the relative permittivity of the liquid crystal material can induce variations in the resonant frequency of the resonator; at different frequency points, the antenna's radiated power and impedance matching performance differ.

[0173] from Figure 6It can be concluded that when the relative permittivity of the liquid crystal is 2.5, the antenna exhibits significant resonance characteristics at 32.1 GHz. At this frequency, 2.5 can be encoded as "1" and 3.3 can be encoded as "0". Simultaneously, the corresponding S11 parameter at this frequency is below -10 dB, indicating that the antenna element has good impedance matching performance. Figure 7 The figure shows the energy distribution of electric and magnetic fields at the CSRR slot. It can be seen from the figure that the electric field energy is mainly distributed at the left and right opening resonant rings of the CSRR slot, and the magnetic field is mainly distributed on the upper and lower sides of the outer ring of the slot. The microstrip line model based on the CSRR slot element can effectively radiate electromagnetic wave energy.

[0174] Four hundred antenna elements were arranged in a two-dimensional planar periodic pattern. According to the transmission principle of periodic leaky wave antennas, the element spacing has a significant impact on the antenna's radiation characteristics. Setting the element spacing as a scanning parameter, a series of comparative simulation experiments revealed that when the element spacing is too large, the 20×20 holographic leaky wave antenna array is prone to generating high-order harmonics; when the spacing is too small, it increases the coupling effect between elements, leading to poor beam scanning performance. Therefore, after optimization, the element spacing was finally determined to be 3.55 mm, and the overall length and width of the antenna were both 70.95 mm, as shown in Figures 8(a) and 8(b).

[0175] The entire antenna array is coaxially fed with the feed port located at the center of the array. As shown in Figure 8(b), the probe length in the dielectric is 2.35 mm, where h t It is 1.45mm, h c It is 0.9mm. The radius w of the coaxial probe. t The diameter is 0.8mm, and the coaxial dielectric material is Teflon. c The diameter is 4.4 mm. By placing absorbing material around the transmission medium, the reflected wave can be reduced.

[0176] To simulate a single-beam scanning two-dimensional leaky antenna array, with the operating frequency set to 32.1 GHz, simulate a two-dimensional leaky antenna array consisting of 400 elements. Set the expected beam pointing of the array to ( θ=0°), substituting these values ​​into equations (28) and (29) yields the discrete amplitude weighted coding sequence. The holographic pattern corresponding to the sequence is as follows: Figure 9 As shown, the red squares represent a relative permittivity of 2.5 for the liquid crystal layer, and the blue area represents 3.3. Based on this holographic distribution, a far-field pattern was obtained through modeling and simulation in HFSS, as shown below. Figure 10 As shown.

[0177] like Figure 10As shown, when the expected direction is (0°, 0°), the actual direction at θ = 0° results in a beam dip problem, which is caused by the inconsistency in the phase of the front and rear waves due to the center feeding method. To address the beam dip problem in the two-dimensional holographic distribution formula (27), a new holographic distribution formula is obtained by setting a 180° phase difference between the two planes. Substituting the expected beam direction back into formulas (30), (31), and (32), the modified holographic distribution of the antenna surface and the far-field pattern are obtained as follows: Figure 11 and Figure 12 As shown, the problem of beam center concavity has been resolved.

[0178] Pick θ can be taken as 0° / -30° / 30° / -60° / 40° respectively. Figure 13 for The antenna holographic distribution diagrams corresponding to each beam pointing to the time are shown. The relative permittivity of the liquid crystal material corresponding to "0" is 3.3 (blue block), and the relative permittivity of the liquid crystal material corresponding to "1" is 2.5 (red block). Figure 14 Gain diagrams for different beam orientations.

[0179] Figure 15 The S11 parameters for each beam pointing direction are shown. At a frequency of 32.1 GHz, the S11 parameters are all below -9 dB, and generally below -10 dB, indicating good impedance matching. From... Figure 15 It can be concluded that different beam directions are consistent with expectations. Table 2 shows the specific angle error and main beam gain for different beam directions.

[0180] Now, regarding multi-beam scanning, combined with the proposed two-dimensional holographic multi-beam method, we take... θ takes values ​​of -10° / 10°, -20° / 20°, -30° / 30°, -60° / 0°, -30° / 0° / 30°, and -60° / -30° / 0° respectively. Substituting these values ​​into formulas (36) and (37) yields the corresponding “0 / 1” encoding sequences. Figure 17 for Holographic distribution of antenna arrays corresponding to different multi-beam pointing directions at different times. Figure 18 Gain diagrams for different multi-beam pointing methods.

[0181] Figure 19 Showing Figure 18 The S11 parameters corresponding to each multi-beam pointing mode are all below -9dB at 32.1GHz, and are basically below -10dB, indicating good impedance matching.

[0182] from Figure 18It can be concluded that different beam directions are consistent with expectations. Table 3 shows the specific angle error and main beam gain for different multi-beam directions. The pointing error is within 2.2° and the beam gain fluctuates around 9dB, realizing multi-beam switching of the array and verifying the effectiveness of the proposed amplitude-weighted two-dimensional holographic leaky wave antenna multi-beam scanning method.

[0183] Figure 20 (a) shows when At that time, the array achieved dual-beam / triple-beam scanning with an elevation angle θ from -30° to 30°, a pointing error within 2.6°, and a beam gain fluctuating around 9dB, reaching a maximum of 10.55dB. The effectiveness of the proposed amplitude-weighted two-dimensional holographic leaky wave antenna array multi-beam scanning method was verified.

[0184] Figure 20 (b) shows when At that time, the array achieved dual-beam scanning with an elevation angle θ from -30° to 30°, a pointing error within 2.5°, and a beam gain of 10.57dB, with fluctuations not exceeding 3dB. The effectiveness of the proposed amplitude-weighted two-dimensional holographic leaky wave antenna array multi-beam scanning method was verified.

[0185] Figure 20 (c) shows when At that time, the array achieved dual-beam scanning with an elevation angle θ from -30° to 30°, a pointing error within 2.9°, and a beam gain of up to 10.74dB. The effectiveness of the proposed amplitude-weighted two-dimensional holographic leaky wave antenna array multi-beam scanning method was verified.

[0186] Figure 20 (d) shows when At that time, the array achieved dual-beam / tri-beam scanning with its elevation angle θ switching from -30° to 30°, a pointing error within 2.5°, and a beam gain of up to 10.60dB. The effectiveness of the proposed amplitude-weighted two-dimensional holographic leaky wave antenna array multi-beam scanning method was verified.

[0187] from Figures 17 to 20 The experimental results show that the antenna array can achieve its beam azimuth angle. Dual / triple beam scanning from -30° to 30° and from -60° to 30° in elevation angle θ demonstrates that the designed two-dimensional antenna array can achieve not only single-beam scanning but also multi-beam scanning. This verifies that the proposed holographic amplitude-weighted two-dimensional antenna array multi-beam scanning method can be well applied to the design and application of two-dimensional leaky wave antenna arrays.

[0188] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

[0189] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. The embodiments of the present invention are described with reference to flowchart illustrations and / or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing terminal equipment to cause a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1The steps of the functions specified in one or more boxes. Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the invention. Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0190] The methods and apparatus provided by the present invention have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

[0191] In the description of this specification, references to terms such as "an embodiment," "some embodiments," "example," "specific example," or "a specific embodiment" or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0192] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A multi-beam scanning method for a two-dimensional antenna array based on holographic amplitude weighting, characterized in that, include: Step S1: Determine the position information of each radiating element in the two-dimensional antenna array, including the element spacing and arrangement; Step S2: Generate the amplitude weighting value of each radiation element according to the target wave direction. The amplitude weighting value of the radiation element is determined by two-dimensional multi-beam holographic amplitude weighting technology. Step S3: Generate a corresponding binary discretized encoding sequence based on the amplitude weighting value to control the excitation amplitude of each radiating unit; Step S4: Design a liquid crystal-based Ka-band two-dimensional holographic beam scanning leaky antenna array, and use the coding sequence to control the radiation pattern of the two-dimensional antenna array to achieve multi-beam scanning; In step S2, the magnitude weighting value is determined using the following method: Holographic patterns are generated based on the interference effect between the reference wave and the target wave; By addressing the beam center concavity problem present in two-dimensional arrays, the phase of the holographic pattern is corrected; The contribution rate of each radiating element to the target beam direction is determined by the holographic pattern. The contribution rate is discretized to obtain a binary discretized encoding sequence; The target wave and amplitude weighting value are determined according to the following formula: （1） （2） Equation (1) represents the target wave, and equation (2) represents the amplitude weighting value. Indicates the first n The ordinate of each radiating element and the excitation source. x m Indicates the first m The x-axis of each radiating element and the excitation source This represents the propagation constant in free space at the same frequency. Indicates the first g Beam pointing at the elevation angle of a target beam. Indicates the first t Beam pointing at the horizontal angle of the target beam. G Indicates the number of target beam elevation angles. T Indicates the number of horizontal angles of the target beam. g Indicates the first g Target beam elevation angle, t Indicates the first t Horizontal angle of the target beam This represents the propagation constant of the reference wave in the transmission medium.

2. The multi-beam scanning method for a two-dimensional antenna array based on holographic amplitude weighting according to claim 1, characterized in that, In step S1, the two-dimensional antenna array includes: Multiple periodically arranged radiating units, each radiating unit including a complementary open resonant ring slot structure and a liquid crystal layer; A center-fed structure is used to provide a reference wave to the radiating element; The control module is used to generate an encoding sequence and adjust the excitation amplitude of each radiating unit through the encoding sequence.

3. The multi-beam scanning method for a two-dimensional antenna array based on holographic amplitude weighting according to claim 1, characterized in that, In step S3, the two-dimensional leaky antenna array successively employs a continuous amplitude weighted excitation amplitude function and a discrete amplitude weighted excitation amplitude function.

4. The multi-beam scanning method for a two-dimensional antenna array based on holographic amplitude weighting according to claim 3, characterized in that, The continuous amplitude weighted excitation amplitude function, after addressing the beam center concavity problem, is determined according to the following formula: In the formula, This represents the propagation constant of the reference wave in the transmission medium. This represents the propagation constant in free space at the same frequency. Indicates the first g Beam pointing at the elevation angle of a target beam. Indicates the first t Beam pointing at the horizontal angle of the target beam. G Indicates the number of target beam elevation angles. T Indicates the number of horizontal angles of the target beam. g Indicates the first g Target beam elevation angle, t Indicates the first t The horizontal angle of the target beam.

5. The multi-beam scanning method for a two-dimensional antenna array based on holographic amplitude weighting according to claim 3, characterized in that, The discrete amplitude weighted excitation amplitude function is determined according to the following formula: In the formula, Indicates the first g Beam pointing at the elevation angle of a target beam. Indicates the first t The beam pointing at the horizontal angle of the target beam.

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