A low-profile full-polarization wide-angle domain far-and-near-field beam two-dimensional adjustable holographic super surface and a regulation and control method thereof

By using a low-profile, fully polarized, wide-angle beamforming two-dimensional tunable holographic metasurface, combined with a T-shaped coupling structure and RF switches, omnidirectional two-dimensional fully polarized wide-angle beam scanning is achieved. This solves the problems of high cost, system complexity, and limited scanning capability of existing holographic antennas, and has the advantages of large-angle scanning capability and low cost.

CN119674557BActive Publication Date: 2025-11-11COMMUNICATION UNIVERSITY OF CHINA
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Patent Information

Application Number
CN202411881020.4
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-12-19
Publication Date
2025-11-11
Estimated Expiration
2044-12-19

AI Technical Summary

Technical Problem

Existing holographic antenna technology suffers from high cost, system complexity, large size, heavy weight, and limited scanning capability. In particular, planar reflective array and transmission array antennas require additional spatial illumination sources, which increases the difficulty of system integration.

Method used

A two-dimensional tunable holographic metasurface based on low-profile, fully polarized, wide-angle, near-field beam scanning is adopted. This metasurface includes a metal plate, a dielectric substrate, an RF feed structure, and a DC feed network. Through a T-shaped coupling structure array and a novel coupling unit, combined with FPGA control circuitry and RF switches, omnidirectional two-dimensional, fully polarized, wide-angle, near-field beam scanning is achieved.

Benefits of technology

It achieves omnidirectional two-dimensional fully polarized wide-angle domain far/near field beam scanning with simple structure and low cost. It has a large scanning range and is easy to control. It is suitable for low profile design and can achieve wide-angle ±70° scanning of far-field pencil beam and wide-angle ±60° scanning of near-field Bessel beam.

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Abstract

This invention provides a two-dimensional tunable holographic metasurface and its control method based on a low-profile, fully polarized, wide-angle, near-field beamforming system. The metasurface includes a top metal plate with a T-shaped coupling structure array on it. The T-shaped coupling structure array includes multiple novel coupling units, and each novel coupling unit has a radio frequency (RF) switch in both the vertical and horizontal directions for controlling coupled radiation. An FPGA control circuit and a direct feed network are located on the lower layer of a second dielectric substrate. The DC feed network applies different DC bias voltages to the center of each novel coupling unit to control the on / off state of the RF switches. This invention has the advantages of simple structure and low cost, and can easily realize multi-polarized beams with arbitrary far / near field orientations, achieving beam scanning in elevation and azimuth angles. It can achieve wide-angle ±70° scanning of far-field pencil beams and wide-angle ±60° scanning of near-field Bessel beams.
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Description

Technical Field

[0001] This invention belongs to the field of holographic metasurface antenna technology, and particularly relates to a two-dimensional tunable holographic metasurface based on low-profile fully polarized wide-angle domain near and far-field beams and its control method. Background Technology

[0002] The holographic principle in the microwave field originates from optical imaging. When object light and reference light meet on a holographic recording medium (such as a holographic plate or photosensitive film), they form an interference pattern. This interference pattern records the phase and amplitude information of the object. The pattern formed by the interference is stored on the recording medium. When the hologram is illuminated with reference light, the reference beam is redirected and diffracts through the hologram. This process allows the light waves to reconstruct the original object.

[0003] To further develop holographic technology in the microwave field, scientists made continuous attempts, and it wasn't until the early 21st century that the method of recording target wave information using the surface impedance values ​​of a printed circuit board structure emerged. When a reference wave illuminates this impedance surface, the pre-designed target wave is reflected. Therefore, holographic antennas can easily achieve target beams with different deflection angles, but because surface impedance is not reconfigurable, it lacks scanning capability.

[0004] O. Yurduseven et al. proposed a reconfigurable holographic metasurface antenna based on a slotted two-dimensional array leaky wave structure, achieving two-dimensional beam scanning (O. Yruduseven and DRSmith, “Dual-Polarization Printed Holographic Multibeam Metasurface Antenna” in IEEE Antennas and Wireless Propagation Letters, vol.16, pp.2738-2741, 2017). However, they did not provide the corresponding feeding structure, making it difficult to directly apply to practical scenarios.

[0005] Application number CN202311528193.3, entitled "Antenna Element with Complementary Slot Resonator Rings, Antenna and Beam Scanning Method," discloses an antenna element with complementary slot resonator rings, an antenna and a beam scanning method. The antenna element comprises, from bottom to top, a copper metal ground plane, a substrate integrated waveguide dielectric substrate, a microstrip line etched with a CSRR structure, and a liquid crystal layer. The substrate integrated waveguide dielectric substrate serves as the transmission structure. This substrate is formed by directly inserting two rows of metal pillars into the middle of the dielectric substrate in the microstrip line transmission structure. The microstrip line etched with the CSRR structure has a CSRR structure in its center, consisting of two metal slot rings with opposite openings and different sizes. An antenna composed of this element can achieve low profile, small size, high gain, and wide-angle beam scanning in the Ka band; it can also achieve multi-beam scanning.

[0006] The antenna element, antenna, and beam scanning method with complementary open-loop resonators (CSRRs) are based on a one-dimensional liquid crystal reconfigurable antenna using holographic theory. The antenna consists of a microstrip line with a CSRR structure and a liquid crystal layer. A substrate-integrated waveguide dielectric substrate serves as the transmission structure. The substrate-integrated waveguide dielectric substrate forms beam pointing patterns of +30° and 0°, -10° and +10°, -30° and +30°, and -30° and +50° by directly inserting two rows of metal pillars into the dielectric substrate within the microstrip line transmission structure. The problems with this approach are: high cost and system complexity, large size and weight; while planar reflective and transmissive array antennas require additional spatial illumination sources, resulting in a high system profile and increased difficulty in system integration. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a two-dimensional tunable holographic metasurface and control method based on low-profile fully polarized wide-angle domain far and near field beams. This antenna is based on binary holography theory and can realize omnidirectional two-dimensional fully polarized wide-angle domain far / near field beam scanning. It also has a simple structure and low cost.

[0008] The present invention adopts the following technical solution:

[0009] Based on a low-profile, fully polarized, wide-angle-domain, near-field beamforming two-dimensional tunable holographic metasurface, the system comprises a metal plate, a dielectric substrate, an RF feed structure, and a DC feed network. A first metal plate is located on the upper surface of a first dielectric substrate, a second metal plate is located on the lower surface of the first dielectric substrate, and the DC feed network is located on the lower surface of the second dielectric substrate. The RF feed structure is an SMA connector, with its metal outer shell penetrating through and connecting to the second dielectric substrate and the second metal plate. The inner probe of the SMA connector penetrates through the second dielectric substrate, the second metal plate, the first dielectric substrate, and the first metal plate.

[0010] A T-shaped coupling structure array is etched onto a first metal plate for leakage radiation. The T-shaped coupling structure array includes multiple novel coupling units that are symmetrically arranged around the perimeter. An annular slot with the inner core probe of the SMA connector as the origin is etched on the first metal plate, and the novel coupling units are distributed around the annular slot.

[0011] Furthermore, a radio frequency switch is loaded in both the vertical and horizontal directions of the novel coupling unit.

[0012] Furthermore, the outer portion of the first metal plate is grounded.

[0013] Furthermore, the length of the novel coupling unit is less than or equal to half the waveguide wavelength, the width is less than or equal to one-sixth the waveguide wavelength, and the spacing between two adjacent novel coupling units along the long side is less than or equal to 0.6 times the waveguide wavelength.

[0014] Furthermore, the novel coupling unit also includes a metal via, which penetrates the first dielectric substrate, the second metal plate, and the second dielectric substrate. One end of the via is connected to the center of the first metal plate, and the other end is connected to the FPGA control circuit and the DC power supply network. RF switches are connected to the outer and inner contours of the novel coupling unit, respectively. The T-shaped coupling structure array includes 21*21 novel coupling units, with the outer contour of the novel coupling unit serving as the negative electrode and the inner contour as the positive electrode.

[0015] Furthermore, the FPGA control circuit and DC power supply network can apply different DC bias voltages to the positive terminal of each RF switch to control the RF switch to turn on or off.

[0016] Furthermore, the difference between the inner diameter of the annular slit and the diameter of the inner core probe is 0.1mm-0.4mm, preferably 0.2mm.

[0017] Furthermore, the RF switch is a PIN diode.

[0018] Furthermore, the thickness of both the first and second dielectric substrates is less than one-quarter of the waveguide wavelength, and the width is approximately ten times the waveguide wavelength.

[0019] The modulation method based on a low-profile, fully polarized, wide-angle-domain, near-field beamforming two-dimensional tunable holographic metasurface includes the following steps:

[0020] Step 1. Based on the beam azimuth and elevation angles and polarization type of the desired far / near field target wave, write the plane wave function expression Ψ for the target wave in free space. obj The cylindrical magnetic field generated by the SMA in the parallel plate waveguide is used as the reference wave Ψ. ref According to interference theory, interference information is obtained by the superposition of phase and amplitude of the target beam and the reference beam interfering with each other on the metasurface aperture.

[0021] Step 2. The reference wave is fed by the embedded central SMA, which causes a central dip in the obtained beam. To avoid this, a 180° phase difference is introduced between the upper and lower halves of the interference field.

[0022] Step 3. Set a certain threshold s, and determine the normalized interference field Ψ based on the threshold. inf The elements in the distribution matrix are used to obtain two binary matrices in the vertical and horizontal directions;

[0023] Step 4. To simplify the antenna feeding structure, a simultaneous vertical / horizontal RF switch control design is implemented. By performing logical judgments on the common parts of the vertical and horizontal binary matrices, the commonalities of the two matrices are identified and the differences are eliminated, retaining the identical parts, thus realizing a multi-polarization function.

[0024] Step 5. If the target wave beam direction (elevation angle or azimuth angle) changes, repeat steps 1 to 4 above.

[0025] Furthermore, step 3 also includes further binarizing the two-dimensional matrix, wherein the binarization threshold s is 0.5-0.9.

[0026] The beneficial effects of this invention are:

[0027] The two-dimensional tunable holographic metasurface based on low-profile, fully polarized, wide-angle-domain near and far-field beamforming provided by this invention has the advantages of simple structure, low profile, and low cost compared with existing planar phased array antennas.

[0028] The novel coupling unit structure of this invention is based on binary radiation holography theory, which can easily realize arbitrarily oriented fully polarized wide-angle domain far / near field beams, as well as beam scanning in elevation and azimuth angles.

[0029] This invention is based on a low-profile, fully polarized, wide-angle, near-field and far-field beam-tunable two-dimensional holographic metasurface. Compared with two-dimensional slot antennas, it is easier to control, easier to add diodes, and more feasible to fabricate. Compared with existing FP resonant cavity antennas, it has the advantage of a larger scanning range, achieving a wide-angle ±70° scanning range for far-field pencil beams and a wide-angle ±60° scanning range for near-field Bessel beams.

[0030] This invention features a novel coupling unit array on a top metal plate, with an RF switch in both the vertical and horizontal directions of each array unit for coupled radiation. An FPGA control circuit and a DC feed network located on the upper surface of the underlying dielectric substrate apply different DC bias voltages to the center of each unit to control the on / off state of the RF switches. Attached Figure Description

[0031] Figure 1 This is a side view of the holographic metasurface.

[0032] Figure 2 This is a top view of the second metal plate of the holographic metasurface.

[0033] Figure 3 This is a three-dimensional schematic diagram of the slit unit structure of a holographic metasurface.

[0034] Figure 4 This is a three-dimensional schematic diagram of the overall structure of the holographic metasurface.

[0035] Figure 5 The simulation results of the far-field pencil beam pattern of the holographic metasurface are shown.

[0036] Figure 6 The image shows the simulation results of the near-field Bessel beam of the holographic metasurface.

[0037] Figure 7 This is a schematic diagram of the structure of a novel coupled array.

[0038] Figure 8 for Figure 4 An enlarged schematic diagram.

[0039] In the figure: 1-First layer metal plate, 2-First layer dielectric substrate, 3-Second layer metal plate, 4-Second layer dielectric substrate, 5-RF feed structure, 6-DC feed network, 101-Annular gap, 103-RF switch, 501-Metal shell of SMA connector, 502-Inner core probe of SMA connector. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some embodiments of this invention, not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0041] Example

[0042] like Figure 1 , Figure 2 , Figure 3As shown, the present invention relates to a two-dimensional tunable holographic metasurface based on low-profile, fully polarized, wide-angle, near-field and far-field beamforming, comprising a first metal plate 1, a second metal plate 3, an RF feed structure 5, and a DC feed network 6. The first metal plate 1 is located on the upper surface of the first dielectric substrate 2, the second metal plate 3 is located on the lower surface of the first dielectric substrate 2, and the second dielectric substrate 4 is located on the lower surface of the second metal plate 3. The RF feed structure 5 is an SMA (Sub-Miniature-A) connector. The metal shell of the SMA connector penetrates the second dielectric substrate 4 and the second metal plate 3, and is connected to the second metal plate 3. The inner probe 502 of the SMA connector penetrates the second dielectric substrate 4, the second metal plate 3, the first dielectric substrate 2, and the first metal plate 1. The DC feed network 6 is located on the lower surface of the second dielectric substrate 4.

[0043] like Figure 8 As shown, a slit is etched with the connection point between the first metal plate 1 and the inner core probe 502 of the SMA connector as the center, forming an annular slit 101 with the inner core probe 502 of the SMA connector as the center. Figure 3 As shown, a T-shaped coupling structure array is etched on the first metal plate 1. The T-shaped coupling structure array is distributed around the annular slit 101. The difference between the inner diameter of the annular slit 101 and the inner diameter of the inner core probe 502 of the SMA connector is 0.1 mm to 0.4 mm, preferably 0.2 mm.

[0044] like Figure 3 , Figure 4 As shown, the T-shaped coupling structure array consists of multiple novel coupling units that are symmetrical around the perimeter. Each novel coupling unit is loaded with two radio frequency switches 103, located in the horizontal and vertical directions respectively. In this embodiment, the radio frequency switches are PIN diodes.

[0045] like Figure 7 As shown, in order to facilitate the representation of the internal structure, the vertical length of the metal via is highlighted in the new coupling unit. The metal via penetrates the first dielectric substrate 2, the second metal plate 3, and the second dielectric substrate 4. One end is connected to the center part of the first metal plate 1, and the other end is connected to the FPGA control circuit and the DC power supply network 6.

[0046] like Figure 7 As shown, the two ends of the RF switch 103 are connected to the outer and inner contours of the novel coupling unit. The T-shaped coupling structure array includes 21*21 novel coupling units, with the outer contour of the novel coupling unit being the negative electrode and the inner contour being the positive electrode. Using an FPGA control circuit and a DC feed network 6 disposed on the lower surface of the second dielectric substrate 4, different DC bias voltages can be applied to the positive electrode of each RF switch 103 to control the RF switch 103 to be turned on or off.

[0047] In this embodiment, the dielectric substrate (including the first dielectric substrate 2 and the second dielectric substrate 4) is made of F4B material with a relative permittivity of 2.65 and an area of ​​230.36 mm × 230.36 mm. The first dielectric substrate 2 has a thickness of 3 mm, and the second dielectric substrate 4 has a thickness of 1.52 mm. The frequency of the electromagnetic wave is 8 GHz. Each novel coupling unit in the T-shaped coupling structure array has a length of 0.29 waveguide wavelengths (the waveguide wavelength is the wavelength in free space divided by the square root of the basic relative permittivity of the dielectric), approximately 10.97 mm, and the number of matrices is 21 × 21.

[0048] Each novel coupling unit integrates two PIN diodes, located vertically and horizontally respectively. When a forward bias voltage is applied to the diodes, they are in a "conducting" state, effectively "cutting off" the coupling unit. The gap at this point is equivalent to two λ / 4-length gaps, therefore the resonant frequency of the gap is 2f0, and no effective radiation is generated at the set frequency f0. When a reverse bias voltage is applied or no bias voltage is applied, the diodes are in a "disconnected" state, and the gap remains a λ / 2-length gap with a resonant frequency of f0, generating radiation. Figure 3 , Figure 4 As shown.

[0049] In addition, the present invention also provides a method for controlling a two-dimensional tunable holographic metasurface based on a low-profile, fully polarized, wide-angle-domain near-field and far-field beam, comprising:

[0050] The conduction status of the PIN diode at each gap is determined by calculating the interference field strength formed by the interference of the reference wave and the target wave using the holographic principle. A cylindrical magnetic field generated by the SMA in the parallel plate waveguide is used as the reference wave Ψ. ref It can be described using a Hankel function of the first kind.

[0051] Where A Hankel The reference amplitude is used. The target beam is reproduced on the metasurface aperture. The condition for reproducing the target beam is to re-excite the interference information with the reference wave. From interference theory, it can be deduced that the interference information is a superposition state of phase and amplitude obtained by the interference of the target beam and the reference beam on the metasurface aperture.

[0052] Therefore, the final expression for the interferometric field strength is: It was found that the doublet part of the above equation represents the target wave Ψ. tar Multiplied by the reference wave Ψ ref The conjugate value. As long as we re-excite the reference wave Ψ ref It is exactly the target wave Ψ tar Multiply by a positive A (amplitude, default is 1). To display the target wave Ψ in more detail... tar The reconstruction process first involves reconstructing the target wave Ψ tar and reference wave Ψ refThe amplitude and phase information are replaced.

[0053]

[0054] Where X / Y represent polarization in different directions, logical derivation shows that the variation of the interferogram is a cosine function of the phase difference between the reference wave and the target wave. This cosine function is the key information of the interferogram we need. It is important to note that the reference wave is fed by an embedded central SMA, which will cause a central dip in the obtained beam. To avoid this, it is necessary to introduce a 180° phase difference between the upper and lower halves of the interferometric field. The design unit has two states, ON and OFF, requiring normalization and a binary algorithm for the continuous phase interferometric field distribution matrix. A certain threshold s is set, and the normalized interferometric field Ψ is determined by the threshold. inf The elements in the distribution matrix are used to obtain a binary matrix.

[0055] After normalization, each element of the two-dimensional matrix is ​​between 0 and 1. Further binarization is performed on the two-dimensional matrix: a binarization threshold s of 0.7 is set. For each element, if the element value is greater than or equal to the threshold, the element value is set to 1; otherwise, it is set to 0. (The binarization threshold can be selected based on the required antenna gain and beam pointing accuracy. If the antenna gain in a certain direction is found to be too low, the threshold can be adjusted to increase the number of radiating slots, thereby improving the gain.) This matrix is ​​fed back to the control circuit. The control circuit applies a corresponding DC bias voltage to all PIN diode switches based on this matrix information: if the matrix element value corresponding to a slot cell is 1, no bias voltage is applied to the PIN diode at that slot, allowing the diode to conduct; otherwise, a forward bias voltage is applied to the PIN diode at that slot, causing it to disconnect.

[0056] The far-field radiation directions of the metasurface of this invention at 8 GHz in various directions are as follows: Figure 5 The image shows the scanning results at 0°, 30°, 45°, and the maximum deflection angle with full polarization, demonstrating the two-dimensional tunability of the beam. The maximum deflection angle of the beam in the elevation plane can reach 70°. The simulation software used is CST Microwave Studio 2022. Figure 6 The image shows the scanning results of the near-field Bessel beam at full polarization of 0°, 30°, 45° and maximum deflection angle, demonstrating the two-dimensional tunability of the beam.

[0057] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention 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; and these 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 the present invention.

Claims

1. A two-dimensional tunable holographic metasurface based on low-profile, fully polarized, wide-angle-domain near and far-field beamforming, characterized in that... The system includes a metal plate, a dielectric substrate, an RF feed structure, and a DC feed network. The first metal plate is located on the upper surface of the first dielectric substrate, and the second metal plate is located on the lower surface of the first dielectric substrate. The DC feed network is located on the lower surface of the second dielectric substrate. The RF feed structure is an SMA connector. The metal shell of the SMA connector penetrates through the second dielectric substrate and the second metal plate and is connected to the second metal plate. The inner core probe of the SMA connector penetrates through the second dielectric substrate, the second metal plate, the first dielectric substrate, and the first metal plate. A T-shaped coupling structure array is etched on the first metal plate. The T-shaped coupling structure array includes multiple novel coupling units symmetrically arranged on all four sides. An annular gap with the inner core probe of the SMA connector as the origin is etched on the first metal plate. The novel coupling units are distributed around the annular gap. An RF switch is loaded in the vertical and horizontal directions of each novel coupling unit.

2. The two-dimensional tunable holographic metasurface based on low-profile, fully polarized, wide-angle-domain near and far-field beamforming as described in claim 1, characterized in that, The length of the novel coupling unit is less than or equal to half the waveguide wavelength, the width is less than or equal to one-sixth the waveguide wavelength, and the spacing between two adjacent novel coupling units along the long side is less than or equal to 0.6 times the waveguide wavelength.

3. The two-dimensional tunable holographic metasurface based on low-profile, fully polarized, wide-angle-domain near and far-field beamforming as described in claim 1, characterized in that, The novel coupling unit also includes a metal via, which penetrates the first dielectric substrate, the second metal plate, and the second dielectric substrate. One end is connected to the center of the first metal plate, and the other end is connected to the FPGA control circuit and the DC power supply network. The radio frequency switch is connected to the outer contour and inner contour of the novel coupling unit respectively. The T-shaped coupling structure array includes 21*21 novel coupling units. The outer contour of the novel coupling unit is the negative electrode, and the inner contour is the positive electrode.

4. The two-dimensional tunable holographic metasurface based on low-profile, fully polarized, wide-angle-domain near and far-field beamforming according to claim 3, characterized in that, The FPGA control circuit and DC power supply network can apply different DC bias voltages to the positive terminal of each RF switch to control the RF switch to turn on or off.

5. The two-dimensional tunable holographic metasurface based on low-profile, fully polarized, wide-angle-domain near and far-field beamforming according to claim 1, characterized in that, The outer part of the first layer of metal plate is grounded.

6. The two-dimensional tunable holographic metasurface based on low-profile, fully polarized, wide-angle-domain near and far-field beamforming according to claim 1, characterized in that, The difference between the inner diameter of the annular slit and the diameter of the inner core probe is 0.1mm-0.4mm.

7. The two-dimensional tunable holographic metasurface based on low-profile, fully polarized, wide-angle-domain near and far-field beamforming according to claim 1, characterized in that, The RF switch is a PIN diode.

8. The two-dimensional tunable holographic metasurface based on low-profile, fully polarized, wide-angle-domain near and far-field beamforming according to claim 1, characterized in that, The thickness of both the first and second dielectric substrates is less than one-quarter of the waveguide wavelength, and the width is ten times the waveguide wavelength.

9. A method for controlling a two-dimensional tunable holographic metasurface with low-profile, fully polarized, wide-angle-domain near and far-field beamforming, characterized in that, Includes the following steps: Step 1. Based on the beam azimuth and elevation angles and polarization type of the desired far / near field target wave, write the plane wave function expression Ψ for the target wave in free space. obj The cylindrical magnetic field generated by the SMA in the parallel plate waveguide is used as the reference wave Ψ. ref According to interference theory, interference information is obtained by the superposition of phase and amplitude of the target beam and the reference beam interfering with each other on the metasurface aperture. Step 2. The reference wave is fed by the embedded central SMA, which causes the center of the obtained beam to be concave, requiring the introduction of a 180° phase difference between the upper and lower halves of the interference field; Step 3. Set a certain threshold s, and determine the normalized interference field Ψ based on the threshold. inf The elements in the distribution matrix are used to obtain two binary matrices in the vertical and horizontal directions; Step 4. Simultaneous control design of RF switches in vertical and horizontal directions: By performing logical judgment on the common parts of the vertical binary matrix and the horizontal binary matrix, the common parts of the two matrices are retained after finding the similarities and eliminating the differences, thus realizing the multipolarization function. Step 5. If the target wave beam direction changes, repeat steps 1 to 4 above.

10. The method according to claim 9, characterized in that, Step 3 also includes further binarization of the binary matrix, with the binarization threshold s ranging from 0.5 to 0.9.

Citation Information

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