A distance deception jamming method based on time-modulated metasurface array

By applying time modulation technology and neural network direction estimation on the metasurface array, combined with linear phase time modulation and harmonic beamforming, the problems of signal energy concentration and poor direction adaptability are solved, and effective distance fraud interference effect is achieved.

CN119805381BActive Publication Date: 2025-05-09UNIV OF ELECTRONICS SCI & TECH OF CHINA
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Patent Information

Application Number
CN202510309118.0
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2025-03-17
Publication Date
2025-05-09
Estimated Expiration
2045-03-17

AI Technical Summary

Technical Problem

The prior art is difficult to concentrate signal energy on false targets in electronic confrontation scenarios, and the direction adaptability is poor, especially when radar signals are incident, the traditional modulation method fails.

Method used

The metasurface array based on time modulation is adopted to predict the direction of the radar incident signal through the incoming wave direction estimation neural network, and linear phase time modulation and harmonic beamforming methods are used to make the reflected wave carry information of false targets, misleading the radar system to judge the distance of the target.

Benefits of technology

It realizes the effective concentration of signal energy on false targets, improves direction adaptability, reduces energy consumption and the risk of being reconnaissance, and has the advantages of low cost and high flexibility.

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Abstract

The present invention discloses a distance deception jamming method based on a time-modulated metasurface array, wherein the method comprises: S1. The surface of the protected device is equipped with a time-modulated programmable metasurface, which works in a receiving mode; S2. The multi-channel received data is sent to an incoming wave direction estimation neural network to predict the direction of the radar incident signal; S3. The radar incident wave is modulated using a linear phase time modulation method; S4. The harmonic beamforming method is used to align the main lobe of the harmonic corresponding array pattern carrying false target information with the direction of the radar incident wave. The present invention moves the incident wave to the harmonic through a time-modulated metasurface, utilizes the distance-Doppler coupling characteristics of the linear frequency modulation signal to form a deception jamming effect, and combines the incoming wave direction estimation and the harmonic beamforming method to solve the problems of false target energy being not concentrated and being unable to cope with oblique incidence in the existing solution. The present invention can be widely used in electronic countermeasures and stealth protection of Internet of Things devices.
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Description

Technical Field

[0001] The invention belongs to the field of radar, and in particular relates to electronic countermeasures and a distance deception interference method based on a time-modulated metasurface array. Background Art

[0002] In the electronic countermeasure scenario of modern radar field, high-power active jamming means face the disadvantages of easy radiation exposure, poor adaptability to complex radar systems, obvious signal characteristics, and high hardware cost, and need to be combined with other jamming methods. Electromagnetic metasurfaces have attracted much attention in the fields of science and engineering due to their fine control over electromagnetic waves. Through time modulation technology, the amplitude and phase of the incident radar signal can be modulated, thereby changing the time domain and frequency domain waveforms of the radar echo, and displaying forged distance deception jamming information after pulse compression. However, in existing public research, it is usually based on the radar signal being incident on the metasurface, combined with amplitude modulation-based methods. However, in practical applications, the signals are mostly obliquely incident, and the energy of the reflected signal is required to be large. At this time, the traditional modulation method will fail. Therefore, how to concentrate energy on the forged target and solve the problem of directional adaptability has important application value. Summary of the invention

[0003] The purpose of the present invention is to provide a distance deception interference method based on a time-modulated metasurface array to solve the technical problems of concentrating signal energy on a false target and direction adaptation.

[0004] In order to solve the above technical problems, the present invention proposes a pulse radar distance deception jamming method based on time-modulated metasurface, which comprises the following steps:

[0005] Step S1: A time-modulated programmable metasurface array is mounted on the surface of the device to be protected, and the time-modulated programmable metasurface array works in a receiving mode;

[0006] Step S2: The antenna radiation patch of the time-modulated programmable metasurface array receives the radar signal, processes the radar signal to obtain radar pulse reception data, and sends the radar pulse reception data to the incoming wave direction estimation neural network to predict the direction of the radar incident signal;

[0007] Step S3: The time-modulated programmable metasurface array turns on the linear phase time modulation to modulate the radar signal radiated to the time-modulated programmable metasurface array, so that the signal spectrum is shifted, and the range-Doppler coupling characteristics of the linear frequency modulation signal are used to make the reflected wave carry the information of the false target;

[0008] Step S4: Using the harmonic beamforming method, the harmonic signal carrying false target information is adjusted through the array pattern so that the main lobe of the harmonic signal is aligned with the direction of the radar incident wave; misleading the radar system to judge the distance of the target and achieving distance deception interference.

[0009] Furthermore, step S1 includes the following steps:

[0010] Step S11: mounting a time-modulated programmable metasurface array on the surface of the protected device, where the time-modulated programmable metasurface array is a conformal multi-channel array;

[0011] Step S12: the time-modulation programmable metasurface array is controlled by FPGA to modulate the space-time coding modulation waveform and modulation frequency;

[0012] Step S13: The time-modulated programmable metasurface array is powered on and operates in a receiving mode to receive radar detection pulse echo signals.

[0013] Further, step S2 includes the following steps:

[0014] Step S21: The antenna radiation patch of the time-modulated programmable metasurface array receives the radar signal;

[0015] Step S22: down-converting, filtering, and analog-to-digital conversion the radar signal to obtain I and Q signals, i.e., radar pulse reception data;

[0016] Step S23: inputting the radar pulse reception data into the complex convolutional neural network of the incoming wave direction estimation neural network to obtain the output of the complex convolutional neural network;

[0017] Step S24: Input the output of the complex convolutional neural network into the Kolmogorov–Arnold neural network to obtain the azimuth and elevation angles of the radar incident signal.

[0018] Further, step S23 includes the following steps:

[0019] Step S231: inputting the I and Q signals into the complex convolution layer of the complex neural network to implement convolution;

[0020] Step S232: Pass the output of the complex convolution layer of the complex convolutional neural network through a complex ReLU activation function layer;

[0021] Step S233: The output of the complex Relu activation function layer is processed by average pooling and flattening to obtain the output of the complex convolutional neural network.

[0022] Further, in step S3,

[0023] Linear phase time modulation is equivalent to multiplying the signal. The linear phase time modulation method is as follows:

[0024] e ( t ) = s echo ( t ) ∗ h ( t ) ⋅ C ( t ) = ∑ q =−∞ ∞ | A nq | Zinc [ B ( t − t + qf p m )] e j 2 π [ qf p ( t − t ) − f c t ]

[0025] in, It represents the radar echo signal after pulse compression after linear phase time modulation of the time-modulated programmable metasurface array, that is, false target information; Represents the radar signal radiated onto the time-modulated programmable metasurface array, A matched filter function representing pulse compression; A linear phase temporal modulation waveform representing a temporally modulated programmable metasurface array; Indicates the linear phase time modulation The amplitude of the first harmonic; represents the pulse width of the radar signal, represents the bandwidth of the radar signal, represents the frequency modulation slope, Indicates time; represents the time delay for the radar signal to return to the receiver, represents the harmonic order, represents the modulation frequency of the time-modulated programmable metasurface array, Indicates the center frequency of the radar signal.

[0026] Furthermore, the expression of the linear phase time modulation waveform of the time-modulated programmable metasurface array is:

[0027]

[0028] In the formula, represents a linear phase time modulated waveform, The cycle is The function of is the number of phase-adjustable states of the time-modulated programmable metasurface array, represents the slope of the phase change rate, Indicates the remainder operation, limiting the time to one within the cycle.

[0029] Further, step S4 includes the following steps:

[0030] Step S41: the radar incident direction is the azimuth and elevation angle of the radar incident signal predicted by the incoming wave direction estimation neural network in step S2;

[0031] Step S42: Harmonics refer to harmonics containing false target information. In order to point to the ideal angle during harmonic scanning, the equivalent phase weighting generated by the time coding pattern on the harmonics is compensated by changing the time delay between adjacent array elements, and the directional angle direction is generated. Scanning the required phase gradient can achieve beamforming at the harmonic, which means reflecting the signal containing false target information to the direction of the radar wave. The time delay is calculated as:

[0032] t n = mod [ β ( x n sin i 0 cos f 0 +y n sin i 0 sin f 0 ) 2 π qf p , 1 ] ⋅ T p

[0033] in, is the remainder operation, is the direction of the incident radar wave, represents the pitch angle, represents the azimuth, is the wave number, are the coordinates of the array element, is the modulation period.

[0034] Compared with the prior art, the present invention has the following beneficial technical effects: the present invention is easy to integrate into the existing platform, adopts passive control mode, has low power consumption, greatly reduces energy consumption, and reduces the risk of enemy reconnaissance and countermeasures; adopts programmable metasurface, can optimize different interference modes according to different needs, and has the advantages of low cost and high flexibility compared with active interference. The present invention can be widely used in electronic countermeasures and stealth protection of Internet of Things devices. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments of the present invention will be briefly introduced below. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative labor.

[0036] Figure 1 This is a flow chart of the pulse radar distance deception jamming method based on the time-modulated metasurface array of the present invention.

[0037] Figure 2 It is the system model of the present invention.

[0038] Figure 3 This is the neural network model for estimating the incoming wave direction in the present invention.

[0039] Figure 4 It is the harmonic beamforming pattern in the present invention. DETAILED DESCRIPTION

[0040] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0041] The present invention proposes a pulse radar distance deception jamming method based on time-modulated metasurface, such as Figure 1 As shown, the method comprises the following steps:

[0042] Step S1: A time-modulated programmable metasurface array is mounted on the surface of the device to be protected, and the time-modulated programmable metasurface array works in a receiving mode. The device to be protected refers to a device that needs to be avoided from being detected by enemy radar, such as a drone.

[0043] Specifically, step S1 includes the following steps:

[0044] Step S11: A time-modulated programmable metasurface array is mounted on the surface of the protected device, where the time-modulated programmable metasurface array is a conformal multi-channel array.

[0045] Step S12: The time-modulated programmable metasurface array is controlled by FPGA to modulate the space-time coded modulation waveform and modulation frequency.

[0046] Step S13: The time-modulated programmable metasurface array is powered on and operates in a receiving mode to receive radar detection pulse echo signals.

[0047] Step S2: The antenna radiation patch of the time-modulated programmable metasurface array receives the radar signal, processes the radar signal to obtain radar pulse reception data, and sends the radar pulse reception data to the incoming wave direction estimation neural network to predict the direction of the radar incident signal.

[0048] Specifically, step S2 includes the following steps:

[0049] Step S21: The antenna radiation patch of the time-modulated programmable metasurface array receives the radar signal.

[0050] Multiple antenna radiation patch units in the metasurface array receive radar signals, and the antenna radiation patch of each unit receives echo signals with different phase and amplitude information, thereby forming a spatially distributed radar signal.

[0051] Step S22: down-converting, filtering, and analog-to-digital conversion are performed on the radar signal to obtain I and Q signals, namely, radar pulse reception data.

[0052] Step S23: inputting the radar pulse receiving data into the complex convolutional neural network of the incoming wave direction estimation neural network to obtain the output of the complex convolutional neural network.

[0053] Radar pulse receiving data is input into the incoming wave direction estimation neural network for direction estimation to achieve high-precision direction finding of radar detection signals.

[0054] The neural network for estimating the direction of arrival includes complex convolutional neural networks and Kolmogorov–Arnold neural networks. Figure 2 As shown in the figure, the complex convolutional neural network includes a complex convolution layer, a complex Relu activation function layer, an average pooling layer and a flattening layer.

[0055] The complex convolutional neural network is used to extract the features of I and Q signals, making full use of the amplitude and phase information of complex operations, improving the ability to extract time-frequency features of radar echo signals, and thus enhancing the ability to resolve target direction information.

[0056] The Kolmogorov–Arnold neural network is used to perform nonlinear mapping and dimensionality reduction on the extracted features, improve the compactness and robustness of feature expression, and reduce the computational complexity. It finally outputs the predicted values ​​of azimuth and elevation angles to achieve high-precision estimation of the target direction.

[0057] Step S231: Input the I and Q signals into the complex convolution layer of the complex neural network to implement convolution. The convolution process is:

[0058]

[0059] in, represents a trainable complex convolution kernel, represents the real part of the trainable complex convolution kernel, represents the imaginary part of the trainable complex convolution kernel, represents the complex features of the input, represents the real part of the complex feature of the input, represents the imaginary part of the complex feature of the input, Represents an imaginary unit.

[0060] Step S232: The output of the complex convolution layer of the complex convolutional neural network is passed through a complex Relu activation function layer. The expression of the complex Relu activation function is:

[0061]

[0062] in, represents the complex Relu activation function, represents the input complex signal vector, express The real part of express The imaginary part of Represents the Relu activation function, the expression is:

[0063]

[0064] Step S233: The output of the complex Relu activation function layer is processed by average pooling and flattening to obtain the output of the complex convolutional neural network.

[0065] Step S24: Input the output of the complex convolutional neural network into the Kolmogorov–Arnold neural network to obtain the azimuth and elevation angles of the radar incident signal.

[0066] In the Kolmogorov–Arnold neural network, the activation function can be trained, and the expression of the activation function is:

[0067]

[0068] in, represents the trainable weights, is the base activation function, is the spline function, is the input value.

[0069] The expression is:

[0070]

[0071] Using the third-order spline function, the expression is:

[0072]

[0073] in, represents the trainable weight parameters, Represents the spline basis function.

[0074] The loss function of the neural network for estimating the direction of arrival is composed of two parts, which are used to estimate the prediction errors of the pitch angle and azimuth angle respectively. The expression is:

[0075]

[0076] in, and denote the predicted losses in azimuth and elevation respectively, and They represent the weights corresponding to the azimuth and elevation angles respectively, and can be adjusted according to the convergence during training.

[0077] The prediction loss of azimuth and elevation angles adopts Huber loss, and the expression of Huber loss is:

[0078]

[0079] in, is the real angle of the incoming wave, is the predicted value of the incoming wave angle, represents the prediction error threshold. In the present invention, = 1. The incoming wave direction estimation neural network of the present invention is an end-to-end prediction model. After training, the azimuth and elevation angles corresponding to the input incoming wave signals will be directly output.

[0080] Step S3: The time-modulated programmable metasurface array turns on the linear phase time modulation to modulate the radar signal radiated to the time-modulated programmable metasurface array, shift the signal spectrum, and use the range-Doppler coupling characteristics of the linear frequency modulation signal to make the reflected wave carry the information of the false target.

[0081] The linear phase time modulation of the time-modulated programmable metasurface array can modify the phase and amplitude of the radar signal radiated to the time-modulated programmable metasurface array. The linear phase time modulation is equivalent to multiplying the signal. The linear phase time modulation method is as follows:

[0082] e ( t ) = s echo ( t ) ∗ h ( t ) ⋅ C ( t ) = ∑ q =−∞ ∞ | A nq | Zinc [ B ( t − t + qf p m )] e j 2 π [ qf p ( t − t ) − f c t ]

[0083] in, It represents the radar echo signal after pulse compression after linear phase time modulation of the time-modulated programmable metasurface array, that is, false target information; Represents the radar signal radiated onto the time-modulated programmable metasurface array, A matched filter function representing pulse compression; A linear phase temporal modulation waveform representing a temporally modulated programmable metasurface array; Indicates the linear phase time modulation The amplitude of the first harmonic; represents the pulse width of the radar signal, represents the bandwidth of the radar signal, represents the frequency modulation slope, Indicates time; represents the time delay for the radar signal to return to the receiver, represents the harmonic order, represents the modulation frequency of the time-modulated programmable metasurface array, Indicates the center frequency of the radar signal. is the Sigmoid function, and its expression is:

[0084]

[0085] The expression of the linear phase time modulation waveform of the time-modulated programmable metasurface array is:

[0086]

[0087] In the formula, represents a linear phase time modulated waveform, The cycle is The function of is the number of phase-adjustable states of the time-modulated programmable metasurface array, represents the slope of the phase change rate, Indicates the remainder operation, limiting the time to one In the present invention, in order to maximize the concentration of harmonic energy on the false target, , at this time it has the highest harmonic efficiency.

[0088] In the linear phase modulation waveform, there are two ways of phase arrangement. Take 2-bit modulation as an example. The corresponding false target is closer than the real target, and The false target generated is farther away than the real target.

[0089] In linear phase time modulation, the modulation frequency Controlled by FPGA, the modulation frequency cannot exceed the maximum switching frequency of the metasurface phase, which is determined by the offset of the preset false target distance, and the expression is:

[0090]

[0091] in, Indicates the offset of the deceptive target relative to the real target, The speed of light.

[0092] The original center frequency is After the signal is modulated by linear phase time, the spectrum is moved to By utilizing the range-Doppler coupling characteristics of the linear frequency modulation signal, the frequency shift of the signal will cause a change in the detection distance, so the reflected harmonic signal will carry the information of the false target, forming a distance deception effect.

[0093] Step S4: Using the harmonic beamforming method, the harmonic signal carrying the false target information is adjusted through the array pattern so that the main lobe of the harmonic signal is aligned with the radar incident wave direction. By accurately adjusting the harmonic frequency and phase, the echo signal of the false target presents similar characteristics to the real target in the receiver, thereby misleading the radar system to judge the distance of the target and achieving distance deception interference.

[0094] Specifically, step S4 includes the following steps:

[0095] Step S41: The radar incident direction is the azimuth and elevation angle of the radar incident signal predicted by the incoming wave direction estimation neural network in step S2.

[0096] Step S42: Harmonics refer to harmonics containing false target information. In order to point to the ideal angle during harmonic scanning, the equivalent phase weighting generated by the time coding pattern on the harmonics is compensated by changing the time delay between adjacent array elements, and the directional angle direction is generated. Scanning the required phase gradient can achieve beamforming at the harmonic, which means reflecting the signal containing false target information to the direction of the radar wave. The time delay is calculated as:

[0097] t n = mod [ β ( x n sin i 0 cos f 0 +y n sin i 0 sin f 0 ) 2 π qf p , 1 ] ⋅ T p

[0098] in, is the remainder operation, is the direction of the incident radar wave, represents the pitch angle, represents the azimuth, is the wave number, are the coordinates of the array element, is the modulation period.

[0099] The following will be combined Figure 3 The pulse radar distance deception jamming method based on the time-modulated metasurface array of the present invention is described in detail. The radar transmission carrier frequency is Linear frequency modulation signal, the signal parameters are: pulse width ,bandwidth , pulse repetition frequency , 256 pulses are accumulated for ranging, and the real target is at 13.0km. The scale of the time-modulated programmable metasurface carried by the drone is 8*8. After receiving the detection signal of the radar, it generates 64 units of receiving data after down-conversion, filtering, and AD sampling. The sample size is 2*64*1000 and is input into the neural network for estimating the direction of the incoming wave. In this network, there are 3 layers of complex convolution layers with channel numbers of 128, 256, and 512, kernel sizes of 1*7, 1*3, and 1*3, complex Relu activation function layers, average pooling layers, flattened cascade Kolmogorov–Arnold networks, and spline functions of order 3. , output two nodes, corresponding to the predicted azimuth and pitch angles.

[0100] At the same time, after the radar signal is detected, the metasurface turns on the linear phase time modulation, and the linear frequency modulation signal is modulated to the harmonic, and the modulation frequency , the energy is concentrated in its positive first harmonic At , this harmonic contains the information of the false target. The time delay between array elements required for harmonic beamforming is calculated. After adding the delay, the main lobe of the directional pattern of the metasurface array points to the predicted direction of the incoming wave, which is the direction of the radar.

[0101] like Figure 4 The figure shows the two-dimensional radiation pattern of the antenna array in this example. At this time, the enemy radar received the information of the false target, which was located at 12.8 km. In this way, the pulse radar distance deception jamming effect based on the time-modulated metasurface array was achieved.

[0102] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A distance deception jamming method based on a time-modulated metasurface array, characterized in that: The method comprises the following steps: Step S1: A time-modulated programmable metasurface array is mounted on the surface of the device to be protected, and the time-modulated programmable metasurface array works in a receiving mode; Step S2: The antenna radiation patch of the time-modulated programmable metasurface array receives the radar signal, processes the radar signal to obtain radar pulse reception data, and sends the radar pulse reception data to the incoming wave direction estimation neural network to predict the direction of the radar incident signal; Step S3: The time-modulated programmable metasurface array turns on the linear phase time modulation to modulate the radar signal radiated to the time-modulated programmable metasurface array, so that the signal spectrum is shifted, and the range-Doppler coupling characteristics of the linear frequency modulation signal are used to make the reflected wave carry the information of the false target; Step S4: using a harmonic beamforming method, the harmonic signal carrying false target information is adjusted through an array pattern so that the main lobe of the harmonic signal is aligned with the radar incident wave direction; misleading the radar system to judge the distance of the target, thereby achieving distance deception interference; In step S3, the linear phase time modulation is equivalent to performing a multiplication operation on the signal, and the linear phase time modulation method is as follows: in, It represents the radar echo signal after pulse compression after linear phase time modulation of the time-modulated programmable metasurface array, that is, false target information; Represents the radar signal radiated onto the time-modulated programmable metasurface array, A matched filter function representing pulse compression; A linear phase temporal modulation waveform representing a temporally modulated programmable metasurface array; Indicates the linear phase time modulation The amplitude of the first harmonic; represents the pulse width of the radar signal, represents the bandwidth of the radar signal, represents the frequency modulation slope, Indicates time; represents the time delay for the radar signal to return to the receiver, represents the harmonic order, represents the modulation frequency of the time-modulated programmable metasurface array, Indicates the center frequency of the radar signal; The expression of the linear phase time modulation waveform of the time-modulated programmable metasurface array is: In the formula, represents a linear phase time modulated waveform, The cycle is The function of is the number of phase-adjustable states of the time-modulated programmable metasurface array, represents the slope of the phase change rate, Indicates the remainder operation, limiting the time to one within the cycle.

2. The distance deception jamming method based on the time-modulated metasurface array according to claim 1 is characterized in that: Step S1 includes the following steps: Step S11: mounting a time-modulated programmable metasurface array on the surface of the protected device, where the time-modulated programmable metasurface array is a conformal multi-channel array; Step S12: the time-modulation programmable metasurface array is controlled by FPGA to modulate the space-time coding modulation waveform and modulation frequency; Step S13: The time-modulated programmable metasurface array is powered on and operates in a receiving mode to receive radar detection pulse echo signals.

3. The distance deception jamming method based on the time-modulated metasurface array according to claim 1 is characterized in that: Step S2 includes the following steps: Step S21: The antenna radiation patch of the time-modulated programmable metasurface array receives the radar signal; Step S22: down-converting, filtering, and analog-to-digital conversion the radar signal to obtain I and Q signals, i.e., radar pulse reception data; Step S23: inputting the radar pulse reception data into the complex convolutional neural network of the incoming wave direction estimation neural network to obtain the output of the complex convolutional neural network; Step S24: Input the output of the complex convolutional neural network into the Kolmogorov–Arnold neural network to obtain the azimuth and elevation angles of the radar incident signal.

4. The distance deception jamming method based on the time-modulated metasurface array according to claim 3 is characterized in that: Step S23 includes the following steps: Step S231: inputting the I and Q signals into the complex convolution layer of the complex neural network to implement convolution; Step S232: Pass the output of the complex convolution layer of the complex convolutional neural network through a complex ReLU activation function layer; Step S233: The output of the complex Relu activation function layer is processed by average pooling and flattening to obtain the output of the complex convolutional neural network.

5. The distance deception jamming method based on time-modulated metasurface array according to claim 1 is characterized in that: Step S4 includes the following steps: Step S41: the radar incident direction is the azimuth and elevation angle of the radar incident signal predicted by the incoming wave direction estimation neural network in step S2; Step S42: Harmonics refer to harmonics containing false target information. In order to point to the ideal angle during harmonic scanning, the equivalent phase weighting generated by the time coding pattern on the harmonics is compensated by changing the time delay between adjacent array elements, and the directional angle direction is generated. Scan the required phase gradient to achieve beamforming at the harmonic, which means that the signal containing false target information is reflected to the direction of the radar wave. The time delay is calculated as: in, is the remainder operation, is the direction of the incident radar wave, represents the pitch angle, represents the azimuth, is the wave number, are the coordinates of the array element, is the modulation period.

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