A radio frequency fingerprint classification method based on contrastive learning network

Through the RF fingerprint classification method of the comparative learning network, the multi-domain feature fusion and supcon comparison learning algorithm are used to solve the problem of vulnerability of wireless communication devices, and the effective identification and classification of RF fingerprints are realized, and the security of wireless communication network is improved.

CN119167133BActive Publication Date: 2025-03-21LANZHOU JIAOTONG UNIV
View PDF 2 Cites 0 Cited by

Patent Information

Application Number
CN202411085515.6
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2024-08-08
Publication Date
2025-03-21
Estimated Expiration
2044-08-08

AI Technical Summary

Technical Problem

Wireless communication devices are vulnerable to malicious attacks, resulting in security problems. It is difficult for the prior art to effectively identify and classify radio frequency fingerprints to ensure network security.

Method used

The RF fingerprint classification method of the comparative learning network is adopted to construct a multi-domain feature fusion data set by preprocessing the RF signal, max-minimum normalization, time domain, frequency domain and high-order spectral domain transformation, and trained using Resnet50 and supcon contrast learning algorithms to achieve effective classification of RF fingerprints.

Benefits of technology

It realizes effective identification of individual communication radiation sources, has good applicability and recognition accuracy, can work effectively in a low signal-to-noise ratio environment, and improves the security of wireless communication network.

✦ Generated by Eureka AI based on patent content.

Smart Images

  • Figure CN119167133B_ABST
    Figure CN119167133B_ABST
Patent Text Reader

Abstract

The present invention discloses a radio frequency fingerprint classification method of a contrastive learning network, and relates to the technical field of radio frequency fingerprint recognition. Traditional radio frequency fingerprint recognition algorithms are easily affected by channel interference, and the recognition accuracy is not high. In view of the above problems, this paper starts with a preprocessing method and a classification algorithm based on deep learning; first, a real data set of radio signals with different modulation modes and powers is constructed by acquiring the IQ signals of 10 hackRF one transmitters; then, multiple transform domain features of the communication radiation source transmission signal are extracted, and these features are combined into multi-domain features, and data enhancement is performed from the signal preprocessing of the time domain, frequency domain and high-order spectral domain respectively, and a multi-channel convolutional neural network is constructed, and multi-domain features are deeply extracted using multi-channel convolution operations; finally, the feature vectors of the signals of different transmitters after data enhancement are compared using a contrastive learning model, the features of the radio frequency fingerprint are extracted, and the identity of the transmitter is identified.
Need to check novelty before this filing date? Find Prior Art

Description

Technical Field

[0001] The present invention relates to the technical field of radio frequency fingerprint recognition, and in particular to a radio frequency fingerprint classification method of a comparative learning network. Background Art

[0002] With the increasing popularity of wireless communication devices and the rapid development of wireless communication technology, wireless communication has become an indispensable part of today's society, penetrating into every aspect of our daily life and bringing great convenience to our daily life. Wireless communication network is the extension of our thoughts and perceptions. With wireless communication technology, we can know what is happening in the world without leaving home and transmit information anytime and anywhere. The development of wireless communication technology has brought about technologies such as smart home, smart city, smart transportation, smart agriculture, and smart medical care. These technologies have simplified and intelligentized our lives, and realized the interconnection of all things and the exchange of information. However, while wireless communication has freed people from the constraints of space and time in communication, it has also brought many security issues.

[0003] Due to the openness and broadcasting of wireless communications, the radio signals emitted by the transmitter are directly broadcast into free space, and any radio receiving device can receive the transmitted radio signals. Therefore, wireless communications are more vulnerable to malicious attacks than wired communications, which makes the security of wireless communications increasingly a huge hidden danger. Various malicious attacks on radio communications, such as replay attacks, man-in-the-middle attacks, and even direct password theft, will cause economic losses to the country, society, and users, as well as personal harm caused by privacy leaks.

[0004] With the continuous research of researchers from various countries on radio frequency fingerprint recognition technology, radio frequency fingerprint recognition technology will be applied to civilian use, unified management of radio transmission equipment, prevention of illegal personnel from attacking wireless communication equipment, and guaranteeing the security of wireless communication networks. This technology has broad application prospects and will surely create a huge market. Therefore, the research on radio frequency fingerprint recognition technology based on deep learning has extremely high theoretical and economic value. Summary of the invention

[0005] The purpose of the present invention is to solve the above-mentioned problems and provide a radio frequency fingerprint classification method based on a comparative learning network.

[0006] To achieve the above object, the technical solution adopted by the present invention is:

[0007] According to one aspect of the present invention, a radio frequency fingerprint classification method of a contrastive learning network is provided, comprising the following contents:

[0008] S1: Collect radio frequency signals and pre-process the collected radio frequency signals;

[0009] S2: Perform maximum-minimum normalization on the preprocessed signal, then perform transformations in the time domain, frequency domain, and high-order spectrum domain respectively, and combine these features into multi-domain features to construct a multi-domain feature fusion dataset;

[0010] S3: According to the multi-domain feature fusion dataset, a specified number of samples are selected as the batch training dataset;

[0011] S4: Calculate the output of all samples after Resnet50 calculation, including the projection vector output;

[0012] S5: Calculate the average loss function value of each batch training process, define label consistency through cross entropy loss function value, and define sample consistency through comparison loss function value;

[0013] S6: Calculate the gradient of the loss function and update the network parameters according to the gradient descent principle. Repeat the above steps until the network parameter stable training ends early or the preset Epoach value iteration is completed. The comparative learning pre-training process based on the original data set and the enhanced data set is completed. The grid parameters are fine-tuned according to the enhanced data set and the corresponding label information. The supcon comparative learning algorithm is used for training until the optimal training result is obtained.

[0014] Furthermore, the step S1 specifically includes: the RF fingerprint data set used in the present invention is a measured data set; the radio transmitters are two walkie-talkies of the same type and batch, ensuring that the deviation of the RF fingerprint is small; the transmitted audio is completely random, reducing the impact of the transmitted signal on the RF fingerprint; data collection is carried out in a laboratory with glass and concrete walls, and each room has some daily electronic equipment, which ensures that the wireless channel is complex enough; the receiving end uses a 3900A radio monitoring receiver to reduce the impact of the receiving end on the RF fingerprint. When collecting data, the position of the transmitter is constantly changing in the room, while the position of the 3900A receiver is fixed. The radio data is transmitted from the transmitter, passes through the channel, is received by the receiver, and then reaches the terminal through the network cable for back-end data processing.

[0015] Furthermore, the step S2 specifically includes: the present invention uses the I / Q data of the signal directly as the time domain feature of the radiation source, separates the I-path and Q-path signals instead of taking the modulus; the frequency domain feature selects the Welch power spectrum data of the signal; in the high-order spectral domain, the integral bispectrum is selected as the signal feature, the I-path and Q-path signals are separated, and the integral bispectrum calculation is performed separately; the domain data of multiple transform domains are combined and encapsulated into 5 parallel data channels, and each data channel has an exclusive channel and does not affect each other; each channel corresponds to I-path data, Q-path data, power spectrum data, I-path integral bispectrum data, and Q-path integral bispectrum data in turn, to construct a multi-domain feature fusion data set.

[0016] Furthermore, the step S3 specifically includes: scaling and rotating the 5-channel data to obtain enhanced data, and for each batch training process, selecting a specified number of samples from the multi-domain feature fusion data set and the enhanced data set as a batch training data set according to the batch size.

[0017] Furthermore, the step S4 specifically includes: calculating the output of all samples after Resnet50 calculation, and for each batch training process, each sample obtains a projection vector p and a probability vector z after passing through the network.

[0018] Furthermore, the step S5 specifically includes: comparing the loss function value to define the sample consistency, assuming batch_size=N, then the input data is , when reading data, the data Two data will be generated through random image transformation and , the data set is , where the label , the supervised contrast loss formula is:

[0019]

[0020] In the formula, is the number of images with the same label in a batch of input data; when hour, Returns 1 if yes, otherwise returns 0; is the output of the feature extraction network, Represents the inner product of two vectors; is a parameter with a fixed value. The supervised contrast loss is used to calculate the correlation between two feature vectors. When the two feature vectors are of the same category, the supervised contrast loss requires that the two vectors are similar enough; when the two feature vectors are of different categories, the two feature vectors are required to be more different.

[0021] The cross entropy loss function value defines label consistency. The more consistent the probability distribution of the predicted value is with the probability distribution of the true value, the smaller the cross entropy loss is. The formula is:

[0022] .

[0023] In the formula, x is the output of the classification network and class is the corresponding label.

[0024] Furthermore, the step S6 specifically includes: updating the network parameters according to the gradient descent principle: , where W is the network parameter, is the learning rate.

[0025] Compared with the prior art, the present invention has the following beneficial effects:

[0026] 1. The present invention proposes a radio frequency fingerprint classification method of a contrastive learning network. In terms of feature fusion, the present invention directly selects the I / Q data of the signal as the time domain feature of the radiation source. As the mainstream method of signal acquisition and storage, I / Q data contains all the information of the signal in the time domain. Secondly, for the frequency domain feature, we use the power spectrum data of the signal. The power spectrum not only reflects the change of signal power with frequency, but also contains information in the frequency domain. Moreover, compared with the spectrum of the signal, the power spectrum has a smaller variance under low signal-to-noise ratio conditions. In the high-order spectral domain, the integrated bispectrum is selected as the signal feature, and the integrated bispectrum is the bispectral information after dimensionality reduction. The time domain I / Q data, the frequency domain power spectrum data, and the high-order frequency domain integrated bispectrum data are combined into multi-domain features, and the radiation source equipment is effectively classified in combination with the supcon contrastive learning network.

[0027] 2. Compared with the radiation source individual identification method based on a single feature, the multi-domain feature fusion method proposed in the present invention makes full use of multiple transform domain features of the communication radiation source emission signal, combined with the powerful subtle feature mining ability of the contrastive learning network, to achieve effective identification of the communication radiation source individual. Moreover, the method proposed in the present invention can be extended to various communication radiation source individual identification scenarios and has good applicability.

[0028] 3. The contrastive learning framework proposed in the present invention uses the residual network as the backbone network and compares the features of different spectrum waterfall diagrams by feature comparison, so that the feature vectors of the same category are similar and the feature vectors of different categories are more different. Then, the feature vectors after calculating the contrast loss are input into the fully connected network with dropout for classification. Compared with other methods, it has higher accuracy in individual recognition of communication radiation sources and can be applied to individual recognition of communication radiation sources in low signal-to-noise ratio environments.

[0029] In summary, the method of the present invention has high robustness, strong generalization ability, and higher accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a flow chart of the radio frequency fingerprint classification method of the comparative learning network of the present invention;

[0031] Figure 2 It is a schematic diagram of feature fusion data;

[0032] Figure 3 It is the segmentation method of Welch algorithm;

[0033] Figure 4 is a schematic diagram of a rectangular integration path;

[0034] Figure 5Schematic diagram of 5-channel feature fusion using neural network; DETAILED DESCRIPTION

[0035] In order to make the technical means, creative features, objectives and effects achieved by the present invention easy to understand, the present invention is further explained below in conjunction with specific implementation methods.

[0036] A radio frequency fingerprint classification method using a contrastive learning network comprises the following steps:

[0037] S1: Collect radio frequency signals and pre-process the collected radio frequency signals;

[0038] Step S1 specifically includes: the RF fingerprint data set used in the present invention is a measured data set; the radio transmitters are two walkie-talkies of the same type and batch, ensuring that the deviation of the RF fingerprint is small; the transmitted audio is completely random, reducing the impact of the transmitted signal on the RF fingerprint; data collection is carried out in a laboratory with glass and concrete walls, and each room has some daily electronic equipment, which ensures that the wireless channel is complex enough; the receiving end uses a 3900A radio monitoring receiver to reduce the impact of the receiving end on the RF fingerprint. When collecting data, the position of the transmitter is constantly changing in the room, while the position of the 3900A receiver is fixed. The radio data is transmitted from the transmitter, passes through the channel, is received by the receiver, and then reaches the terminal through the network cable for back-end data processing.

[0039] S2: Perform maximum-minimum normalization on the preprocessed signal, then perform transformations in the time domain, frequency domain, and high-order spectrum domain respectively, and combine these features into multi-domain features to construct a multi-domain feature fusion dataset;

[0040] Step S2 specifically includes: the present invention uses the I / Q data of the signal directly as the time domain feature of the radiation source, separates the I-path and Q-path signals instead of taking the modulus; the frequency domain feature selects the Welch power spectrum data of the signal; in the high-order spectral domain, the integral bispectrum is selected as the signal feature, the I-path and Q-path signals are separated, and the integral bispectrum calculation is performed separately; the domain data of multiple transform domains are combined and encapsulated into 5 parallel data channels, and each data channel has an exclusive channel and does not affect each other; each channel corresponds to I-path data, Q-path data, power spectrum data, I-path integral bispectrum data, and Q-path integral bispectrum data in turn, to construct a multi-domain feature fusion data set.

[0041] S3: According to the multi-domain feature fusion dataset, a specified number of samples are selected as the batch training dataset;

[0042] Step S3 specifically includes: scaling and rotating the 5-channel data to obtain enhanced data, and for each batch training process, selecting a specified number of samples from the multi-domain feature fusion dataset and the enhanced dataset as a batch training dataset according to the batch size.

[0043] S4: Calculate the output of all samples after Resnet50 calculation, including the projection vector output;

[0044] Step S4 specifically includes: calculating the output of all samples after Resnet50 calculation. For each batch training process, each sample obtains a projection vector p and a probability vector z after passing through the network.

[0045] S5: Calculate the average loss function value of each batch training process, define label consistency through cross entropy loss function value, and define sample consistency through comparison loss function value;

[0046] Step S5 specifically includes: comparing the loss function value to define sample consistency, assuming batch_size=N, then the input data is , when reading data, the data Two data will be generated through random image transformation and , the data set is , where the label , the supervised contrast loss formula is:

[0047]

[0048] In the formula, is the number of images with the same label in a batch of input data; when hour, Returns 1 if yes, otherwise returns 0; is the output of the feature extraction network, Represents the inner product of two vectors; is a parameter with a fixed value. The supervised contrast loss is used to calculate the correlation between two feature vectors. When the two feature vectors are of the same category, the supervised contrast loss requires that the two vectors are similar enough; when the two feature vectors are of different categories, the two feature vectors are required to be more different.

[0049] The cross entropy loss function value defines label consistency. The more consistent the probability distribution of the predicted value is with the probability distribution of the true value, the smaller the cross entropy loss is. The formula is:

[0050] .

[0051] In the formula, x is the output of the classification network and class is the corresponding label.

[0052] S6: Calculate the gradient of the loss function and update the network parameters according to the gradient descent principle. Repeat the above steps until the network parameter stable training ends early or the preset Epoach value iteration is completed. The comparative learning pre-training process based on the original data set and the enhanced data set is completed. The grid parameters are fine-tuned according to the enhanced data set and the corresponding label information. The supcon comparative learning algorithm is used for training until the optimal training result is obtained.

[0053] Step S6 specifically includes: updating the network parameters according to the gradient descent principle: , where W is the network parameter and is the learning rate.

[0054] like Figure 1 and Figure 2 The figure is a schematic diagram of multi-domain feature fusion. First of all, the current analysis and research on communication radiation source signals is mostly based on I / Q data collected by real-time spectrum analyzers and down-converted to baseband. These data contain all the characteristics of the radiation source signal in the time domain. The present invention directly uses the I / Q data of the signal as the time domain feature of the radiation source. As the mainstream method for pre-signal acquisition and storage, I / Q data contains all the information of the signal in the time domain. The ideal baseband I / Q signal model of the radiation source is as follows:

[0055] like Figure 3 As shown, the power spectrum describes the distribution of signal power in the frequency domain and is defined as the signal power per unit frequency. Classical calculation methods for the power spectrum include the periodogram method and the autocorrelation method, but these methods have two obvious disadvantages: on the one hand, their variance is large under noise ratio conditions; on the other hand, when the data length is too long, the power spectrum has serious fluctuations, and when the data length is too short, the resolution of the power spectrum is poor. The Welch power spectrum algorithm solves these two problems well. It divides the signal into segments and overlaps two adjacent segments to reduce the variance. At the same time, it uses a non-rectangular window to eliminate the spectral distortion of adjacent sequences and increase the correlation between them, so that the resolution of the power spectrum is higher. The Welch power spectrum has good performance and is widely used in communications and mechanical engineering. The signal power spectrum of the i-th segment is

[0056]

[0057] Where: U is the normalization factor; For a non-rectangular window function, the power spectrum of the signal is defined as

[0058]

[0059] Selecting the power spectrum as the feature input significantly improves the network's recognition performance under low signal-to-noise ratio.

[0060] like Figure 4As shown in the figure, the high-order spectrum can well preserve the amplitude and phase information of the signal, and can suppress the influence of Gaussian white noise. Since the bispectrum has the characteristics of time shift, scale invariance and phase retention, it has been widely used in high-order spectrum feature extraction methods. The bispectrum can be used to describe the asymmetry and nonlinearity of the signal, and measure the degree to which the signal deviates from the Gaussian distribution. However, when using the bispectral features, it is necessary to calculate complex two-dimensional matching templates, which significantly increases the amount of calculation. Therefore, the researchers proposed the concept of integral bispectrum to convert the two-dimensional bispectrum into a one-dimensional function. The rectangular integral bispectrum is as follows Figure 4 The integral path extraction is shown in Figure 1. Each point in the figure represents the bispectral value of the signal, and the dotted line represents the integral path. Integrating according to the integral path can well maintain the integrity of the bispectral information and will not cause the reuse of some bispectral values. The calculation result is

[0061]

[0062] Where: The integral path is shown in the figure; l is the number of integral paths.

[0063] The present invention will be described below with an example. If the I / Q data representing the time domain features is to be sent to the convolutional neural network for convolution operation, the real and imaginary data must be separated separately or replaced by the modulus value of the signal. After experimental verification, the recognition effect of sending the modulus value of the signal to the neural network is far inferior to sending the I and Q channels to the convolutional neural network in parallel. Therefore, the I and Q signals of the I / Q data are separated to obtain data with a dimension of 2×1 280×1 to characterize the time domain features of the signal. For the power spectrum data in the frequency domain, the signal power spectrum has a clear physical definition, and the power spectrum data can be directly used as a transform domain feature. Since the dimension of the power spectrum data is closely related to the number of FFT operation points, in order to keep the data dimension of the fusion feature consistent, the Welch power spectrum method based on 1280-point FFT operation is used to obtain power spectrum data with a signal dimension of 1×1280×1. In summary, the article uses power spectrum data with a dimension of 1×1280×1 to characterize the frequency domain features of the signal. High-order spectrum data is similar to time-domain I / Q data. The recognition effects of the integrated bispectrum obtained by signal modulus operation and the integrated bispectrum operation of I and Q channels respectively and then sent to the network in parallel are very different, and the physical definition of the high-order spectrum is relatively vague. Therefore, the integrated bispectrum data obtained from the I and Q channels are used to characterize its characteristics in this domain. The dimension of the bispectrum data is also closely related to the number of FFT operation points. In order to maintain the consistency of the dimension, the I-channel data is first subjected to a bispectrum operation based on a 2560-point FFT to obtain bispectrum data with a dimension of 2560×2560. Secondly, through Figure 4From the symmetry of the integral path, it can be seen that if the dimension of the bispectrum is 2560×2560, then the number of integral paths l is 2560 / 2=1280. Therefore, a rectangular integral operation of l=1280 is performed on the bispectrum data to obtain an integral bispectrum data with a dimension of 1×1280×1. The operation process of the Q-path data is similar. After the above-mentioned integral bispectrum extraction process, this paper finally uses the integral bispectrum data with a dimension of 2×1280×1 to represent the high-order frequency domain characteristics of the signal. By analyzing several transform domain data, the domain data of multiple transform domains are combined and encapsulated into 5 parallel data paths instead of simply connecting them end to end. The fused data dimension is 5×1 280×1. The advantage of this combination method is that it is convenient for the neural network to process each data path in parallel, and each data path has its own channel and does not affect each other. After the first layer of convolution operation, the operation results of each path are summed, and the summed data can more comprehensively characterize the multi-domain subtle characteristics of the communication radiation source.

[0064] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

[0065] In addition, it should be understood that although the present specification is described according to implementation modes, not every implementation mode contains only one independent technical solution. This description of the specification is only for the sake of clarity. Those skilled in the art should regard the specification as a whole. The technical solutions in each embodiment may also be appropriately combined to form other implementation modes that can be understood by those skilled in the art.

Claims

1. A radio frequency fingerprint classification method based on a contrastive learning network, characterized in that: The following steps are involved: S1: Collect radio frequency signals and pre-process the collected radio frequency signals; S2: Perform maximum-minimum normalization on the preprocessed signal, and then perform transformations in the time domain, frequency domain, and high-order spectrum domain respectively, and combine these features into multi-domain features to construct a multi-domain feature fusion data set, as follows: The I / Q data of the signal is directly used as the time domain feature of the radiation source, and the I-channel and Q-channel signals are separated instead of taking the modulus; the Welch power spectrum data of the signal is used as the frequency domain feature; the integrated bispectrum is selected as the signal feature in the high-order spectrum domain, and the I-channel and Q-channel signals are separated, and the integrated bispectrum calculation is performed separately; The domain data of multiple transform domains are combined and encapsulated into 5 parallel data channels, and each data channel occupies a channel without affecting each other; each channel corresponds to I-channel data, Q-channel data, power spectrum data, I-channel integrated bispectral data, and Q-channel integrated bispectral data in sequence to construct a multi-domain feature fusion data set; S3: According to the multi-domain feature fusion dataset, a specified number of samples are selected as the batch training dataset; The 5-channel data is scaled and rotated to obtain enhanced data. For each batch training process, a specified number of samples are selected from the multi-domain feature fusion dataset and the enhanced dataset as the batch training dataset according to the batch size; S4: Calculate the output of all samples after Resnet50 calculation, including the projection vector output; S5: Calculate the average loss function value of each batch training process, define label consistency through cross entropy loss function value, and define sample consistency through comparison loss function value; S6: Calculate the gradient of the loss function and update the network parameters according to the gradient descent principle. Repeat the above steps until the network parameter stable training ends early or the preset Epoach value iteration is completed. The comparative learning pre-training process based on the original data set and the enhanced data set is completed. The grid parameters are fine-tuned according to the enhanced data set and the corresponding label information. The supcon comparative learning algorithm is used for training until the optimal training result is obtained.

2. The radio frequency fingerprint classification method of the contrastive learning network as claimed in claim 1, characterized in that: The step S1 specifically includes: The RF fingerprint dataset is a measured dataset; The radio transmitters are two walkie-talkies of the same type and batch, ensuring that the deviation of the RF fingerprint is small; The transmitted audio is completely random, reducing the impact of the transmitted signal on the RF fingerprint.

3. The radio frequency fingerprint classification method of the contrastive learning network as claimed in claim 1, characterized in that: The step S4 specifically includes: calculating the output of all samples after Resnet50 calculation, and for each batch training process, each sample obtains a projection vector p and a probability vector z after passing through the network.

4. The radio frequency fingerprint classification method of the contrastive learning network according to claim 1, characterized in that: The step S5 specifically includes: comparing the loss function value to define the sample consistency, assuming batch_size=N, then the input data is , when reading data, the data Two data will be generated through random image transformation and , the data set is , where the label , the supervised contrast loss formula is: In the formula, is the number of images with the same label in a batch of input data; when hour, Returns 1 if yes, otherwise returns 0; is the output of the feature extraction network, Represents the inner product of two vectors; is a parameter with a fixed value. The supervised contrast loss is used to calculate the correlation between two feature vectors. When the two feature vectors are of the same category, the supervised contrast loss requires that the two vectors are similar enough. When the two feature vectors are of different categories, the two feature vectors are required to be more different. The cross entropy loss function value defines label consistency. The more consistent the probability distribution of the predicted value is with the probability distribution of the true value, the smaller the cross entropy loss is. The formula is: ; In the formula, x is the output of the classification network and class is the corresponding label.

5. The radio frequency fingerprint classification method of the contrastive learning network as claimed in claim 1, characterized in that: The step S6 specifically includes: updating the network parameters according to the gradient descent principle: , where W is the network parameter, is the learning rate.

Citation Information

Patent Citations

  • Radio frequency fingerprint identification method and device based on slice combination convolutional neural network

    CN115526214A

  • Radio frequency fingerprint identification method based on sample enhancement and deep learning

    CN116257750A