Adaptive modulation and radio frequency fingerprint combined identification method based on multi-task learning

Abstract

The invention discloses an adaptive modulation and radio frequency fingerprint combined identification method based on multi-task learning. A dual-task joint recognition model used in the method comprises a feature extraction expert network and a multi-head classifier. The feature extraction expert network comprises a plurality of shared convolutional neural network modules serving as expert networks, and further comprises two gating networks in one-to-one correspondence with two recognition tasks; the gating network obtains probabilities in one-to-one correspondence with the expert networks according to the input multi-label signals, and then performs weighted fusion with the output features of all the expert networks according to the probabilities; and the output features after weight fusion are sent to the corresponding classifiers to obtain recognition results of the corresponding tasks. According to the method, a multi-task architecture of a multi-gate hybrid expert network is adopted, two tasks of modulation mode and radio frequency fingerprint identification can be completed at the same time, meanwhile, technical means such as an attention mechanism and loss weight dynamic optimization are introduced, and the identification accuracy is improved.

Description

Technical Field

[0001] The present invention belongs to the field of wireless signal recognition, and particularly relates to a method for joint recognition of adaptive modulation and radio frequency fingerprinting. Background Art

[0002] With the continuous progress of networking, informatization, and intelligent technologies, the number of radio devices has increased significantly. Adaptive modulation recognition (AMR) and radio frequency fingerprint recognition (RFFI) are common recognition means in the field of wireless signals. Adaptive modulation recognition refers to automatically identifying the modulation mode of a signal after it arrives at the receiver and before demodulation, providing a basis for subsequent signal processing. In non-cooperative communication scenarios, correctly identifying the modulation mode helps reduce communication overhead and better identify unknown signals. Radio frequency fingerprint recognition technology stems from the differences in wireless device hardware, which are difficult to imitate and replicate. Therefore, it can enhance the security of wireless networks, protect data privacy, and improve anti-spoofing capabilities. This technology has been developed with emphasis in civilian fields such as the Global Positioning System (GPS) and Automatic Dependent Surveillance-Broadcast (ADS-B) systems, improving the detection and situational awareness capabilities of the electromagnetic spectrum.

[0003] In some scenarios, it is necessary to perform adaptive modulation recognition and radio frequency fingerprint recognition simultaneously. For example, in a satellite communication system, multiple ground stations or satellite devices may take turns sending signals at different time periods. To achieve efficient communication under limited spectrum resources, different devices will adopt different modulation modes and sometimes adjust the modulation mode according to changes in communication quality (such as signal interference or noise). In existing deep learning-based communication signal radio frequency fingerprint recognition algorithms, the coupling relationship between the signal modulation mode and the individual recognition of radiation sources is not considered, and only a single radio frequency fingerprint recognition task can be completed. Summary of the Invention

[0004] The present invention proposes a method for joint recognition of adaptive modulation and radio frequency fingerprinting based on multi-task learning, and its purpose is to solve the problem that the existing technology cannot simultaneously complete modulation mode and radio frequency fingerprint recognition.

[0005] The technical solution of the present invention is as follows: A method for joint recognition of adaptive modulation and radio frequency fingerprinting based on multi-task learning uses a dual-task joint recognition model to recognize the multi-label signals sampled by the receiver, and obtains the adaptive modulation recognition result and the radio frequency fingerprint recognition result; The dual-task joint recognition model includes a feature extraction expert network and a multi-head classifier; The feature extraction expert network includes multiple shared convolutional neural network modules serving as expert networks, and also includes two gating networks, one of which corresponds to the adaptive modulation recognition task and the other corresponds to the radio frequency fingerprint recognition task; The gating network obtains probabilities corresponding to each expert network according to the input multi-label signal, and then performs weighted fusion based on the probabilities and the output features of all expert networks; The multi-head classifier part includes an AMR classifier corresponding to the adaptive modulation recognition task and an RFFI head classifier corresponding to the radio frequency fingerprint recognition task; The gating network sends the output features after weighted fusion into the corresponding classifier to obtain the recognition results of the corresponding tasks.

[0006] As a further improvement of the above-mentioned joint recognition method of adaptive modulation and radio frequency fingerprint based on multi-task learning: the shared convolutional neural network module includes multiple feature extraction blocks, several max pooling layers and 1 adaptive average pooling flattening layer; the max pooling layers are respectively arranged at the rear of a part of the feature extraction blocks; the adaptive average pooling flattening layer is located at the end of the shared convolutional neural network module, converting the high-dimensional features into low-dimensional output features.

[0007] As a further improvement of the above-mentioned joint recognition method of adaptive modulation and radio frequency fingerprint based on multi-task learning: the feature extraction block contains a convolutional layer, a normalization layer and a ReLU activation function arranged in sequence.

[0008] As a further improvement of the above-mentioned joint recognition method of adaptive modulation and radio frequency fingerprint based on multi-task learning: the gating network performs a linear transformation on the input multi-label signal and then inputs the result of the linear transformation into the softmax layer, so as to obtain probabilities corresponding to each expert network: ; where, is the parameter matrix of the th gating network, , is the number of expert networks, is the flattened feature dimension of the multi-label signal , is the probability vector obtained by the th gating network, and each element in it is the probability corresponding to each expert network, .

[0009] As a further improvement of the above-mentioned joint recognition method of adaptive modulation and radio frequency fingerprint based on multi-task learning, the output feature obtained after weighted fusion by the th gating network is: ; where, is the number of expert networks, Represents the output features of the th expert network, which is the probability vector obtained by the th gating network and is the probability corresponding to the th expert network in it.

[0010] As a further improvement to the above-mentioned joint recognition method of adaptive modulation and radio frequency fingerprint based on multi-task learning: the classifier performs classification based on the Transformer encoder module and the fully connected layer; after the Transformer encoder extracts the features of the current task from the output features of the corresponding gating network, it outputs the classification result of the corresponding task through the fully connected layer, that is, the adaptive modulation recognition result or the radio frequency fingerprint recognition result.

[0011] As a further improvement to the above-mentioned joint recognition method of adaptive modulation and radio frequency fingerprint based on multi-task learning, the training method of the dual-task joint recognition model is as follows: Step T1, construct a training set and divide the training set into multiple batches, each batch including training samples; Step T2, train in batches. After each batch of training samples is input into the dual-task joint recognition model, calculate the multi-task training loss and adjust the network parameters of the dual-task joint recognition model according to the loss.

[0012] As a further improvement to the above-mentioned joint recognition method of adaptive modulation and radio frequency fingerprint based on multi-task learning, for the th batch, the corresponding multi-task training loss is: ; where is the cross-entropy loss function of the radio frequency fingerprint recognition task for the th batch, is the cross-entropy loss function of the adaptive modulation recognition task for the th batch, is the loss weight of the radio frequency fingerprint recognition task for the th batch, is the loss weight of the adaptive modulation recognition task for the th batch.

[0013] As a further improvement to the above-mentioned joint recognition method of adaptive modulation and radio frequency fingerprint based on multi-task learning: For any batch, the calculation method of the cross-entropy loss function of the radio frequency fingerprint recognition task is: = ; in, The number of categories for the RF fingerprinting task; For the The first one in the real label of RF fingerprint recognition corresponding to the training sample The value of the category, if the training sample belongs to If there are multiple categories, the value is 1, otherwise it is 0; For the The RF fingerprint recognition result obtained by inputting the training samples into the dual-task joint recognition model is The probability of each category; For any batch, the cross entropy loss function of the adaptive modulation recognition task is The calculation method is: = ; in, The number of categories for the adaptive modulation recognition task; For the The first one in the true label of adaptive modulation recognition corresponding to the training sample The value of the category, if the training sample belongs to If there are multiple categories, the value is 1, otherwise it is 0; For the The adaptive modulation recognition results obtained by inputting the training samples into the dual-task joint recognition model are The probability of a class.

[0014] As a further improvement of the adaptive modulation and RF fingerprint joint recognition method based on multi-task learning: For batches, RF fingerprint recognition task loss weight and adaptive modulation recognition task loss weights The calculation method is: ; ; in, , ,and , , is a preset constant.

[0015] Compared with the prior art, the present invention has the following beneficial effects: 1. The present invention adopts a multi-task architecture of a multi-gate hybrid expert network, and controls each part of the network to fully learn a set of parameters that contributes the most to each task, thereby completing the two tasks of modulation mode and radio frequency fingerprint recognition at the same time.

[0016] 2. The multi - head classifier part uses a Transformer encoder module, which combines technologies such as self - attention mechanism, global attention mechanism, and residual connection. It can effectively encode the input sequence, transmit information between different positions, capture long - range dependencies in the sequence at the head of each task, thereby helping each task extract better task - specific features outside the shared network and improving the recognition accuracy.

[0017] 3. In the training stage, a multi - task optimization strategy is adopted to dynamically optimize the multi - task loss function, eliminating the need for manual adjustment of multi - task loss weights and improving the prediction accuracy of each task. Description of the Drawings

[0018] Figure 1 It is a schematic structural diagram of a communication radiation source information joint recognition system in a single - carrier scenario; Figure 2 It is an architecture diagram of the dual - task joint recognition model in the present invention; Figure 3 It is a structural diagram of a shared convolutional neural network; Figure 4 It is an architecture diagram of the Transformer encoder used in the multi - head classifier; Figure 5 It is a comparison diagram of ablation experiments;

[0019] Figure 6 It is the multi - task accuracy under grid search for different weights. Detailed Embodiment

[0020] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments.

[0021] A method for joint recognition of adaptive modulation and RF fingerprint based on multi - task learning is used for a communication radiation source information joint recognition system in a single - carrier scenario as Figure 1 shown. In this scenario, the transmitting end includes multiple similar communication devices. Only one of these devices is in the signal - transmitting state at any given time, and the single - carrier modulation mode it uses is not fixed but constantly changing. The signal monitoring end first captures the air signal and then identifies the radiation source information contained in the signal. Among them, the modulation mode information is used for subsequent signal content analysis, and the RF fingerprint information is used to judge the security and reliability of signal transmission.

[0022] This method uses a dual - task joint recognition model for multi - label signals (i.e., complex baseband sequences at points, which can be denoted as )Perform identification to obtain the adaptive modulation identification result and the radio frequency fingerprint identification result. The real part of the sequence represents the in-phase component of the baseband signal, and the imaginary part of the sequence represents the quadrature component of the baseband signal.

[0023] Such as Figure 2 , the dual-task joint identification model includes two parts: a feature extraction expert network and a multi-head classifier.

[0024] (I) Feature extraction expert network.

[0025] The feature extraction expert network includes multiple shared convolutional neural network modules serving as expert networks, and also includes two gating networks. One of the gating networks corresponds to the adaptive modulation identification task, and the other gating network corresponds to the radio frequency fingerprint identification task.

[0026] Such as Figure 3 , the shared convolutional neural network module includes 11 feature extraction blocks, several max pooling layers, and 1 adaptive average pooling flattening layer. Each feature extraction block gradually extracts higher-dimensional features by increasing the number of channels. Each feature extraction block contains a convolutional layer, a normalization layer, and a ReLU activation function arranged in sequence to ensure the stability and efficiency of training. In the deep part of the shared convolutional neural network module, continuous convolutional operations are adopted to further enhance the feature extraction ability. The max pooling layers are respectively arranged at the rear of a part of the feature extraction blocks, and the data dimension is gradually compressed through downsampling to retain important features. The adaptive average pooling flattening layer is located at the end of the shared convolutional neural network module, converting the high-dimensional features into low-dimensional output features.

[0027] Such as Figure 2 , the gating network performs a linear transformation on the input multi-label signal , and then inputs the result of the linear transformation into the softmax layer to obtain the probabilities corresponding to each expert network one by one: ; Among them, is the parameter matrix of the th gating network, , is the number of expert networks, is the flattened feature dimension of the multi-label signal ; is the probability vector obtained by the th gating network, and each element in it is the probability corresponding to each expert network one by one, .

[0028] In the feature extraction expert network, the output features of each expert network are weighted and fused based on the probability vector output by the gating network. The The output features obtained after weighted fusion of a gating network are as follows: ; Among them, is the number of expert networks, represents the output features of the th expert network, is the probability vector obtained by the th gating network and the probability corresponding to the

[0029] (2) Multi-head classifier.

[0030] As Figure 2 , the multi-head classifier part includes an AMR classifier corresponding to the adaptive modulation recognition task and an RFFI head classifier corresponding to the radio frequency fingerprint recognition task.

[0031] Each classifier performs classification based on a Transformer encoder module and a fully connected layer. The structure of the Transformer encoder module is as Figure 4 shown. It uses the attention mechanism to better extract the features of the AMR task and the RFFI task. The self-attention mechanism allows the output at each position to consider the information of all other positions in the input sequence, thereby capturing global dependencies. In signal processing, this means that the model can consider the features of the entire signal simultaneously without being limited by the local window size. After the Transformer encoder extracts the features of the current task from the output features of the corresponding gating network, it passes through a fully connected layer to output the classification result of the corresponding task, that is, the adaptive modulation recognition result or the radio frequency fingerprint recognition result.

[0032] The training method of the dual-task joint recognition model is as follows: Step T1, construct a training set and divide the training set into multiple batches, each batch including training samples.

[0033] The dataset Multidata used in this embodiment is real radio data generated by a Signal Hound VSG60A signal generator and collected by a Signal Hound BB60C collector. The data acquisition system consists of a signal generator (VSG60A), a signal receiver (BB60C), a personal computer (PC), and six target power amplifiers (PAs). The stable hardware characteristics of the transmitter, such as signal amplitude, phase, and frequency distortion, are reflected in the nonlinear distortion of the power amplifier. The VSG60A is connected to the computer via USB 3.0, and the power amplifiers are connected to the BB60C and VSG60A respectively via SMA radio frequency coaxial connection lines. The collected signals are transmitted from the BB60C to the PC via USB 3.0, and many parameters of the BB60C can be adjusted through the spike spectrum analysis software. The center frequency of the collected signals is 2.4 GHz, and the sampling rate is 10 Msample / s. The size of the original data is 17.8 GB, which contains a total of eight modulation schemes, namely BPSK, QPSK, 8PSK, 16PSK, 16QAM, 64QAM, 256QAM, and 1024QAM from six PAs, with a total of 36,000 IQ sequence signals. 28,800 signals from the dataset are used as the training set, 3,600 for validation, and 3,600 for testing.

[0034] Step T2: Train in batches. After each batch of training samples is input into the dual-task joint recognition model, calculate the multi-task training loss in the following manner and adjust the network parameters of the dual-task joint recognition model according to the loss: For the th batch, the corresponding multi-task training loss is: ; where is the cross-entropy loss function of the radio frequency fingerprint recognition task for the th batch, is the cross-entropy loss function of the adaptive modulation recognition task for the th batch, is the loss weight of the radio frequency fingerprint recognition task for the th batch, is the loss weight of the adaptive modulation recognition task for the th batch.

[0035] For any batch, the calculation method of the cross-entropy loss function of the radio frequency fingerprint recognition task is: = ; Among them, is the number of categories of the radio frequency fingerprint recognition task; is the -th value of the -th category in the true label of radio frequency fingerprint recognition corresponding to the -th training sample. If the training sample belongs to the -th category, the value is 1; otherwise, it is 0; is the probability of the -th value of the -th category in the radio frequency fingerprint recognition result obtained by inputting the -th training sample into the dual-task joint recognition model.

[0036] For any batch, the calculation method of the cross-entropy loss function of the adaptive modulation recognition task is: = ; Among them, is the number of categories of the adaptive modulation recognition task; is the -th value of the -th category in the true label of adaptive modulation recognition corresponding to the -th training sample. If the training sample belongs to the -th category, the value is 1; otherwise, it is 0; is the probability of the -th value of the -th category in the adaptive modulation recognition result obtained by inputting the -th training sample into the dual-task joint recognition model.

[0037] For the -th batch, the calculation methods of the loss weight of the radio frequency fingerprint recognition task and the loss weight of the adaptive modulation recognition task are: ; ; Among them, , , and , , is a preset constant.

[0038] The effectiveness of the multi-task learning model largely depends on the weighting scheme between the loss functions of different tasks. The commonly used method currently is to weight the losses of each task to obtain the total loss. However, the present invention uses the DWA strategy to learn the average task weights over time by considering the loss change rate of each task, thereby reducing the uncertainty of stochastic gradient descent and stochastic training data selection. This method can achieve better performance in preventing loss pulling and improving the prediction accuracy of each task.

[0039] Table 1 below shows the experimental comparison results of four networks: the method (MCNT) adopted in the present invention, the multi-task learning convolutional neural network (MTL-CNN), the hard-sharing multi-task architecture network (SB-CNN-Transformer, with the same configuration as this embodiment), and the single-task network (CNN-Transformer, with the same configuration as this embodiment). The suffixes -RFF and -AMR respectively represent the recognition accuracies of the corresponding network architectures in the radio frequency fingerprint recognition task and the adaptive modulation recognition task.

[0040] Table 1 - Experimental comparison of four network architectures.

[0041] ; From the data analysis in Table 1, it can be concluded that the method (MCNT) proposed in the present invention has an accuracy rate of almost 100% in the adaptive modulation recognition (AMR) task and significantly reduces the error of radio frequency fingerprint recognition (RFFI). Obviously, by integrating the characteristics of radio frequency fingerprint recognition and adaptive modulation recognition, the present invention realizes information sharing between the two tasks, reveals the connection between them, and significantly improves the overall performance. Especially in the radio frequency fingerprint recognition task, since the transmitter individual may generate unexpected modulation due to various factors, and the intentional modulation features extracted in the modulation recognition task theoretically help RFFI filter out redundant features irrelevant to the individual, thus more effectively extracting unique fingerprint features.

[0042] In addition, ablation experiments were also conducted in this embodiment to evaluate the impact of the Transformer encoder in the multi-task architecture and the multi-head classifier on the task performance. The experiments explored the contributions of each step through different configurations: First, multi-task learning (MTL) was simplified to a single task-specific head to examine whether information sharing between tasks can effectively improve the performance of radio frequency fingerprint recognition (RFFI). These configurations are respectively called single-head AMR and single-head RFFI, and the corresponding single-task structures are respectively represented as MCNT-A and MCNT-R. Second, the Transformer encoder module was removed, and only the classification head was retained, forming the MMOE-CNN configuration. Among them, MMOE-CNN-RFF represents the recognition accuracy of RFFI, and MMOE-CNN-AMR represents the AMR recognition accuracy under this configuration.

[0043] Figure 5Shows the performance of AMR and RFFI on the dataset under different network configurations. Notably, in the multi-task architecture, the performance of AMR almost reaches 100% at five signal-to-noise ratios. Among the three configurations, the performance of RFFI significantly drops at 0 dB and 5 dB signal-to-noise ratios in the MMOE-CNN configuration. Additionally, the multi-task method of the present invention has a significant improvement compared to the MMOE-CNN Transformer-R configuration at low signal-to-noise ratios, indicating that multi-task knowledge sharing helps the RFFI task extract more difficult-to-capture features and obtain information from a single task to accurately identify individuals. From Figure 5 It can be seen that the RFFI task performance of the network of the present invention always leads at five signal-to-noise ratios. The designed network significantly improves the recognition performance of the RFFI task while hardly affecting the modulation recognition task.

[0044] To evaluate the performance of the multi-task learning optimization strategy DWA, this embodiment conducts a comparison of three different optimization strategies: uniform (a baseline method representing equal weights for task losses), grid search, and uncertain (an uncertainty method). Figure 6 Shows the situation of finding the optimal weights for two tasks during the grid search process, and the results show that the best effect is achieved when the task weights are equal. Table 2 lists the accuracy performances under different optimization strategies.

[0045] Table 2 - Accuracy of different optimization strategies.

[0046] ; Table 2 shows the specific results of different task balancing methods. Among these methods, the strategy (DWA) of the present invention balances the training progress of the two tasks by dynamically adjusting the weights. For the adaptive modulation recognition (AMR) task, the accuracies of various balancing methods are similar. However, under the conditions of 0, 5, 10, and 20 dB, the DWA method has the highest accuracy in the radio frequency fingerprint identification (RFFI) task. At 15 dB, the accuracy of the DWA method in the RFFI task is only 0.28% lower than that of the grid search method. This indicates that the adopted optimization strategy can effectively balance the optimization processes of different tasks without the need for complex grid search, thereby improving the overall accuracy of multi-task learning.

[0047] It should be noted that for those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and without departing from the spirit or basic characteristics of the present invention, the present invention can be implemented in other specific forms. The scope of the present invention is defined by the claims rather than the above description.

Claims

1. A method for joint recognition of adaptive modulation and radio frequency fingerprint based on multi-task learning, characterized in that: The dual-task joint recognition model is used to identify the multi-tag signal sampled by the receiver, and the adaptive modulation recognition result and the RF fingerprint recognition result are obtained; The dual-task joint recognition model includes a feature extraction expert network and a multi-head classifier; The feature extraction expert network includes a plurality of shared convolutional neural network modules as expert networks, and also includes two gating networks, wherein one gating network corresponds to the adaptive modulation recognition task, and the other gating network corresponds to the radio frequency fingerprint recognition task; The gating network obtains the probability corresponding to each expert network according to the input multi-label signal, and then performs weighted fusion with the output features of all expert networks according to the probability; The multi-head classifier part includes an AMR classifier corresponding to the adaptive modulation recognition task and an RFFI head classifier corresponding to the radio frequency fingerprint recognition task; The gated network sends the weighted fused output features to the corresponding classifier to obtain the recognition results of the corresponding task.

2. The method for joint recognition of adaptive modulation and radio frequency fingerprint based on multi-task learning according to claim 1, characterized in that: The shared convolutional neural network module includes multiple feature extraction blocks, several maximum pooling layers and one adaptive average pooling flattening layer; the maximum pooling layers are respectively arranged on the back side of some of the feature extraction blocks; the adaptive average pooling flattening layer is located at the tail end of the shared convolutional neural network module to convert high-dimensional features into low-dimensional output features.

3. The method for joint recognition of adaptive modulation and radio frequency fingerprint based on multi-task learning according to claim 2, characterized in that: The feature extraction block contains convolutional layers, normalization layers, and ReLU activation functions set in sequence.

4. The method for joint recognition of adaptive modulation and radio frequency fingerprint based on multi-task learning according to claim 1, characterized in that: The gating network is used to input multi-label signals Perform a linear transformation, and then input the result of the linear transformation into the softmax layer to obtain the probability corresponding to each expert network: ； in, For the The parameter matrix of the gating network, , is the number of expert networks, It is a multi-label signal The flattened feature dimension of For the The probability vector obtained by the gating network, each element of which is the probability corresponding to each expert network. .

5. The method for joint recognition of adaptive modulation and radio frequency fingerprint based on multi-task learning according to claim 4, characterized in that: No. The output features obtained after weighted fusion of gating networks for: ； in, is the number of expert networks, Indicates The output features of the expert network are For the The probability vector obtained by the gating network Middle and The probability corresponding to an expert network.

6. The method for joint recognition of adaptive modulation and radio frequency fingerprint based on multi-task learning according to claim 1, characterized in that: The classifier performs classification based on the Transformer encoder module and the fully connected layer; after the Transformer encoder extracts the features of the current task from the output features of the corresponding gating network, it outputs the classification result of the corresponding task through the fully connected layer, that is, the adaptive modulation recognition result or the RF fingerprint recognition result.

7. The method for joint recognition of adaptive modulation and radio frequency fingerprint based on multi-task learning according to any one of claims 1 to 6, characterized in that: The training method of the dual-task joint recognition model is: Step T1: Build a training set and divide it into multiple batches. Each batch includes training samples; Step T2: training in batches. After inputting a batch of training samples into the dual-task joint recognition model, the multi-task training loss is calculated and the network parameters of the dual-task joint recognition model are adjusted according to the loss.

8. The method for joint recognition of adaptive modulation and radio frequency fingerprint based on multi-task learning according to claim 7, characterized in that: For batches, corresponding multi-task training loss for: ； in, For the The cross entropy loss function of the RF fingerprint recognition task for batches, For the The cross entropy loss function of the adaptive modulation recognition task in batches, For the The loss weight of the RF fingerprint recognition task for batches, For the Adaptive modulation recognition task loss weights for batches.

9. The method for joint recognition of adaptive modulation and radio frequency fingerprint based on multi-task learning according to claim 8, characterized in that: For any batch, the cross entropy loss function of the RF fingerprint recognition task is The calculation method is: = ； in, The number of categories for the RF fingerprinting task; For the The first one in the real label of RF fingerprint recognition corresponding to the training sample The value of the category, if the training sample belongs to If there are multiple categories, the value is 1, otherwise it is 0; For the The RF fingerprint recognition result obtained by inputting the training samples into the dual-task joint recognition model is The probability of each category; For any batch, the cross entropy loss function of the adaptive modulation recognition task is The calculation method is: = ； in, The number of categories for the adaptive modulation recognition task; For the The first one in the true label of adaptive modulation recognition corresponding to the training sample The value of the category, if the training sample belongs to If there are multiple categories, the value is 1, otherwise it is 0; For the The adaptive modulation recognition results obtained by inputting the training samples into the dual-task joint recognition model are The probability of a class.

10. The method for joint recognition of adaptive modulation and radio frequency fingerprint based on multi-task learning according to claim 8, characterized in that: For batches, loss weight of RF fingerprint recognition task and adaptive modulation recognition task loss weights The calculation method is: ； ； in, , ,and , , is a preset constant.

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