Radio frequency fingerprint identification method and system based on a learnable mahalanobis distance discriminant model
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SOUTHEAST UNIV
- Filing Date
- 2026-06-22
- Publication Date
- 2026-08-07
AI Technical Summary
然后这种方法对特征空间建模过程与闭集分类网络训练独立，未将特征空间分布建模引入闭集分类网络训练来优化特征空间形成更利于开集识别的结构；且使用极值理论对设备类别特征空间建模，对固定先验分布形式有较强的依赖，可能与实际的特征空间分布并不符合，存在局限性
[0066] 1. By directly introducing feature space distribution modeling into the training process of deep neural networks, the feature space distribution can be constrained to be more separable between classes, thereby improving recognition accuracy;
Smart Images
Figure CN122534439A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of radio frequency fingerprint recognition technology, and particularly relates to a radio frequency fingerprint recognition method and system based on a learnable Mahalanobis distance discrimination model. Technical Background
[0002] With the rapid development of wireless communication technology, the Internet of Things (IoT) has enabled intelligent interaction and collaboration between people and devices, profoundly changing social life and industrial production. However, in open wireless communication environments, due to the broadcast characteristics of channels and the openness of access, networks are highly vulnerable to attacks such as spoofed access by unauthorized devices and injection of malicious signals. To address these security issues, it is urgent to introduce highly reliable authentication mechanisms in the physical layer or cross-layer architecture.
[0003] Against this backdrop, Radio Frequency Fingerprint Identification (RFFI) technology has gradually attracted widespread attention. RF fingerprints originate from hardware defects in the manufacturing process of RF devices; these unclonable physical features can serve as device identification. With the rapid development of deep learning, researchers are using deep neural networks to extract RF features, overcoming the limitations of manual feature extraction. Deep learning models can adaptively extract multi-level, high-dimensional feature representations from signals, improving recognition accuracy and robustness in complex real-world IoT application scenarios.
[0004] However, most existing RFID fingerprinting methods lack the ability to detect and reject unknown device categories in open-set recognition scenarios, leading to decreased recognition accuracy. Current research approaches modeling the feature space of known device categories, using extremum theory to depict the boundaries or uncertainties of feature distributions for each category, enabling the model to distinguish between known and unknown devices. However, this method separates feature space modeling from closed-set classification network training, failing to incorporate feature space distribution modeling into closed-set classification network training to optimize the feature space into a structure more conducive to open-set recognition. Furthermore, using extremum theory to model the device category feature space relies heavily on fixed prior distributions, potentially contradicting the actual feature space distribution and thus presenting limitations. Summary of the Invention
[0005] To address the aforementioned technical issues, this invention proposes an RFID fingerprinting method and system based on a learnable Mahalanobis distance discriminant model. During the training of the feature extraction network, the statistical quantities distributed in the feature space for each category are explicitly learned: the feature center and the covariance matrix. Simultaneously, the learnable statistical quantities are used to calculate the Mahalanobis distance between the sample and the feature center of the category, and a discriminant boundary is constructed for each known category in the feature space to detect whether the sample belongs to an unknown category.
[0006] Firstly, a radio frequency fingerprint recognition method based on a learnable Mahalanobis distance discrimination model is provided, the method including a training process and a testing process.
[0007] The training process includes the following steps:
[0008] Receive radio frequency signals;
[0009] Training the received radio frequency signal includes:
[0010] Normalize the radio frequency signal;
[0011] A time-frequency characterization is obtained by performing a short-time Fourier transform on the normalized radio frequency signal;
[0012] The time-frequency representation is passed through a backbone network to obtain the feature vector of the feature space, and then a classifier is used to obtain the device label of the closed set classification.
[0013] The feature vectors and closed-set classification labels are input into the learnable Mahalanobis distance discriminant model to update the learnable statistics for each known class, namely the feature center and covariance matrix; a joint loss function is constructed based on the cross-entropy loss function and Mahalanobis distance to update the network parameters of the backbone network and the classifier.
[0014] The received radio frequency signals are repeatedly trained until the network converges.
[0015] The testing method includes the following steps:
[0016] The received test radio frequency signal is then processed sequentially through normalization, short-time Fourier transform, and backbone network to obtain the feature vector;
[0017] Using the feature centers and covariance matrices of each known category obtained during training, the Mahalanobis distance between the feature vector and the predicted category is calculated;
[0018] Based on the comparison result between the Mahalanobis distance and the threshold, it is determined whether the device is of an unknown category, and the open set identification result is output.
[0019] Preferably, the normalization processing of the radio frequency signal specifically includes:
[0020] Assume the received radio frequency complex signal discrete sequence is , N is the total length of the sequence. The maximum values of the real and imaginary parts of the complex signal sequence are calculated using the following formula. and minimum value :
[0021]
[0022]
[0023] The received RF complex signal is normalized by performing maximum-minimum normalization to obtain the normalized RF complex signal. , :
[0024] .
[0025] Preferably, the step of performing a short-time Fourier transform on the normalized radio frequency signal to obtain a two-dimensional time-frequency characterization specifically includes:
[0026] One-dimensional Point radio frequency complex signal sequence The two-dimensional complex matrix is obtained by performing a short-time Fourier transform. :
[0027]
[0028] in, A two-dimensional complex matrix The Line 1 Column corresponding elements, The number of points in the Fourier transform. This represents the number of time windows for the short-time Fourier transform. For the length of the window The Hanning window function, The sliding step of the window function. , ;
[0029] Take two-dimensional complex matrices respectively The real and imaginary parts are concatenated to form a dual-channel time-frequency representation. As subsequent network input.
[0030] Preferably, the step of obtaining feature vectors in the feature space from the time-frequency representation through a backbone network, and then obtaining device labels for closed-set classification through a classifier, specifically includes:
[0031] First, the dual-channel time-frequency characterization is performed. The backbone network maps the input to feature vectors in the feature space. d is the dimension of the feature vector:
[0032]
[0033] The classifier uses the feature vectors output by the backbone network to determine the closed set classification probability distribution of devices with known class information.
[0034]
[0035] in Belonging to A predicted probability vector for a known category.
[0036] Finally, the device labels for closed-set classification are obtained:
[0037] .
[0038] Preferably, the step of inputting the feature vector and closed-set classification label into the learnable Mahalanobis distance discriminant model to update the learnable statistics for each known category, namely the feature center and covariance matrix, specifically includes:
[0039] In each batch, for all known categories Give the feature center estimate of the feature space Estimation of covariance matrix ,as follows:
[0040]
[0041]
[0042] Then, to improve the stability of the statistics, a moving average algorithm was used for all known categories. Feature center Covariance Matrix Update:
[0043]
[0044]
[0045] in and These are the smoothing update coefficients for the moving average algorithm.
[0046] Preferably, the step of constructing a joint loss function based on the cross-entropy loss function and the Mahalanobis distance to update the network parameters of the backbone network and the classifier specifically includes:
[0047] For closed-set classification, the cross-entropy loss function is chosen, and for open-set classification, the Mahalanobis distance loss function is chosen. The two are weighted and summed to construct a joint loss function, which is then used to update parameters using the Adam optimizer. The formula for the joint loss function is as follows:
[0048]
[0049] in It is the device category label to which the radio frequency signal belongs.
[0050] Secondly, a radio frequency fingerprint recognition system based on a learnable Mahalanobis distance discrimination model is provided, the system comprising the following modules:
[0051] The receiver module is used to receive radio frequency signals;
[0052] The training module, used to train the received radio frequency signal, includes:
[0053] The normalization processing module is used to perform maximum-minimum value normalization processing on the received radio frequency signal;
[0054] The short-time Fourier transform module is used to transform a one-dimensional radio frequency signal into a time-frequency representation;
[0055] The closed-set classification module is used to obtain feature vectors in the feature space and device labels for closed-set classification based on time-frequency representation.
[0056] The open-set statistics learning module is used during the training phase to update the learnable statistics for each known class, namely the feature center and covariance matrix, based on the feature vector and the closed-set classification device label.
[0057] The loss function building module is used to construct a joint loss function based on the cross-entropy loss function and the Mahalanobis distance;
[0058] The update module is used to update the network parameters of the backbone network and the classifier based on the joint loss function;
[0059] The iterative training module is used to repeatedly train the received radio frequency signals until the network converges.
[0060] The test discrimination module is used during the test phase to receive the test radio frequency signal, calculate the Mahalanobis distance between the feature vector and the predicted category, and determine whether it is an unknown category based on the comparison result of the Mahalanobis distance and the threshold.
[0061] The output module is used to output the open set classification results.
[0062] Thirdly, a computer-readable storage medium is provided for storing one or more programs, the one or more programs including instructions that, when executed by a computing device, cause the computing device to perform any of the methods described.
[0063] Fourthly, a computing device is provided, comprising:
[0064] One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the one or more programs include instructions for performing any of the methods described.
[0065] The beneficial effects of this invention are as follows:
[0066] 1. By directly introducing feature space distribution modeling into the training process of deep neural networks, the feature space distribution can be constrained to be more separable between classes, thereby improving recognition accuracy;
[0067] 2. The learnable Mahalanobis distance discrimination model directly learns the feature centers and covariance matrix, and can learn the anisotropy of the feature space and construct the Mahalanobis distance, which is more consistent with the actual radio frequency characteristics than the Euclidean distance;
[0068] 3. A moving average algorithm was designed to update the learnable statistics, so that changes in the statistics do not affect the network's convergence speed. Attached Figure Description
[0069] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are merely some examples of the present invention, and those skilled in the art can obtain other drawings based on these drawings without any creative effort.
[0070] Appendix Figure 1 This is a flowchart illustrating the training process of the radio frequency fingerprint recognition algorithm based on the learnable Mahalanobis distance discrimination model of the present invention.
[0071] Appendix Figure 2This is a simplified network structure diagram of the radio frequency fingerprint recognition algorithm based on the learnable Mahalanobis distance discrimination model of the present invention;
[0072] Appendix Figure 3 This is a network structure diagram of the residual blocks used in the backbone network of this invention. Detailed Implementation
[0073] To make the objectives and technical solutions of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be described more clearly and completely below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.
[0074] Since this invention is based on deep neural networks, the description of specific implementation methods will be separated into two aspects: the training process and the testing process.
[0075] like Figure 1-3 As shown, the present invention provides a radio frequency fingerprint recognition method based on a learnable Mahalanobis distance discrimination model, the method including a training process and a testing process.
[0076] The training process includes:
[0077] Receive radio frequency signals;
[0078] Training the received radio frequency signal includes:
[0079] Normalize the radio frequency signal;
[0080] A time-frequency characterization is obtained by performing a short-time Fourier transform on the normalized radio frequency signal;
[0081] The time-frequency representation is passed through a backbone network to obtain the feature vector of the feature space, and then a classifier is used to obtain the device label of the closed set classification.
[0082] The feature vectors and closed-set classification labels are input into the learnable Mahalanobis distance discriminant model to update the learnable statistics for each known class, namely the feature centers and covariance matrix.
[0083] A joint loss function is constructed based on the cross-entropy loss function and Mahalanobis distance, and the network parameters of the backbone network and the classifier are updated.
[0084] The received radio frequency signals are repeatedly trained until the network converges.
[0085] The testing process includes:
[0086] The received test radio frequency signal is then processed sequentially through normalization, short-time Fourier transform, and backbone network to obtain the feature vector;
[0087] Using the feature centers and covariance matrices of each known category obtained during training, the Mahalanobis distance between the feature vector and the predicted category is calculated;
[0088] Based on the comparison result between the Mahalanobis distance and the threshold, it is determined whether the device is of an unknown category, and the open set identification result is output.
[0089] Specifically, the normalization process for radio frequency signals includes the following steps:
[0090] (1.1) Assume the discrete sequence of the received radio frequency complex signal is as follows: , N is the total length of the sequence. The maximum values of the real and imaginary parts of the complex signal sequence are calculated using the following formula. and minimum value :
[0091]
[0092]
[0093] (1.2) Perform maximum-minimum normalization on the received RF complex signal to obtain the normalized RF complex signal. , :
[0094] .
[0095] Specifically, the time-frequency characterization is obtained by performing a short-time Fourier transform on the normalized radio frequency signal, including the following steps:
[0096] (2.1) One-dimensional Point radio frequency complex signal sequence The two-dimensional complex matrix is obtained by performing a short-time Fourier transform. :
[0097]
[0098] in, A two-dimensional complex matrix The Line 1 Column corresponding elements, The number of points in the Fourier transform. This represents the number of time windows for the short-time Fourier transform. For the length of the window The Hanning window function, The sliding step of the window function. , ;
[0099] (2.2) Take two-dimensional complex matrices respectively The real and imaginary parts are concatenated to form a dual-channel time-frequency representation. As subsequent network input.
[0100] Specifically, the time-frequency representation is processed through a backbone network to obtain feature vectors in the feature space, and then a classifier is used to obtain device labels for closed-set classification. This includes the following steps:
[0101] (3.1) Dual-channel time-frequency characterization The backbone network maps the input to feature vectors in the feature space. d is the dimension of the feature vector:
[0102]
[0103] (3.2) The classifier uses the feature vectors output by the backbone network to determine the closed set classification probability distribution of devices with known categories:
[0104]
[0105] in Belonging to A predicted probability vector for a known category.
[0106] (3.3) Obtain the device labels for closed set classification:
[0107] .
[0108] Specifically, the feature vectors and closed-set classification labels are input into the learnable Mahalanobis distance discriminant model to update the learnable statistics for each known class, namely the feature centers and covariance matrix, including the following steps:
[0109] (4.1) In each batch, for all known categories Give the feature center estimate of the feature space Estimation of covariance matrix ,as follows:
[0110]
[0111]
[0112] (4.2) To improve the stability of the statistics, a moving average algorithm is used for all known categories. Feature center Covariance Matrix Update:
[0113]
[0114]
[0115] in and These are the smoothing update coefficients for the moving average algorithm.
[0116] Specifically, a joint loss function is constructed based on the cross-entropy loss function and the Mahalanobis distance to update the network parameters of the backbone network and the classifier, including the following steps:
[0117] (5.1) For closed-set classification, the cross-entropy loss function is selected, and for open-set classification, the Mahalanobis distance loss function is selected. The two are weighted and added together to construct the joint loss function, and the calculation formula is as follows:
[0118]
[0119] in It is the device category label to which the radio frequency signal belongs.
[0120] (5.2) Use the Adam optimizer to update parameters.
[0121] The network parameters are determined during the training phase. The testing process consists of seven steps. The first six steps are the same as the training process (because the network parameters are determined during training, no parameter updates are needed). Step seven, "Repeatedly train the network using the received RF signals until the network converges," is modified as follows:
[0122] Step 7: Output the device category labels for the open set classification.
[0123] (7.1) Calculate the eigenvectors according to the following formula. Classification of Closed Sets Mahalanobis distance from the feature center :
[0124]
[0125] (7.2) If Larger than the number of classes during training If the maximum Mahalanobis distance is found, the input is treated as an unknown category device, and the output is an open-set classification device category label M (representing the unknown category); otherwise, the output is an open-set classification device category label. .
[0126] This invention provides an RFID fingerprint recognition system based on a learnable Mahalanobis distance discrimination model, the system comprising the following modules:
[0127] The receiver module is used to receive radio frequency signals;
[0128] The training module, used to train the received radio frequency signal, includes:
[0129] The normalization processing module is used to perform maximum-minimum value normalization processing on the received radio frequency signal;
[0130] The short-time Fourier transform module is used to transform a one-dimensional radio frequency signal into a time-frequency representation;
[0131] The closed-set classification module is used to obtain feature vectors in the feature space and device labels for closed-set classification based on time-frequency representation.
[0132] The open-set statistics learning module is used during the training phase to update the learnable statistics for each known class, namely the feature center and covariance matrix, based on the feature vector and the closed-set classification device label.
[0133] The loss function building module is used to construct a joint loss function based on the cross-entropy loss function and the Mahalanobis distance;
[0134] The update module is used to update the network parameters of the backbone network and the classifier based on the joint loss function;
[0135] The iterative training module is used to repeatedly train the received radio frequency signals until the network converges.
[0136] The test discrimination module is used during the test phase to receive the test radio frequency signal, calculate the Mahalanobis distance between the feature vector and the predicted category, and determine whether it is an unknown category based on the comparison result of the Mahalanobis distance and the threshold.
[0137] The output module is used to output the open set classification results.
[0138] Embodiments of this application may be provided as methods or computer program products. Therefore, this application may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. The solutions in the embodiments of this application may be implemented in various computer languages, such as the object-oriented programming language Java and the interpreted scripting language JavaScript.
[0139] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0140] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0141] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0142] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.
Claims
1. A radio frequency fingerprint recognition method based on a learnable Mahalanobis distance discrimination model, characterized in that, The method includes a training process and a testing process: The training process includes: Receive radio frequency signals; Training the received radio frequency signal includes: Normalize the radio frequency signal; A time-frequency characterization is obtained by performing a short-time Fourier transform on the normalized radio frequency signal; The time-frequency representation is passed through a backbone network to obtain the feature vector of the feature space, and then a classifier is used to obtain the device label of the closed set classification. The feature vectors and closed-set classification labels are input into the learnable Mahalanobis distance discriminant model to update the learnable statistics for each known class, namely the feature centers and covariance matrix. A joint loss function is constructed based on the cross-entropy loss function and Mahalanobis distance, and the network parameters of the backbone network and the classifier are updated. Repeat the training process on the received radio frequency signals until the network converges; The testing process includes: The received test radio frequency signal is then processed sequentially through normalization, short-time Fourier transform, and backbone network to obtain the feature vector; Using the feature centers and covariance matrices of each known category obtained during training, the Mahalanobis distance between the feature vector and the predicted category is calculated; Based on the comparison result between the Mahalanobis distance and the threshold, it is determined whether the device is of an unknown category, and the open set identification result is output.
2. The radio frequency fingerprint recognition method based on a learnable Mahalanobis distance discrimination model according to claim 1, characterized in that, The normalization process for the radio frequency signal specifically includes: Assume the received radio frequency complex signal discrete sequence is , N is the total length of the sequence. The maximum values of the real and imaginary parts of the complex signal sequence are calculated using the following formula. and minimum value : ； ； The received RF complex signal is normalized by performing maximum-minimum normalization to obtain the normalized RF complex signal. : 。 3. The radio frequency fingerprint recognition method based on a learnable Mahalanobis distance discrimination model according to claim 2, characterized in that, The process of performing a short-time Fourier transform on the normalized radio frequency signal to obtain a time-frequency characterization specifically includes: One-dimensional Point radio frequency complex signal sequence The two-dimensional complex matrix is obtained by performing a short-time Fourier transform. : ； in, A two-dimensional complex matrix The Line 1 Column corresponding elements, The number of points in the Fourier transform. This represents the number of time windows for the short-time Fourier transform. For the length of the window The Hanning window function, The sliding step of the window function. , ; Take two-dimensional complex matrices respectively The real and imaginary parts are concatenated to form a dual-channel time-frequency representation. As subsequent network input.
4. The radio frequency fingerprint recognition method based on a learnable Mahalanobis distance discrimination model according to claim 3, characterized in that, The process of obtaining feature vectors in the feature space from the time-frequency representation through a backbone network, and then obtaining device labels for closed-set classification through a classifier, specifically includes: First, the dual-channel time-frequency characterization is performed. The backbone network maps the input to feature vectors in the feature space. d is the dimension of the feature vector: ； The classifier uses the feature vectors output by the backbone network to determine the closed set classification probability distribution of devices with known class information. ； in For the sample A predicted probability vector for a known category; Finally, the device labels for closed-set classification are obtained: 。 5. The radio frequency fingerprint recognition method based on a learnable Mahalanobis distance discrimination model according to claim 4, characterized in that, The step of inputting the feature vector and closed-set classification label into the learnable Mahalanobis distance discriminant model to update the learnable statistics for each known class, namely the feature center and covariance matrix, specifically includes: In each batch, for all known categories Give the feature center estimate of the feature space Estimation of covariance matrix , ,as follows: ； ； Indicates the category in the current batch The set of eigenvectors; Then, the moving average algorithm is used for all known categories. Feature center Covariance Matrix Update: ； ； in and These are the smoothing update coefficients for the moving average algorithm.
6. The radio frequency fingerprint recognition method based on a learnable Mahalanobis distance discrimination model according to claim 5, characterized in that, A joint loss function is constructed based on the cross-entropy loss function and Mahalanobis distance to update the network parameters of the backbone network and the classifier, specifically including: For closed-set classification, the cross-entropy loss function is chosen, and for open-set classification, the Mahalanobis distance loss function is chosen. The two are weighted and summed to construct a joint loss function, which is then used to update parameters using the Adam optimizer. The formula for the joint loss function is as follows: ； in It is the device category label to which the radio frequency signal belongs.
7. The radio frequency fingerprint recognition method based on a learnable Mahalanobis distance discrimination model according to claim 1, characterized in that, The covariance matrix Perform regularization before inverting: ,in The regularization coefficient is . It is an identity matrix.
8. The radio frequency fingerprint recognition method based on a learnable Mahalanobis distance discrimination model according to claim 1, characterized in that, The threshold in the testing process applies to each known category. , is set to the maximum Mahalanobis distance of all samples of this category during training; If the Mahalanobis distance of the test sample is greater than the maximum value, it is classified as an unknown category; otherwise, the closed set classification label is output.
9. The radio frequency fingerprint recognition method based on a learnable Mahalanobis distance discrimination model according to claim 1, characterized in that, The backbone network includes at least one residual block, each residual block including a convolutional kernel, a ReLU activation function, a batch normalization layer, and a residual connection that adds the input and output in sequence.
10. A radio frequency fingerprint recognition system based on a learnable Mahalanobis distance discrimination model, characterized in that, The system includes the following modules: The receiver module is used to receive radio frequency signals; The training module, used to train the received radio frequency signal, includes: The normalization processing module is used to perform maximum-minimum value normalization processing on the received radio frequency signal; The short-time Fourier transform module is used to transform a one-dimensional radio frequency signal into a time-frequency representation; The closed-set classification module is used to obtain feature vectors in the feature space and device labels for closed-set classification based on time-frequency representation. The open-set statistics learning module is used during the training phase to update the learnable statistics for each known class, namely the feature center and covariance matrix, based on the feature vector and the closed-set classification device label. The loss function building module is used to construct a joint loss function based on the cross-entropy loss function and the Mahalanobis distance; The update module is used to update the network parameters of the backbone network and the classifier based on the joint loss function; The iterative training module is used to repeatedly train the received radio frequency signals until the network converges. The test discrimination module is used during the test phase to receive the test radio frequency signal, calculate the Mahalanobis distance between the feature vector and the predicted category, and determine whether it is an unknown category based on the comparison result of the Mahalanobis distance and the threshold. The output module is used to output the open set classification results.