Radio frequency fingerprinting method and device based on complex neural network, and medium

Abstract

This invention provides a radio frequency fingerprinting method, device, and medium based on a complex neural network. The radio frequency fingerprinting method based on a complex neural network includes: converting acquired raw complex channel state information (CSI) data into amplitude data, and adding all-zero imaginary parts to the amplitude data to construct complex form data conforming to the input format of a complex neural network; dividing the complex form data into a training set and a test set; constructing a complex neural network model for feature extraction from the input complex form data; training the complex neural network model using the training set; inputting the CSI data to be identified, after being constructed into complex form data, into the trained complex neural network model, and determining the device category to which the CSI data to be identified belongs based on the amplitude value of the complex result output by the model. This achieves accurate and stable identification of device identity in complex wireless environments.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and in particular relates to a radio frequency fingerprinting method, device and medium based on complex neural networks. Background Technology

[0002] Channel State Information (CSI) encompasses the complex characteristics of a wireless channel. It is typically represented in complex form, meaning it includes both amplitude and phase information. A complex number can be viewed as a two-dimensional vector representing a point in the complex plane, where the real and imaginary parts correspond to amplitude and phase, respectively. Therefore, CSI data can be considered a vector field data that reflects the state and characteristics of the channel.

[0003] Complex networks are highly effective at processing complex CSI (Channel State Information) data. They fully utilize the amplitude contained in CSI data and easily decouple phase information interference, which is often crucial in wireless signal analysis. Traditional real-number models, when processing complex data, typically need to decompose the complex number into independent real and imaginary parts, or only use the amplitude, which may lead to information loss or reduced model expressive power. Complex neural networks can operate directly in the complex domain, clearly capturing deeper and more discriminative patterns in the data. Therefore, complex deep network models will be widely used in fields dominated by vector field data (complex data), such as RF fingerprinting, radar and sonar signal processing, medical imaging (magnetic resonance imaging), power systems, speech and audio signal processing, quantum mechanics, optics, and image processing.

[0004] CSI encompasses the complex characteristics of wireless channels, which can be broadly divided into two parts: Channel Information: This part is time-varying and greatly affected by the environment, such as multipath effects, fading, and blockage. It typically contains a large amount of environmental noise and disturbances unrelated to the transmitting equipment itself.

[0005] Radio Frequency Fingerprint Information (RFFI): This part is relatively stable and unique, originating from non-ideals in the device hardware, such as I / Q imbalance, power amplifier nonlinearity, and local oscillator leakage. It is an inherent characteristic of the device that needs to be captured.

[0006] The two types of information are coupled; the complex vector of the CSI measurement is the result of the combined effect of the device fingerprint and channel multipath. If the unprocessed CSI is used directly as the fingerprint, the model is likely to misinterpret channel multipath features (e.g., CSI variations due to human movement) as the device fingerprint. During training, the model may memorize the CSI characteristics of a particular device under specific conditions. Decoupling aims to extract the stable, constant device fingerprint from the unstable CSI measurement and remove the unstable channel multipath component.

[0007] If the channel is not decoupled, the traditional model will face the following challenges: 1. Interference from Channel Environment Information: Channel environment information (multipath, fading, noise, etc.) is highly dynamic and time-varying. This information is independent of device identity. If raw, undecoupled CSI is directly input into a traditional real-number DNN (deep neural network), the model will see a large number of seemingly random fluctuations caused by environmental changes.

[0008] 2. Ambiguous Learning Objectives: Traditional DNNs struggle to distinguish between inherent device "fingerprint" features and constantly changing "environmental noise" in highly coupled environments. They attempt to find patterns from all inputs, potentially leading to: Overfitting: The model may overlearn specific patterns of channel effects in the training environment, rather than the true device fingerprint. Poor Generalization: When deployed to new and different environments (even with minor changes like footsteps or temperature variations), the model's performance drops sharply due to the difference in environmental information, as it never learns a "pure" device fingerprint. The learned fingerprint is mixed with too many environmental imprints. Low Accuracy: If the environment changes significantly, the model may even fail to achieve good accuracy on the test set because it is misled by irrelevant environmental information.

[0009] Therefore, traditional deep neural network models need to decouple channel information, that is, separate channel environment information and radio frequency fingerprint information from CSI information, in order to obtain pure fingerprint features and focus on processing these real-valued feature data. Decoupling the channel environment information and radio frequency fingerprint information in CSI is a crucial and often necessary step. When CSI is input as complex data, it usually needs to be converted into real-valued form, for example, taking only the amplitude (losing phase information), extracting the real and imaginary parts separately, and then concatenating them as independent real-valued feature vectors.

[0010] Both methods suffer from a fundamental flaw: they disrupt the inherent complex structure and mathematical properties of CSI. Clearly, regardless of the transformation method, information loss or alteration occurs. When phase information is lost, the model cannot capture the fine temporal characteristics and spatial geometry of the signal during propagation, severely limiting its ability to perceive channel changes. Furthermore, when the real and imaginary parts are extracted separately and simply concatenated into a long real vector, this natural complex structure and operations (such as rotation and scaling corresponding to complex multiplication) are broken. The model needs to relearn this correlation through complex real-number operations, which is typically inefficient and prone to losing the geometric meaning specific to the complex domain. Summary of the Invention

[0011] In view of the problems existing in the prior art, the present invention provides a radio frequency fingerprinting method, device and medium based on complex neural networks, which at least partially solves the problems of information loss, feature coupling and model inefficiency in complex CSI data processing in the prior art.

[0012] In a first aspect, embodiments of this disclosure provide a radio frequency fingerprint recognition method based on a complex neural network, comprising: The acquired raw complex channel state information (CSI) data is converted into amplitude data, and an all-zero imaginary part is added to the amplitude data to construct complex form data that conforms to the input format of a complex neural network. The complex number data is divided into a training set and a test set; Construct a complex neural network model for feature extraction from input complex form data; The complex neural network model is trained using the training set; wherein, when calculating the loss function, the magnitude of the complex result output by the model is calculated, and the classification loss is calculated based on the magnitude value. After the CSI data to be identified is constructed into complex number form, it is input into a trained complex neural network model. The device category to which the CSI data to be identified belongs is determined based on the magnitude value of the complex number result output by the model.

[0013] Optionally, the constructed complex neural network model includes at least one complex linear layer and at least one complex activation function.

[0014] Optionally, the complex neural network model is a classification model, including: The input layer is used for data in complex form. The first complex linear layer is used to map complex features of the input dimension to complex features of the hidden dimension; A complex activation function layer applies an activation function to the magnitude of the complex features of the hidden dimension while preserving their phase; The second complex linear layer is used to map the complex features of the hidden size dimension to the complex features of the digit category dimension, where the digit category is the total number of device categories.

[0015] Optionally, it also includes calculating the magnitude of each complex value based on the output of the second complex linear layer, thereby obtaining the real-valued confidence score for each sample corresponding to each category.

[0016] Optionally, after the step of dividing the complex data into training and test sets, the method includes using dimensionality reduction techniques to map the high-dimensional feature data of the training set onto a two-dimensional plane and generating a scatter plot to visually verify the separability of data points of different device categories in the feature space.

[0017] Optionally, training the complex neural network model using the training set includes: The number of samples in each category in the training set is counted, and the weights that are inversely proportional to the category frequencies are calculated. During training, the weights are passed to the loss function, which penalizes the model more when it makes a class error with a small number of samples.

[0018] Optionally, training the complex neural network model using the training set includes: The real channel state information amplitude data in the training set, which has the shape of the number of samples multiplied by the number of features, is expanded into a complex data structure with the shape of the number of samples multiplied by the number of features multiplied by two by adding an imaginary part dimension of all zeros. Convert the expanded numerical computation library array into a deep learning framework tensor; Pack deep learning framework tensors into a data loader for batch processing and data shuffling during model training.

[0019] Secondly, embodiments of this disclosure also provide an electronic device, the electronic device comprising: At least one processor; and, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions executable by the at least one processor, which, when executed, enable the at least one processor to perform the radio frequency fingerprinting method based on complex neural networks as described in any of the first aspects.

[0020] Thirdly, embodiments of this disclosure also provide a computer-readable storage medium storing computer instructions for causing a computer to perform the radio frequency fingerprinting method based on complex neural networks as described in any of the first aspects.

[0021] Fourthly, embodiments of this disclosure also provide a computer program product, including a computer program / instructions that, when executed by a processor, implement the radio frequency fingerprint recognition method based on complex neural networks as described in any of the first aspects.

[0022] This invention provides a radio frequency fingerprinting method, device, and medium based on complex neural networks. The method converts CSI data into amplitude data for effective decoupling and enhances the identification process using a complex neural network model. This achieves accurate and stable device identification in complex wireless environments. Attached Figure Description

[0023] The above and other objects, features and advantages of this disclosure will become more apparent from the accompanying drawings, in which like reference numerals generally denote like parts.

[0024] Figure 1 A schematic diagram of the raw complex channel state information (CSI) data provided in the embodiments of this disclosure; Figure 2 A schematic diagram illustrating the mapping of high-dimensional CSI feature data to a two-dimensional plane, provided for embodiments of this disclosure; Figure 3 A schematic diagram of the complex network model provided in the embodiments of this disclosure; Figure 4 A schematic block diagram of an electronic device provided in an embodiment of this disclosure. Detailed Implementation

[0025] The embodiments of this disclosure will now be described in detail with reference to the accompanying drawings.

[0026] It should be understood that the following specific examples illustrate the implementation of this disclosure, and those skilled in the art can easily understand other advantages and effects of this disclosure from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this disclosure, and not all of them. This disclosure can also be implemented or applied through other different specific implementation methods, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this disclosure. It should be noted that, in the absence of conflict, the following embodiments and features in the embodiments can be combined with each other. Based on the embodiments in this disclosure, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this disclosure.

[0027] It should also be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of this disclosure. The illustrations only show the components related to this disclosure and are not drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0028] Furthermore, specific details are provided in the following description to facilitate a thorough understanding of the examples. However, those skilled in the art will understand that the described aspects can be practiced without these specific details.

[0029] In this embodiment, the hidden size Viter refers to the number of output features of the first complex linear layer inside the complex neural network model.

[0030] This embodiment discloses a radio frequency fingerprint recognition method based on a complex neural network, including: The acquired raw complex channel state information (CSI) data is converted into amplitude data, and an all-zero imaginary part is added to the amplitude data to construct complex form data conforming to the input format of a complex neural network. Specifically, the acquired raw complex channel state information (CSI) data is converted into amplitude data after noise reduction and normalization processing. The raw complex channel state information (CSI) data is as follows: Figure 1 As shown; The complex number data is divided into a training set and a test set; Construct a complex neural network model for feature extraction from input complex form data; The complex neural network model is trained using the training set; wherein, when calculating the loss function, the magnitude of the complex result output by the model is calculated, and the classification loss is calculated based on the magnitude value. After the CSI data to be identified is constructed into complex number form, it is input into a trained complex neural network model. The device category to which the CSI data to be identified belongs is determined based on the magnitude value of the complex number result output by the model.

[0031] Optionally, the constructed complex neural network model includes at least one complex linear layer and at least one complex activation function.

[0032] Optionally, the complex neural network model is a classification model, including: The input layer is used for data in complex form. The first complex linear layer is used to map complex features of the input dimension to complex features of the hidden dimension; A complex activation function layer applies an activation function to the magnitude of the complex features of the hidden dimension while preserving their phase; The second complex linear layer is used to map the complex features of the hidden size dimension to the complex features of the digit category dimension, where the digit category is the total number of device categories.

[0033] Optionally, it also includes calculating the magnitude of each complex value based on the output of the second complex linear layer, thereby obtaining the real-valued confidence score for each sample corresponding to each category.

[0034] Optionally, after the step of dividing the complex data into training and test sets, the method includes using dimensionality reduction techniques to map the high-dimensional feature data of the training set onto a two-dimensional plane and generating a scatter plot to visually verify the separability of data points of different device categories in the feature space.

[0035] Optionally, training the complex neural network model using the training set includes: The number of samples in each category in the training set is counted, and the weights that are inversely proportional to the category frequencies are calculated. During training, the weights are passed to the loss function, which penalizes the model more when it makes a class error with a small number of samples.

[0036] Optionally, training the complex neural network model using the training set includes: The real channel state information amplitude data in the training set, which has the shape of the number of samples multiplied by the number of features, is expanded into a complex data structure with the shape of the number of samples multiplied by the number of features multiplied by two by adding an imaginary part dimension of all zeros. Convert the expanded numerical computation library array into a deep learning framework tensor; Pack deep learning framework tensors into a data loader for batch processing and data shuffling during model training.

[0037] Specifically as follows: Vector fields are naturally well-suited for modeling continuous dynamic systems, thus representing temporal relationships between frames effectively. For example, in video processing or time series analysis, vector fields can capture motion, trends, or geometric transformations between frames. Compared to attention mechanisms, vector fields may be better at modeling local continuity or smoothness. Vector fields can explicitly model geometric transformations between frames (such as rotation, translation, scaling, etc.), which can be very useful for certain tasks (such as video action recognition, physical system modeling). Attention mechanisms typically model relationships implicitly and may not directly capture geometric structures. The core of attention mechanisms is establishing global dependencies, but this may not be necessary for some tasks. For example, in video frames, the relationship between adjacent frames may be more important than that between distant frames. Vector fields can more naturally model local dependencies, thus avoiding unnecessary global computations. Furthermore, there is a natural connection between vector fields and complex network models. Simply put, a vector field associates a vector with every point in space (or higher-dimensional space). This vector typically represents the force, velocity, or direction at that point. Complex numbers can be mathematically viewed as two-dimensional vectors. A complex number z = a + b * i can uniquely correspond to a vector (a, b) in a two-dimensional plane. Its magnitude corresponds to the length of the vector, and its phase corresponds to the angle (direction) between the vector and the positive real axis. This correspondence makes complex numbers a powerful tool for describing two-dimensional vector fields or signals with amplitude and phase information.

[0038] However, even with complex networks, "more information is not always better." In high-noise real-world environments, channel multipath noise in the phase information can overwhelm the weak device fingerprint signal it contains. The method disclosed in this embodiment cleverly combines these two decisions. Instead of using traditional real networks, it employs a more advanced complex network. Simultaneously, it abandons the high-noise phase information, using only the more stable and robust amplitude information as input.

[0039] Overall, traditional real-number models struggle to effectively capture and utilize the rotational properties and phase sensitivity of complex signals. They may require more layers and parameters to approximate the inherent advantages of complex operations in complex networks, leading to more difficult training, lower model efficiency, and poor performance when dealing with scenarios involving phase changes.

[0040] Complex networks are powerful tools for handling CSI (Convolutional Segmentation Indicators), but how to preprocess the data for effective decoupling remains crucial to determining the final performance. In some scenarios, using only magnitude data is a successful decoupling strategy. When the model uses only magnitude data, it is a dataset of purely real numbers. The reason for not using traditional real networks (such as a standard convolutional or fully connected network) to handle magnitude data is that, although complex networks can handle complex numbers, their mathematical structure and computational methods are inherently superior to traditional real networks, even when dealing with purely real data.

[0041] Complex models have stronger expressive power. Each neuron in a complex network contains both real and imaginary parts, and the weights are also complex numbers. A complex multiplication... This is actually equivalent to a combination of real number multiplication and addition: This means that the operation of a complex neuron internally involves four real number multiplications and two real number additions / subtractions. In contrast, a traditional real number neuron contains only one real number multiplication and one addition.

[0042] Therefore, each neuron in a complex network possesses a more powerful feature extraction capability and a more complex nonlinear expression capability than an equivalent neuron in a real network. It can capture deeper patterns and correlations in data with fewer parameters and fewer layers.

[0043] The complex model has more natural geometric transformations. In the complex domain, multiplication is not just a simple numerical multiplication, but also includes two geometric transformations: rotation and scaling.

[0044] A complex number Multiply by another complex number The result is .

[0045] This corresponds to rotating a vector by an angle θ and scaling it by a factor of B.

[0046] Although the input is purely real numbers (with an imaginary part of 0), the network weights are complex numbers. This means that when complex networks process amplitude data, their internal operations still involve more advanced rotation and scaling transformations. This inherent geometric transformation capability makes complex networks more efficient than real networks when processing data with periodic, oscillatory, or structural patterns. They are better able to capture the "frequency domain" and "phase" features of the data, even if these features are hidden within pure amplitude variations.

[0047] Complex networks, through their unique mathematical structure, can extract features from amplitude data more effectively than real networks. Simultaneously, by discarding phase, they achieve an effective decoupling operation, preventing the model from being misled by channel noise and thus achieving higher accuracy. This method's advantage doesn't stem from discarding phase, but rather from the fact that using only amplitude in noisy environments is a more effective decoupling technique, and complex networks can utilize this processed data better than traditional models.

[0048] The complex network model in this embodiment maintains the original form of complex CSI, I+j*Q, and directly uses it as input to the complex network. By directly using the amplitude information without complex transformations (and supplementing it with a zero imaginary part to adapt to the complex network structure), the original "fingerprint" of the data is preserved, allowing the model to learn directly from these original patterns.

[0049] First, the original complex CSI data is converted into amplitude data that has been denoised and normalized, and the input format is prepared for the subsequent complex neural network model (i.e., a zero imaginary part dimension is added).

[0050] Then, all the data is split into training and test sets. The training set is used for the model to learn patterns, and the test set is used to evaluate the model's performance on unseen data. Figure 2 As shown, t-SNE (t-Distributed Stochastic Neighbor Embedding) dimensionality reduction technology is used to map high-dimensional CSI feature data to a two-dimensional plane, thus allowing for a direct observation of whether data points from different device categories can be effectively separated. The CSI data is first flattened and then reduced to 2D using the t-SNE algorithm. When plotting the scatter plot, data points from different devices (labels) are represented by different colors. If points of the same type cluster together and points of different types are separated, it indicates that the original features have good separability.

[0051] Next, a complex neural network model is defined and instantiated, creating a ComplexClassifier that contains a complex linear layer (ComplexLinear) and a complex activation function (ComplexReLU). input_size determines the feature dimension of each sample (flattened CSI amplitude data), hidden_size defines the number of neurons in the intermediate layers, and num_classes is the total number of device categories to be identified.

[0052] The NumPy format data is converted to PyTorch tensors, and the data shape is adjusted to fit the complex network. The CSI amplitude data is initially real. To train the complex network, an imaginary dimension with all zeros needs to be added, changing it from (N, Features, 1) to (N, Features, 2). These NumPy arrays are then converted to PyTorch Tensor types and packaged into a DataLoader for batch processing and data shuffling during training.

[0053] To address potential class imbalance in the dataset and prevent the model from favoring classes with larger sample sizes, we count the number of samples for each class in the training set and calculate weights inversely proportional to class frequency. Classes with fewer samples receive higher weights, meaning the model is penalized more when mispredicting these minority classes, thus encouraging the model to focus more on them. These weights are then passed to the loss function. We choose `nn.CrossEntropyLoss` as the loss function, passing in the `class_weights_tensor` calculated in the previous step. This measures the difference between the model's predicted class probabilities and the true labels.

[0054] By iteratively feeding training data into the model, it learns how to recognize the RFID fingerprints of different devices. Finally, the performance of the trained model on unseen data is measured.

[0055] Complex network models such as Figure 3 As shown, it includes: Input features (A): are preprocessed CSI data. Each data point (sample) is a set of complex numbers.

[0056] The shape (Batch_Size, Input_Size, 2) indicates that there are Batch_Size samples, and each sample has Input_Size complex features. The 2 indicates that each complex feature is represented by its real part (index 0) and imaginary part (index 1). For example, if the original CSI has 512 features, this would be (Batch_Size, 512, 2).

[0057] Flattened feature vector (B): Represents the x.view(x.size(0),-1,2) operation performed in the forward method of ComplexClassifier (or before the model input). It ensures that the input data is in the correct format (Batch_Size, N_features,2) for the ComplexLinear layer to process, where N_features is the input_size passed to the classifier.

[0058] Complex linear transformation (fc1) (C): self.fc1=ComplexLinear(input_size,hidden_size). It performs matrix multiplication in the complex domain. This operation involves multiplying and combining the real and imaginary parts of the input with the real and imaginary parts of the weights (according to the formula). and The output is still a set of complex numbers, but now each sample has hidden_size features.

[0059] Complex ReLU activation (D): self.relu=ComplexReLU(). It applies the ReLU function to the magnitude of each complex number while preserving its original phase. This introduces nonlinearity in the complex domain. The output is still a set of complex numbers with hidden_size features.

[0060] Complex linear transformation (fc2)(E): self.fc2=ComplexLinear(hidden_size,num_classes). Another complex linear transformation maps the hidden_size features to num_classes features. The output is num_classes complex numbers for each sample. These can be considered as complex numerical scores for each class.

[0061] Magnitude Calculation (F): Before applying the final classification (such as Softmax), the code calculates the magnitude of these complex output scores: magnitude = torch.sqrt(outputs[...,0]*2 + outputs[...,1]*2). This converts the complex numerical scores into real-valued positive scores, representing the "strength" or confidence level of each category.

[0062] Softmax (implicitly included in CrossEntropyLoss) (G): Although not explicitly represented as a layer in ComplexClassifier, nn.CrossEntropyLoss used for training implicitly applies the Softmax function to the magnitudes of these real values. Softmax converts the scores into probabilities for each class, summing to 1.

[0063] Predicted Category (H): During the inference phase, torch.max(magnitude,1) is used to find the category with the highest probability (or magnitude score). This is the final predicted device category.

[0064] Complex networks are highly effective at processing complex CSI (Channel State Information) data. They fully utilize the amplitude information contained in CSI data and decouple interference such as multipath noise from phase information, which is often crucial in wireless signal analysis. Traditional real-number models, when processing complex data, typically need to decompose the complex number into independent real and imaginary parts, or only use the amplitude, which may lead to information loss or reduced model expressive power. Complex neural networks can operate directly in the complex domain, clearly capturing deeper and more discriminative patterns in the data. Therefore, complex deep network models will be widely used in fields dominated by vector field data (complex data), such as RF fingerprinting, radar and sonar signal processing, medical imaging (magnetic resonance imaging), power systems, speech and audio signal processing, quantum mechanics, optics, and image processing.

[0065] The electronic device disclosed in this embodiment includes a memory and a processor. The memory is used to store non-transitory computer-readable instructions. Specifically, the memory may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may, for example, include random access memory (RAM) and / or cache memory. The non-volatile memory may, for example, include read-only memory (ROM), hard disk, flash memory, etc.

[0066] The processor may be a central processing unit (CPU) or other form of processing unit with data processing capabilities and / or instruction execution capabilities, and may control other components in the electronic device to perform desired functions. In one embodiment of this disclosure, the processor is used to execute computer-readable instructions stored in the memory, causing the electronic device to perform all or part of the steps of the complex neural network-based radio frequency fingerprinting method of the foregoing embodiments of this disclosure.

[0067] Those skilled in the art will understand that, in order to solve the technical problem of how to achieve a good user experience, this embodiment may also include well-known structures such as communication buses and interfaces, and these well-known structures should also be included within the protection scope of this disclosure.

[0068] like Figure 4 This is a schematic diagram of the structure of an electronic device provided in an embodiment of the present disclosure. It illustrates a structural schematic diagram suitable for implementing the electronic device in the embodiment of the present disclosure. Figure 4 The electronic device shown is merely an example and should not be construed as limiting the functionality and scope of the embodiments disclosed herein.

[0069] like Figure 4 As shown, an electronic device may include a processing unit (such as a central processing unit, graphics processing unit, etc.) that can perform various appropriate actions and processes based on a program stored in read-only memory (ROM) or a program loaded from a storage device into random access memory (RAM). The RAM also stores various programs and data required for the operation of the electronic device. The processing unit, ROM, and RAM are interconnected via a bus. Input / output (I / O) interfaces are also connected to the bus.

[0070] Typically, the following devices can be connected to the I / O interface: input devices, such as sensors or visual information acquisition devices; output devices, such as displays; storage devices, such as magnetic tapes or hard drives; and communication devices. Communication devices allow electronic devices to exchange data wirelessly or via wired communication with other devices, such as edge computing devices. Although Figure 4 Electronic devices with various devices are shown, but it should be understood that it is not required to implement or have all of the devices shown. More or fewer devices may be implemented or have alternatively.

[0071] In particular, according to embodiments of this disclosure, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a non-transitory computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via a communication device, or installed from a storage device, or installed from a ROM. When the computer program is executed by a processing device, all or part of the steps of the radio frequency fingerprinting method based on complex neural networks according to embodiments of this disclosure are performed.

[0072] For a detailed description of this embodiment, please refer to the corresponding descriptions in the foregoing embodiments, which will not be repeated here.

[0073] A computer-readable storage medium according to embodiments of the present disclosure stores non-transitory computer-readable instructions. When these non-transitory computer-readable instructions are executed by a processor, all or part of the steps of the radio frequency fingerprinting method based on a complex neural network according to the foregoing embodiments of the present disclosure are performed.

[0074] The aforementioned computer-readable storage media include, but are not limited to: optical storage media (e.g., CD-ROM and DVD), magneto-optical storage media (e.g., MO), magnetic storage media (e.g., magnetic tape or portable hard drive), media with built-in rewritable non-volatile memory (e.g., memory card), and media with built-in ROM (e.g., ROM cartridge).

[0075] For a detailed description of this embodiment, please refer to the corresponding descriptions in the foregoing embodiments, which will not be repeated here.

[0076] The basic principles of this disclosure have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in this disclosure are merely examples and not limitations, and should not be considered as essential features of each embodiment of this disclosure. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not limit the scope of this disclosure to the necessity of employing the aforementioned specific details for implementation.

[0077] In this disclosure, relational terms such as "first" and "second" are used merely 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. The block diagrams of devices, apparatuses, devices, and systems involved in this disclosure are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these devices, apparatuses, devices, and systems can be connected, arranged, and configured in any manner. Words such as "comprising," "including," "having," etc., are open-ended terms meaning "including but not limited to," and are used interchangeably with them. The terms "or" and "and" as used herein refer to the terms "and / or," and are used interchangeably with them unless the context clearly indicates otherwise. The term "such as" as used herein refers to the phrase "such as but not limited to," and is used interchangeably with it.

[0078] Additionally, as used herein, the "or" used in a list of items beginning with "at least one" indicates a separate list, such that a list of, for example, "at least one of A, B, or C" means A or B or C, or AB or AC or BC, or ABC (i.e., A and B and C). Furthermore, the word "exemplary" does not imply that the described example is preferred or better than other examples.

[0079] It should also be noted that in the systems and methods of this disclosure, the components or steps can be decomposed and / or recombined. These decompositions and / or recombinations should be considered as equivalent solutions to this disclosure.

[0080] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use this disclosure. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other aspects without departing from the scope of this disclosure. Therefore, this disclosure is not intended to be limited to the aspects shown herein, but rather to be carried out within the widest scope consistent with the principles and novel features disclosed herein.

[0081] The above description has been given for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of this disclosure to the forms disclosed herein. Although numerous exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations therein.

Claims

1. A radio frequency fingerprint recognition method based on a complex neural network, characterized in that, include: The acquired raw complex channel state information (CSI) data is converted into amplitude data, and an all-zero imaginary part is added to the amplitude data to construct complex form data that conforms to the input format of a complex neural network. The complex number data is divided into a training set and a test set; Construct a complex neural network model for feature extraction from input complex form data; The complex neural network model is trained using the training set; wherein, when calculating the loss function, the magnitude of the complex result output by the model is calculated, and the classification loss is calculated based on this magnitude; the training process includes: The matrix multiplication is performed in the complex domain by performing the first complex linear transformation, multiplying and combining the real and imaginary parts of the input with the real and imaginary parts of the weights, and outputting a complex number. The ReLU function is applied to the magnitude of each complex number by the complex ReLU activation function, while preserving its original phase, and a set of complex numbers is output. The matrix multiplication is performed in the complex domain by performing a second complex linear transformation, which multiplies and combines the real and imaginary parts of the input with the real and imaginary parts of the weights to output a set of complex numbers. The amplitude of the complex output fraction is calculated by the amplitude calculation function, and the complex value fraction is converted into a real value positive fraction. The scores are converted into probabilities for each category using the Softmax function; The category with the highest probability will be used as the final predicted device category; After the CSI data to be identified is constructed into complex number form, it is input into a trained complex neural network model. The device category to which the CSI data to be identified belongs is determined based on the magnitude value of the complex number result output by the model.

2. The radio frequency fingerprint recognition method based on complex neural networks according to claim 1, characterized in that, The constructed complex neural network model includes at least one complex linear layer and at least one complex activation function.

3. The radio frequency fingerprint recognition method based on complex neural networks according to claim 2, characterized in that, The complex neural network model is a classification model, including: The input layer is used for data in complex form. The first complex linear layer is used to map complex features of the input dimension to complex features of the hidden dimension; A complex activation function layer applies an activation function to the magnitude of the complex features of the hidden dimension while preserving their phase; The second complex linear layer is used to map the complex features of the hidden size dimension to the complex features of the digit category dimension, where the digit category is the total number of device categories.

4. The radio frequency fingerprint recognition method based on a complex neural network according to claim 3, characterized in that, It also includes calculating the magnitude of each complex value based on the output of the second complex linear layer, thereby obtaining the real-valued confidence score for each sample corresponding to each category.

5. The radio frequency fingerprint recognition method based on a complex neural network according to claim 1, characterized in that, After the step of dividing the complex data into training and test sets, the method includes using dimensionality reduction techniques to map the high-dimensional feature data of the training set onto a two-dimensional plane and generating a scatter plot to visually verify the separability of data points of different device categories in the feature space.

6. The radio frequency fingerprint recognition method based on a complex neural network according to claim 1, characterized in that, Training the complex neural network model using the training set includes: The number of samples in each category in the training set is counted, and the weights that are inversely proportional to the category frequencies are calculated. During training, the weights are passed to the loss function, which penalizes the model more when it makes a class error with a small number of samples.

7. The radio frequency fingerprint recognition method based on a complex neural network according to claim 1, characterized in that, Training the complex neural network model using the training set includes: The real channel state information amplitude data in the training set, which has the shape of the number of samples multiplied by the number of features, is expanded into a complex data structure with the shape of the number of samples multiplied by the number of features multiplied by two by adding an imaginary part dimension of all zeros. Convert the expanded numerical computation library array into a deep learning framework tensor; Pack deep learning framework tensors into a data loader for batch processing and data shuffling during model training.

8. An electronic device, characterized in that, The electronic device includes: At least one processor; and, A memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, which, when executed by the at least one processor, enables the at least one processor to perform the radio frequency fingerprinting method based on a complex neural network as described in any one of claims 1-7.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions for causing a computer to perform the radio frequency fingerprinting method based on a complex neural network as described in any one of claims 1-7.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the radio frequency fingerprinting method based on complex neural networks as described in any one of claims 1-7.

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