Multi-domain feature fusion unmanned aerial vehicle radio frequency fingerprint identification method and device based on Mama

Abstract

The invention discloses a Mama-based multi-domain feature fusion unmanned aerial vehicle radio frequency fingerprint identification method and device, and relates to the technical field of wireless communication and target identification, and the method comprises the steps: fusing the in-phase / orthogonal feature, the bispectrum feature and the short-time Fourier spectrum feature of a signal, so as to achieve the enhanced representation of a radio frequency fingerprint. Aiming at the bottleneck of computation complexity and real-time performance brought by multi-domain feature fusion, an efficient fusion framework based on Mama and Vision-Mama is constructed, the framework gives full play to the linear computation complexity advantage of a Mama model in long sequence modeling, and is combined with an algorithm optimization strategy of hardware perception, so that the computation overhead is remarkably reduced while high recognition precision is kept. In order to solve the problem that redundancy and complementarity are difficult to balance in the feature fusion process, a self-adaptive feature interaction module based on a cross attention mechanism is introduced, the module can dynamically model the dependency relationship among multi-source features, self-adaptive distribution of fusion weights is achieved, and therefore the feature degradation phenomenon caused by environmental interference is effectively restrained.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication and target recognition technology, specifically relating to a method and device for radio frequency fingerprinting of unmanned aerial vehicles based on Mamba multi-domain feature fusion. Background Technology

[0002] With the rapid development of the low-altitude economy and unmanned systems, drones are widely used in logistics, environmental monitoring, and security patrols. However, a large number of unauthorized drones frequently appear in low-altitude airspace, causing electromagnetic interference, information leaks, and public safety hazards, posing a serious challenge to low-altitude airspace management.

[0003] Traditional UAV identification relies on communication protocol parsing, which makes reliable identification of non-cooperative targets difficult in complex electromagnetic environments. Current research on non-cooperative UAV target identification mainly focuses on vision and radar sensors. Although some progress has been made in target detection and model identification, there are still significant limitations in the individual identification of non-cooperative UAV targets. Existing methods are mostly based on visual analysis or expert system rules, relying on the macroscopic statistical characteristics of signals and ignoring subtle physical differences caused by hardware non-ideal characteristics, resulting in insufficient individual-level discrimination.

[0004] Therefore, there is an urgent need to provide a method for drone identification in order to improve the aforementioned deficiencies in existing technologies. Summary of the Invention

[0005] To address the aforementioned problems in the existing technology, this invention provides a method and apparatus for UAV radio frequency fingerprinting based on Mamba multi-domain feature fusion. The technical problem to be solved by this invention is achieved through the following technical solution: In a first aspect, the present invention provides a multi-domain feature fusion method for UAV radio frequency fingerprinting based on Mamba, comprising: The UAV radio frequency signal is acquired and represented by in-phase and quadrature components; bispectral features are obtained based on the UAV radio frequency signal; short-time Fourier transform features are obtained based on the UAV radio frequency signal. The trained network processes the UAV radio frequency signal, bispectral features, and short-time Fourier transform features to obtain classification results. The first branch module of the Mamba-based multi-domain feature fusion network in the trained network processes the UAV radio frequency signal to obtain time-domain features. The second branch module of the Mamba-based multi-domain feature fusion network in the trained network processes the bispectral features to obtain higher-order statistical features. The third branch module of the Mamba-based multi-domain feature fusion network in the trained network processes the short-time Fourier transform features to obtain spectral features. The cross-attention module in the trained network fuses the time-domain features, higher-order statistical features, and spectral features to obtain a first fused feature and a second fused feature. The first fused feature and the second fused feature are then fused to obtain a fused feature. The classification head in the trained network classifies the fused feature to obtain classification results. The first fused feature integrates the UAV radio frequency signal and short-time Fourier transform features, while the second fused feature integrates the bispectral features and short-time Fourier transform features.

[0006] Secondly, the present invention also provides a multi-domain feature fusion unmanned aerial vehicle (UAV) radio frequency fingerprinting device based on Mamba, comprising: The feature acquisition module is used to acquire the UAV radio frequency signal, and to represent the UAV radio frequency signal using in-phase and quadrature components; to acquire bispectral features based on the UAV radio frequency signal; and to acquire short-time Fourier transform features based on the UAV radio frequency signal. The feature processing and fusion module is used to process the UAV radio frequency signal, bispectral features, and short-time Fourier transform features using a trained network to obtain classification results. The first branch module of the Mamba-based multi-domain feature fusion network in the trained network processes the UAV radio frequency signal to obtain time-domain features. The second branch module of the Mamba-based multi-domain feature fusion network in the trained network processes the bispectral features to obtain higher-order statistical features. The third branch module of the Mamba-based multi-domain feature fusion network in the trained network processes the short-time Fourier transform features to obtain spectral features. The cross-attention module in the trained network fuses the time-domain features, higher-order statistical features, and spectral features to obtain a first fused feature and a second fused feature. The first fused feature and the second fused feature are then fused to obtain a fused feature. The classification head in the trained network classifies the fused feature to obtain classification results. Specifically, the first fused feature fuses the UAV radio frequency signal and the short-time Fourier transform features, and the second fused feature fuses the bispectral features and the short-time Fourier transform features.

[0007] The beneficial effects of this invention are: This invention provides a multi-domain feature fusion method for UAV radio frequency fingerprinting based on Mamba. First, starting from the physical mechanism of the transmitter hardware, the causes of radio frequency fingerprint generation are analyzed, focusing on the formation mechanisms of non-ideal features such as power amplifier nonlinearity, phase noise, and carrier frequency offset, thereby extracting stable and distinguishable physical layer features. Then, a multi-domain feature collaborative representation method for UAV radio frequency signals is studied. By extracting multi-source features such as I / Q signals, short-time Fourier spectra, and bispectral data, a multi-domain feature representation that comprehensively reflects time-domain, frequency-domain, and higher-order statistical characteristics is constructed. Further, the Mamba and ViM architectures are introduced to design a low-complexity multi-domain feature fusion recognition model. Leveraging the efficiency of Mamba in long sequence modeling, a cross-attention mechanism is combined to achieve adaptive fusion and deep discrimination of cross-domain features. Finally, an individual UAV recognition and open-set detection model is constructed, and field verification is completed in a complex electromagnetic environment. This achieves high-precision, low-complexity intelligent recognition of non-cooperative UAVs, providing technical support for low-altitude airspace safety management and UAV behavior monitoring.

[0008] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0009] Figure 1 This is a flowchart of a multi-domain feature fusion UAV radio frequency fingerprinting method based on Mamba provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of a signal transmitter radio frequency fingerprint generation structure provided in an embodiment of the present invention; Figure 3 This is a schematic diagram of a trained network structure provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of selective scanning provided in an embodiment of the present invention; Figure 5 This is a schematic diagram of a cross-attention mechanism structure provided in an embodiment of the present invention; Figure 6 This is a schematic diagram of the experimental conditions provided in an embodiment of the present invention; Figure 7 This is a schematic diagram of a signal receiver based on ADRV9009 provided in an embodiment of the present invention; Figure 8 This is a schematic diagram of the loss curve and accuracy change curve provided in an embodiment of the present invention; Figure 9 This is a schematic diagram of a drone classification confusion matrix provided in an embodiment of the present invention; Figure 10 This is a schematic diagram of the feature distribution UMAP visualization result provided in an embodiment of the present invention; Figure 11 This is a schematic diagram illustrating the variation in verification accuracy across different branches provided in an embodiment of the present invention; Figure 12 This is a schematic diagram illustrating the performance comparison of models (with / without cross-attention mechanism) provided in an embodiment of the present invention; Figure 13 This is a schematic diagram illustrating the performance comparison of models under different signal-to-noise ratios provided in an embodiment of the present invention; Figure 14 This is a schematic diagram illustrating the performance comparison of different models provided in an embodiment of the present invention; Figure 15a This is a schematic diagram of the sample Mahalanobis distance distribution provided in an embodiment of the present invention; Figure 15b This is a schematic diagram of the classification results under open set conditions provided in an embodiment of the present invention; Figure 15c This is a schematic diagram of the t-SNE visualization results provided in an embodiment of the present invention. Detailed Implementation

[0010] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0011] In existing technologies, radio frequency fingerprinting utilizes physical characteristics such as amplitude imbalance, phase noise, and nonlinear distortion generated during the manufacturing process of device transmitters to identify devices at the signal physical layer. It possesses significant advantages such as being unforgeable and difficult to tamper with, attracting widespread attention in the field of non-cooperative drone identification. Meanwhile, with the development of intelligent methods such as neural networks and deep learning, the effectiveness of data-driven intelligent identification is continuously improving. Therefore, research on intelligent identification methods for non-cooperative drones based on radio frequency fingerprinting can not only overcome the performance bottlenecks of traditional feature-dependent methods but also achieve robust, non-contact identification in complex environments. This has significant scientific and engineering value for ensuring low-altitude communication security, strengthening airspace management, and supporting intelligent supervision of unmanned systems.

[0012] In view of this, this invention proposes a multi-domain feature fusion method and device for UAV radio frequency fingerprinting based on Mamba, aiming to improve the individual identification capability of non-cooperative low-altitude UAVs. By exploring the generation mechanism of UAV radio frequency fingerprints, a non-cooperative UAV target identification method based on radio frequency fingerprints is proposed. By utilizing multi-domain feature extraction and efficient cross-domain fusion identification technology, the method improves identification accuracy and environmental adaptability, achieving high-precision and low-complexity identification of UAVs. The method is verified through field experiments, providing technical support for low-altitude safety protection and intelligent airspace management.

[0013] Please see Figure 1 , Figure 1This is a flowchart of a multi-domain feature fusion UAV radio frequency fingerprinting method based on Mamba provided in an embodiment of the present invention. The multi-domain feature fusion UAV radio frequency fingerprinting method based on Mamba provided by the present invention includes: S101. Acquire the UAV radio frequency signal and represent it using in-phase and quadrature components; obtain bispectral features based on the UAV radio frequency signal; obtain short-time Fourier transform features based on the UAV radio frequency signal.

[0014] Specifically, in this embodiment, three computationally efficient radio frequency fingerprint features are used for identification: the original I / Q signal features of the UAV radio frequency signal, bispectral features, and short-time Fourier transform features. These features are complementary; among them, First, the raw I / Q signal characteristics of the UAV's radio frequency (RF) signal are obtained. These raw I / Q signal characteristics inherently contain distortions caused by hardware non-ideal characteristics, which constitute a unique radio frequency fingerprint (RFF). For example... Figure 2 As shown, these unique RFF characteristics mainly stem from subtle differences between key analog front-end devices such as digital-to-analog converters, bandpass filters, mixers, and power amplifiers.

[0015] The manufacturing tolerances of each component collectively cause characteristic distortions in the electromagnetic waveform, which manifest as a unique radio frequency fingerprint in the transmitted signal. The resulting radio frequency signal is represented as follows: ; in, Indicates in-phase components, Indicates orthogonal components, It represents the imaginary unit.

[0016] I / Q data captured directly from the quadrature downconversion process of the RF front end retains complete amplitude and phase information, effectively revealing inherent hardware defects in devices such as digital-to-analog converters, mixers, and power amplifiers. These defects include I / Q imbalance, carrier leakage, and power amplifier nonlinear distortion, which manifest as unique harmonic intermodulation modes in the complex domain. Compared with derived features such as power spectrum, raw I / Q data avoids information loss, and its bivariate distribution supports the extraction of higher-order statistics, thereby improving sensitivity to minute hardware differences.

[0017] Secondly, bispectral signature (BIS) is obtained. Higher-order spectra can effectively reveal the nonlinear characteristics of target signals and are widely used in signal feature extraction. BIS is easier to compute than other higher-order spectra and is often chosen as the preferred method for processing nonlinear signals. Assuming that the radio frequency signal satisfies the generalized stationarity condition, its third-order cumulant can be calculated as follows: ; in, and Indicates different time delays, Represents the expectation operator; Performing a two-dimensional Fourier transform on the third-order cumulants yields the bispectral features. , is represented as: ; In practical engineering applications, compared to using the definition of bispectrum to calculate the bispectrum of a signal, people prefer to use bispectral estimation methods to obtain the bispectrum. Bispectral estimation is a technique used in signal processing and spectrum analysis. Based on the second-order statistical properties of the spectrum, it can be used to detect and analyze nonlinear interactions in signals. The steps of the indirect method for bispectral estimation are as follows: will Individual observation data by Each sample can be divided into groups of 1, resulting in a total of 10 groups. part; set up For the division of the first For data segments, the third-order cumulative of each segment can be expressed as: ; , ; The average of all third-order cumulants is taken as the estimate of the third-order cumulant for the entire observation dataset, i.e.: ; The bispectral estimate is calculated as follows: ; in, ,and It is a two-dimensional hysteresis window function.

[0018] Finally, the short-time Fourier transform features are obtained. UAV radio frequency signals usually exhibit non-stationary time-frequency characteristics. Therefore, the short-time Fourier transform (STFT) can be used to effectively extract its time-frequency characteristics. Specifically, the STFT method obtains the spectrum of the signal as time changes by segmenting the signal on the time axis and performing a Fourier transform on each segment, thereby realizing the extraction of the time-frequency characteristics of the radio frequency fingerprint.

[0019] The short-time Fourier transform characteristics are expressed as follows: ; in, Indicates the length of time. Represents angular frequency. Indicates the duration as Sliding window functions (such as Hamming window or Hanning window). Indicates time.

[0020] pass Energy spectrum analysis can extract the spectral envelope, instantaneous frequency, and other RF hardware-related features of radio frequency signals. Short-time Fourier spectrum analysis can simultaneously analyze the time and frequency domain characteristics of signals, making it suitable for processing non-stationary signals. The extracted time-frequency features contain rich RF fingerprint information and have high discrimination ability, which will be verified in the experimental results.

[0021] S102. The trained network is used to process the UAV radio frequency signal, bispectral features, and short-time Fourier transform features to obtain classification results. The first branch module of the Mamba-based multi-domain feature fusion network in the trained network is used to process the UAV radio frequency signal to obtain time-domain features. The second branch module of the Mamba-based multi-domain feature fusion network in the trained network is used to process the bispectral features to obtain higher-order statistical features. The third branch module of the Mamba-based multi-domain feature fusion network in the trained network is used to process the short-time Fourier transform features to obtain spectral features. The cross-attention module in the trained network is used to fuse the time-domain features, higher-order statistical features, and spectral features to obtain a first fused feature and a second fused feature. The first fused feature and the second fused feature are then fused to obtain a fused feature. The classification head in the trained network is used to classify the fused feature to obtain classification results. The first fused feature fuses the UAV radio frequency signal and the short-time Fourier transform features, and the second fused feature fuses the bispectral features and the short-time Fourier transform features.

[0022] Specifically, this embodiment proposes a multi-domain feature fusion network for UAV radio frequency feature recognition, which includes a feature extraction module that uses hybrid Mamba and Vision-Mamba (ViM) feature encoding and uses a cross-attention mechanism to fuse features, so as to achieve an efficient recognition method based on closed sets and open sets.

[0023] First, the basic theory of state-space models and the derivation of Mamba are briefly introduced, followed by an explanation of ViM and its application in STFT and bispectral features. Then, a cross-attention mechanism is introduced to construct a three-branch fusion architecture. Finally, the loss function and training process are explained. The Mamba-based multi-domain feature fusion network structure proposed in this embodiment is as follows: Figure 3 As shown.

[0024] State-space models (SSMs) were originally designed to characterize the states of continuous-time systems and predict subsequent state transitions based on given inputs. They are typically expressed in the form of linear ordinary differential equations, i.e.: ; ; in, Indicates a hidden state. Represents the transformation matrix. and Represents the projection matrix; The SSM evolved into the Structured State Space Model (S4). This model describes the continuous-time system on different time scales. It is obtained by discretization with zero-order hold (ZOH), that is: ; ; ; ; in, and Indicates parameters and Discretized form, and Represents the hidden state under discrete time constant; To overcome the inefficiency of discrete-time SSM recursion in hardware implementation, S4 reformulates the state update process as a convolution operation and utilizes Fast Fourier Transform for efficient computation in the frequency domain, thereby significantly improving training speed and achieving GPU parallelization. ; ; Among them, convolution kernel Discrete parameters of SMM Export, Indicates the sequence length. and These represent the discrete Fourier transform and its inverse transform, respectively. This represents element-wise multiplication in the frequency domain.

[0025] Building upon S4, Mamba introduces a dynamic input selection mechanism and hardware-aware design, enabling the model to adaptively adjust parameters at each time step based on the input content, achieving context-aware dynamic modulation. The specific process is shown in the algorithm in Table 1. This model forms a Selective State-Space Model (S6), the definition of which involves batch size. Sequence length Number of input channels and hidden dimensions In the algorithm, , , , , This represents the linear projection operator.

[0026] Table 1. Algorithm SSM+Selectivity Mechanism

[0027] Furthermore, in this embodiment, the Mamba-based multi-domain feature fusion network in the trained network includes a first branch module, a second branch module, and a third branch module; wherein, The first branch module includes a first normalization layer, a first learnable linear layer, a second learnable linear layer, a first convolutional layer, a first nonlinear activation function, a second nonlinear activation function, a selective state-space model, and a global average pooling layer. The second branch module includes a second convolutional layer, a third nonlinear activation function, a first normalized layer, a second normalized layer, a third learnable linear layer, a fourth learnable linear layer, a first forward one-dimensional convolutional layer, a fourth nonlinear activation function, a first forward state space model, a first backward one-dimensional convolutional layer, a fifth nonlinear activation function, a first backward state space model, a sixth nonlinear activation function, and a first linear layer. The third branch module includes the third convolutional layer, the seventh nonlinear activation function, the second normalized layer, the third normalized layer, the fifth learnable linear layer, the sixth learnable linear layer, the second forward one-dimensional convolutional layer, the eighth nonlinear activation function, the second forward state space model, the second backward one-dimensional convolutional layer, the ninth nonlinear activation function, the second backward state space model, the tenth nonlinear activation function, and the second linear layer. The cross-attention module in the trained network includes a linear mapping feature embedding module, a first softmax function, a second softmax function, a first nonlinear transformation module, and a second nonlinear transformation module; The trained network's classification head includes a third linear layer, a seventh nonlinear activation function, a regularization constraint layer, and a classification layer.

[0028] In this embodiment, the UAV radio frequency signal is processed through the first branch module of the Mamba-based multi-domain feature fusion network in the trained network. That is, the Mamba network is used to efficiently and context-awarely extract features from the UAV IQ data to obtain temporal features, including: The IQ sequence is obtained by downsampling the radio frequency signal of the UAV. ; The IQ sequence is normalized using the first normalization layer to obtain the first feature; The first feature is processed by a first learnable linear layer and a second learnable linear layer, and then projected into two different feature spaces to obtain the second feature. and third feature , is represented as: ; ; in, This represents the feature mapping module. Represents the real number field. Indicates the length of the input feature map. Indicates the width of the input feature map; The second feature is convolved using a first convolutional layer, and the convolved feature is processed using a first nonlinear activation function to obtain the fourth feature; the fourth feature is then processed using a selective state-space model to obtain the fifth feature. , is represented as: ; in, Representing a state-space model, This represents the activation function. This represents one-dimensional convolution; The third feature is processed using a second nonlinear activation function to obtain the sixth feature, which is expressed as: ; The fifth and sixth features are fused together through element-wise multiplication to obtain the seventh feature, which is represented as: ; in, This represents element-wise multiplication; The seventh feature is added to the IQ sequence to obtain the eighth feature; a global average pooling layer is then used to process the eighth feature to obtain the temporal feature. , is represented as: ; in, This represents the index of the input feature map. This represents a compact representation of the time-series radio frequency fingerprint features extracted from the original IQ signal.

[0029] In this embodiment, ViM extends the core ideas of Mamba to the field of visual representation learning, achieving efficient visual feature modeling by combining a state-space model with image understanding. This model features a global receptive field, input-dependent dynamic weights, and a hardware-friendly design.

[0030] To adapt one-dimensional sequence modeling to two-dimensional image input, ViM employs a Selective Scan Module (SCM) that divides the image into small blocks and decomposes it into a one-dimensional sequence along four directions. Building upon this, this embodiment further proposes a bidirectional scanning strategy to reduce computational costs. This design maintains the advantages of the S6 model while achieving complete spatial coverage and efficient visual processing.

[0031] Since both STFT features and BIS features are represented in two-dimensional image form, their processing procedures are similar.

[0032] Furthermore, the bispectral features are processed through the second branch module of the Mamba-based multi-domain feature fusion network in the trained network to obtain higher-order statistical features, including: The bispectral features are converted into amplitude spectrum features, and the amplitude spectrum features are segmented into several patches, such as... Figure 4 As shown, a second convolutional layer is used to convolve several patches, and a third non-linear activation function is used to process the features after convolution to achieve image patch embedding, obtaining the embedding features corresponding to each patch, as shown below: ; in, This represents the feature blocks into which the amplitude spectrum features are divided. This represents the SiLU activation function. This represents a learnable convolutional kernel. Indicates amplitude spectrum characteristics, Indicates the number of output channels. , , Indicates the downsampling factor. The width of the amplitude spectrum feature is represented. Indicates the height of the amplitude spectrum feature; The embedded features corresponding to each patch are flattened in the spatial dimension and injected with learnable two-dimensional positional encoding. , This allows the model to perceive the original spatial location of each token, ensuring efficient and information-fidelity conversion from image to sequence. A first normalization layer is then used for layer normalization to obtain the ninth feature. , is represented as: ; in, Presentation layer normalization operation, Indicates the flattening operation; The ninth feature is normalized using a second normalization layer to obtain the tenth feature; The tenth feature is processed using the third and fourth learnable linear layers respectively, and projected into two different feature spaces to obtain the eleventh feature. and the twelfth feature , is represented as: ; ; in, and Represents different linear layer mappings, This indicates a normalization operation; The eleventh feature is convolved using a first forward one-dimensional convolutional layer, and the convolved feature is further processed using a fourth nonlinear activation function to obtain the thirteenth feature. Finally, the thirteenth feature is processed using a first forward state-space model to obtain the fourteenth feature. , is represented as: ; in, This represents the processing procedure of the forward state-space model; The eleventh feature is convolved using a first backward one-dimensional convolutional layer, and the convolved feature is processed using a fifth nonlinear activation function to obtain the fifteenth feature; the fifteenth feature is then processed using a first backward state-space model to obtain the sixteenth feature. , is represented as: ; in, This represents the processing procedure of the backward state-space model; The twelfth feature is processed using the sixth nonlinear activation function to obtain the seventeenth feature; the seventeenth feature is then fused with the fourteenth feature through element-wise multiplication to obtain the eighteenth feature, expressed as: ; The seventeenth feature is obtained by fusing the sixteenth feature with the element-wise multiplication, and is represented as follows: ; Adding the eighteenth feature to the nineteenth feature yields the twentieth feature. , is represented as: ; The twentieth feature is processed using the first linear layer. The processed feature is then added to the ninth feature to obtain the higher-order statistical feature. .

[0033] Furthermore, the short-time Fourier transform features are processed through the third branch module of the Mamba-based multi-domain feature fusion network in the trained network to obtain spectral features, including: The short-time Fourier transform features are segmented into several patches, such as Figure 4 As shown, the third convolutional layer is used to convolve several patches, and the seventh non-linear activation function is used to process the features after convolution to achieve image patch embedding, obtaining the embedding features corresponding to each patch, as shown below: ; in, This represents a feature map where the short-time Fourier transform features are divided into small blocks. This represents the SiLU activation function. This represents a learnable convolutional kernel. Indicates the short-time Fourier spectrum characteristics. Indicates the number of output channels. , , Indicates the downsampling factor. The width of the short-time Fourier spectral feature is represented. Indicates the height of the short-time Fourier spectral features; The embedded features corresponding to each patch are flattened in the spatial dimension and injected with learnable two-dimensional positional encoding. , This allows the model to perceive the original spatial location of each token, ensuring efficient and information-fidelity conversion from image to sequence. A second normalization layer is then used for layer normalization processing to obtain the twenty-first feature. , is represented as: ; in, Presentation layer normalization operation, Indicates the flattening operation; The twenty-first feature is normalized using the third normalization layer to obtain the twenty-second feature; The twenty-second feature is processed using the fifth and sixth learnable linear layers respectively, and projected into two different feature spaces to obtain the twenty-third feature. Twenty-fourth feature , is represented as: ; ; in, and Represents different linear layer mappings, This indicates a normalization operation; The 23rd feature is convolved using a second forward one-dimensional convolutional layer, and the convolved feature is further processed using an eighth nonlinear activation function to obtain the 25th feature. Finally, the 25th feature is processed using a second forward state space model to obtain the 26th feature. , is represented as: ; in, This represents the processing procedure of the forward state-space model; The 23rd feature is convolved using a second backward one-dimensional convolutional layer, and the convolved feature is processed using a ninth nonlinear activation function to obtain the 27th feature; the 27th feature is then processed using a second backward state-space model to obtain the 28th feature. , is represented as: ; in, This represents the processing procedure of the backward state-space model; The 24th feature is processed using the 10th nonlinear activation function to obtain the 29th feature; the 29th feature and the 26th feature are then fused together by element-wise multiplication to obtain the 30th feature, expressed as: ; The 29th feature and the 28th feature are fused together by element-wise multiplication to obtain the 31st feature, which is represented as: ; Adding the thirtieth feature to the thirty-first feature yields the thirty-second feature. , is represented as: ; The 32nd feature is processed using a second linear layer. This processed feature is then added to the 21st feature to obtain the spectral feature. .

[0034] It should be noted that the above process employs a bidirectional scanning mechanism that enables global interaction between sequence elements, thereby forming a more comprehensive and flexible receptive field. Subsequently, the output vectors from both directions are aggregated through element-wise summation to generate a high-level RF fingerprint representation corresponding to the STFT and BIS features.

[0035] Furthermore, in this embodiment, to achieve complementary representation of multi-source features, a cross-attention mechanism is introduced during feature extraction. The structure of this mechanism is as follows: Figure 5 As shown.

[0036] The cross-attention mechanism proposed in this embodiment borrows from the self-attention mechanism in the Transformer model to achieve interactive modeling and fusion between time-domain features (IQ signals), higher-order statistical features (bispectral), and STFT spectral features. The proposed cross-attention can adaptively allocate weights between modes, and the model tends to focus attention on reliable feature units in another mode, thus achieving robust fusion. Residual and normalization designs ensure that the fused features retain the structural advantages of the query mode while incorporating reliable information from other modes, avoiding unilateral loss of control in attention output.

[0037] The cross-attention module in the trained network fuses temporal features, higher-order statistical features, and spectral features to obtain a first fused feature and a second fused feature. The first fused feature and the second fused feature are then fused together to obtain a fused feature, which includes: Employing a feature embedding module for temporal features Higher-order statistical features and spectral characteristics Embedding is performed, represented as: ; ; ; in, , and These represent the projection of time-domain features onto the query. ,key Sum The vector after, , and Representing the projection time domain features The corresponding learnable weights, , and These represent the projection of spectral features onto the query. ,key Sum The vector after, , and Representing the characteristics of the projected spectrum The corresponding learnable weights, , and These represent the projection of higher-order statistical features onto the query. ,key Sum The vector after, , and Represents higher-order statistical features of projection The corresponding learnable weights; A cross-attention mechanism is employed, combining the first and second softmax functions to calculate the temporal attention matrix. and , is represented as: ; ; in, express Dimensions express Dimensions Indicates matrix transpose; The first nonlinear transformation module is used to process the time-domain attention matrix. Processing is performed, and the results are compared with higher-order statistical features. Adding them together yields the first fusion feature. , is represented as: ; The second nonlinear transformation module is used to process the time-domain attention matrix. Processing is performed, and the results are compared with higher-order statistical features. Adding them together yields the second fusion feature. , is represented as: ; in, Represents a nonlinear transformation function; The first fusion feature Second fusion features The fusion is performed to obtain the fusion feature, which is represented as: ; in, This represents the fusion factor.

[0038] It should be noted that the first fusion feature integrates the UAV radio frequency signal and the short-time Fourier transform feature, while the second fusion feature integrates the bispectral feature and the short-time Fourier transform feature.

[0039] Furthermore, in this embodiment, the training process of the trained network includes: Data of a preset category is obtained as samples, and the true labels of the samples are obtained to construct a training dataset; the samples include UAV radio frequency signals, bispectral features, and short-time Fourier transform features; Input a portion of the samples from the training dataset into the first... The network to be trained is trained again to obtain the first... The prediction results output by the classification head during each training process; According to the The prediction results output by the classification head during the training process are consistent with those of the training... The true labels of the samples in the network to be trained are used to calculate the classification loss, which is then used as the first classification loss. Classification loss during each training process; According to the The classification loss from the first training process is backpropagated to update the classification loss from the second training process. The network parameters of the network to be trained are obtained. The network to be trained is repeated until the number of training iterations or the degree of convergence meets the preset conditions, at which point a trained network is obtained.

[0040] In this embodiment, the expression for calculating the classification loss is: ; in, This represents the Focal Loss function. Indicates the true category The predicted probability, , This represents the weighting coefficient used to handle class imbalance. This represents the focusing parameter, used to adjust the weights of difficult-to-classify samples.

[0041] In summary, the Mamba-based multi-domain feature fusion method for UAV radio frequency fingerprinting provided by this invention has the following beneficial effects: First, to address the significant limitations of single-domain feature representation of UAV radio frequency fingerprints—namely, weak noise resistance of time-domain features, insufficient dynamic representation of frequency-domain features, and lack of high-order statistical information in time-frequency features—we propose multi-domain feature fusion to enhance the representation of UAV radio frequency fingerprint features.

[0042] Second, to address the issue of balancing feature redundancy and complementarity caused by feature fusion, we study an adaptive feature selection mechanism to dynamically optimize the fusion weights of multi-source data, overcome feature degradation caused by environmental interference, and explore the collaborative representation capabilities of cross-domain features.

[0043] Third, to address the bottlenecks of high computational complexity and insufficient real-time performance caused by feature fusion, a lightweight multimodal fusion framework based on the Mamba architecture is studied. This framework fully utilizes the linear computational complexity advantage of the Mamba model in long sequence modeling, as well as hardware-aware algorithms such as kernel fusion, parallel scanning, and recalculation, to significantly reduce the computational load while ensuring recognition accuracy.

[0044] Based on the same inventive concept, this invention also provides a Mamba-based multi-domain feature fusion UAV radio frequency fingerprinting device, used to implement the Mamba-based multi-domain feature fusion UAV radio frequency fingerprinting method provided in the above embodiments of this invention. Examples of the identification method are described above and will not be repeated here. The device includes: The feature acquisition module is used to acquire the UAV radio frequency signal, and to represent the UAV radio frequency signal using in-phase and quadrature components; to acquire bispectral features based on the UAV radio frequency signal; and to acquire short-time Fourier transform features based on the UAV radio frequency signal. The feature processing and fusion module is used to process the UAV radio frequency signal, bispectral features, and short-time Fourier transform features using a trained network to obtain classification results. The first branch module of the Mamba-based multi-domain feature fusion network in the trained network processes the UAV radio frequency signal to obtain time-domain features. The second branch module of the Mamba-based multi-domain feature fusion network in the trained network processes the bispectral features to obtain higher-order statistical features. The third branch module of the Mamba-based multi-domain feature fusion network in the trained network processes the short-time Fourier transform features to obtain spectral features. The cross-attention module in the trained network fuses the time-domain features, higher-order statistical features, and spectral features to obtain a first fused feature and a second fused feature. The first fused feature and the second fused feature are then fused to obtain a fused feature. The classification head in the trained network classifies the fused feature to obtain classification results. Specifically, the first fused feature fuses the UAV radio frequency signal and the short-time Fourier transform features, and the second fused feature fuses the bispectral features and the short-time Fourier transform features.

[0045] This invention provides a multi-domain feature fusion-based UAV radio frequency fingerprinting device based on Mamba. The research results can be directly applied to scenarios such as low-altitude UAV monitoring systems, radio spectrum security monitoring, anti-UAV defense systems, and electromagnetic space security assessment. Simultaneously, relying on the hardware uniqueness, environmental interference resistance, and non-contact sensing advantages of radio frequency signals, UAV radio frequency fingerprinting technology is gradually breaking through the limitations of traditional UAV control methods, demonstrating broad application potential in multiple fields. Examples include identity verification of cooperative UAVs without hardware modifications, and equipment traceability and responsibility tracking in large-scale UAV applications such as logistics, agriculture, and inspection. In the short term, this technology will focus on scenarios such as security control in sensitive areas and compliance supervision of UAVs in various industries, addressing the current pain points of "difficulty in controlling unauthorized flights and difficulty in tracing identities." In the medium to long term, with technological integration and industrial maturity, it will be deeply integrated into low-altitude traffic management, cross-domain security, and intelligent logistics systems, forming a collaborative industrial ecosystem and providing key support for the safe, efficient, and large-scale development of the low-altitude economy.

[0046] In an optional embodiment of the present invention, the effectiveness of the Mamba-based multi-domain feature fusion UAV radio frequency fingerprinting method provided in the above embodiment is verified through simulation experiments, specifically as follows: I. Simulation Conditions 1. Closed-loop drone radio frequency fingerprint recognition.

[0047] First, an existing publicly available dataset containing raw radio frequency signals collected from various commercial drones was used. This dataset was preprocessed, and five types of drones (DJI Phantom 3, DJI Air 2S, DJI Inspire 2, DJI Mini 2, and DJI Phantom 4 Pro) were selected to construct a dataset containing 24,610 samples, of which 19,080 were used for training, 4,770 for validation, and 760 for testing. Each sample was processed to obtain IQ features, BIS features, and STFT features.

[0048] The experiment was conducted using the PyTorch framework on an NVIDIA RTX 4090 GPU (24GB VRAM). All models were trained using the AdamW optimizer with an initial learning rate of [missing value]. The weight decays to The batch size was 32, and the number of training epochs was 100. To improve the robustness of the model, data augmentation strategies were applied: the IQ data was vertically flipped with a probability of 0.5, and the STFT and BIS features were horizontally flipped; Gaussian noise with a mean of 0 and a standard deviation of 0.03 was added to the IQ data with a probability of 0.3. Fusion factor Set to 0.4, the class weighting coefficient in the loss function. Set to 1, focus parameter Set it to 2.

[0049] In addition, to evaluate the model's detection capabilities in real-world scenarios, a field experiment was conducted using a DJI Mini 4 Pro drone equipped with a high-precision 2.4 / 5.8GHz radio frequency signal transmission module. Data acquisition was carried out in an outdoor campus environment, collecting a total of 500 samples, all derived from signals emitted by the drone under stable operating conditions. A complete acquisition system was designed to achieve this, including a computer, monitor, DC power supply, and a self-developed radio frequency signal receiver. The data acquisition environment and system are as follows: Figure 6 As shown.

[0050] The receiving front end uses the ADRV9009 RF chip, such as Figure 7As shown, this module supports a wide input frequency range of 75MHz to 6000MHz and provides two independent receiving channels with a maximum signal receiving bandwidth of 200MHz. Its analog-to-digital conversion sampling rate is 125 megasamples per second (MSPS), enabling high-resolution RF signal acquisition. With its wide bandwidth and dual-channel characteristics, the ADRV9009 is ideally suited for multi-antenna signal acquisition and high-fidelity UAV RF fingerprinting tasks.

[0051] II. Simulation Content and Result Analysis Please see Figure 8 , Figure 8 This is a schematic diagram of the loss curves of the training set and validation set provided in an embodiment of the present invention. Figure 8 The corresponding recognition accuracy curves are also provided. As can be seen from the figure, both the loss and accuracy show a stable convergence trend, and the performance on the validation set is highly consistent with that during the training process, indicating that the model optimization is effective and has strong generalization ability.

[0052] Precision, recall, and F1 score can be calculated from the true positives (TP), false positives (FP), and false negatives (FN) in the recognition results, and their definitions are as follows: ; ; ; Please refer to Table 2. The multi-feature fusion-based recognition model proposed in this invention has achieved stable high performance across all UAV categories, with an overall accuracy of 97.76% on the validation set, indicating that the method has strong discriminative ability and robustness.

[0053] Table 2 Performance Indicators for UAV Classification

[0054] Please see Figure 9 , Figure 9 This is a schematic diagram of a classification result confusion matrix provided in an embodiment of the present invention. The recognition accuracy rates on the validation set and test set are 97.7% and 97.2%, respectively. Furthermore, Figure 10The UMAP (Uniform Manifold Approximation and Projection) visualization results of the proposed drone recognition performance are presented, where stars indicate the center of each drone category cluster. The UMAP visualization results clearly show that the feature clusters corresponding to different DJI drone categories are well distributed and separated from each other, indicating that there are significant differences in the feature space representation extracted by this invention.

[0055] 2. Ablation experiment.

[0056] 2.1 Feature fusion effect.

[0057] To verify the effectiveness of the proposed multi-branch architecture, ablation experiments were conducted on the proposed three-branch fusion method (IQ+BIS+STFT) and each independent branch on a UAV RF fingerprint dataset. All experiments used the same training parameters. As shown in Table 3, the proposed feature fusion method achieved an overall accuracy of 97.7%, outperforming all single-branch and dual-branch structures.

[0058] Table 3 Performance Comparison of Different Input Features

[0059] exist Figure 11 The diagram illustrates how validation accuracy on the validation set changes with the number of training epochs. It shows that the fusion model improves the final accuracy by 18.7% compared to the best-performing single branch (STFT branch), and by 5% compared to the best-performing pairwise fusion branch (STFT+BIS branch). Furthermore, the fusion architecture proposed in this invention exhibits higher stability during training.

[0060] Subsequently, the classification accuracy of various input features under different signal-to-noise ratios (SNRs) was compared. To evaluate the robustness of the method under different signal qualities, additive white Gaussian noise with different SNRs was applied to the original IQ data to simulate instability in real-world scenarios. The SNR is defined as follows: ; in, Represents the original IQ signal. This represents superimposed noise. The expectation operator is used to represent the average power. Different interference environments were simulated by varying the SNR level to test the model's performance under noise interference, as shown in Table 4.

[0061] Table 4. Comparison of model performance under different signal-to-noise ratios

[0062] like Figure 12 As shown, the proposed fusion method (red curve) exhibits excellent generalization ability, maintaining a classification accuracy of over 94% within an SNR range of 15dB to 30dB. Compared to single-domain features (IQ / STFT / BIS branches), it achieves a performance improvement of over 20% at low SNR (5~10dB). Notably, even at 0dB SNR, the proposed feature fusion-based model maintains an accuracy of over 80% and exhibits smooth attenuation characteristics; from 30dB to 0dB, the accuracy decreases by only 12.9%, which is superior to the over 29.5% decrease of the single-branch model. This performance advantage stems from the synergistic fusion of IQ, STFT, and BIS feature representations. The cross-domain fusion mechanism effectively compensates for the inherent limitations of a single feature space, enabling robust UAV RF fingerprint recognition performance even in highly harsh electromagnetic environments.

[0063] 2.2 The impact of cross-attention mechanism.

[0064] To evaluate the impact of the cross-attention mechanism, a controlled ablation experiment was designed to compare the performance differences of the model with and without the cross-attention module. Figure 13 As shown in the experimental results, the model employing the cross-attention architecture achieves a 4.55% improvement in classification accuracy compared to the baseline model, while also exhibiting a faster convergence speed. This dual advantage of improved accuracy and accelerated convergence fully demonstrates the effectiveness of the cross-attention mechanism in enhancing feature learning efficiency.

[0065] 2.3 Performance comparison of different recognition models.

[0066] Next, the recognition performance of different models was compared. During the experiment, all network model architectures were configured strictly according to the same conditions. First, the accuracy of each method on the validation set was compared, such as... Figure 14 As shown, apart from the Transformer & ViT model, the other multi-domain feature fusion methods (including the proposed method) exhibit similar performance throughout the training process, with only slight fluctuations.

[0067] Table 5 shows a comprehensive performance comparison between the proposed method and existing methods, including MobileNetV2, ResNet, EfficientNet, CNN-LSTM, DenseNet, and Transformer&ViT. The proposed method requires only 0.11G MACs and 19.66M parameters, significantly less than traditional models such as ResNet, DenseNet, and Transformer&ViT. Furthermore, this model consumes the least GPU memory (148.05MB) and has the fastest inference speed (1.90ms), demonstrating its practical applicability in low-resource or real-time RF signal classification tasks.

[0068] Table 5 Comparison of performance of different recognition networks

[0069] Although the average classification accuracy (97.76%) is slightly lower than some large models (such as ResNet and DenseNet), the method proposed in this invention remains highly competitive, significantly reducing computational costs and memory overhead. This balance between performance and efficiency fully demonstrates the effectiveness of the Mamba architecture in achieving compact, high-performance UAV RF fingerprint recognition.

[0070] 2.4 Identification of Unknown Unmanned Aerial Vehicles.

[0071] To further validate the effectiveness of the hybrid framework, supplementary experiments were conducted for unknown sample detection. A framework for identifying unknown identities of unmanned aerial vehicles (UAVs) is proposed, which achieves radio frequency fingerprint analysis through the synergistic fusion of deep representation learning and statistical anomaly detection.

[0072] The processed features before the fully connected layer in the classification module are represented as follows: This method projects multi-domain radio frequency inputs onto a unified discrimination subspace through nonlinear transformation. It includes multi-domain inputs... , as well as , obtained through transformation : ; To quantify the similarity between unknown drones and known categories, an enhanced Mahalanobis distance detector is proposed to calculate anomaly scores, namely: ; in, and It is estimated from the embedding features of known categories.

[0073] then, This represents the threshold used to balance the trade-off between recognizing known categories and detecting unknown samples. To achieve optimal system performance, an adaptive threshold optimization method is constructed using a multi-objective minimization function, namely: ; Among them, the weighting coefficient The accuracy of classification for known drone categories Detection rate of unknown intrusion samples A balance must be established between them. This balancing optimization strategy prevents the model from sacrificing the performance of one metric while improving the performance of another, which is especially crucial for real-world deployment scenarios.

[0074] Experimental results on the DJI drone dataset show a classification accuracy of 98.64% for known categories and a detection rate of 97.83% for unknown samples. The Mahalanobis distance distribution of the fused drone samples is as follows: Figure 15a As shown. The classification results under the open set condition are as follows. Figure 15b As shown, the architecture proposed in this invention performs excellently in open set classification tasks.

[0075] also, Figure 15c The t-SNE visualization results are presented, showing that the five known UAV models form a clear cluster structure in the learned feature space, and the unknown samples (red) are effectively separated.

[0076] In summary, this invention addresses the limited single-domain feature representation capability in UAV RF fingerprinting by proposing a multi-domain feature fusion enhancement method. By deeply fusing cross-domain information from IQ signals, bispectral features, and STFT spectra, the proposed fusion architecture effectively integrates the complementary advantages of different feature spaces, significantly improving recognition accuracy while enhancing the model's generalization ability. To overcome the computational complexity and real-time bottlenecks caused by feature fusion, this invention innovatively designs an efficient fusion framework based on Mamba and ViM architectures. This framework fully leverages Mamba's linear computational complexity advantage in long sequence modeling and, combined with hardware-aware algorithm optimization, significantly reduces computational overhead while maintaining high recognition accuracy. To address the challenge of balancing redundancy and complementarity in feature fusion, this invention proposes an adaptive feature interaction mechanism based on cross-attention. This mechanism dynamically models the dependencies between multi-source features, achieving online optimization of fusion weights and effectively suppressing feature degradation caused by environmental interference. Experimental results show that the proposed method achieves a recognition accuracy of 97.76% while maintaining low computational overhead and fast inference speed, demonstrating significant effectiveness and superiority.

[0077] It should be noted that, in this document, 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. Furthermore, the terms "comprising," "including," or any other variations are intended to cover non-exclusive inclusion, such that an article or device comprising a list of elements includes not only those elements but also other elements not expressly listed. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or device comprising said element. Terms such as "connected" or "linked" are not limited to physical or mechanical connections but can include electrical connections, whether direct or indirect. The orientations or positional relationships indicated by terms such as "upper," "lower," "left," and "right" are based on the orientations or positional relationships shown in the accompanying drawings and are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as limiting the invention.

[0078] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Furthermore, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0079] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A multi-domain feature fusion method for UAV radio frequency fingerprinting based on Mamba, characterized in that, include: Acquire the radio frequency signal of the drone and represent it using in-phase and quadrature components; Based on the UAV radio frequency signal, bispectral features are obtained; Based on the UAV radio frequency signal, obtain the short-time Fourier transform characteristics; The trained network processes the UAV radio frequency signal, the bispectral features, and the short-time Fourier transform features to obtain a classification result. The first branch module of the Mamba-based multi-domain feature fusion network in the trained network processes the UAV radio frequency signal to obtain time-domain features. The second branch module of the Mamba-based multi-domain feature fusion network in the trained network processes the bispectral features to obtain higher-order statistical features. The third branch module of the Mamba-based multi-domain feature fusion network in the trained network processes the short-time Fourier transform features to obtain spectral features. The cross-attention module in the trained network fuses the time-domain features, the higher-order statistical features, and the spectral features to obtain a first fused feature and a second fused feature. The first fused feature and the second fused feature are then fused to obtain a fused feature. The fused features are classified using a classification head in a trained network to obtain a classification result; wherein, the first fused feature combines UAV radio frequency signals and short-time Fourier transform features, and the second fused feature combines bispectral features and short-time Fourier transform features.

2. The Mamba-based multi-domain feature fusion UAV radio frequency fingerprinting method according to claim 1, characterized in that, The trained network, based on Mamba, includes a multi-domain feature fusion network comprising a first branch module, a second branch module, and a third branch module; wherein... The first branch module includes a first normalization layer, a first learnable linear layer, a second learnable linear layer, a first convolutional layer, a first nonlinear activation function, a second nonlinear activation function, a selective state space model, and a global average pooling layer. The second branch module includes a second convolutional layer, a third nonlinear activation function, a first normalized layer, a second normalized layer, a third learnable linear layer, a fourth learnable linear layer, a first forward one-dimensional convolutional layer, a fourth nonlinear activation function, a first forward state space model, a first backward one-dimensional convolutional layer, a fifth nonlinear activation function, a first backward state space model, a sixth nonlinear activation function, and a first linear layer. The third branch module includes a third convolutional layer, a seventh nonlinear activation function, a second normalized layer, a third normalized layer, a fifth learnable linear layer, a sixth learnable linear layer, a second forward one-dimensional convolutional layer, an eighth nonlinear activation function, a second forward state space model, a second backward one-dimensional convolutional layer, a ninth nonlinear activation function, a second backward state space model, a tenth nonlinear activation function, and a second linear layer. The cross-attention module in the trained network includes a linear mapping feature embedding module, a first softmax function, a second softmax function, a first nonlinear transformation module, and a second nonlinear transformation module. The trained network's classification head includes a third linear layer, a seventh nonlinear activation function, a regularization constraint layer, and a classification layer.

3. The Mamba-based multi-domain feature fusion UAV radio frequency fingerprinting method according to claim 2, characterized in that, The UAV radio frequency signal is processed by the first branch module of the Mamba-based multi-domain feature fusion network in the trained network to obtain time-domain features, including: The UAV radio frequency signal is downsampled to obtain the IQ sequence. ; The IQ sequence is normalized using the first normalization layer to obtain the first feature; The first feature is processed using both the first learnable linear layer and the second learnable linear layer, and then projected into two different feature spaces to obtain the second feature. and third feature , is represented as: ； ； in, This represents the feature mapping module. Represents the real number field. Indicates the length of the input feature map. Indicates the width of the input feature map; The second feature is convolved using the first convolutional layer, and the convolved feature is processed using the first nonlinear activation function to obtain the fourth feature; the fourth feature is then processed using the selective state-space model to obtain the fifth feature. , is represented as: ； in, Representing a state-space model, This represents the activation function. This represents one-dimensional convolution; The third feature is processed using the second nonlinear activation function to obtain the sixth feature, which is expressed as follows: ； The fifth and sixth features are fused together by element-wise multiplication to obtain the seventh feature, which is represented as follows: ； in, This represents element-wise multiplication; The seventh feature is added to the IQ sequence to obtain the eighth feature; the eighth feature is then processed using the global average pooling layer to obtain the temporal feature. , is represented as: ； in, Indicates the index of the input feature map.

4. The Mamba-based multi-domain feature fusion UAV radio frequency fingerprinting method according to claim 2, characterized in that, The bispectral features are processed by the second branch module of the Mamba-based multi-domain feature fusion network in the trained network to obtain higher-order statistical features, including: The bispectral features are converted into amplitude spectrum features, which are then segmented into several patches. The second convolutional layer is used to convolve these patches, and the third nonlinear activation function is applied to process the convolutionally processed features to achieve image patch embedding. The resulting embedding features for each patch are expressed as follows: ； in, This represents the feature blocks into which the amplitude spectrum features are divided. This represents the SiLU activation function. This represents a learnable convolutional kernel. Indicates amplitude spectrum characteristics, Indicates the number of output channels. , , Indicates the downsampling factor. The width of the amplitude spectrum feature is represented. Indicates the height of the amplitude spectrum feature; The embedded features corresponding to each patch are flattened in the spatial dimension and injected with learnable two-dimensional positional encoding. , Then, the first normalization layer is used for layer normalization to obtain the ninth feature. , is represented as: ； in, Presentation layer normalization operation, Indicates the flattening operation; The ninth feature is normalized using the second normalization layer to obtain the tenth feature; The tenth feature is processed using the third and fourth learnable linear layers respectively, and projected into two different feature spaces to obtain the eleventh feature. and the twelfth feature , is represented as: ； ； in, and Represents different linear layer mappings, This indicates a normalization operation; The eleventh feature is convolved using the first forward one-dimensional convolutional layer, and the convolved feature is processed using the fourth nonlinear activation function to obtain the thirteenth feature; the thirteenth feature is then processed using the first forward state space model to obtain the fourteenth feature. , is represented as: ； in, This represents the processing procedure of the forward state-space model; The eleventh feature is convolved using the first backward one-dimensional convolutional layer, and the convolved feature is processed using the fifth nonlinear activation function to obtain the fifteenth feature; the fifteenth feature is then processed using the first backward state space model to obtain the sixteenth feature. , is represented as: ； in, This represents the processing procedure of the backward state-space model; The twelfth feature is processed using the sixth nonlinear activation function to obtain the seventeenth feature; the seventeenth feature is then fused with the fourteenth feature through element-wise multiplication to obtain the eighteenth feature, expressed as follows: ； The seventeenth feature is fused with the sixteenth feature through element-wise multiplication to obtain the nineteenth feature, which is represented as follows: ； Adding the eighteenth feature to the nineteenth feature yields the twentieth feature. , is represented as: ； The twentieth feature is processed using the first linear layer, and the processed feature is added to the ninth feature to obtain the higher-order statistical feature. .

5. The Mamba-based multi-domain feature fusion UAV radio frequency fingerprinting method according to claim 2, characterized in that, The short-time Fourier transform features are processed by the third branch module of the Mamba-based multi-domain feature fusion network in the trained network to obtain spectral features, including: The short-time Fourier transform features are divided into several patches. The third convolutional layer is used to convolve the patches, and the seventh nonlinear activation function is used to process the convolutional features to achieve image patch embedding, obtaining the embedding features corresponding to each patch, as shown below: ； in, This represents a feature map where the short-time Fourier transform features are divided into small blocks. This represents the SiLU activation function. This represents a learnable convolutional kernel. Indicates the short-time Fourier spectrum characteristics. Indicates the number of output channels. , , Indicates the downsampling factor. The width of the short-time Fourier spectral feature is represented. Indicates the height of the short-time Fourier spectral features; The embedded features corresponding to each patch are flattened in the spatial dimension and injected with learnable two-dimensional positional encoding. , Then, the second normalization layer is used for layer normalization processing to obtain the twenty-first feature. , is represented as: ； in, Presentation layer normalization operation, Indicates the flattening operation; The second-first feature is normalized using the third normalization layer to obtain the second-second feature; The 22nd feature is processed using the fifth and sixth learnable linear layers respectively, and projected into two different feature spaces to obtain the 23rd feature. Twenty-fourth feature , is represented as: ； ； in, and Represents different linear layer mappings, This indicates a normalization operation; The second forward one-dimensional convolutional layer is used to convolve the twenty-third feature, and the eighth nonlinear activation function is used to process the convolutional feature to obtain the twenty-fifth feature; the second forward state space model is then used to process the twenty-fifth feature to obtain the twenty-sixth feature. , is represented as: ； in, This represents the processing procedure of the forward state-space model; The second backward one-dimensional convolutional layer is used to convolve the twenty-third feature, and the ninth nonlinear activation function is used to process the convolutional feature to obtain the twenty-seventh feature; the second backward state space model is then used to process the twenty-seventh feature to obtain the twenty-eighth feature. , is represented as: ； in, This represents the processing procedure of the backward state-space model; The twenty-fourth feature is processed using the tenth nonlinear activation function to obtain the twenty-ninth feature; the twenty-ninth feature and the twenty-sixth feature are then fused together by element-wise multiplication to obtain the thirtieth feature, expressed as follows: ； The 29th feature and the 28th feature are fused together by element-wise multiplication to obtain the 31st feature, which is represented as: ； Add the thirtieth feature to the thirty-first feature to obtain the thirty-second feature. , is represented as: ； The third-second feature is processed using the second linear layer, and the processed feature is added to the second-first feature to obtain the spectral feature. .

6. The Mamba-based multi-domain feature fusion UAV radio frequency fingerprinting method according to claim 2, characterized in that, The time-domain features, higher-order statistical features, and spectral features are fused using a cross-attention module in the trained network to obtain a first fused feature and a second fused feature. The first fused feature and the second fused feature are then fused to obtain a fused feature, including: The time-domain features are processed using the feature embedding module. The higher-order statistical features and the spectral features Embedding is performed, represented as: ； ； ； in, , and These represent the projection of time-domain features onto the query. ,key Sum The vector after, , and Representing the projection time domain features The corresponding learnable weights, , and These represent the projection of spectral features onto the query. ,key Sum The vector after, , and Representing the characteristics of the projected spectrum The corresponding learnable weights, , and These represent the projection of higher-order statistical features onto the query. ,key Sum The vector after, , and Represents higher-order statistical features of projection The corresponding learnable weights; A cross-attention mechanism is employed, combining the first softmax function and the second softmax function to calculate the temporal attention matrix. and , is represented as: ； ； in, express Dimensions express Dimensions Indicates matrix transpose; The first nonlinear transformation module is used to process the time-domain attention matrix. The processing is performed, and the result is compared with the higher-order statistical features. Adding them together yields the first fusion feature. , is represented as: ； The second nonlinear transformation module is used to process the time-domain attention matrix. The processing is performed, and the result is compared with the higher-order statistical features. Adding them together yields the second fusion feature. , is represented as: ； in, Represents a nonlinear transformation function; The first fusion feature and the second fusion feature The fusion is performed to obtain the fusion feature, which is represented as: ； in, This represents the fusion factor.

7. The Mamba-based multi-domain feature fusion UAV radio frequency fingerprinting method according to claim 1, characterized in that, The training process of the trained network includes: Data of a preset category is obtained as samples, and the true labels of the samples are obtained to construct a training dataset; the samples include UAV radio frequency signals, bispectral features, and short-time Fourier transform features; Input a portion of the samples from the training dataset into the first... The network to be trained is trained again to obtain the first... The prediction results output by the classification head during each training process; According to the The prediction results output by the classification head during the training process are consistent with those of the training... The true labels of the samples in the network to be trained are used to calculate the classification loss, which is then used as the first classification loss. Classification loss during each training process; According to the The classification loss from the first training process is backpropagated to update the classification loss from the second training process. The network parameters of the network to be trained are obtained. The network to be trained is iterated in this way until the number of training iterations or the degree of convergence meets the preset conditions, and the trained network is obtained.

8. The Mamba-based multi-domain feature fusion UAV radio frequency fingerprinting method according to claim 7, characterized in that, The expression for calculating the classification loss is: ； in, This represents the Focal Loss function. Indicates the true category The predicted probability, This represents the weighting coefficient used to handle class imbalance. This indicates the focus parameter.

9. The Mamba-based multi-domain feature fusion UAV radio frequency fingerprinting method according to claim 1, characterized in that, The drone radio frequency signal Represented as: ； in, Indicates in-phase components, Indicates orthogonal components, Represents the imaginary unit; Calculate its third-order cumulant based on the UAV's radio frequency signal. , is represented as: ； in, and Indicates different time delays, Represents the expectation operator; Perform a two-dimensional Fourier transform on the third-order cumulants to obtain bispectral features. , is represented as: ； On the time axis, the UAV radio frequency signal is segmented, and a Fourier transform is performed on each segment to obtain the signal's spectrum over time, i.e., the short-time Fourier transform characteristic, which is expressed as: ； in, Indicates the length of time. Represents angular frequency. Indicates the duration as The sliding window function, Indicates time.

10. A multi-domain feature fusion radio frequency fingerprinting device for unmanned aerial vehicles based on Mamba, characterized in that, include: The feature acquisition module is used to acquire the UAV radio frequency signal, and represent the UAV radio frequency signal using in-phase and quadrature components; and acquire bispectral features based on the UAV radio frequency signal. Based on the UAV radio frequency signal, obtain the short-time Fourier transform characteristics; The feature processing and fusion module is used to process the UAV radio frequency signal, the bispectral features, and the short-time Fourier transform features using a trained network to obtain a classification result; to process the UAV radio frequency signal through a first branch module of the Mamba-based multi-domain feature fusion network in the trained network to obtain time-domain features; to process the bispectral features through a second branch module of the Mamba-based multi-domain feature fusion network in the trained network to obtain higher-order statistical features; to process the short-time Fourier transform features through a third branch module of the Mamba-based multi-domain feature fusion network in the trained network to obtain spectral features; and to fuse the time-domain features, the higher-order statistical features, and the spectral features through a cross-attention module in the trained network to obtain a first fused feature and a second fused feature, and then fuse the first fused feature and the second fused feature to obtain a fused feature. The fused features are classified using a classification head in a trained network to obtain a classification result; wherein, the first fused feature combines UAV radio frequency signals and short-time Fourier transform features, and the second fused feature combines bispectral features and short-time Fourier transform features.

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