Nomenclature
- Symbol
-
Description
- AUC
-
area under the curve
- AUC
-
regularisation parameter in SVM
- CNN
-
convolutional neural network
- dB/Hz
-
decibels per Hertz (unit of power spectral density)
- EMD
-
empirical mode decomposition
- FFT
-
fast Fourier transform
- GHz
-
Gigahertz
- H(t,f)
-
time-varying transfer function of the complex envelope
- IMF
-
intrinsic mode function
- I/Q
-
in-phase/quadrature (signal representation)
- KNN
-
K-nearest neighbours
- RBF
-
radial basis function
1.0 Introduction
Unmanned aerial vehicles (UAVs) have become increasingly integrated into a wide range of devices, operating in coordination with ground control systems. Initially developed for military applications, UAVs have been employed in tasks such as search and destroy missions, surveillance, aerial photography and reconnaissance. Their capacity to operate at low altitudes enables them to capture higher spatial resolution over small areas [Reference Gómez-Candón, De Castro and López-Granados1]. As the cost of UAV platforms has declined, the technology has proliferated rapidly. Over the past decade, a growing number of entities – including scientific institutions, government agencies, private individuals and commercial operators – have adopted UAVs for data acquisition. These platforms are now widely used in fields such as land management [Reference Kaushal and Bhatnagar2], cultural heritage and archaeological site documentation [Reference Li3], disaster response [Reference Restas4] and high-resolution surface reconstruction in Earth sciences [Reference Mestre-Runge5]. However, the widespread adoption of UAVs has also raised significant security concerns, including threats to airspace security, risks of privacy violations and the potential for malicious use in illegal activities. Notable incidents include an attempted attack on the president of Venezuela using a UAV and a UAV crashing onto the White House lawn [Reference Batabyal6]. Such events not only disrupt aviation order but also pose serious risks to the safety of civilian passenger aircraft. UAVs can interfere with flight safety warning mechanisms and may collide with other aircraft while flying at low altitudes, with potentially catastrophic consequences. In recent years, numerous international airports and cities have experienced unauthorised drone intrusions, leading to flight delays and significant disruptions to airport operations and urban life [Reference Farber7]. Furthermore, as drone technology becomes more widespread, incidents involving privacy breaches have increased – such as drones being used to photograph individuals without consent or serving as tools in military and industrial espionage. In addition, the communication and remote control signals of drones are vulnerable to malicious attacks; hackers may hijack control signals to alter a drone’s course or exploit it for espionage purposes. Consequently, ensuring safe drone operations and enabling effective regulatory identification have become urgent priorities for nations worldwide.
UAV recognition system based on RFF.
Figure 1. Long description
The diagram illustrates a UAV recognition system based on RFF. It features a UAV, background noise, a flight controller, acquisition equipment, and signal processing. The UAV receives flight control signals and transmits map signals. The flight controller captures these signals, which are then processed by the acquisition equipment. The processed signals are displayed on a monitor.
Traditional drone identification methods, such as visual observation and radar detection, can monitor drones under certain conditions but suffer from significant limitations. Visual recognition is highly dependent on environmental factors and performs poorly in low light or adverse weather. Radar technology, whilst effective in some scenarios, lacks adaptability to complex backgrounds and exhibits low recognition accuracy for low-altitude flights. Moreover, these conventional methods primarily rely on the external characteristics of the target and are unable to analyse its communication signal features in depth, limiting their effectiveness in many practical situations.
To address these challenges more effectively, radio frequency fingerprint (RFF) recognition technology has emerged as a promising approach for UAV identification and classification. The general architecture of such a system is illustrated in Fig. 1. RFF technology extracts distinctive features from the flight control and image transmission signals embedded in UAV communications, enabling accurate identification and classification of UAVs and thereby facilitating effective monitoring and management of UAV activities. The concept of RFF, inspired by biological fingerprints, was pioneered by Hall et al. [Reference Hall, Barbeau and Kranakis8] in 2003. Based on the nature of the signal features exploited, RFF methods can be broadly categorised into three types: transient-based, steady-state-based and those focusing on unique signal parts. Transient-based methods analyse signal segments captured during power-on or power-off transitions, which contain device-specific startup characteristics but are brief and sensitive to noise. Steady-state-based methods utilise the continuous signal during regular operation, offering more data for analysis but requiring longer observation times. The third category focuses on deterministic and repeatable signal components, such as synchronisation preambles or specific protocol fields, which are protocol-dependent but highly reproducible.
Since its introduction, RFF has been extensively studied across its three primary categories. Transient-based methods analyse signal segments captured during power-on or power-off transitions. In this category, Danev et al. [Reference Danev and Capkun9] demonstrated the feasibility of transient-based identification for CC2420 wireless sensor nodes, achieving robustness to variations in distance, antenna polarisation and voltage. Zhuo et al. [Reference Zhuo, Huang and Chen11] proposed an energy envelope feature extraction method for transient signals, explaining the generation process using a nonlinear system model. More recently, Almashaqbeh et al. [Reference Almashaqbeh, Dalveren and Kara13] applied transient RFF to narrowband Bluetooth signals using a dual-tree complex wavelet transform, opening new possibilities for UAV research. Steady-state-based methods utilise the continuous signal during regular operation. Klein et al. [Reference Klein, Temple and Mendenhall10] successfully distinguished Cisco devices with subtle hardware differences using steady-state RFF. Nie et al. [Reference Nie12] extended this approach to UAVs by developing a WiFi-based detection system that extracts fractal dimension and bispectrum features from steady-state signals. Methods focusing on unique signal parts exploit deterministic and repeatable components such as synchronisation preambles. Mohammed et al. [Reference Mohammed14] employed Mel spectrograms and the YAMNet neural network with transfer learning to classify UAVs, effectively capturing unique spectral patterns. Cai et al. [Reference Cai15] designed a lightweight backbone network using multi-scale convolution blocks, significantly reducing model size while enhancing feature extraction capability.
Despite its potential, existing RFF-based methods still exhibit several limitations. Transient-based approaches demand high signal quality and are susceptible to noise interference. Steady-state methods, whilst more stable, often suffer from insufficient recognition accuracy. Moreover, the performance of current RFF techniques degrades markedly in low signal-to-noise ratio (SNR) environments or under strong interference, leading to increased misclassification and missed detection rates.
It is worth noting that while remote identification (RID) mandates broadcast of identity information and enhances accountability, its unencrypted transmissions remain susceptible to spoofing attacks. RFF overcomes this vulnerability by extracting hardware-intrinsic features from the physical layer – characteristics that are inherently difficult to clone or tamper with. Consequently, RFF and RID are complementary: RID provides protocol-level identification, whereas RFF adds an immutable physical-layer verification layer, ensuring robust identification even when RID messages are forged.
Different from the literature, this paper proposes a novel UAV recognition method that integrates an improved empirical mode decomposition (EMD) with RFF. The key contributions are threefold: (i) an adaptive wavelet denoising technique that selectively removes environmental noise while preserving hardware-specific fingerprints; (ii) an enhanced EMD algorithm incorporating cross-correlation and spectral kurtosis to extract the most informative intrinsic mode functions; and (iii) an optimised support vector machine (SVM) classifier with systematic hyperparameter tuning. Collectively, these innovations enhance recognition accuracy and robustness, particularly under low SNR conditions where existing methods often fail.
In addressing these challenges, this study introduces a new method for UAV recognition that combines an enhanced EMD with RFF, aiming to improve both the precision and speed of UAV identification. EMD, as an adaptive signal decomposition technique, is able to decompose a complex non-smooth signal into a series of intrinsic modal components to extract more representative features. In the case of UAV signals, the EMD technique adaptively decomposes the RF signal so that each component contains different frequency information of the UAV signal, thus helping to extract more representative parts of the RF fingerprint. Combining the signal decomposition capability of EMD with the fingerprint feature extraction advantage of RFF, the method in this paper is able to analyse the RF features of UAVs more accurately and provide higher recognition robustness in low SNR and complex environments. The main contributions of this paper are as follows:
-
1. A signal processing method based on adaptive wavelet denoising is proposed, which effectively removes the noise in the UAV radio frequency (RF) signal and ensures the accuracy of the signal in the feature extraction process. In addition, for the characteristics of UAV signals that are affected by different environmental conditions over time, this paper introduces a feature extraction method based on the time window in combination with the time factor, which enables the system to dynamically capture the characteristics of the signals over time, thus enhancing the robustness and adaptability of the system and improving the recognition accuracy.
-
2. An improved EMD method is used to extract the power spectral density (PSD) features in combination with Welch’s algorithm, which successfully extracts effective RF fingerprints. By combining EMD with RFF, this paper is able to improve the accuracy of UAV identification under strong interference and low SNR environments, overcoming the lack of identification accuracy of traditional RF fingerprinting methods in noisy environments.
-
3. An optimised statistical classifier is proposed, and the accuracy and robustness of UAV signal classification and recognition in complex electromagnetic environments are significantly improved by the normalisation of feature vectors and cross-validation optimisation.
The subsequent sections of this document are arranged in the following manner: Section 2 illustrates the EMD decomposition algorithm and the method for extracting UAV fingerprint features. Section 3 describes the specific steps of signal preprocessing, the feature extraction process and the configuration of the classifier. Section 4 outlines the experimental findings of this investigation and provides an in-depth analysis and discussion of the results. Section 5 summarises the main findings and contributions of this research, identifies its limitations and discusses future research directions.
2.0 Methods
This paper proposes an innovative method for recognising UAV signals based on RFF, with the overall process depicted in Fig. 2. This method integrates signal preprocessing techniques, feature extraction algorithms and optimised classifier design to significantly enhance the accuracy and reliability of UAV signal recognition.
Overall process of the proposed RFF-based UAV signal recognition method.
Figure 2. Long description
The diagram illustrates the process of the proposed RFF-based UAV signal recognition method. It begins with UAV signals undergoing an adaptive wavelet transform. The transformed signals are then subjected to EMD decomposition as part of the EMD-Welch algorithm. Following this, RFF feature extraction is performed. The extracted features are then passed to a classifier, which ultimately identifies the drones.
In the signal preprocessing stage, an adaptive wavelet signal processing technique is employed. This technique can adjust the wavelet parameters adaptively according to the characteristics of the signal, thereby more effectively filtering out noise interference. By enhancing the SNR, this not only refines the data quality but also establishes a robust basis for feature extraction tasks to follow. The reduction of noise means that the feature extraction process can be more precise, thereby contributing to higher final recognition accuracy. Next is the feature extraction phase, where an improved EMD-Welch algorithm is used. This algorithm can finely decompose UAV RF signals and successfully extract PSD features. These features retain critical information about the signals while greatly simplifying the data complexity, enabling the classifier to process the information more efficiently. Finally, in the classification stage, an optimised SVM classifier is utilised. By adjusting the parameters of the classifier and combining the previously extracted features, efficient classification of UAV signals is achieved. This optimisation not only enhances classification accuracy but also improves system robustness, ensuring that the proposed method can operate stably in various complex environments.
Adaptive filter based on wavelet transform.
Figure 3. Long description
The diagram illustrates an adaptive filter system based on wavelet transform. The input signal x[n] undergoes wavelet denoising to produce a cleaned signal S[n]. This signal is then processed through multiple levels, from Level 1 to Level 5. Each level’s output is weighted by factors w1, w2, and w5, respectively. These weighted outputs are summed to produce the output signal Y[n]. The error signal E[n] is calculated by subtracting Y[n] from the input signal x[n]. This error signal is fed into a Least Mean Squares (LMS) block, which adjusts the weights w1, w2, and w5 to minimize the error.
2.1 Adaptive denoising algorithm based on the Morlet wavelet
The UAV RF signal is significantly affected by a multi-path effect and electromagnetic interference. This paper proposes an adaptive denoising method based on the Morlet wavelet, and the filter principle is shown in Fig 3. The main idea of this approach is to use the multi-scale characteristics of the wavelet transform to decompose the signal into multiple levels and then perform threshold processing on the wavelet coefficients at different levels to achieve denoising. It is important to distinguish the unwanted noise from the hardware-specific fingerprints that enable device identification. The fingerprints arise from inherent imperfections in the UAV’s transmitter (e.g. oscillator drift) and are stable over time. Noise refers to random disturbances independent of device identity, such as multi-path effects and thermal noise. The proposed wavelet denoising is designed to suppress only the noise while preserving the fingerprints by exploiting the multi-scale correlation: fingerprint features correlate across scales, whereas noise does not. The detailed procedure is outlined below:
-
1. Selection of Wavelet Basis: Choose the Morlet wavelet as the wavelet basis function and set a five-level wavelet decomposition. Perform a wavelet transform on the I/Q data of the UAV to obtain the wavelet detail coefficients dj, k at each level.
-
2. Adaptive Threshold Determination: Automatically determine the adaptive threshold using the least mean square (LMS) algorithm based on the noise intensity. Utilise the threshold function to refine the wavelet detail coefficients, thereby obtaining the enhanced wavelet detail coefficients.
-
3. Signal Reconstruction: Use the processed wavelet detail coefficients to reconstruct the signal, obtaining the denoised I/Q signal data of the UAV. This process can be represented by the following formula:
(1)
\begin{align} x'(t) = \sum\limits_j {\sum\limits_k {{{\bar d}_{j,k}}{\psi _{\alpha ,\,\beta }}(t)}} \end{align}
Here is an instance of the wavelet basis function, used to reconstruct the signal at specific scales and positions. α represents the scale parameter, and β represents the translation parameter.
2.2 Improved EMD decomposition algorithm
In this paper, an improved algorithm based on EMD and combining with spectral kurtosis is used to improve the accuracy of signal decomposition and the effect of fault feature extraction. The EMD method itself is an adaptive signal decomposition technique, which is able to decompose a non-smooth signal into a series of intrinsic modal components (intrinsic mode function (IMF)), but in practice, EMD may face problems such as mode aliasing and endpoint effects. To overcome these shortcomings, spectral kurtosis analysis plays a key role, which leads to a more accurate decomposition of the signal and can effectively extract useful feature information from complex UAV RF signals.
2.2.1 Overview of the EMD algorithm
The EMD method decomposes a complex non-smooth signal into components at multiple frequency levels by extracting the IMF of the signal step by step. Each order IMF component represents a different feature in the signal, usually including high-frequency noise and low-frequency trend components.
-
1. Envelope calculation
First, determine the local maximum and minimum points of the signal, and then connect the local maximum points into the upper envelope and the local minimum points into the lower envelope through the cubic spline curve. The upper and lower envelopes contain all the data points. Next, the mean value of the upper and lower envelopes is calculated, which can be expressed as [Reference Nandi and Subba Reddy16]:
(2)
\begin{align} m(t) = (U(t) + L(t))/2 \end{align}
The new signal h1(t) is obtained by subtracting the mean value from the original signal and determining whether the signal satisfies the conditions of the IMF, which can be expressed as:
(3)
\begin{align} {h_1}(t) = x(t) - m(t) \end{align}
-
2. IMF decomposition
If the signal h1(t) satisfies the conditions of IMF (i.e. the number of extreme and zero intersection points is equal and the mean value of the envelope is close to zero), it is taken as the first IMF component C1(t). The iterative process continues for the remaining signal r1(t) = x(t) – m(t) to extract more IMF components.
-
3. Signal reconstruction
Ultimately, the original signal x(t) is represented as a sum of the individual IMF components and residuals [Reference Nandi and Subba Reddy16]:
(4)where C1(t) is the ith IMF component and rn(t) is the residual term.
\begin{align} x(t) = \sum\nolimits_{i = 1}^n {{c_i}(t) + {r_n}(t)} \end{align}
2.2.2 Improvement of correlation number and spectral kurtosis
In order to enhance the decomposition of EMD, this paper introduces the analysis of the correlation coefficient [Reference Zhao, Chen and Wei17] and the spectral kurtosis. The correlation coefficient is used to measure the similarity between each IMF component and the original signal, while the spectral kurtosis value helps to identify the shock components in the signal. These two metrics help to filter out those IMF components that reflect the signal characteristics and contain valid RF fingerprint information.
-
1. Introduction of correlation number
The correlation number is used to measure the similarity between two signals, especially the relationship between the IMF component and the original signal. The larger the correlation number, the higher the similarity between that IMF component and the original signal, which may contain more useful signal information. Therefore, the correlation number is used as a key criterion for screening valid IMF components. The correlation coefficient is calculated by the formula [Reference Zhao, Chen and Wei17]:
(5)where x(i) and
\begin{align} CIMF({\xi _n}) = \frac{{\sum\nolimits_{i = 1}^N {(x(i) - \overline x )({\xi _n}(i) - \overline {{\xi _n}} )} }}{{\sqrt {\sum\nolimits_{i = 1}^N {{{(x(i) - \overline x )}^2}\sum\nolimits_{i = 1}^N {{{({\xi _n}(i) - \overline {{\xi _n}})}^2}}}}}} \end{align}
$\xi$
n(i) denote the original signal x(t) and the ith sample of the nth IMF component
$\xi$
n, xand
$\xi$
n are the mean values of the signals x(t) and
$\xi$
n, respectively, and N is the number of samples of the signal.
The calculated intercorrelation number is between −1 and 1, with values closer to 1 indicating that the two signals are more similar. In the algorithm, when the intercorrelation number is greater than a set threshold, it means that the IMF component better reflects the characteristics of the original signal and should be retained for subsequent analysis.
-
2. Introduction of spectral kurtosis
Spectral kurtosis is an important metric used to measure the suddenness or shock characteristics of a signal. It evaluates the sharpness of a signal through the energy distribution at each frequency point in the frequency domain. By calculating the spectral kurtosis of the IMF component, frequency bands with strong shock characteristics can be effectively identified, which is especially important for fault characterisation. The formula for calculating the spectral kurtosis is [Reference Xiang, Li and Wang18]:
(6)where S2(f) and S4(f) denote the second-order and fourth-order instantaneous power spectral accumulations of the signal in the frequency domain, respectively, as follows:
\begin{align} {K_Y}(\,f) = \frac{{{S_4}(\,f)}}{{S_2^2(\,f)}} - 2 \end{align}
(7)where H(t, f) is the time-varying transfer function of the complex envelope of the signal
\begin{align} \left\{ \begin{array}{l}{S_{\rm{2}}}(\,f) = {\displaystyle\int_{ - \infty }^\infty {\left| {H(t,\,f)} \right|} ^2}df \\[6pt]{S_4}(\,f) = {\displaystyle\int_{ - \infty }^\infty {\left| {H(t,\,f)} \right|} ^4}df\end{array} \right.\end{align}
$\xi$
n, obtained by a short-time Fourier transform.
Spectral kurtosis highlights the changing characteristics of a signal’s spectrum by analysing the signal’s components in the frequency domain. In the identification of RF signals, a higher spectral kurtosis value usually means that the signal contains more unique spectral distribution features, which is especially important for identifying different signal sources. For each IMF component, after calculating its spectral kurtosis, the IMF components with spectral kurtosis greater than a threshold value are filtered out to improve the extraction of RF fingerprint features.
Algorithmic pseudo-code.
Figure 4. Long description
The image displays an algorithm titled Improved EMD Algorithm with Cross-Correlation and Spectral Kurtosis. The algorithm takes an original signal x(t) and threshold values for cross-correlation and spectral kurtosis as inputs. It also requires the number of IMFs to select Nf and the population size for selection of IMFs Npo. The algorithm initializes the input signal and performs EMD decomposition to get initial IMFs. It then initializes a valid IMF list and enters a loop that continues until a convergence criterion is met. Within the loop, for each IMF, it calculates the cross-correlation between the IMF and the original signal, computes the cross-correlation coefficient, and calculates the spectral kurtosis of each IMF. If the cross-correlation and spectral kurtosis exceed the thresholds, the IMF is added to the valid IMF list. The loop breaks when the length of the valid IMF list meets or exceeds Nf. The valid IMF list is then updated with the best Nf IMFs based on cross-correlation and kurtosis. Finally, the signal is reconstructed from the selected IMFs and returned.
2.2.3 Improved EMD algorithm flow
The improved EMD algorithm mainly includes the steps of signal decomposition, feature screening and signal reconstruction. Through the introduction of the number of interrelationships and spectral kurtosis analysis, it can screen those components that best reflect the signal features from the IMF components obtained from the decomposition, so as to improve the reconstruction accuracy of the signal. The specific algorithm flow is as follows:
-
1. Signal preprocessing and EMD decomposition
First, the original signal x(t) is obtained, and its EMD decomposition is performed to obtain multiple IMF components. Each IMF component represents a different frequency feature in the signal, which usually includes high-frequency noise and low-frequency trend components. The purpose of EMD decomposition is to decompose a complex non-smooth signal into a series of IMFs for further analysis and feature extraction.
-
2. Correlation coefficient and spectral kurtosis calculation
For each IMF component, the inter-correlation number and the spectral kurtosis value between it and the original signal are calculated. The correlation number is used to evaluate the similarity between the IMF component and the original signal, while the spectral kurtosis is used to measure the variability of the IMF component’s frequency domain features. Based on these two metrics, it is possible to filter those IMF components that have high similarity to the original signal and contain meaningful spectral features.
-
3. IMF screening and updating of effective IMFs
Valid IMF components are screened according to the threshold conditions of the number of correlations and spectral kurtosis. If the number of interrelationships and spectral kurtosis of an IMF component are greater than the set threshold, the IMF component is considered to contain valid signal features and should be retained for signal reconstruction. In this way, irrelevant IMF components can be removed, and the parts with distinctive features can be retained.
-
4. Signal reconstruction
Finally, an optimised version of the original signal is reconstructed by summing the filtered valid IMF components. The reconstructed signal will contain more effective feature information, especially in the RF fingerprint signal recognition task, which can effectively improve the classification and recognition accuracy of the signal.
The pseudo-code of the algorithm is shown in Fig. 4. First, EMD decomposition of the original signal is performed to obtain the IMF components. Second, the number of correlations between each IMF component and the original signal is computed to evaluate the similarity between them. Then, the spectral kurtosis of each IMF component is calculated to identify the feature variations in the frequency domain. Finally, the valid IMF components are filtered based on the thresholds of the number of interrelationships and the spectral kurtosis, and the signal is reconstructed by summing the valid IMF components.
In this section, the improved EMD algorithm is introduced, which improves the traditional EMD decomposition by introducing the mutual correlation number and the spectral kurtosis value, ensuring that the extracted intrinsic modal components truly reflect the signal characteristics, improving the quality of the signal decomposition and providing a reliable basis for subsequent feature extraction and identification.
2.3 Drone RF fingerprint extraction
The UAV RF fingerprints are extracted by analysing the random defects generated during the production process of wireless transmitting devices. These imperfections originate from small variations in electronic components (e.g. capacitors, resistors, transistors, etc.) during the production process, in addition to factors such as the operating environment of the device, temperature variations and the aging of the components, which also have an impact on the RF signal. These imperfections are manifested in the signals as features such as frequency drift, phase shift and clock offset, thus making the RF signal unique to each device. By analysing the frequency domain features of the signal, especially the PSD, the device-specific RF fingerprints can be extracted, thus enabling accurate device identification. Therefore, the PSD is selected as the primary fingerprint feature because it captures the subtle frequency-domain variations caused by hardware imperfections, is robust to noise and is independent of modulation schemes.
In this paper, PSD is used as the main RF fingerprint feature. PSD can reflect the overall frequency domain characteristics of the signal and can better capture the long time variation of the signal compared to the transient features. At the same time, PSD does not depend on a specific modulation method, has wide applicability and is relatively simple to calculate, making it suitable for real-time monitoring.
2.3.1 Feature extraction
Welch’s algorithm is employed to estimate the PSD of the reconstructed signal obtained after improved EMD processing [19]. The algorithm proceeds as follows: the signal is first segmented into overlapping windows of length 1,024 samples (approximately 20 ms at 40 MHz sampling rate), with a 50% overlap between consecutive segments to reduce variance in the estimate. Each segment is multiplied by a Hamming window, defined as
$\omega (n) = 0.54 - 0.46\cos (2\pi n/(L - 1))$
for
$n = 0,1, \ldots ,L - 1$
with L = 1,024. The Hamming window is chosen because it provides a good trade-off between main lobe width (frequency resolution) and side lobe attenuation (spectral leakage suppression), which is essential for accurately capturing the fine frequency-domain features that distinguish different UAV hardware.
After windowing, a fast Fourier transform (FFT) is applied to each segment, and the squared magnitude of the FFT coefficients is computed to obtain the periodogram for that segment. The final PSD estimate is obtained by averaging the periodograms across all segments, which reduces noise and variance. The resulting PSD is a vector of power values at discrete frequencies, covering the 40 MHz bandwidth. This PSD vector serves as the RF fingerprint feature for classification. The use of PSD is motivated by its ability to capture device-specific hardware imperfections (e.g. oscillator drift, power amplifier nonlinearities) that manifest as subtle variations in the spectral distribution, while being robust to transient noise and independent of the specific modulation or protocol used by the UAV.
The detailed steps for signal PSD estimation using Welch’s algorithm are given below.
-
1. Fourier transform
The Fourier transform performs an (FFT) on each windowed sub-segment of the EMD decomposed signal, converting it from the time domain to the frequency domain. The FFT is an efficient algorithm for calculating the discrete Fourier transform (DFT), which results in complex numbers that represent the magnitude and phase information of the signal at different frequencies. The transform equation can be expressed as:
(8)where
\begin{align} X(\,f) = F\{ {x_\omega }(n)\} \end{align}
$\omega$
(n) is the signal after windowing, F denotes the Fourier transform and X(f) is the frequency domain signal. Specifically, given a discrete signal x(n) of length N (where n is the sampling point in the time series, n = 0, 1, 2, …, N−1), the formula for its Fourier transform can be expressed as:(9)where X(k) is the complex value of the signal in the frequency domain, representing the magnitude and phase at the kth frequency point. x(n) is the sampled value of the signal in the time domain. k is the frequency index, corresponding to the N frequency points.
\begin{align} X({\rm{k}}) = \sum\limits_{n = 0}^{N - 1} {x(n) \cdot {e^{ - j\frac{{2\pi }}{N}kn}}} \end{align}
-
2. Power calculation
Let the length of a UAV signal segment be M. For each output frequency point of the FFT, the square of its mode, i.e. the power at that frequency point, is calculated. The power of all sub-segments at the same frequency point is averaged to obtain an estimate of the PSD at that frequency point. The power spectrum of the segment can then be expressed as:
(10)where Px(f) is the PSD and Xm(f) is the spectrum of the mth segment.
\begin{align} {P_x}(\,f) = \frac{1}{M}{\left| {\sum\limits_{m = 0}^{M - 1} {{X_m}(\,f)} } \right|^2} \end{align}
-
3. The role of the window function
The window function reduces the spectral leakage, which allows the signal energy to leak from its dominant frequency to other frequencies. The window function
$w(n)$
is multiplied point by point with the sub-segment signals, thus weighting the signal in the time domain [Reference Xiong, Song and Su20]. The window function is used to weight the signal and thus reduce the spectral leakage. The window function is multiplied point by point with the signal segments, which makes the transition between the two ends of the signal smoother and avoids the leakage of signal energy. The specific window function processing formula is:(11)where
\begin{align} {x_\omega }(n) = x(n) \cdot \omega (n) \end{align}
$\omega$
(n) is the window function,
${x}\omega$
(n) is the signal after adding the window.
-
4. Improved Welch algorithm
According to the literature [Reference Zhao, Chen and Wei17], the Welch algorithm has been improved in terms of discretisation assessment and spectral variations, making it possible to further improve the accuracy of power spectrum estimation in the presence of noise. The effect of noise on spectrum estimation is reduced by spectral averaging of multiple overlapping signal segments, resulting in a smoother and more reliable power spectrum.
Through the above steps, the Welch algorithm is able to accurately extract the PSD of the signal, a feature that reflects the overall frequency domain characteristics of the signal. As the main feature of RFF, the PSD can effectively capture the unique characteristics of the device RF signal, which lays the foundation for the subsequent classifier design and device identification.
2.3.2 Feature classification
In the extraction process of UAV RFF, the extracted frequency domain features provide key data for subsequent device identification. However, how to effectively transform these features into accurate identification results relies on designing efficient and innovative classifiers. To this end, this paper adopts a classification framework based on traditional machine learning models and optimises it to improve the accuracy and real-time recognition of UAV devices.
SVM distinguishes different classes of data by constructing an optimal hyperplane, which is particularly suitable for high-dimensional data. To improve the performance of SVM, this paper adopts a radial basis function (RBF) kernel, which is capable of handling complex nonlinear data. The RBF kernel has been widely used in RF fingerprint classification due to its flexibility and effectiveness in capturing nonlinear relationships between features.
Parameter information of the DroneRF dataset
Table 1. Long description
The table presents the parameter information of the DroneRF dataset. It contains five rows and two columns. The first row details the dataset name as DroneRF. The second row indicates the source as publicly available and referenced in a specific document. The third row describes the content, which includes 227 RF recording segments collected from three different UAVs and background RF activity recordings. The fourth row explains the structure, stating that the dataset is divided into two parts: UAV present and UAV absent, each containing multiple RF recording segments. The fifth row mentions the data volume, which is over 40 gigabytes of RF data.
3.0 Experiments
In this study, the publicly available DroneRF dataset [Reference Al-Sa’d21] was used for the experiments. Gathered by intercepting the transmissions between UAVs and their control units, this dataset covers a frequency range of 1.2 to 6 GHz and includes a bandwidth of 40 MHz. The DroneRF dataset includes RF signals from various UAVs under different operating conditions, including the RF background signals of the UAVs and the RF signals of the UAVs connected to controllers. Figure 6 shows the classification structure of the DroneRF dataset, detailing the classification of RF signals from different types of UAVs within the dataset. The parameter information of the dataset is provided in Table 1.
Classification structure of the DroneRF dataset.
Figure 5. Long description
The flowchart illustrates the classification structure of the DroneRF dataset. At the top, the dataset is divided into four categories: None drone, Bebop drone, AR drone, and Phantom drone. Each category branches out to a specific label: None drone leads to None, Bebop drone leads to UAV1, AR drone leads to UAV2, and Phantom drone leads to UAV3. The flowchart visually represents the hierarchical organization of the dataset, showing how different types of drones are categorized and labeled within the DroneRF dataset.
Comparison of original and wavelet-denoised UAV time-domain waveforms (0–1.75 ms). The blue curve represents the raw signal, and the red curve shows the signal after the adaptive wavelet transform.
Figure 6. Long description
The line graph displays two data lines representing UAV time-domain waveforms over a duration of 01.75 milliseconds. The x-axis is labeled ’Time (s)’ and ranges from 0.00025 to 0.00175 seconds. The y-axis ranges from -6000 to 6000. The blue line represents the original signal, while the red line shows the signal after adaptive wavelet transforms. The graph illustrates the denoising effect of the wavelet transform on the UAV signal, with the red line generally following the blue line but with reduced noise. All values are approximated.
As shown in Fig. 5, the DroneRF dataset is divided into four main categories: No Drone, Bebop Drone, AR Drone and Phantom Drone. The specific RF signals corresponding to each category are labelled as None, UAV1, UAV2 and UAV3, respectively. The No Drone category contains RF background signals when there is no UAV present, while the other three categories correspond to the RF signals of different types of UAVs when connected to their controllers. This classification structure allows for the effective labelling of different types of UAV signals, facilitating subsequent feature extraction and classification experiments.
It should be noted that each drone model in the DroneRF dataset corresponds to a single physical unit. Therefore, the classification task in this study is to distinguish between drone types (models) rather than between individual devices of the same model.
3.1 Signal preprocessing
3.1.1 Adaptive wavelet transform
Figure 6 illustrates a comparison plot of the UAV signal in its original state and after an adaptive wavelet transform.
Figure 6 illustrates a comparison of the original UAV signal and the signal after adaptive wavelet denoising over a 0–1.75 ms time window. The blue curve represents the raw signal, while the red curve shows the denoised signal. The original signal, sampled at 40 MHz with a central frequency of 2.4 GHz, exhibits evident periodic features and noise components. After applying the adaptive wavelet transform, the noise is effectively suppressed while the important signal characteristics are preserved, resulting in a smoother and clearer waveform, which facilitates more accurate recognition and classification of different UAV operating modes.
3.1.2 EMD decomposition
In Section 3.1.1, this paper demonstrated the effectiveness of a wavelet transform in signal denoising and feature extraction by comparing the original UAV signal with the signal processed by the adaptive wavelet transform. However, while a wavelet transform performs well in handling linear and approximately linear signals, it has certain limitations when dealing with the complex nonlinear and non-stationary components of UAV signals. To further enhance the accuracy and depth of signal analysis, this paper employs the EMD method.
The EMD is an advanced adaptive method for signal processing that breaks down intricate signals into a collection of IMFs, each carrying meaningful physical information. These IMFs can reflect the local characteristics and multi-scale information of the signal, providing richer signal analysis capabilities compared to the wavelet transform. This paper applies EMD decomposition to the I/Q data of UAVs, focusing on the first ten IMF components (IMF1 to IMF10). Using the algorithm described in Section 2.2 and iterative calculations from Equations (1) to (5), the 2.4 GHz control signals of UAV1 and UAV3 are decomposed into their IMF components (n = 10), as shown in Fig. 7.
(a) Original signal and the first ten IMF components of UAV1. (b) Original signal and the first 10 IMF components of UAV3.
Figure 7. Long description
The image contains two sets of graphs labeled (a) and (b). Each set includes an original signal and its first ten intrinsic mode function (IMF) components. The graphs in set (a) represent the original signal and the first ten IMFs of UAV1, while the graphs in set (b) represent the original signal and the first ten IMFs of UAV3. Each graph plots amplitude against time in milliseconds. The original signals are shown at the top of each set, followed by the ten IMF components below. The amplitude values vary across the components, with each IMF displaying distinct frequency and amplitude characteristics. The graphs illustrate the decomposition of the original signals into their constituent IMFs, highlighting the different frequency components present in the signals. All values are approximated.
By analysing Fig. 7, we can observe the characteristic differences of different UAVs in each IMF component. The original signals of UAV1 and UAV3, both recorded at a central frequency of 2.4 GHz and a sampling frequency of 40 MHz, contain evident periodic components and noise. Through EMD decomposition, the signals of UAV1 and UAV3 are decomposed into the first ten IMF components. IMF1 contains more high-frequency noise components; IMF2 to IMF5 exhibit mid-to-high-frequency characteristics of the signal; IMF6 to IMF10 mainly represent low-frequency components and trend changes of the signal. These decomposition results provide a reliable data foundation for further UAV feature extraction.
This section describes the adaptive wavelet transform technique in the signal preprocessing stage, which removes the noise from the signal through multi-scale processing, improves the SNR of the signal and provides a clean signal base for subsequent feature extraction.
3.2 Feature extraction
This section focuses on extracting power spectral features from UAV signals for further UAV detection and classification. Power spectral features provide information about the signal in the frequency domain, helping to identify the RF characteristics of different UAVs. Based on the EMD decomposed IMF functions, this paper uses the Welch algorithm to extract the PSD and observe the power distribution characteristics of UAV RF signals at different frequencies. Power spectral features were extracted from the signals of UAV1 and UAV3. The specific process and results of power spectral feature extraction are detailed below.
Firstly, the signals of UAV1 and UAV3 were subjected to power spectral analysis, and the average power spectrum values were calculated using Equation (10). Figure 9 presents the visual representation of the PSD of UAV1 and UAV3.
From Fig. 8, it can be observed that UAV1 and UAV3 exhibit significant differences in their frequency domain characteristics. UAV3 shows higher PSD in certain frequency bands, while UAV1 displays different characteristics in other bands.
PSD of UAV1 and UAV3.
Figure 8. Long description
A line graph compares the power spectral density of two unmanned aerial vehicles, UAV1 and UAV3, across a frequency range from 0 to 20 megahertz. The x-axis represents frequency in megahertz, ranging from 0 to 20, while the y-axis represents power spectral density in decibels per hertz, ranging from 10 to the power of negative 7 to 10 to the power of negative 5. The graph features two data lines: one in blue for UAV1 and one in red for UAV3. The blue line for UAV1 shows relatively lower and more consistent power spectral density values across the frequency range, with minor peaks around 5 and 17.5 megahertz. The red line for UAV3 exhibits higher and more variable power spectral density values, with significant peaks around 5, 10, and 15 megahertz. All values are approximated.
For a more detailed analysis, the following features were extracted from the power spectra of UAV1 and UAV3: mean PSD, variance, peak frequency and bandwidth. Table 2 presents the results of the power spectral feature extraction for UAV1 and UAV3. UAV1 has a mean PSD of 0.0213 dB/Hz, a variance of 0.0014, a peak frequency of 10.0 MHz and a bandwidth of 1.40625 MHz. In contrast, UAV3 has a mean PSD of 0.0035 dB/Hz, a variance of 0.000014, a peak frequency of 10.5859375 MHz and a bandwidth of 8.4375 MHz.
Power spectral feature extraction results for UAV1 and UAV3
Table 2. Long description
The table presents a comparison of power spectral features extracted from UAV1 and UAV3. It consists of two columns labeled UAV1 and UAV3, and four rows labeled Mean PSD, Variance, Peak frequency, and Bandwidth. UAV1 has a mean PSD of 0.0213 decibels per hertz, a variance of 0.0014, a peak frequency of 10.0 megahertz, and a bandwidth of 1.40625 megahertz. In contrast, UAV3 has a mean PSD of 0.0035 decibels per hertz, a variance of 0.000014, a peak frequency of 10.5859375 megahertz, and a bandwidth of 8.4375 megahertz.
By experimentally comparing the power spectral features of UAV1 and UAV3, this paper identified significant differences in their frequency domain characteristics. UAV1 exhibits a higher and more variable signal energy distribution, with the main frequency components concentrated in a narrower frequency band. Conversely, UAV3 has a more uniform signal energy distribution and a broader range of frequency components. The extraction and analysis of these features provide important foundations for further UAV signal detection and classification.
In the feature extraction section, this section describes how the PSD is computed by Welch’s algorithm based on the signal after EMD decomposition to further extract the frequency domain features reflecting the signal characteristics. This process provides strong feature support for UAV identification.
3.3 Classifier setup
In the classifier setup, this paper selects the SVM as the classifier from statistical classifiers and optimises its parameters. SVM seeks the optimal hyperplane in a high-dimensional space to maximise the margin between different classes of samples, thereby achieving classification. This study uses an SVM equipped with an RBF kernel, which can handle non-linearly separable cases.
Prior to classification, the extracted PSD feature vectors are normalised to zero mean and unit variance based on the training set statistics. This normalisation ensures that all frequency components contribute equally to the classifier’s decision and prevents features with larger numerical ranges from dominating the distance calculations in the SVM.
To further enhance the model’s performance and ensure robust evaluation, a five-fold cross-validation strategy is employed. The entire dataset is randomly partitioned into five folds; in each iteration, four folds are used for training and the remaining fold for validation. The process is repeated five times, and the validation results from all folds are aggregated to compute several evaluation metrics: overall accuracy, per-class confusion matrices, receiver operating characteristic (ROC) curves and the area under the ROC curve (AUC). Accuracy provides a global measure of correct predictions, while confusion matrices reveal classification details for each class. ROC curves and AUC assess the classifier’s discriminative ability across different thresholds.
Hyperparameter optimisation is performed via grid search over the parameter space
$c \in \{ {2^3},{2^4}, \ldots ,{2^9}\} $
and
$r \in \{ {2^3},{2^4}, \ldots ,{2^9}\} $
. For each combination of C and γ, the five-fold cross-validation accuracy is computed, and the combination yielding the highest average accuracy is selected as optimal. For the binary classification task (drone vs. no drone), the optimal parameters were
$c = {2^5}$
and
$r = {2^3}$
; for the quaternary classification task (four drone models), the optimal parameters were
$c = {2^6}$
and
$r = {2^4}$
.
After identifying the optimal hyperparameters, the final SVM model is trained on the entire training set using these parameters. Its performance is then evaluated on the held-out test set (or using cross-validation results) to obtain the metrics reported in Section 4 (accuracy, confusion matrices, ROC curves). The implementation was carried out using the LIBSVM library . The parameters of the classifier and their descriptions are summarised in Table 3.
Parameters of the classifier
Table 3. Long description
The table presents the parameters of a classifier, detailing their descriptions and value ranges. It consists of three columns: Parameter, Description, and Value range. The Parameter column lists the names of the parameters, which are C and r. The Description column provides explanations for each parameter. For instance, C is described as a regularization parameter that controls the complexity of the model and overfitting, with larger values tending to make the model overfit and smaller values helping prevent overfitting. The r parameter is described as controlling the influence range of a single training sample for the RBF kernel, with larger values making the model more complex and smaller values making it smoother. The Value range column specifies the range of values for each parameter, which is 2 to the power of 3 to 2 to the power of 9 for both C and r.
This section describes in detail the design of the classifier, which employs a statistical type classifier and further improves the accuracy and robustness of the classification by optimising the hyperparameters (C and gamma) to ensure the stability and reliability of the whole recognition system.
4.0 Results and discussion
The proposed method demonstrates excellent performance in UAV recognition and classification. In detecting the presence of UAVs, the method achieved a remarkable accuracy of 97%. This result indicates that the proposed method is highly reliable in determining whether a UAV is present. In terms of identifying specific UAV models, the method also performed well. Compared to traditional classifiers such as K-nearest neighbours (KNN) and SVM, the proposed method achieves higher accuracy in UAV model recognition. Experimental results show that our method reaches 84.7% accuracy, demonstrating its effectiveness in addressing intricate classification challenges.
Confusion matrix of cross-validation. (a) Confusion matrix of the first cross-validation. (b) Confusion matrix of the second cross-validation. (c) Confusion matrix of the third cross-validation. (d) Confusion matrix of the fourth cross-validation. (e) Confusion matrix of the fifth cross-validation.
Figure 9. Long description
The image displays five confusion matrices representing cross-validation results for UAV identification. Each matrix compares true labels against predicted labels for UAV1, UAV2, UAV3, and None. The matrices show varying levels of accuracy and misclassification across different cross-validation sets. Matrix (a) shows UAV1 with 0.64 accuracy, UAV2 with 0.76, and UAV3 with 0.85. Matrix (b) shows UAV1 with 0.67 accuracy, UAV2 with 0.75, and UAV3 with 0.92. Matrix (c) shows UAV1 with 0.7 accuracy, UAV2 with 0.75, and UAV3 with 0.92. Matrix (d) shows UAV1 with 0.72 accuracy, UAV2 with 0.66, and UAV3 with 0.87. Matrix (e) shows UAV1 with 0.66 accuracy, UAV2 with 0.82, and UAV3 with 0.83. Each matrix includes a color gradient indicating the proportion of correct and incorrect classifications.
To visually demonstrate the classification results, five-fold cross-validation was conducted, and a confusion matrix of the classification process was plotted. Figure 9 presents the confusion matrix for the classification process. From these matrices, it is evident that the classification accuracy for each category is high. Samples from the ‘No drone’ class were correctly classified with a recall of approximately 70%, while drone samples (UAV1, UAV2, UAV3) were classified with high accuracy (over 90% in most folds). Additionally, the classification results for UAV2 and UAV3 were also satisfactory, with low misclassification rates. This indicates that the proposed method performed consistently well from the first to the fifth cross-validation. This stability in accuracy for the four-class classification problem of UAV signals highlights the robustness and reliability of the proposed method. The relatively low misclassification rates between different categories further validate the method’s stability and accuracy.
To further evaluate the performance of the classifier, ROC curves for each category were plotted, and the AUC values were calculated. The ROC curves and their corresponding AUC values are shown in Fig. 10. From Fig. 10, it can be seen that the classifier’s recognition performance varies across different categories. Class 0 (None) has an AUC of 0.71, indicating that the classifier’s performance in recognising the absence of a UAV is moderate. Class 1 (UAV1) has an AUC of 0.77, suggesting that the classifier performs well in recognising the Bebop Drone. Class 2 (UAV2) has an AUC of 0.85, showing good recognition performance for the AR Drone. Class 3 (UAV3) has an AUC of 0.95, indicating excellent recognition performance for the Phantom Drone. The average AUC value is 0.84, demonstrating that the classifier performs well overall.
Performance comparison
Table 4. Long description
The table presents a performance comparison of various technologies used in binary and multi-drone classification. It includes five rows and four columns. The columns are labeled ’Reference’, ’Main technology’, ’Binary classification’, and ’Multi-drone classification’. Each row lists a different reference, the main technology used, and the corresponding percentages for binary and multi-drone classification. The references include [22], [12], [23], [24], and ’This work’. The main technologies listed are ’energy-time domain+RF’, ’square integrated bispectra+RFF’, ’ML + RFF + DT’, ’FM signal’, and ’EMD + PSD + RFF’. The binary classification percentages range from 84.00% to 97.00%, and the multi-drone classification percentages range from 80.00% to 93.5%. Notable trends include ’This work’ achieving the highest binary classification percentage at 97.00% and the highest multi-drone classification percentage at 84.7%. The table provides a clear comparison of the effectiveness of different technologies in drone classification tasks.
ROC curves.
Figure 10. Long description
A line graph titled Receiver Operating Characteristic (ROC) Curves displays the true Positive Rate on the y axis and the false Positive Rate on the x axis. The graph includes multiple data lines representing different classes. The ROC curve of class 0 is shown in cyan with an area of 0.71. The ROC curve of class 1 is depicted in yellow with an area of 0.77. The ROC curve of class 2 is illustrated in blue with an area of 0.85. The ROC curve of class 3 is represented in red with an area of 0.95. Additionally, a micro-average ROC curve is shown in pink with an area of 0.84. All values are approximated.
It is worth noting that while the overall binary classification accuracy reaches 97%, the AUC for the ‘No drone’ class (Class 0) is 0.71. This apparent discrepancy can be explained by two factors. First, accuracy is a global metric that reflects performance across all samples, while AUC measures the classifier’s ability to distinguish a specific class from the others. Second, the DroneRF dataset contains fewer ‘No drone’ samples compared to drone samples, creating a class imbalance. As shown in the confusion matrices (Fig. 9), the ‘No drone’ class has a recall of approximately 70%, meaning that some background RF signals are misclassified as drones. This contributes to the lower AUC while still allowing high overall accuracy, as the majority class (drones) is correctly classified. Future work will explore techniques such as class weighting or synthetic sampling to further improve the recognition of background signals.
Table 4 presents a comparative analysis of various UAV detection methods. In binary classification (drone vs. no drone), the proposed EMD + PSD + RFF method achieves 97.0% accuracy, which is slightly higher than the 96.30% reported in Ref. [Reference Ezuma, Erden, Anjinappa, Ozdemir and Guvenc22] and 96.11% in Ref. [Reference Nie12]. While this improvement is modest, it demonstrates that the proposed method performs competitively in basic drone detection tasks.
In multi-drone classification (distinguishing between different drone models), the proposed method achieves 84.7% accuracy. This result is comparable to the 83.59% reported in Ref. [Reference Zuo, Xie, Zhang and Yang23] and higher than the 80.00% in Ref. [Reference Ye24]. However, it is lower than the 88.15% in Ref. [Reference Ezuma, Erden, Anjinappa, Ozdemir and Guvenc22] and 93.5% in Ref. [Reference Nie12]. Several factors may contribute to these differences, including variations in dataset splits, feature extraction approaches and classifier configurations. A direct comparison should therefore be interpreted with caution.
Importantly, the contribution of this work extends beyond raw classification accuracy. The proposed method is specifically designed to improve robustness in low SNR environments and under complex interference conditions – scenarios where traditional methods often degrade significantly. The adaptive wavelet denoising and improved EMD-based feature selection aim to preserve hardware-specific fingerprints while suppressing environmental noise, as discussed in Sections 2.1 and 2.2. This focus on robustness, rather than marginal gains in clean-signal accuracy, distinguishes the proposed approach from existing methods.
5.0 Conclusion
This paper proposes a UAV recognition method based on improved EMD and RFF. This method preprocesses the signal using an adaptive wavelet filter, decomposes the UAV signal with the improved EMD, and extracts PSD features as RFF using the Welch algorithm. Then, a statistical classifier SVM with hyperparameters optimised by grid search is employed to recognise the UAVs. The experimental results demonstrate that RFF features perform excellently in UAV signal classification tasks. During validation, the average accuracy for binary classification reached 97%, the average accuracy for four-class classification was 84.7% and the AUC value for UAV3 classification reached 0.95. These findings suggest that the introduced technique demonstrates exceptional dependability and stability in addressing intricate UAV signal classification challenges.
Despite the promising results, this study has some limitations that warrant further investigation. First, the DroneRF dataset contains only a single physical unit per drone model, restricting the current work to type-level identification. Future research should collect datasets with multiple units of the same model to enable device-level recognition. Second, the method’s robustness under lower SNR conditions and against various interference types should be systematically evaluated. Third, exploring deep learning classifiers, such as convolutional neural networks (CNNs), could potentially improve feature extraction and classification performance. Finally, class-balancing techniques (e.g. synthetic sampling) may be employed to enhance the recognition of background signals, addressing the current class imbalance issue.
