Overview of Radio Frequency Fingerprint Extraction in Specific Emitter Identification（in English）

1. Introduction

Specific Emitter Identification (SEI), also known as Radio Frequency Fingerprinting (RFF), was first proposed by Northrop Grumman of the United States in the 1960s^[1]. It refers to the technology of extracting information reflecting a transmitter’s identity (referred to as a “radio frequency fingerprint”) by only using the external characteristics of the received signal and comparing the fingerprint information with a database, thereby determining the specific emitter. The fingerprint of an emitter is an inherent characteristic of the hardware of the transmitting device, which is unforgeable, unavoidable, and unchangeable. Moreover, it a weak signal is attached to the transmitting signal in the form of unintentional modulation.

SEI technology has a unique role in identifying specific originating individuals and has attracted widespread attention in the fields of spectrum management, network security, cognitive radio, and electronic countermeasures. Particularly, in military applications, SEI technology can identify specific signals from the complex electromagnetic environment and associate them with individual radiation sources, their platforms and weapon systems, and strategic and tactical targets^[1]. It is of great significance for quickly grasping battlefield situations and grasping initiatives during wars.

SEI extracts features containing individual information that characterizes a specific transmitter from the received time series for classification and recognition. Therefore, it is essentially a pattern recognition problem.

The structure of a typical SEI system, proposed by Talbot et al.^[1] in 2003, is presented in Fig. 1. The general processing flow of SEI is as follows: First, the signal is obtained through the radio frequency-receiving subsystem. Second, signal preprocessing is performed, where the received signal is subjected to various processes, such as filtering, denoizing, pulse detection, and signal demodulation. Then, extract the fine features containing the individual information of the radiation source device. Finally, the feature is compared with data in a database and used in classification and recognition algorithms to determine the specific emitter.

Figure  1.  Structural diagram of typical system for specific emitter identification^[1]

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In the traditional SEI (different from the deep learning-based intelligent SEI method) system, the definition and extraction of fingerprint features are of significant importance. Therefore, the fingerprint feature extraction of SEI is specifically analyzed in this study.

The structure of this paper is as follows: Section 2 briefly introduces the basic connotation of the fingerprint features of SEI. Section 3 briefly describes the two currently commonly used taxonomies. Section 4 is the main content of this article and proposes a detailed fingerprint feature taxonomy framework. It also presents a detailed review and analysis of the research progress of various fingerprint features under this framework. Section 5 focuses on the current status of Artificial Intelligence (AI) technology applied to SEI. Section 6 summarizes and presents the future prospects of the fingerprint feature extraction of SEI.

2. Fingerprint Features

The imperfection of the emitter hardware chain leads to the inevitable deviation of modulated signals, i.e., it unintentionally modulates the hardware information to the signal within the allowable range of the normal operation of the system. These subtle differences vary from different transmitters, such that the unintentional modulation carries transmitter-specific information. This physical-layer difference is caused by hardware, which is inevitably attached to the intentional modulation and is nearly impossible to mimic, particularly with radio frequency fingerprints.

However, related research on the description and characterization of radio frequency fingerprints is very challenging, mainly due to the following three reasons:

(1) The generation mechanism of radio frequency fingerprints is complex, and the performance is not intuitive and easy to understand like biological fingerprints. It does not have an accurate definition and cannot be accurately modeled and expressed with mathematical tools.

(2) The fingerprint differences caused by hardware between emitters are very subtle, especially for transmitters of the same model and batch of the same manufacturer.

(3) A fingerprint is an unintentional modulation attached to a transmitted signal. Compared with the main part of a signal, its energy is weak and easily affected by many factors, such as complex channel conditions, multipath effects, and environmental noise.

Therefore, SEI needs to extract effective features from as many perspectives as possible to depict real radio frequency fingerprints. These characteristics are called “radio frequency fingerprint features,” which should meet the following basic requirements^[2–4]:

(1) Universality: The fingerprint features of a transmitter should be universally present in all individual transmitters and all signal samples.

(2) Uniqueness: Feature parameters are different in the samples of different individual transmitters, i.e., the fingerprint features of different emitters are unique, different, and distinguishable.

(3) Stability: The feature of the same individual remains stable or does not change significantly within a certain period of time.

(4) Independence: The individual features of an emitter should be independent of the signal pattern and only related to the transmitter hardware.

(5) Measurability: Feature parameters can be extracted and detected from observed samples using relevant technologies, and the measurement accuracy can meet the requirements of classification.

3. Common Taxonomy of RFF Features

The commonly used taxonomies of fingerprint feature methods for SEI are as follows: Based on the signal type of the analysis object, RFF features can be divided into radar SEI fingerprint features and communication SEI fingerprint features. Based on the signal state of the analysis object, it is divided into transient-state and steady-state features. These taxonomy methods are mainly aimed at the analysis objects of SEI and do not fully consider the performances of features in describing fingerprints and the correlation between different features.

3.1 Radar and communication SEI fingerprint features

Related research on radar signals started in the mid-1960s, and conventional radar parameters were initially used as the identification basis^[1], the most typical of which is the use of pulse description words (PDWs) (PDW = {RF, PA, PW, TOA, DOA}) to identify specific radar equipment. As the radar system becomes more complex, the waveform design becomes more complicated, the working frequency band of the radar continues to expand, and the working frequency bands of different radars overlap in a wider range, especially the use of phased-array and agile radars. Therefore, conventional radar parameters can no longer provide enough effective information to meet the corresponding identification requirements^[5]. The intra-pulse characteristics of radar signals are increasingly used in SEI.

Compared with radar signals, the research on SEI of communication radiation sources started a little later^[6]. SEI of the communication system is also more difficult: communication signal systems are diverse, modulation types are complex and carry a large amount of modulation information, and subtle fingerprint features are usually submerged in the main intentional modulation information. Hence, it is highly difficult to extract fingerprints accurately. Commonly used fingerprint features of communication signals include signal modulation curve-based features and high-dimensional transform domain-based features.

In addition to radar and communication signals in SEI, some studies have focused on other types of signals, such as satellite signals, navigation signals, wireless network signals (e.g., IEEE802.11 series protocol signals), Global System for Mobile communications system signals, electronic tags (Radio Frequency IDentification, RFID), and related radio frequency signals of other Internet of Things devices.

3.2 Transient-state and steady-state features

Based on the inherent manifestations of signal states, i.e., noise, transient, and steady states, fingerprint features can be divided into transient-state and steady-state features.

The transient state refers to the process of equipment switching, mode conversion, symbol conversion of the digital communication system, and external excitation changes in the system. The signals in these processes do not contain any modulated communication data and are only related to the physical-layer characteristics of the device, which can better reflect the unintentional modulation characteristics of emitters^[7,8]. The fingerprint features extracted in this process are called transient features.

The premise of transient feature extraction is to accurately obtain complete transient signals. However, the detection of transient signals is relatively complicated, and the main difficulties are as follows. (1)The duration of the transient state is short. (2)Due to noise, the start and end points of the transient state cannot be accurately determined. (3)The amplitude, phase, and frequency characteristics of transient signals are easily affected by nonideal complex channel conditions^[9]. Guo et al.^[10] compared typical transient analysis methods, focusing on the analysis of five transient characteristics, namely, fractal dimension estimation, entropy, energy trajectory, and inherent shape of the rising edge.

A steady-state signal refers to the part of the signal transmitted by the transmitting device after the power is stabilized. The communication signal mainly contains the data part to be transmitted and a small amount of noise. Compared with transient signals, steady-state signals are easier to obtain. When the emitter is working in a stable state, the individual difference caused by numerous hardware units (components or modules) in the physical layer is displayed on the signal in the form of “combined forces”, which is stable. However, the state fingerprint features are hidden deep in the modulated signal and noise, making it difficult to extract.

4. Feature Framework based on the Inherent Logic of the Fingerprint Analysis

Considering the inherent logic of fingerprint feature extraction in SEI, this study combined the mathematical principles of feature tools based on the feature extraction method, proposed a new fingerprint feature framework, and divided the existing fingerprint features into two categories, namely, direct measurement features (primary features) and dimensionality reduction transformation features (secondary features). Moreover, combined with the principle of the fingerprint feature analysis, each category is classified in more detail. The features are divided into three levels for SEI.

The direct measurement feature refers to the feature directly extracted from the received signal based on the basic signal analysis process (e.g., basic parameter information and basic transformation information). Under normal circumstances, the input for calculating direct measurement features can only be the preprocessed signal series. The results can be directly used as a fingerprint feature for SEI. Features with higher dimensionality can also be further subjected to secondary feature transformation, and the final result after the calculation (i.e., dimensionality reduction transformation feature) is used as the fingerprint feature.

The dimensionality reduction transformation feature is not closely integrated with the signal characteristics and does not rely on the basic knowledge of electromagnetic signal analysis. However, these features are usually considered feature description methods to optimize the direct measurement features. i.e., on the basis of the primary features, the secondary features are extracted based on a certain mathematical transformation. In special cases, it can also be used directly to extract the features of the original signal.

To facilitate understanding and discussion, let $x(n)$ denote the preprocessed data, ${F_1}\{ \cdot \}$ be the direct measurement feature calculation, ${F_{\rm{2}}}{\rm{\{ }} \cdot {\rm{\} }}$ be the dimensionality reduction transformation feature extraction, and $y(m)$ denotes the final fingerprint feature result, i.e., the input of the classifier. The extracted fingerprint features are

where ${y_1}$ and ${y_2}$ represent the direct measurement feature and dimensionality reduction transformation, respectively, and ${M_1}$ , ${M_2}$ ( ${M_2} \le {M_1}$ ) is the corresponding feature dimension. However, in theory, it is also possible to directly extract the dimensionality reduction transform characteristics of a signal, i.e., ${y_2}({m_2}) =$ ${F_2}\{ x(n)\}$ . For example, the fractal dimension estimation of the original signal can be directly used for SEI. In practical applications, this situation is relatively rare, and it usually needs to meet certain prerequisites, such as a specific signal pattern or specific processing. In the taxonomy proposed in this paper, such features that rely on the special structure of the signal and the basic signal analysis methods are classified as direct measurement features. Thus, in a strict sense, the above situation can be expressed by Eq. (2). In short, in this taxonomy, ${F_1}\{ \cdot \}$ , ${F_2}\{ \cdot \}$ are serial, usually first ${F_1}\{ \cdot \}$ and then comes ${F_2}\{ \cdot \}$ . ${F_2}\{ \cdot \}$ can be omitted in some cases.

Compared with the current methods, the framework refines the classification of fingerprint features, and it is consistent with the inherent logic of fingerprint feature processing and analysis. In addition, it covers all commonly used fingerprint features at this stage and minimizes the overlap of feature methods as much as possible. Hence, researchers should further refine and improve the features and study their combinations.

The following is a detailed analysis of the classification framework and development status of fingerprint features under various categories. In the taxonomy framework based on the inherent logic of the fingerprint analysis, the two major categories of features are shown in Tab. 1 and 2. Tab. 1 shows the direct measurement feature, and Tab. 2 shows the dimensionality reduction transformation feature.

Table  1.  Direct measurement features under the feature framework based on the inherent logic of fingerprint feature extraction

Feature method		Reference
Basic parameter information	General parameter	[1,11,12]
	Envelope feature	[13–18]
	Instantaneous feature	[19–23]
	Modulation parameter	[24–26]
	Spectrum feature	[3–27]
Basic transformation information	Time-frequency analysis	[28–32]
	High-order spectrum	[33–37]
	Cyclic spectrum	[38,39]
	Hilbert spectrum	[40–43]
Signal special structure	Signal preamble	[23,44,45]
	Radar signal analysis	[46–51]
Decomposition and reconstruction information	EMD	[42,43,52–55]
	ITD	[56–63]
	VMD	[9,43,64,65]
	Phase space analysis	[2,66–69]
	Segmentation reconstruction	[70,71]
Transmitter hardware characteristics	Equivalent circuit model	[72]
	Nonlinear circuit model	[73]
	Frequency source circuit	[74]

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Table  2.  Dimensionality reduction feature under feature framework based on the inherent logic of fingerprint feature extraction

Feature Method	Reference
Waveform skeleton	[75–78]
Fractal and complexity	[42,79,80]
Specific path integration/slicing	[38,39,81]
Entropy	[59,65,82–84]
SVD	[36,38,85]
Traditional dimensionality reduction	[3,86–88]

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4.1 Direct measurement feature

The direct measurement feature refers to the fingerprint feature that is closely related to the common basic signal analysis methods. This type of feature directly acts on the preprocessed signal to obtain or retain as much of the original signal’s fingerprint information as possible. This study mainly considers the following aspects of the direct measurement fingerprint features of SEI:

Basic parameter information: commonly used communication signal parameters, radar signal parameters, time-domain and frequency-domain basic parameter information, and other parameters that can be used to identify individual information in the conventional signal processing process;

Basic transformation information: basic signal transformation, including time-frequency transformation, high-order spectrum analysis, and cyclic spectrum analysis;

Signal special structure: specific structures contained in the transmitted signal, such as the IEEE802.11 series protocol signal frame header and handshake signal in digital radio transmission, which are used to meet specific communication requirements or corresponding standards;

Decomposition and reconstruction information: corresponding transformations of the received time series to improve the data dimension, including adaptive signal decomposition methods and phase space reconstruction methods;

Transmitter hardware characteristics: the fingerprint feature generation mechanism modeling analysis carried out according to the nonideal characteristics of the related hardware in the signal transmission process.

4.1.1   Basic parameter information

Basic parameter information refers to the conventional parameters of the signal, such as the conventional parameters of the radar signal (e.g., PDW); envelope shape; rising edge time; intra-pulse characteristics, including Instantaneous Frequency (IF) and Instantaneous Phase (IP); symbol rate of the communication signal; carrier frequency deviation; spectral characteristics; modulation parameters; and modulation domain errors (including IQ imbalance and constellation offset). Such features are mainly concentrated in the time and frequency domains and are common in various signal processing procedures. Compared with other signal processing processes, SEI usually requires high accuracy for estimating such parameters.

Fingerprint features based on the basic parameter information are divided into five categories in this paper: conventional parameters, envelope characteristics, instantaneous parameters, modulation errors, and spectral distribution characteristics. The following describes their applications in SEI.

(1) General parameter

The SEI technology based on the features of conventional radar parameters mainly relies on the features directly measured or estimated by the signal measurement and detection systems^[1,11], such as carrier frequency, pulse azimuth, pulse coding method, pulse width, pulse arrival time, and pulse amplitude. Then, these features are compared with the known signal parameters in the database to obtain relevant information about the intercepted pulse signal^[12]. The early radar system was relatively simple, the electromagnetic signal density was small, the pulse signal frequency domain span was small and less overlapped, the signal form was simple, and the parameters were relatively stable, so the corresponding signal identification based on the conventional parameters was effective before. Nowadays, as the electromagnetic environment is becoming increasingly complex, the signal is diversified, and the difference in signal parameters is constantly shrinking. Thus, it is difficult to accurately confirm the specific emitter using conventional parameters directly as fingerprint features.

(2) Envelope feature

Due to the nonideality of the electronic device itself, there is inevitably a slight difference in transmitter performance. This subtle difference can be mapped on the shape of the signal’s time-domain pulse envelope, so the waveform is accompanied by the characteristics of a specific transmitter, which can be used as a basis for individual identification. The pulse envelope waveform of the radar signal is shown in Fig. 2.

Figure  2.  Radar pulse envelope

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The received signal can be affected by the multipath effect, transmitter phase noise, and additive noise, and its pulse envelope will produce varying degrees of distortion and fading^[13]. When the influence of the multipath effect is large, the pulse envelope shape may even change. Studies have found that the rising edge of the pulse envelope is the least affected by the multipath among the envelope parameters. Therefore, the front edge of the envelope (including the rising edge and part of the pulse top waveform) is often used as the fingerprint feature of the radiation source^[14,15].

In Ref. [16], the wavelet transform technology for the envelope analysis was combined, and high-precision envelope information was extracted as the fingerprint feature of SEI. In Ref. [14], Liu Xu et al. combined the recurrence rate analysis method to detect the start and end points of a signal and defined three new variables, namely, fitting rising angle, fitting falling angle, and P/S, to describe the envelope shape of pulses. In Ref. [15], two envelope features R and J excavated the spurious characteristics of the spurious modulation of the signal envelope to a certain extent. Rehman et al.^[17] used the short-time Fourier transform spectrogram to detect the transient energy envelope curve of the Bluetooth signal and extracted the area under the normalized curve, duration of the transient, kurtosis, skewness, and variance of the curve to describe the subtle characteristics of the envelope. In Ref. [18], four envelope features, namely, Linear Envelope (LE), Tangent Envelope (TE), Quadratic Envelope (QE), and Sigmoid function Envelope (SE), were defined.

Particularly, the radar pulse waveform is susceptible to atmospheric propagation effects, making incidental amplitude modulation an unreliable parameter.

(3) Instantaneous feature

Instantaneous features include IF, IP, and Instantaneous Amplitude (IA). The estimation methods of the instantaneous parameters mainly include the Hilbert Transform (HT), energy separation, generalized zero crossings, empirical Amplitude Modulated (AM)-Frequency Modulated (FM) decomposition, direct quadrature, and normalized HT^[19]. Among them, the HT is the most commonly used.

The transient features are mainly used in the transient state of the signal and the frame header structure (preamble) of specific signals. The changes in amplitude, phase, and frequency of the processes often become different over time. Fig. 3 shows the IF features of secondary response signals when four civil aviation aircraft communicate with the ground. Hall et al.^[20] extracted a number of features from the IF, IP, and IA of the transient state, including the standard deviation of normalized instantaneous features, variance of change in amplitude, standard deviation of normalized I/Q data, power per section, and average change in DWT coefficients. In Ref. [21], the five-dimensional feature vector was defined based on the IA, which effectively realizes the identification of wireless network cards and Bluetooth devices. Huang et al.^[22] specifically addressed the problem of individual identification of Frequency-Shift Keying (FSK) radio stations, completed the estimation of FSK frequency distortion parameters, and established the basis of the IF fingerprint model. In Ref. [23], an envelope and IP were combined to extract the individual characteristics of radar signals, and the influence of the radar operating mode on device-specific features was analyzed based on measured data.

Figure  3.  Instantaneous phase characteristics of the secondary response signals of four civil aviation aircrafts

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(4) Modulation parameter

The fingerprint feature based on the modulation domain error is also called the constellation shape error fingerprint feature. It is a steady-state fingerprint feature (i.e., PAssive RAdiometric Device Identification System, PARADIS) proposed by Brik et al.^[24] in 2008. This method takes into account the influence of various nonideal characteristics of a device on the modulation signal, including the I/Q channel offset, frequency offset, and limiting effect on the amplitude, which usually appear as constellation deterioration in the modulation domain. The nonlinear characteristics of the oscillator source, mixer, power amplifier, and other devices in different radiation source hardware devices are slightly different. Therefore, the shape of the signal constellation diagram is different. Based on the differences in the constellation diagram shape, we can determine the radiation source where the signal comes from.

Brik et al.^[24] compared the difference in the distribution of scattered points on the constellation diagram; defined fingerprint features, such as phase error, amplitude error, and I/Q channel offset; and successfully realized the identification of 138 wireless network cards (quadrature phase shift keying modulation). In Refs. [25,26], further research was performed on the modulation domain error based on the work of Brik et al.^[24]. The former extracts constellation diagrams on the basis of carrier recovery, symbol rate estimation, and timing estimation and uses the Hausdorff distance to measure the similarity of transmitters. The latter analyzes the influence of phase noise on the modulation domain, dynamically clusters the observation points of the received signal, obtains a reconstructed constellation, and completes the classification of the constellation according to the maximum likelihood criterion.

The fingerprint feature based on the constellation error gets rid of the dependence on the signal time-domain waveform, suppresses the influence of noise and bad channel effect to a certain extent, and is easily implemented in the hardware. However, its shortcomings are also prominent. First, it is only applicable to digital modulation signals. Second, it is necessary to accurately estimate information, such as frequency, code rate, and modulation pattern, and the recognition effect largely depends on the results of the digital demodulation.

(5) Spectrum feature

The reference frequency of the signal generated by the individual crystal oscillators of different emitters is different, which causes the difference between the carrier frequency and the code rate of the signal, and the relative deviation (the ratio of the deviation to the standard deviation) has nothing to do with the standard deviation. In Ref. [3], the accurate estimation of the carrier frequency and code rate was examined, and the effectiveness of frequency deviation as a fingerprint feature to identify specific emitters was verified.

Although the relative deviation between the carrier frequency and the code rate is distinguishable, the implementation of SEI requires an extremely high estimation accuracy, and it is difficult to obtain the standard value of the signal parameter in practical applications. Thus, it is impossible to obtain an accurate relative deviation for SEI.

In addition, the asymmetric characteristics of the spectrum can be used as fingerprint features to identify individual radiation sources^[27].

4.1.2   Basic transformation information

On the basis of basic parameters, transform-domain information, such as time-frequency spectrum, high-order spectrum, and Hilbert spectrum, have recently been widely used for RFF.

(1) Time-frequency analysis

Time-frequency analysis, particularly Joint Time-Frequency Analysis (JTFA), provides joint distribution information of the time and frequency domains. It clearly describes the relationship between the signal frequency and time and is a powerful tool for analyzing time-varying non-stationary signals. The most common time-frequency analysis methods include the Short-Time Fourier Transform (STFT), wavelet transform, Wegener distribution, and quadratic time-frequency distribution.

Fingerprint features based on STFT were analyzed in Ref. [28]. In Ref. [29], the time–frequency characteristics of binary signals were systematically analyzed. In Ref. [30], the wavelet transform was used to extract the unintentional modulation of RFID. In Ref. [31], transmitter identification methods based on the wavelet transform were systematically analyzed. In Ref. [32], the improved Choi-Williams Distribution (CWD) of Wigner-Ville distribution was introduced, the CWD was used to convert the one-dimensional (1D) time-domain signal to a two-dimensional (2D) time-frequency domain image, and the modulation information was extracted in the time-frequency plane.

Such fingerprint features are often limited by the inherent drawbacks of time-frequency tools and face a series of problems. For example, (1)STFT has shortcomings in solving nonlinear problems. (2)A contradiction exists between the choice of window function and its length and the resolution of the spectrogram. (3)The wavelet transform method relies on the choice of wavelet packet and has low precision and poor adaptability. (4)There are serious cross terms in quadratic time-frequency analysis methods, and the energy of the entire time-frequency plane may appear negative.

(2) High-order spectrum

Actual signals do not strictly obey the Gaussian distribution, and the signals emitted by different emitters show non-Gaussian characteristics. A high-order spectrum, like the Fourier transform of high-order cumulants, is an effective non-Gaussian analysis tool. The high-order spectrum does not affect the time, can retain the signal amplitude and phase information, and suppress the Gaussian noise. Among them, the third-order spectrum, also known as the bispectrum, with the characteristics of a time-shift invariance, scale variability, and phase retention, is the most widely used in SEI. Fig. 4 shows the bispectrum feature distribution of two FM radio signals, which indicates that there are significant differences in the bispectrum features of signals from different radiation sources.

Figure  4.  Bispectrum characteristic images of two FM radio signal

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The bispectrum feature is a third-order statistical feature with a relatively large complexity, and the unique information of the transmitter is scattered in a high-dimensional space, making classification and recognition difficult. Therefore, when utilizing high-order spectrum features, the dimensionality reduction transform algorithms, such as representative slice integration, should be combined, and the dimensionality reduction feature based on the distribution of high-dimensional data should be extracted.

In Refs. [33–37], high-order spectra were chosen as the preliminary high-dimensional features, and different mathematical tools were used to extract the secondary features. In Ref. [3], Locally Linear Embedding (LLE) manifold reduction was used to perform a dimensionality reduction analysis on high-dimensional Square Integral Bispectra (SIB) features and improves the distance definition of LLE samples and output dimension estimation method for SEI.

(3) Cyclic spectrum

Cyclo-stationarity is an important characteristic of a modulated signal. The cyclic spectral density function contains information, such as frequency and phase related to the modulated signal. Cyclic spectrum analysis can distinguish the signal from the noise with non-cyclic stationery. Therefore, the anti-interference, signal analysis, and characterization ability of the cyclic spectrum analysis are stronger than those of the power spectrum^[38]. The most commonly used non-parametric cyclic spectrum estimation methods are the time-domain and frequency-domain smooth periodogram methods.

In Ref. [39], the $\alpha$ cross-sectional spectrum (cyclic spectrum slice) of the cyclic spectrum density $f = 0$ was chosen as the initial high-dimensional feature, and the cyclic spectrum difference in the signal was analyzed to achieve the purpose of SEI.

(4) Hilbert spectrum

The Hilbert spectrum is derived from the Hilbert-Huang Transform (HHT). Intrinsic Mode Functions (IMFs) can be obtained after the Empirical Mode Decomposition (EMD) of the signal is subjected to the HT. After the HT, the relationship among time, frequency, and amplitude of the IMF can be obtained. The distribution of amplitude on the time-frequency plane is the Hilbert spectrum $H\left( {t,\omega } \right)$ .

Wang et al.^[40] used the improved HHT algorithm to calculate the signal Hilbert spectrum . Wang Li^[41] summarized some of the fingerprint features that can be extracted on the basis of the HHT. In Ref. [42], the Hilbert edge spectrum was extracted. In Ref. [43], the performance of the HHT fingerprint features in a single-hop scenario and relaying scenario and in different channels was paid attention to.

4.1.3   Signal special structure

Some signals have unique structural characteristics and can be used for SEI, such as the preamble of the wireless signal under the 802.11 protocols, and its format is shown in Fig. 5. Under the same standard, the preamble contains the same content, which can avoid the impact of different modulation information, is more robust than other features, and is suitable for the identification of different wireless network devices.

Figure  5.  Preamble format of standard IEEE802.11b

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In Refs. [23,44], a Wi-Fi signal preamble was used to identify wireless network cards. In Ref. [45], seven software radio peripheral transmitters (Universal Software Radio Peripheral, USRP) were combined with the signal generated by the protocol simulation to identify emitters.

However, most types of signals do not have a preamble, and in the case of non-cooperation, it is usually impossible to obtain a complete data frame header.

Similar to the preamble, radar signals also have special structures or parameters that can be used for identification, such as the Ambiguity Function (AF) and Doppler^[46]. Among them, the AF was first used for radar analysis and waveform design, and now it is also often used to characterize the individual differences of different signals. In Ref. [47], radar signal sorting was performed by extracting the main ridge slice of the ambiguity function. In Ref. [48], the local AF slice was defined, and its fast estimation algorithm was proposed on the basis of the method in Ref. [47] to extract and identify different radar pulse data. Wang Lei et al.^[49–51] further optimized the fingerprinting features of the AF .

4.1.4   Decomposition and reconstruction information

SEI does not focus on the main information conveyed in the signal transmission process, but it pays attention to details other than the main components of the signal. Using decomposition and reconstruction algorithms to improve the original signal dimension, fingerprint-related features can be extracted from a higher level, and at the same time, a new idea for separating the main component and secondary component (spurious component) of the signal can be provided.

Commonly used decomposition methods include EMD, Intrinsic Time-scale Decomposition (ITD), and Variational Mode Decomposition (VMD). Reconstruction methods include phase space reconstruction and segmentation reconstruction.

Decomposition and reconstruction make the data have higher dimensions, more variables, and more complex forms. Therefore, understanding the differences and connections between different signal components in a high-dimensional space and extracting the truly meaningful information are the keys to use such features to realize SEI. Otherwise, mapping data to high-dimensional space can only result in greater computational pressure and information redundancy.

(1) EMD

EMD was first proposed by Norden et al.^[52] in 1998, which is a posterior adaptive time-frequency analysis method for nonlinear and non-stationary signals.

The basic calculation method of EMD is to use the tertiary spline interpolation method to continuously and iteratively search for the upper and lower envelopes of the local maximum and minimum points of the original signal, obtain the IMF components, and complete the decomposition process. Fig. 6 shows the time-domain waveforms of a signal and all the decomposed IMFs after EMD. The first layer of the sub-pictures is the original signal waveform, and the remaining sub-pictures correspond to each IMF. The figure shows that EMD basically works according to the frequency from high to low. The first few layers of IMF components with high frequency and low amplitude can be roughly understood as high-frequency spurious components attached to the signal.

Figure  6.  Schematic of empirical mode decomposition results

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In the past 20 years, there have been many SEI-related studies based on EMD at home and abroad. In Ref. [53], EMD was first used for SEI and compared with wavelet decomposition. In Ref. [54], IMF was used to reconstruct signals to obtain stable time-frequency distribution characteristics. Liang et al.^[55] used EMD to separate the main components and spurious components containing individual information about the radiation source. In Ref. [42], the fractal features of IMF in the time and frequency domains were extracted, combining IF and Hilbert edge spectrum as fingerprint features. In Ref. [43], three different features based on EMD were proposed, and its performance was explored for the first time in the relay scene.

(2) ITD

In 2007, Frei M G et al.^[56] proposed ITD, which decomposes a signal into the sum of several inherent rotation components and a monotonic trend. Compared with EMD, the process of filtering and interpolation is subtracted.

In Ref. [57], the instantaneous parameters of ITD were used to reconstruct the time spectrum, and the spectral symmetry deviation coefficient of the signal spectrum was defined as a feature. In Ref. [58], the fractal features, RJ features, and edge spectrum features of different rotation components after ITD were extracted. In Ref. [59], ITD was combined with the nonlinear analysis method, the correlation coefficient was used to filter out the appropriate signal components, and the entropy data of each layer of the signal were extracted. Ren et al.^[60] combined ITD and image processing methods to extract corresponding fingerprint features. In addition, ITD has a wide range of applications in the fields of the biological signal^[61], fault diagnosis^[62], and system detection^[61,63].

(3) VMD

VMD was proposed by Dragomiretskiy et al.^[64] in 2014. It is a non-recursive adaptive quasi-orthogonal signal decomposition method in the time and frequency domains. It plays an important role in the nonlinear signal analysis^[65]. The VMD method has stable decomposition results with simple calculations and no modal aliasing problems. The decomposed basic component IMF has the characteristics of AM–FM modulated narrowband signals, and its IF has a practical physical meaning, which has natural advantages for SEI. Satija et al.^[9] applied VMD to fingerprint recognition based on the method proposed in Ref. [43] and constructed VMD entropy (VMD-Entropy) and cumulant (VMD-EM²) as fingerprint features.

(4) Signal reconstruction

The received signal can be understood as a 1D time series formed by high-dimensional data projections carrying transmission information and emitter-specific fingerprint information. Therefore, the reconstruction of the signal can also be called ascending-dimensional restoration. Common reconstruction methods include phase space reconstruction based on nonlinear signal characteristics, segmentation reconstruction, and parameter imaging.

The phase space analysis is one of the basic analysis methods of nonlinear dynamics. Each phase point in the phase space corresponds to a state of the dynamic system, and the change in the phase point corresponds to the state evolution of the system. The use of a time series to construct a phase space equivalent to the original phase space of the system, i.e., phase space reconstruction, is the first step to analyze the nonlinearity of the time series^[66].

Theoretically, different transmitters correspond to different nonlinear systems, and there must be hardware fingerprint characteristics inherent to the specific transmitter in the reconstructed phase space. Carrol^[67] first used the phase space reconstruction method to solve the SEI problem. Xu Dan^[2], Yuan Yingjun^[68], and Zhu Shengli^[69] discussed in detail the application of phase space theory to SEI in their doctoral dissertations.

In addition to phase space reconstruction, domestic and foreign scholars have also tried other segmentation reconstruction methods. For example, T. J. Bihl et al.^[70] proposed a signal segmentation and feature vector combination method based on a sliding window function. Zhu^[71] reconstructed a time series into a Horizontal Visibility Graph (HVG).

4.1.5   Transmitter hardware characteristics

The analysis of the fingerprint mechanism is an important research content of SEI, which is of great significance for exploring the physical nature of signal fingerprint features and extracting effective fingerprint features.

In Ref. [72], the hardware structure of transmitters was first introduced, the equivalent circuit model of the radio frequency oscillator for the transmitter with a free-running oscillator was constructed, and a modeled SEI technology was proposed. When the modulation voltage greatly changes, this method can make up for the shortcomings of traditional methods in measuring the rising- and falling-edge delays. Xu Zhijun et al.^[73] specifically studied the nonlinear distortion of nonlinear power amplifiers by performing a Taylor series analysis on the signal. Huang Yuanling et al.^[74] analyzed the equivalent Mathematical model of the transmitter frequency source circuit and established an Autoregressive Moving Average (ARMA) model to describe the phase noise characteristics of a transmitter. They proposed to construct the fingerprint characteristics of the radiation source through the ARMA parameter estimation, thereby completing SEI.

With the development of hardware, particularly the development of programmable device technology, the exploration of a fingerprint mechanism of a radiation source and extraction of an effective feature method by modeling and analyzing the transmitter hardware have become increasingly difficult.

4.2 Dimensionality reduction transformation

In the SEI field, the direct measurement features extracted above can be directly inputted to the classifier for identification. However, due to some specific reasons, such as high dimensionality and limited characterization capabilities, some direct measurement features need to be further purified into the secondary feature. Secondary feature extraction refers to feature transformation or dimensionality reduction on the premise of keeping the original information of the feature as much as possible, exploring deeper and more accurate fingerprint features, and facilitating easy classification or recognition by the classifier. In this paper, this type of secondary feature is also called the dimensionality reduction transform feature.

The dimensionality reduction transformation feature is essentially a feature analysis and processing method, which is mainly considered from two perspectives in this paper:

(1) High-dimensional feature transformation: This involves secondary features that are closely related to the original signal structure and primary features (direct measurement features). Statistical tools are commonly used to characterize directly extracted high-dimensional features to achieve feature dimensionality reduction or feature transformation according to the feature distribution.

(2) Traditional feature dimensionality reduction: The traditional dimensionality reduction method of machine learning is directly used, and the mathematical correlation is used to achieve dimensionality reduction.

Parts of the dimensionality reduction transformation features are shown in Tab. 2.

4.2.1   High-dimensional feature transformation

(1) Waveform skeleton

According to the principle of non-increasing information in signal processing, the signal waveform itself is the carrier of the subtle features of a radiator signal that is more robust and contains the most information. The waveform skeleton method aims to minimize the influence of the transmission channel and restore the signal waveform emitted by the emitter, which includes the manifold learning-master curve method and compressed sensing.

The master curve belongs to the category of manifold learning, which refers to a smooth curve that passes through the center of the data distribution and satisfies self-consistency. This curve is the skeleton of the data collection, which can better describe the characteristics of the data distribution and retain the information of the data, as shown in Fig. 7. Using a smooth curve instead of the principal component line to analyze the data and finding the smooth curve between the symmetrical variables is an extension of the nonlinear method that more accurately describes the actual problem^[75].

Figure  7.  Data skeleton extracted by principal curve

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In Refs. [76,77], the signal was analyzed by combining the non-parametric power spectrum and direct bispectrum, extract the spectrum skeleton of the spectral line distribution, and then combine the multifractal dimension to describe the skeleton as the signal fingerprint feature. However, the power spectrum and bispectrum of many signals are not suitable for extracting the skeleton structure, and their representation ability is not strong in some cases. Hence, a lot of information will be lost.

In addition to the above-mentioned master curve method, compressed sensing^[78] can also be used to extract the waveform skeleton.

(2) Fractal and complexity

A fractal is a powerful tool used to analyze the irregularity of non-stationary series and has been widely used in non-stationary and nonlinear signal processing in recent years. Fractal features commonly used in fingerprint feature extraction are the information dimension, box dimension, variance dimension, and Lempel–Ziv complexity. Gui Yunchuan et al.^[42] calculated the fractal features of eigenmode functions (i.e., IMF) in the time and frequency domains on the basis of the EMD, combined with the fractal dimension on the Hilbert edge spectrum and spectral symmetry coefficient to form the feature vector. Tang et al.^[79] calculated the variance fractal dimension of a modulated radio signal and the Mandelbrot singular fractal dimension spectrum and projected the modulation feature and nonlinear transformation feature of the signal to the fractal feature space. In Ref. [80], the box dimension and variance dimension were used to characterize each segment of the signal segmentation to realize SEI.

(3) Specific path integration/slicing

Taking a bispectrum as an example, the direct use of a bispectrum matrix for feature extraction and recognition requires the calculation of complex 2D templates, and the computational efficiency is relatively low. Therefore, it is necessary to convert the 2D function into 1D by integrating the bispectrum. Specific path integrals can be divided into the Radial Integral Bispectrum (RIB), Axial Integral Bispectrum (AIB), Circular Integral Bispectrum (CIB), and SIB according to different paths^[4,81], as shown in Fig. 8.

Figure  8.  Integral paths of bispectrum

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In addition, the idea of slicing high-dimensional spectrograms is similar to that of specific path integration, but some slices are still high in dimensionality. Hence, further feature dimensionality reduction is needed. The dimensionality reduction method of cyclic spectrum features often uses slices^[38,39].

(4) Entropy

Entropy is an indicator that measures the degree of chaos in a system. In information theory, it is also called Shannon entropy or information entropy. After the received time series is decomposed and reconstructed, the dimensionality reduction transformation feature can be extracted in combination with the basic principle of entropy calculation. In Ref. [82], a method for extracting the individual characteristics of emitters based on the permutation entropy of communication signals was proposed, and entropies that characterize the subtle features of an original system were extracted. In addition to permutation entropy, other entropy algorithms include sample entropy^[59], energy entropy^[65], wavelet entropy^[83], and correlation entropy^[84].

(5) Singular value decomposition

Liu Ting^[38] performed singular value decomposition (SVD) on a matrix obtained via the cyclic spectrum transformation, which extracted comprehensive and subtle inherent characteristics of a radiation source signal. Some scholars also performed SVD of 2D full-plane information after time–frequency spectrum transformation and then combined the eigenvalue and eigenvectors into a fingerprint feature. Sahmel^[85] used the singular value space method to study the identification of SEI for OFDM signals. They also converted high-dimensional features into images and converted the extraction and identification of subtle features of radiation sources into image recognition problems.

In addition, high-order statistics^[36] can achieve a certain dimensionality reduction effect in SEI.

4.2.2   Traditional dimensionality reduction

The traditional dimensionality reduction methods in pattern recognition can also be used as a means of extracting secondary fingerprint features, which mainly include linear discriminant analysis^[86] and principal component analysis^[3,87,88]. However, this kind of method does not fully integrate the structural characteristics of fingerprint features, such as a high degree of non-correlation and nonlinearity, and cannot maintain the original information well. Moreover, the direct application of mathematical correlation to SEI ignores the distribution characteristics of features, and there are many adaptability problems.

5. AI and Fingerprint Feature Extraction

In recent years, the popularity of deep learning AI methods has continued to rise, and breakthroughs have been made in the fields of image processing and natural language understanding. Regarding the identification of individual radiation sources, the addition of AI not only improves the identification effect to a certain extent but also affects the original classic SEI framework and redefines the analysis and processing process.

Early related research tended to use neural networks as a classifier. The input of the network is generally fingerprint features extracted with expert knowledge, usually high-dimensional features, and the network structure is mainly a Convolutional Neural Network (CNN). In Ref. [88], an STFT time spectrogram was taken as an input. In Ref. [89], the bispectrum feature was used after dimensionality reduction. In Ref. [90], the author considered the energy of the time-frequency distribution and compared the CNN’s classification performance with those of traditional classifiers, such as Support Vector Machines (SVM), naive Bayes, random forests, decision trees, and K-nearest neighbors).

Later, some studies have merged two links, namely, feature extraction and classification recognition, directly inputted the received original I/Q complex data, and outputted radiation source recognition results, which achieved a certain recognition effect^[91]. At this stage, the end-to-end approach has become increasingly common^[92,93].

With the development of neural networks, new research ideas, such as network structure improvements and adaptive testing of different signal styles, have gradually appeared in the SEI field^[93–95]. In addition, due to the inherent advantages of deep learning, such as strong learning and computing capabilities, research on fingerprint recognition in specific scenarios can be performed, such as the use of a generative adversarial network, to identify illegally confronted devices in large-scale autonomous networks^[96].

However, deep learning itself is poor in interpretability. Its feature extraction and analysis logic are similar to a black box. In addition, the corresponding mechanism behind fingerprint features has not been completely solved. Therefore, although the AI method has significantly improved the recognition effect, the possibility of overfitting is still large, and its performance in new data and new scenarios is often unsatisfactory. This bottleneck also limits the transformation of fingerprint identification methods based on deep learning to practical application systems.

At this stage, two main solutions for such problems are proposed:

(1) Data enhancement of original data

Common methods include changing the signal-to-noise ratio of the training data and adjusting the signal carrier frequency. In Ref. [97], inspired by the image data enhancement technology, the data enhancement of SEI through the random integration method was realized.

(2) Research combining the mechanism of fingerprint features

Expert knowledge can be used to remove interference information, artificially strip out non-hardware circuit fingerprint factors, and guide the neural network to learn real fingerprint features. For example, in Ref. [98], the carrier frequency offset was estimated and removed; the influence of the channel environment, parameter changes, and other related factors were reduced or eliminated; and finally, the time-domain complex baseband error signal was obtained as the input of the deep CNN network. The recognition rate reached 92.29%.

Compared with the previous end-to-end methods, the idea of combining fingerprint mechanisms to improve the performance of SEI systems based on deep learning puts forward higher requirements for signal analysis and fingerprint understanding.

6. Conclusions and Outlooks

After decades of development, the issue in SEI has become more profound, and related technology applications have gradually matured. Nowadays, traditional SEI largely relies on the definition and extraction of fingerprint features. Many types and numbers of features are involved, and the angles of extraction and analysis and the theoretical knowledge based on them are also different. However, as the electromagnetic environment is becoming increasingly complex, the manufacturing process of related electronic devices has been greatly improved, and the physical differences have been shrinking, making it more difficult to extract effective fingerprint features. In the future, the related methods of SEI technology, especially the feature extraction method, still need in-depth research on the following three aspects:

6.1 Intelligent extraction of signal features

Deep learning-based SEI methods can get rid of the dependence on expert knowledge, change the traditional processing procedures that require manual pre-definition, realize automatic learning of fingerprint features, and improve the adaptability of feature methods to a certain extent. Using AI methods to mine the individual information of radiation sources contained in electromagnetic signals will certainly play a great role in SEI issues in the future.

However, at this stage, the intelligent and automatic fingerprint feature extraction is still in the trial and exploration stage. In particular, how to combine expert experience, make better use of the advantages of intelligent computing, and extract the truly stable and effective fingerprint features of the radiation source, among other issues, require more detailed and in-depth research.

6.2 Comprehensive utilization of multiple features

There are many types of existing features, the scope of application of a single feature is limited, and the advantages of different features are different. Therefore, comprehensive utilization of features will characterize the radio frequency fingerprints of emitters from other angles and provide more comprehensive information for SEI.

In the field of SEI, the comprehensive utilization of feature methods not only includes the traditional problem of multi-feature fusion in pattern recognition but also emphasizes the dependence on the understanding of signals and aims to combine the advantages of different types of fingerprint features in the ability to describe the fingerprint from different angles. We need to avoid useless redundancy and prevent the omission of information. For example, the time- and frequency-domain features were integrated after VMD decomposition in Ref. [9], while the decision tree was used to select the optimal feature combination subset in Ref. [99].

Aiming at the problem of SEI, the basic idea of the comprehensive utilization of multiple features in the future should be to improve the adaptability of fingerprint features to different signals, enhance the pertinence of specific signals, and promote the complementary advantages of original features. In other words, future SEI-related research should improve the use of original excellent features while defining and extracting new features.

6.3 Adaptability and scalability

Most features can only be adapted to limited signal types, and their scope and conditions of applications are unclear. When a new signal form appears, it is usually necessary to combine expert knowledge to explore and screen the available features. In addition, the original recognition effect in the face of a new situation is often greatly compromised or even invalid. The electromagnetic environment is becoming increasingly complex, and the types and patterns of signals are increasing, which changes the adaptability and scalability of fingerprint features. In addition, the boundary characteristics of the fingerprint feature of SEI are worthy of attention.

As the application of SEI technology becomes increasingly extensive, growing requirements are put forward for fingerprint features. Whether it is manually defined by expert knowledge or automatic learning based on AI technology, the fingerprint features of SEI technology in the future will need to be developed in a more refined, intelligent, complex, and in-depth direction.