Radio frequency fingerprint feature extraction method and system based on high-order difference

Abstract

The invention discloses a radio frequency fingerprint feature extraction method and system based on high-order difference. The method comprises the following steps: acquiring a Wi-Fi equipment wireless transmission signal collected under a specified signal-to-noise ratio condition, and preprocessing the Wi-Fi equipment wireless transmission signal; on the basis of the preprocessed signal, two long training domain symbols in a preamble of the preprocessed signal are obtained, and an average value is solved in a time domain; the long training domain symbols after averaging are converted to a frequency domain, and channel state information, namely CSI, is calculated by using a least square method according to frequency domain representation and an effective subcarrier sequence specified by an IEEE 802.11 protocol; on the basis of the CSI, modulus and logarithm calculation are utilized to obtain a logarithm domain amplitude; and according to the CSI amplitude of the logarithm domain, acquiring radio frequency fingerprint features by using a high-order difference method. According to the method, the continuity of channel influence on a frequency domain and the correlation on adjacent subcarriers are utilized, the channel influence is eliminated on a CSI amplitude of a logarithm domain by utilizing a high-order difference algorithm, and radio frequency fingerprint features irrelevant to the channel are extracted.

Description

Technical Field

[0001] This invention relates to the field of communication and information security technology, specifically to a method and system for extracting radio frequency fingerprint features based on high-order differential methods. Background Technology

[0002] With the rapid development of IoT technology, the massive number of connected devices poses a severe challenge to authentication systems in wireless communication. Current communication networks typically employ traditional cryptographic methods such as symmetric encryption and public-key cryptography for protection, and generally use challenge-response protocols for authentication. However, due to stringent constraints on power consumption and computing resources, these methods are often unsuitable for IoT devices.

[0003] As a non-cryptographic authentication method, radio frequency fingerprinting provides a physical layer-based solution that utilizes hardware damage characteristics introduced by manufacturing process variations, such as mixer imbalance, oscillator defects, and power amplifier nonlinearity. These radio frequency fingerprint features are often more distinctive in low-cost electronic components and are inherently carried by wireless transmission signals, thus allowing for IoT device authentication without requiring modifications to the end device.

[0004] It should be noted that, since the RF fingerprint characteristics in the received signal are intertwined with channel propagation effects, and the broadband characteristics of Wi-Fi signals make them sensitive to multipath fading, eliminating channel effects is crucial for building a robust Wi-Fi RF fingerprinting system. However, existing methods typically require direct acquisition of physical layer I / Q sample interfaces. For example, Reference 1 (“Y. Xing, A. Hu, J. Zhang, L. Peng, and X. Wang, “Design of a channelrobust radio frequency fingerprint identification scheme,” IEEE InternetThings J., vol. 10, no. 8, pp. 6946–6959, 2023) utilizes IEEE 802.11 short training domain symbols for RF fingerprint feature extraction; while Reference 2 (L. Xie, L. Peng, and J. Zhang, “Towards robust RF fingerprint identification using spectral regrowth and carrier frequency offset,” in Proc. IEEE INFOCOM, London, United Kingdom, May 2025, pp. 1–10.) leverages the spectral regeneration effect on inactive Wi-Fi subcarriers to achieve device identification. Since the signal preprocessing procedures of existing access points are usually fixed and generally do not open I / Q sample interfaces, such methods often require additional equipment for I / Q data acquisition, resulting in significant resource overhead.

[0005] Recently, with the inclusion of wireless sensing capabilities in the IEEE 802.11bf standard, future commercial Wi-Fi devices are expected to provide obtainable Channel State Information (CSI) estimation results. This will not only support emerging applications such as wireless sensing and positioning, but also facilitate the realization of CSI-based channel-robust Wi-Fi RF fingerprint feature identification. Since CSI estimation relies on received signals containing distortions introduced by inherent hardware defects, its estimation results naturally incorporate channel information and hardware-related features, making it suitable for RF fingerprint feature extraction. Therefore, utilizing CSI for channel-robust RF fingerprint feature extraction provides a more resource-efficient approach that can be seamlessly integrated with existing signal processing chains. In summary, how to extract channel-robust RF fingerprint features from Wi-Fi signals using CSI has become a critical problem that urgently needs to be solved. Summary of the Invention

[0006] Purpose of the invention: In order to solve the above-mentioned problems in the current radio frequency fingerprint feature extraction technology, this invention uses a high-order differential algorithm based on the CSI of Wi-Fi signals to eliminate channel interference and extract radio frequency fingerprint features.

[0007] Technical Solution: To achieve the above-mentioned objectives, the present invention adopts the following technical solution:

[0008] A method for extracting radio frequency fingerprint features based on higher-order differences includes the following steps:

[0009] The wireless transmission signal of the Wi-Fi device is acquired under a specified signal-to-noise ratio condition and preprocessed. The preprocessing includes signal interception, synchronization, carrier frequency offset compensation and energy normalization.

[0010] Based on the preprocessed signal, the two long training domain symbols in its leading edge are obtained and the average value is calculated in the time domain.

[0011] The long training domain symbols after averaging are converted to the frequency domain. The least squares method is used to calculate the channel state information, i.e., CSI, based on the frequency domain representation and the effective subcarrier sequence specified by the IEEE 802.11 protocol.

[0012] Based on CSI, its logarithmic domain magnitude is obtained by modulo and logarithmic calculations.

[0013] Radio frequency fingerprint features are obtained using a higher-order difference method based on the CSI amplitude in the logarithmic field.

[0014] Furthermore, the specified signal-to-noise ratio condition is not less than 25dB.

[0015] Furthermore, the mean of the two long training domain symbols in the preamble is calculated in the time domain, including:

[0016] Let the time-domain representations of the two long training domain symbols be as follows: and ,in and These represent the indices of the first and second long training domain symbols, respectively. Represents the received signal in the time domain; the result after averaging is expressed as .

[0017] Furthermore, the long training domain symbols after averaging are transformed to the frequency domain, including:

[0018] For the long training domain symbols after averaging Perform a Fourier transform on it to convert it to the frequency domain, and the result is expressed as ,in Subcarrier sequence number, Fourier transform;

[0019] Channel state information (CSI) is calculated using the least squares method based on the frequency domain representation and the effective subcarrier sequence specified in the IEEE 802.11 protocol. The result is expressed as follows: ,in It is a long training OFDM symbol sequence as specified in the IEEE 802.11 protocol, and has .

[0020] Furthermore, based on CSI, its logarithmic domain magnitude is obtained using modulo and logarithmic calculations, including:

[0021] The calculated CSI is denoted as Take its logarithmic magnitude, and express it as ,in For logarithmic operations defined over the positive real number field, This is the modulo operation for complex numbers.

[0022] Furthermore, based on the CSI amplitude in the logarithmic domain, higher-order difference methods are used to obtain radio frequency fingerprint features, including:

[0023] For sequences Its first-order difference result is defined as ,That The order difference result is ;

[0024] Based on the above definitions, the obtained logarithmic domain spectrum is then analyzed. The first-order difference is used to obtain the radio frequency fingerprint feature, denoted as . ,in , Subcarrier sequence number, for Subcarrier set under order difference.

[0025] A radio frequency fingerprint feature extraction system based on high-order difference includes:

[0026] The signal preprocessing module is used to acquire the wireless transmission signal of the Wi-Fi device under a specified signal-to-noise ratio condition and perform preprocessing, including signal interception, synchronization, carrier frequency offset compensation and energy normalization.

[0027] The preamble symbol calculation module is used to obtain two long training domain symbols in the preamble of the preprocessed signal and calculate their average in the time domain.

[0028] The channel state information calculation module is used to convert the long training domain symbols after averaging to the frequency domain, and calculate the channel state information, i.e., CSI, using the least squares method according to the frequency domain representation and the effective subcarrier sequence specified by the IEEE 802.11 protocol.

[0029] The logarithmic domain calculation module is used to obtain the logarithmic domain magnitude based on CSI by using modulo and logarithmic calculations.

[0030] The high-order difference calculation module is used to obtain radio frequency fingerprint features based on the CSI amplitude in the logarithmic field using a high-order difference method.

[0031] The present invention also provides an electronic device, comprising: a memory; one or more processors; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the high-order differential-based radio frequency fingerprint feature extraction method as described above.

[0032] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the radio frequency fingerprint feature extraction method based on higher-order differences as described above.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] (1) Extracting radio frequency fingerprint features using CSI of Wi-Fi signals. This process can be seamlessly integrated with the existing signal processing chain, and has high resource utilization efficiency.

[0035] (2) By utilizing the continuity of channel influence in the frequency domain and the correlation in adjacent subcarriers, a high-order difference algorithm was used to eliminate channel influence on the CSI amplitude in the logarithmic domain, and channel-independent RF fingerprint features were extracted. Attached Figure Description

[0036] Figure 1 This is a flowchart of the method of the present invention;

[0037] Figure 2 It is the signal preamble structure specified in the IEEE 802.11 protocol;

[0038] Figure 3 This is a schematic diagram of an experimental scenario according to an embodiment of the present invention;

[0039] Figure 4 yes Figure 3 The two devices in this embodiment obtain radio frequency fingerprint features according to the method provided by the present invention. Detailed Implementation

[0040] To provide a clearer understanding of the features and advantages of the technical solution of the present invention, the composition and implementation of the specific solution are described below in conjunction with the accompanying drawings.

[0041] The flowchart of the radio frequency fingerprint feature extraction method based on high-order difference provided by this invention is as follows: Figure 1 As shown, it includes the following steps:

[0042] (1) Collect wireless transmission signals from Wi-Fi devices. The conditions for collecting Wi-Fi signals include certain requirements for the signal-to-noise ratio of the received signal (not less than 25dB), but no restrictions on channel conditions (e.g., line-of-sight and non-line-of-sight conditions). In the time domain, the received signal can be represented as:

[0043] ,

[0044] in For an ideal signal, The impact is due to the characteristics of the transmitter hardware. For convolution operations, For time-domain channel impulse response, This represents additive white Gaussian noise.

[0045] (2) Preprocessing is performed on the acquired wireless received signal, including signal interception, synchronization, carrier frequency offset compensation, and energy normalization. Any effective signal interception, synchronization, frequency offset compensation, and energy normalization method can be used, and this invention does not limit this. The object of preprocessing is any single frame signal acquired by the wireless receiver.

[0046] (3) For the preprocessed signal, obtain the two long training domain symbols in its preamble and average them in the time domain to improve the signal-to-noise ratio. According to the IEEE 802.11 protocol, a preamble exists at the beginning of each frame of signal. The preamble structure is as follows: Figure 2 As shown, it contains two long training domain symbols. Ideally, these two symbols are identical and can be denoted as . and ,in and These represent the indices of the first and second long training domain symbols, respectively. The process of calculating the mean can be represented as:

[0047] .

[0048] (4) For the long training domain symbols after averaging, Fourier transform and least squares method are used, and channel state information (CSI) is calculated according to the effective subcarrier sequence specified in the IEEE 802.11 protocol. The specific operation is as follows:

[0049] For the long training domain symbols after averaging, performing a Fourier transform to convert them to the frequency domain can be represented as follows:

[0050] ,

[0051] in Subcarrier sequence number, This is a Fourier transform.

[0052] After Fourier transform, the channel influence and RF fingerprint characteristics in the received signal are transformed from a convolutional relationship in the time domain to a multiplicative relationship in the frequency domain.

[0053] ,

[0054] in , and These are the frequency domain representations of channel effects, transmitted signals containing fingerprint features, and the mean of Gaussian white noise, respectively.

[0055] The channel state information (CSI) is further calculated using the least squares method, and the result is expressed as follows:

[0056] ,

[0057] in It is a long training OFDM symbol sequence as specified in the IEEE 802.11 protocol, and has .

[0058] According to the effective subcarriers defined in the IEEE 802.11 protocol, the domain here is defined as follows: Taking a 20 MHz bandwidth Wi-Fi signal as an example, This example only uses a 20 MHz bandwidth; the present invention does not impose any limitations on the bandwidth size.

[0059] (5) For CSI, its logarithmic domain magnitude is obtained using modulo and logarithmic calculations. The specific operation is as follows:

[0060] For CSI, take its logarithmic domain magnitude, denoted as

[0061] ,

[0062] in For logarithmic operations defined over the positive real number field, This is the modulo operation for complex numbers. Because... When the noise is so weak as to be negligible, the magnitude in the logarithmic domain can be further expressed as:

[0063] ,

[0064] in , This transforms the multiplicative relationship between channel influence and fingerprint features in the frequency domain into an additive relationship in the logarithmic domain.

[0065] (6) For the CSI amplitude in the logarithmic domain, the radio frequency fingerprint features are obtained using a higher-order difference method. The specific process is as follows:

[0066] Define the difference operator For a certain sequence Its first-order difference result is ,That The order difference result is .

[0067] Based on the above definitions, the obtained logarithmic domain spectrum is then analyzed. The first-order difference can be used to obtain the radio frequency fingerprint features, denoted as .

[0068] ,

[0069] in Because the underlying requirement of difference operations is that the domain is... The value interval is 1, to satisfy... The computational operation is valid, and taking a 20 MHz bandwidth Wi-Fi signal as an example, the effective subcarrier sequence specified in the IEEE 802.11 protocol... exist There is a missing part, therefore, the corresponding The subcarrier set under the first-order differential is This example only uses a 20 MHz bandwidth; the present invention does not impose any limitations on the bandwidth size. Furthermore, regarding the differential order... The present invention does not limit the value of , but recommends a range of values ​​of . .

[0070] The radio frequency fingerprint features obtained through the above operations are channel robust because the channel effects are eliminated while the fingerprint features are preserved. The specific principle is as follows:

[0071] For continuous frequency domain channel response within the bandwidth ,in Let be the angular frequency, and its logarithmic domain amplitude. Continuous. Therefore, according to Weierstrass's theorem, for... There exists a polynomial satisfy

[0072] ,

[0073] in Let be the order of the polynomial, representing , Define the bandwidth range.

[0074] For the subcarrier sequence specified in IEEE 802.11, its corresponding angular frequency can be expressed as:

[0075] ,

[0076] in The center angular frequency, ( (The subcarrier spacing specified in the protocol).

[0077] Therefore, polynomial approximation can be used. ,Right now

[0078] .

[0079] Furthermore, it can be proven The proof is as follows:

[0080] Proposition: One polynomial of degree The order difference is a constant.

[0081] Basic Information ( ):

[0082] make Its first-order difference can be expressed as:

[0083]

[0084] The result is a constant, verifying that when The proposition holds true at that time.

[0085] Inductive hypothesis:

[0086] Suppose for some integer , any polynomial of degree of The order difference is equal to a constant. .

[0087] Summarize the steps ( ):

[0088] consider polynomial of degree ,in The highest number of times Its first-order difference can be described as:

[0089] .

[0090] According to the binomial theorem It is about of A polynomial of degree n, whose first term is Therefore, applying the inductive hypothesis, of The order difference can be expressed as:

[0091]

[0092] in Let represent the set of all lower-degree terms in a polynomial expansion. These terms have a degree lower than the first term. And with It increases to the point of being negligible.

[0093] In summary, due to A constant, the inductive proof is complete.

[0094] From the above proof, it can be concluded that So, going a step further, The difference result is

[0095] .

[0096] Therefore, for Given ,have

[0097] ,

[0098] This indicates that the channel effect has been eliminated, and for the difference order... The parameter settings have tolerance. The above proof process demonstrates that: this invention utilizes the continuity of channel influence in the frequency domain and its correlation on adjacent subcarriers, and can use a high-order differential algorithm to eliminate channel influence in the CSI amplitude in the logarithmic domain.

[0099] In addition, for radio frequency fingerprint features This can be viewed as a fixed sequence related to the transmitter's hardware characteristics. After... The result of the order difference calculation can be expressed as:

[0100] ,

[0101] It retains the characteristics of radio frequency fingerprints.

[0102] In this embodiment of the invention, 10 Wi-Fi devices were used to perform cross-validation in three different real-world usage scenarios, achieving an average accuracy of over 95%, which verifies that the extracted radio frequency fingerprint features have good channel robustness.

[0103] Specifically, based on the actual usage of Wi-Fi devices, this embodiment of the invention designs three signal acquisition scenarios within a large office: a semi-stationary scenario, a stationary scenario, and a mobile scenario. For example... Figure 3 As shown, the three scenarios contain a total of five transmitter locations. The semi-static scenario includes two locations, denoted as L1 and N1 (L indicates a line-of-sight (LOS) scenario between the transmitter and receiver, and N indicates a non-line-of-sight (NLOS) scenario). In this scenario, the Wi-Fi transmitter is held by the experimenter and experiences slight shaking during use; there are also moving objects such as pedestrians in the environment. The static scenario includes two locations, denoted as L2 and N2. The Wi-Fi transmitters at these two locations are stationary on the ground and a table, respectively, and there are no visible moving objects in the environment. The moving scenario includes one location, denoted as M, where the experimenter holds the transmitter and moves freely within the office. Additionally, the receiver, denoted as Rx, is stationary on the table.

[0104] The data acquisition process utilized 10 Wi-Fi devices as transmitters, with each device collecting 1800 frames of signal from five different transmitter locations. The Wi-Fi signal protocol used was IEEE 802.11 n / ac, with a carrier frequency of 5.825 GHz and a bandwidth of 20 MHz. Furthermore, the acquisition process used a USRP X310 as the receiver, with a sampling rate set to 20 MS / s.

[0105] Figure 4 The paper presents the radio frequency fingerprint features extracted from signals collected by two devices at five transmitter locations. It can be seen that the radio frequency fingerprint features obtained based on the method proposed in this invention exhibit high similarity among the five different locations for a single device; however, they show significant inconsistency among different devices. This demonstrates that the proposed method can effectively eliminate the influence of the channel and extract distinguishable features. Furthermore, cross-validation based on fingerprint features obtained from five different transmitter locations (e.g., using feature samples from 10 devices at location L1 as the training set, and samples from the other four locations as the test set, and so on) achieves an average classification accuracy of over 95%, further validating the channel robustness and distinguishability of the extracted radio frequency fingerprint features.

[0106] Another embodiment of the present invention provides a radio frequency fingerprint feature extraction system based on high-order difference, comprising:

[0107] The signal preprocessing module is used to acquire the wireless transmission signal of the Wi-Fi device under a specified signal-to-noise ratio condition and perform preprocessing, including signal interception, synchronization, carrier frequency offset compensation and energy normalization.

[0108] The preamble symbol calculation module is used to obtain two long training domain symbols in the preamble of the preprocessed signal and calculate their average in the time domain.

[0109] The channel state information calculation module is used to convert the long training domain symbols after averaging to the frequency domain, and calculate the channel state information, i.e., CSI, using the least squares method according to the frequency domain representation and the effective subcarrier sequence specified by the IEEE 802.11 protocol.

[0110] The logarithmic domain calculation module is used to obtain the logarithmic domain magnitude based on CSI by using modulo and logarithmic calculations.

[0111] The high-order difference calculation module is used to obtain radio frequency fingerprint features based on the CSI amplitude in the logarithmic field using a high-order difference method.

[0112] The specific calculation process in each module is described in the above method and will not be repeated here.

[0113] Another embodiment of the present invention provides an electronic device, including: a memory; one or more processors; and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, and the programs, when executed by the processors, implement the high-order differential-based radio frequency fingerprint feature extraction method as described above.

[0114] Another embodiment of the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the radio frequency fingerprint feature extraction method based on higher-order differences as described above.

[0115] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, apparatus (systems), electronic devices, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0116] This invention is described with reference to a flowchart of a method according to embodiments of the invention. It should be understood that each step in the flowchart and combinations thereof can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing device, generate instructions for implementing the process. Figure 1 A device for a function specified in one or more processes.

[0117] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 The function specified in one or more processes.

[0118] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 Steps of a specified function in one or more processes.

Claims

1. A method for extracting radio frequency fingerprint features based on high-order difference, characterized in that, Includes the following steps: The wireless transmission signal of the Wi-Fi device is acquired under a specified signal-to-noise ratio condition and preprocessed. The preprocessing includes signal interception, synchronization, carrier frequency offset compensation and energy normalization. Based on the preprocessed signal, the two long training domain symbols in its leading edge are obtained and the average value is calculated in the time domain. The long training domain symbols after averaging are converted to the frequency domain. The least squares method is used to calculate the channel state information, i.e., CSI, based on the frequency domain representation and the effective subcarrier sequence specified by the IEEE 802.11 protocol. Based on CSI, its logarithmic domain magnitude is obtained by modulo and logarithmic calculations. Radio frequency fingerprint features are obtained using a higher-order difference method based on the CSI amplitude in the logarithmic field.

2. The method according to claim 1, characterized in that, The specified signal-to-noise ratio condition is not less than 25dB.

3. The method according to claim 1, characterized in that, The mean of the two long training domain symbols in the preceding part is calculated in the time domain, including: Let the time-domain representations of the two long training domain symbols be as follows: and ,in and These represent the indices of the first and second long training domain symbols, respectively. Represents the received signal in the time domain; the result after averaging is expressed as .

4. The method according to claim 1, characterized in that, Transform the symbols of the long training domain after averaging to the frequency domain, including: For the long training domain symbols after averaging Perform a Fourier transform on it to convert it to the frequency domain, and the result is expressed as ,in Subcarrier sequence number, Fourier transform; Channel state information (CSI) is calculated using the least squares method based on the frequency domain representation and the effective subcarrier sequence specified in the IEEE 802.11 protocol. The result is expressed as follows: ,in It is a long training OFDM symbol sequence as specified in the IEEE 802.11 protocol, and has .

5. The method according to claim 1, characterized in that, Based on CSI, its logarithmic domain magnitude is obtained using modulo and logarithmic calculations, including: The calculated CSI is denoted as Take its logarithmic magnitude, and express it as ,in For logarithmic operations defined over the positive real number field, This is the modulo operation for complex numbers.

6. The method according to claim 1, characterized in that, Based on the CSI amplitude in the logarithmic domain, radio frequency fingerprint features are obtained using a higher-order difference method, including: For sequences Its first-order difference result is defined as ,That The order difference result is ; Based on the above definitions, the obtained logarithmic domain spectrum is then analyzed. The first-order difference is used to obtain the radio frequency fingerprint feature, denoted as . ,in , Subcarrier sequence number, for Subcarrier set under order difference.

7. A radio frequency fingerprint feature extraction system based on high-order difference, characterized in that, include: The signal preprocessing module is used to acquire the wireless transmission signal of the Wi-Fi device under a specified signal-to-noise ratio condition and perform preprocessing, including signal interception, synchronization, carrier frequency offset compensation and energy normalization. The preamble symbol calculation module is used to obtain two long training domain symbols in the preamble of the preprocessed signal and calculate their average in the time domain. The channel state information calculation module is used to convert the long training domain symbols after averaging to the frequency domain, and calculate the channel state information, i.e., CSI, using the least squares method according to the frequency domain representation and the effective subcarrier sequence specified by the IEEE 802.11 protocol. The logarithmic domain calculation module is used to obtain the logarithmic domain magnitude based on CSI by using modulo and logarithmic calculations. The high-order difference calculation module is used to obtain radio frequency fingerprint features based on the CSI amplitude in the logarithmic field using a high-order difference method.

8. An electronic device, characterized in that, include: Memory; One or more processors; And one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, wherein when the programs are executed by the processors, they implement the radio frequency fingerprint feature extraction method based on higher-order differences as described in any one of claims 1-6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the radio frequency fingerprint feature extraction method based on higher-order differences as described in any one of claims 1-6.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the radio frequency fingerprint feature extraction method based on higher-order differences as described in any one of claims 1-6.

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