Nonlinear dynamics based multipath fading robustness emitter signal characterization method

Abstract

The application discloses a kind of based on nonlinear dynamics multipath fading robustness radiation source signal characterization method, comprising: S1, receive the signal data of radiation source and carry out data preprocessing, obtain signal x (t) ;S2, calculate time delay parameter tau and embedding dimension m, and reconstruct the phase space to the signal x (t) and obtain matrix S;S3, to matrix S is carried out row direction transformation and channel elimination and obtains matrix S4, to matrix is carried out column direction transformation and logarithmic transformation and obtains reconstructed phase space matrix two-dimensional Fourier transform logarithmic spectrum Θ.The application combines the advantages of nonlinear analysis and spectral analysis, designs and constructs the phase space two-dimensional Fourier transform logarithmic frequency spectrum, by the frequency domain transformation of two-dimensional row and column direction between phase points, the characteristic analysis of nonlinear dynamic system is carried out in frequency domain, on the basis of realizing the elimination of channel influence by the frequency domain mean value between cancellation phase points, without channel estimation and channel compensation, and without affecting the measurement of radiation source fingerprint information.

Description

Technical Field

[0001] This invention relates to the field of radiation source signal characterization technology, and more specifically, to a multipath fading robust radiation source signal characterization method based on nonlinear dynamics. Background Technology

[0002] Radiation source fingerprinting (RFF) is a technique that determines the source of a signal emission and identifies a specific transmitter by measuring the external characteristics of the received signal. These external characteristics are inevitably attached to the signal during modulation due to the inherent non-ideals of the transmitter hardware. They are related to the radiation source hardware system and cannot be forged. Therefore, this technique is used as a lightweight device authentication method.

[0003] The fingerprint information of radiation sources, i.e., the non-ideal differences between hardware components, is extremely subtle compared to the actual transmitted information. Therefore, fingerprint feature extraction methods need to accurately characterize and measure these subtle differences. However, transmission is inevitably affected by the channel, and channel characteristics affect the measurement of signal characteristics. However, most existing research does not specifically address eliminating channel effects in radiation source fingerprint recognition, often unintentionally extracting channel information as part of the fingerprint information. Consequently, the recognition performance of the original feature methods significantly decreases or even fails when faced with channel variations.

[0004] Existing research either ignores the influence of the channel or simplifies the channel model to a static channel. However, there is limited research on dynamic multipath channels, and the existing approaches involve estimating and equalizing the channel using prior knowledge. This increases the computational burden and inevitably introduces estimation errors, further affecting the measurement of subtle fingerprint features.

[0005] Channel effects are mostly linear, thus nonlinear characterization methods theoretically possess a natural robustness advantage. Among existing characterization methods, those based on nonlinear dynamics aim to fingerprint radiation sources by mining the nonlinear information of the signal. While these methods have achieved good recognition results in testing, their performance in multipath channels is currently lacking. Furthermore, current research on this type of method is mainly limited to the time domain, making it highly susceptible to noise. Therefore, it is indeed necessary to develop a multipath fading robust radiation source signal characterization method based on nonlinear dynamics. Summary of the Invention

[0006] The purpose of this invention is to provide a multipath fading robust radiation source signal characterization method based on nonlinear dynamics, so as to overcome the defects of the existing technology.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] A method for characterizing multipath fading robust radiation source signals based on nonlinear dynamics includes the following steps:

[0009] S1. Receive signal data from the radiation source and perform data preprocessing to obtain signal x(t);

[0010] S2. Calculate the time delay parameter τ and the embedding dimension m, and reconstruct the phase space of the signal x(t) to obtain the matrix S;

[0011] S3. Perform row direction transformation and channel cancellation on matrix S to obtain matrix γ;

[0012] S4. Perform column direction transformation and logarithmic transformation on matrix γ to obtain the two-dimensional Fourier transform logarithmic spectrum Θ of the reconstructed phase space matrix.

[0013] Further, step S1 specifically includes:

[0014] S10. The receiver receives the signal data from the radiation source and performs detection, filtering, and noise reduction processing on the signal to obtain the signal sample x0(t) to be processed.

[0015] S11. Estimate the frequency offset value f0 of the signal sample x0(t) to be processed based on the Fourier interpolation algorithm;

[0016] S12. The root frequency offset value f0 shifts the signal sample x0(t) to be processed to zero frequency to obtain the baseband signal. Then, the baseband signal is de-meaned and the energy is normalized to obtain the signal x(t) to be extracted.

[0017] Further, step S2 specifically includes:

[0018] S20. Calculate the time delay parameter τ corresponding to the signal x(t) through correlation integration;

[0019] S21. Calculate the embedding dimension m;

[0020] S22. According to Takens' theorem, the phase space is reconstructed, and the RPS of the signal x(t) is expressed as:

[0021]

[0022] In the formula, each row of matrix S is an m-dimensional phase point, which represents the current state of the system in nonlinear dynamics. The i-th row s i Let S represent the i-th phase point, which is a 1×m row vector. S consists of N row vectors, which are considered as N phase points.

[0023] Furthermore, step S3 specifically includes:

[0024] S30. The actual received signal after passing through channel h(t) is represented by y(t), and expressed in the frequency domain as:

[0025]

[0026] In the formula, X, H, and Y represent the frequency domain responses of the original signal x(t), the channel h(t), and the received signal y(t), respectively. The symbol represents convolution operation, and DFT[.] represents one-dimensional Fourier transform;

[0027] S31. Calculate the phase space matrix RPS of the received signal y(t):

[0028]

[0029] S32, Use each phase point separately... It means, that is For a single phase point In other words, to perform N r The point DFT can be used to obtain the frequency domain response.

[0030]

[0031] S33, Simultaneously perform N on all phase points r Point DFT, the results are still placed in each row to form a new matrix Γ. r , for S Y Perform a line-wise DFT transformation, using DFT. r [·] indicates the row direction N. r Point DFT yields:

[0032]

[0033] Considering only the magnitude term, Γ r The corresponding spectrum can be represented as:

[0034] |Γ r |=[|H1|·|s1(k)| |H2|·|s2(k)| … |H N |·|s N (k)|] T ;

[0035] S34, Calculate matrix Γ r The frequency domain mean corresponding to the line direction transformation is used This indicates the result after processing:

[0036]

[0037] Right now

[0038] With the channel remaining unchanged, the above equation can be further simplified to:

[0039]

[0040] In the formula, Let be the mean of the channel response at frequency k, and This represents the mean of the spectrum of all phase points at k;

[0041] S35, Using frequency domain mean For matrix |Γ r | Perform a row-by-row channel effect elimination operation, denoted by γ, where the eliminated matrix represents the channel effect:

[0042]

[0043] Use z i，k Represent the element in the i-th row and k-th column of matrix γ:

[0044]

[0045] Furthermore, step S4 specifically includes:

[0046] S40. Perform N-axis rotation on matrix γ in the column direction. c The point FFT yields a new matrix Π

[0047]

[0048] In the formula, Z i，k This represents the element in the i-th row and k-th column of matrix Π;

[0049] S41. Calculate the energy value of matrix Π and perform a logarithmic transformation. The resulting matrix is ​​the reconstructed phase space matrix. The two-dimensional Fourier transform logarithmic spectrum is represented by Θ.

[0050] Θ = 10log 10 (|Π(g)|).

[0051] Compared with the prior art, the advantages of the present invention are as follows: The present invention fully combines the advantages of nonlinear analysis and spectrum analysis, designs and constructs a two-dimensional Fourier transform logarithmic spectrum in phase space, performs characteristic analysis of nonlinear dynamic system in frequency domain through frequency domain transformation in two-dimensional row and column directions between phase points, and eliminates channel influence by canceling the frequency domain mean between phase points. It does not require channel estimation and channel compensation, and does not affect the measurement of radiation source fingerprint information. Attached Figure Description

[0052] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0053] Figure 1 This is a flowchart of the multipath fading robust radiation source signal characterization method based on nonlinear dynamics of the present invention.

[0054] Figure 2 This invention simulates QPSK signal data from three targets with different radiation sources.

[0055] Figure 3 This invention is Figure 2 The phase space two-dimensional Fourier transform logarithmic spectrum of QPSK signal data from three different radiation sources in the simulation was calculated under the condition of adding multipath fading channel. Detailed Implementation

[0056] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby providing a clearer and more explicit definition of the scope of protection of the present invention.

[0057] See Figure 1 As shown, this embodiment discloses a method for characterizing multipath fading robust radiation source signals based on nonlinear dynamics, including the following steps:

[0058] Step S1: Receive signal data from the radiation source and perform data preprocessing to obtain signal x(t), specifically including:

[0059] Step S10: The receiver receives the signal data from the radiation source and performs detection, filtering, noise reduction and other processing on the signal to obtain the signal sample x0(t) to be processed.

[0060] Step S11: The actual received signal frequency value may have some difference. The existence of the frequency offset value will cause some deviation in subsequent signal processing. Therefore, it is necessary to accurately estimate the frequency offset f0 of the signal sample x0(t) to be processed. The frequency offset value f0 of the signal sample x0(t) to be processed is estimated based on the Fourier interpolation algorithm. (For the specific estimation method, see Aboutanios E, Mulgrew B. Iterative frequency estimation by interpolation on Fourier coefficients. IEEE Transactions on signal processing 2005; 53(4):1237-42.).

[0061] Step S12: Shift the signal sample x0(t) to be processed to zero frequency based on the root frequency offset f0 to obtain the baseband signal. Then, remove the mean from the baseband signal and normalize the energy to obtain the signal x(t) to be extracted.

[0062] Step S2: Calculate the time delay parameter τ and the embedding dimension m, and reconstruct the phase space of the signal x(t) to obtain the matrix S.

[0063] Nonlinear characteristics can effectively characterize individual differences in radiation sources and have a natural advantage for channel analysis. The following section describes phase space reconstruction based on the signal x(t). Phase space reconstruction requires two important parameters: the embedding dimension m and the time delay τ.

[0064] Step S20: The time delay parameter τ corresponding to the signal x(t) can be calculated by referring to the CC algorithm through correlation integration. This method has the advantages of accurate calculation, small computational cost, and the ability to combine autocorrelation function and mutual information method. (For the specific method, see Kim H, Eykholt R, Salas J. Nonlinear dynamics, delay times, and embedding windows[J]. Physica D: Nonlinear Phenomena, 1999, 127(1-2): 48~60.)

[0065] Step S21: The embedding dimension m can be calculated using the Cao method, also known as False Nearest Neighbors (FNN). (For details, see Cao L, Mees A, Judd K. Dynamics from multivariatetime series[J]. Physical D Nonlinear Phenomena, 1998, 121(1-2): 75-88.)

[0066] Step S22: According to Takens' theorem, perform phase space reconstruction. The RPS of signal x(t) is expressed as:

[0067]

[0068] In the formula, each row of matrix S is an m-dimensional phase point, which represents the current state of the system in nonlinear dynamics. The i-th row s i Let S represent the i-th phase point, which is a 1×m row vector. S consists of N row vectors, which can be regarded as N phase points.

[0069] Step S3: Perform row direction transformation and channel cancellation on matrix S to obtain matrix γ. The main task is to construct the independent spectrum of the channel within the phase point through the intra-phase FFT, that is, to perform DFT and channel cancellation operations according to the rows of the RPS matrix.

[0070] Step S30: Considering the influence of the channel, the actual received signal after passing through the channel h(t) is represented by y(t), and expressed in the frequency domain as:

[0071]

[0072] In the formula, X, H, and Y represent the frequency domain responses of the original signal x(t), the channel h(t), and the received signal y(t), respectively. represents the convolution operation, and DFT[·] represents the one-dimensional Fourier transform.

[0073] Step S31: Calculate the phase space matrix RPS of the received signal y(t):

[0074]

[0075] Step S32: Use each phase point separately... It means, that is For a single phase point In other words, to perform N r The point DFT can be used to obtain the frequency domain response.

[0076]

[0077] Step S33: Simultaneously perform N on all phase points. r Point DFT, the results are still placed in each row to form a new matrix Γ. r , for S Y Perform a line-wise DFT transformation, using DFT. r [·] indicates the row direction N. r Point DFT yields:

[0078]

[0079] Considering only the magnitude term, Γ r The corresponding spectrum can be represented as:

[0080] |Γ r |=[|H1|·|s1(k)| |H2|·|S2(k)| … |H N |·|S N (k)|] T (6)

[0081] Step S34: Calculate matrix Γ r The frequency domain mean corresponding to the line direction transformation is used This indicates the result after processing:

[0082]

[0083] Right now

[0084] With the channel remaining unchanged, the above equation can be further simplified to:

[0085]

[0086] In the formula, Let be the mean of the channel response at frequency k, and This represents the mean of the spectrum of all phase points at k;

[0087] Step S35: Utilize frequency domain mean For matrix |Γ r | Perform a row-by-row channel effect elimination operation, denoted by γ, where the eliminated matrix represents the channel effect:

[0088]

[0089] Use z i，k Represent the element in the i-th row and k-th column of matrix γ:

[0090]

[0091] In the channel elimination process, besides eliminating common channels, a portion of the mean is inevitably eliminated as well. However, since the above operation is the same for all phase points, especially the information ratios are the same, meaning the relationships between phase points remain unchanged, the fingerprint information is still preserved. The equivalent topology in phase space undergoes a certain scaling transformation, which does not affect its shape or the distribution of radiation source fingerprint information, thus not affecting the accuracy of subsequent fingerprint feature measurement and individual radiation source identification. Similarly, for each column vector, all N elements are simply scaled proportionally, and the relationships between them still exist.

[0092] Step S4: Perform column direction transformation and logarithmic transformation on matrix γ to obtain the two-dimensional Fourier transform logarithmic spectrum Θ of the reconstructed phase space matrix, specifically including:

[0093] Step S40: According to formula (1), the signal in the same column direction is actually a truncated portion of the original signal at N points. Performing a DFT along the column direction can also reflect the signal change relationship, and the transformed signal here has already eliminated channel influence. Next, we perform a DFT along the N-column direction on matrix γ. r The point FFT yields a new matrix Π:

[0094]

[0095] In the formula, Z i，k This represents the element in the i-th row and k-th column of matrix Π;

[0096] Step S41: Calculate the energy value of matrix Π and perform a logarithmic transformation. The resulting matrix is ​​the reconstructed phase space matrix. The two-dimensional Fourier transform logarithmic spectrum is represented by Θ.

[0097] Θ = 10log 10 (|Π(g)|).

[0098] Thus, the reconstructed two-dimensional Fourier transform logarithmic spectrum Θ of the phase space matrix no longer contains channel influences and is formally a two-dimensional matrix. When performing radiation source fingerprinting, different radiation sources can be distinguished by comparing the two-dimensional matrices Θ of their signals. The method of this invention, while eliminating channel influences, can convert subtle differences in the signal into image features, facilitating subsequent extraction and analysis. Specific feature extraction methods can be combined with image recognition techniques, such as the extraction of texture and structural features.

[0099] It is worth noting that the processing in this invention processes each signal individually and eliminates the channel effects of each signal separately. Therefore, the method of this invention can adapt to time-varying channels, especially complex channel conditions with time-varying multipath fading.

[0100] like Figure 2 As shown, this is a simulation of QPSK signal data from three different radiation sources, with the phase space two-dimensional Fourier transform logarithmic spectrum calculated under noise-free and multipath-fading channel conditions. The test signals are identical except for the hardware parameter settings of the radiation sources. It can be seen that the signals from different radiation sources differ subtly; for example, the characteristics at the top of the three images are different. This difference represents the radio frequency fingerprint.

[0101] like Figure 3 As shown, it is Figure 2The phase space two-dimensional Fourier transform logarithmic spectrum of QPSK signal data from three different radiation sources was calculated under the condition of adding a multipath fading channel. The channel model adopted is a typical indoor multipath model h(t) = 0.9960δ(t) + 0.0628δ(t-1) + 0.0079δ(t-2). The signals from different radiation sources still have subtle differences, such as... Figure 2 The three images at the top exhibit consistent characteristics, indicating that significant differences in RF fingerprints persist even under multipath channels. Then, the signals from the same radiation source are compared separately. Figure 2 and Figure 3 In this case, we can see that the image is almost unchanged, which shows that the proposed two-dimensional Fourier transform logarithmic spectrum in phase space is almost unaffected by multipath channels, thus eliminating channel influence. On the other hand, it does not affect the radiation source fingerprint information contained in the signal, and can convert subtle differences in the signal into image features, which is convenient for subsequent extraction and analysis.

[0102] Although embodiments of the present invention have been described in conjunction with the accompanying drawings, the patent owner may make various modifications or alterations within the scope of the appended claims, and such modifications or alterations shall be within the scope of protection of the present invention as long as they do not exceed the scope of protection described in the claims.

Claims

1. A method for characterizing multipath fading robust radiation source signals based on nonlinear dynamics, characterized in that, Includes the following steps: S1. Receive signal data from the radiation source and perform data preprocessing to obtain the signal. ; S2, Calculate time delay parameters and embedding dimension and the signal Phase space reconstruction yields the matrix ; S3, for the matrix The matrix is ​​obtained by performing row direction transformation and channel cancellation. ; S4, for the matrix Perform column direction transformation and logarithmic transformation to obtain the reconstructed phase space matrix and two-dimensional Fourier transform logarithmic spectrum. ; Step S3 specifically includes: S30, will be transmitted through the channel The actual received signal is used This is represented in the frequency domain as: In the formula, , , Representing the original signal respectively Channel and received signals The frequency domain response, This represents the convolution operation. This represents a one-dimensional Fourier transform. S31. Calculate the phase space matrix RPS of the received signal y(t): S32, Use each phase point separately... It means, that is For a single phase point In other words, to carry out The point DFT can be used to obtain the frequency domain response. : S33, Simultaneously perform [action] on all phase points. Point DFT, the results are still placed in rows to form a new matrix. ,right Perform a line-wise DFT transformation, using... Indicates line direction Point DFT yields: Considering only the magnitude term, The corresponding spectrum can be represented as: ； S34, Calculate the matrix The frequency domain mean corresponding to the line direction transformation is used This indicates the result after processing: Right now With the channel remaining unchanged, the above equation can be further simplified to: In the formula, For the channel response in the frequency domain The mean at that point, and Represents the spectrum of all phase points in The mean at; S35, Using frequency domain mean For matrix Perform line-by-line channel effect cancellation operation, using The matrix representing the elimination of the channel: use Representation matrix No. Line number Column elements: 。 2. The method for characterizing multipath fading robust radiation source signals based on nonlinear dynamics according to claim 1, characterized in that: Step S1 specifically includes: S10. The receiver receives the signal data from the radiation source and performs detection, filtering, and noise reduction processing on the signal to obtain a sample of the signal to be processed. ; S11. Signal samples to be processed based on Fourier interpolation algorithm frequency offset value Make an estimate; S12, Root Frequency Offset Data The signal sample to be processed The signal is shifted to zero frequency to obtain the baseband signal. Then, the baseband signal is de-meaned and the energy is normalized to obtain the signal for feature extraction. .

3. The method for characterizing multipath fading robust radiation source signals based on nonlinear dynamics according to claim 1, characterized in that: Step S2 specifically includes: S20. Calculate the signal through correlation integral. Corresponding time delay parameters ; S21, Calculate the embedding dimension ; S22. According to Takens' theorem, phase space reconstruction is performed, and the signal... The RPS is represented as: In the formula, the matrix Each row represents an m-dimensional phase point, which in nonlinear dynamics reflects the current state of the system. OK Indicates the first Each phase point is The row vector, Total It consists of N row vectors, which can be regarded as N phase points.

4. The method for characterizing multipath fading robust radiation source signals based on nonlinear dynamics according to claim 1, characterized in that: Step S4 specifically includes: S40, For the matrix Perform column direction Point FFT yields a new matrix In the formula, Representation matrix No. Line number Column elements; S41, Calculate the matrix The energy values ​​are then logarithmically transformed, and the resulting matrix is ​​the reconstructed phase space matrix. The two-dimensional Fourier transform logarithmic spectrum is then used... express: 。

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