Robustness nonlinear frequency modulation signal identification method under complex conditions

Abstract

The invention belongs to the technical field of radar radiation source signal intra-pulse analysis, and particularly relates to a robust nonlinear frequency modulation signal identification method under complex conditions. Direct identification of nonlinear frequency modulation signals is realized through signal time-frequency structure characteristic analysis, self-adaptive parameter setting, self-adaptive preprocessing, multi-feature-domain characteristic measurement, multi-index joint judgment and the like, the radar signal in-pulse processing flow is greatly shortened, and influences of acquisition conditions, signal parameters, random interference and the like are avoided. The method can adapt to actual complex application scenes, and has the advantages of low calculation complexity, high robustness and the like.

Description

Technical Field

[0001] The invention belongs to the technical field of intra-pulse analysis of radar radiation source signals, and in particular relates to a robust nonlinear frequency modulation signal recognition method under complex conditions. Background Art

[0002] In modern electromagnetic environments, high signal density, diversified signal forms, and new radar systems and new uses are constantly being put into use, all of which pose a great challenge to the analysis and identification of radar signals. In addition, the existing radar signal intra-pulse analysis technology, namely radar modulation identification technology, is difficult to meet the requirements of robustness and accuracy under complex conditions such as low signal-to-noise ratio caused by non-ideal factors in the transmission and reception links, the presence of interference signals, changes in transmission conditions, and changes in signal parameters.

[0003] There are many commonly used radar modulation recognition methods, among which the commonly used index parameter methods include wavelet transform method, instantaneous feature method, time-frequency analysis method and high-order statistical method (Tang Yan. Radar signal parameter detection and intra-pulse recognition [D]. University of Electronic Science and Technology of China, 2021, Liu Fangjian, Li He, Chen Yunfan, et al. Algorithm simulation and verification based on radar signal intra-pulse modulation recognition [J]. Journal of Qingdao University (Engineering Technology Edition) 2023.38(2):68–74.). These methods often rely on a single index and set up a special process based on this index to determine the type of signal one by one. However, a single index cannot completely distinguish all types, and can only identify specific types of signals with obvious distinguishable characteristics. The scope of application of the algorithm is limited. According to a specific serial process, it is compared with the threshold of the alternative type one by one, and it is directly judged if certain conditions are met. This method takes too long to process, has limited analysis ability for a certain modulation type signal, and needs to process different signals differently when facing complex situations, especially when the signal acquisition is incomplete during reception and transmission, and there is noise and interference. The single judgment criterion of the serial process is difficult to apply directly.

[0004] Nonlinear frequency modulation signal (NLFM), also known as polynomial frequency modulation signal, has a nonlinear relationship between frequency and time. Its advantage is that pulse compression can be directly performed without weighting to obtain lower side lobes, thus avoiding the problem of low main-side lobe ratio. In terms of spectrum, the shape of this type of signal is similar to that of linear frequency modulation signal, but the spectrum edge is smoother and the spectrum peak is not flat, which is related to the use of window algorithm, so it is difficult to describe directly; in terms of time-phase characteristics, compared with linear frequency modulation signal, which is a straight diagonal line, NLFM signal is an inclined curve with the degree of inclination being the modulation slope, but the curve shape has no obvious distinguishing characteristics. In addition, considering that in actual applications, the phase and frequency will change to a certain extent after being affected by noise, interference, etc., and the instantaneous frequency has random fluctuations and glitches, the difficulty of direct confirmation is increased. Therefore, in order to obtain accurate signal information and quickly and accurately determine the signal type, it is necessary to process and identify the radar signal in a targeted manner according to the signal modulation characteristics.

[0005] The commonly used identification method for nonlinear frequency modulation signals is to fit the time-phase curve or instantaneous frequency curve with a cubic polynomial, and identify conventional radar signals, linear frequency modulation signals, and nonlinear frequency modulation signals respectively through the fitting coefficients (Xue Yanyan. Research on radar signal modulation identification and parameter estimation algorithm [D]. Nanjing University of Aeronautics and Astronautics, 2012. DOI: CNKI: CDMD: 2.1012.041669.); some studies use fractal dimension and phase similarity coefficient as intra-pulse characteristics of the signal to distinguish linear frequency modulation signals, nonlinear frequency modulation signals, two-phase coded signals, and four-phase coded signals (Qu Zhi, Huang Gaoming, Cheng Yuanguo, et al. Radar signal modulation identification method based on intra-pulse characteristic parameters [J]. Electronic Information Countermeasure Technology, 2012, 27(2): 5. DOI: 10.3969 / j.issn.1674-2230.2012.02.002). These identification methods are basically based on a single indicator to directly determine whether it is a nonlinear frequency modulation signal at a time, and only compare it with a limited number of other types, which is difficult to meet the application requirements under actual complex conditions. Summary of the invention

[0006] In order to accurately identify nonlinear frequency modulation signals in actual application scenarios, the present invention designs a robust nonlinear frequency modulation signal recognition method under complex conditions based on the structural characteristics of NLFM signals in the time and frequency domains. Direct recognition of NLFM signals is achieved through signal time-frequency structural characteristic analysis, adaptive parameter setting, adaptive preprocessing, multi-feature domain characteristic measurement, and multi-index joint judgment, which greatly shortens the radar signal pulse processing process and is not affected by acquisition conditions, signal parameters, random interference, etc. It can adapt to actual complex application scenarios and has the advantages of low computational complexity and high robustness.

[0007] The technical solution adopted by the present invention is: a robust nonlinear frequency modulation signal recognition method under complex conditions, which is divided into the following steps:

[0008] S1. Signal reception

[0009] The received signal to be processed is represented by s0(n0), where n0 represents the index value of the sampling point, n0 = 1, 2, ..., N0, N0 represents the initial signal length, and the signal sampling rate is f s .

[0010] S2. Adaptive filtering

[0011] S2.1 uses the real sinusoidal signal frequency estimation method based on DFT to estimate the peak frequency point f0 of the signal s0(n0) (for specific methods, see the document "Guo Luxiang. Research on real sinusoidal signal frequency estimation algorithm based on DFT [D], Southeast University, 2019.").

[0012] S2.2 estimates the bandwidth BW0 of the signal s0(n0), the specific steps are as follows:

[0013] S2.2.1 According to the non-parametric power spectrum estimation method, the power spectrum S(f) of the signal s0(n0) is obtained, where f represents the frequency index value of the power spectrum, and f = -f s / 2,...,f s / 2.

[0014] S2.2.2 Find the peak position f of S(f) max , and from f max Search to both sides and record the frequency value f when S(f) drops to 3dB of the peak value l and f r , f l Indicates the frequency value 3dB to the left of the peak, f r Indicates the frequency value 3dB to the right of the peak.

[0015] S2.2.3 Calculation of f l and f r The distance between them gives the bandwidth of the signal s0(n0) BW0=f r -f l .

[0016] S2.3 Adaptively filter the signal using an FFT filter with f0 as the center frequency according to the estimated peak frequency position f0 and bandwidth BW0. The specific steps are as follows:

[0017] S2.3.1 Set the filter bandwidth factor δ and set the starting frequency of the frequency domain filter to f start =f0-δ·BW0, the cut-off frequency is f end=f0+δ·BW0. In practical applications, δ is generally set to 0.85~1.2.

[0018] S2.3.2 Perform N on s0(n0) FFT Fourier transform of the point, convert it to the frequency domain, and then keep f start and f end The frequency components between them are set to zero, and the remaining frequency components are all set to zero. Finally, an inverse Fourier transform is performed to obtain the filtered signal s1(n0), n0 = 1, 2, ..., N0, usually N FFT Take 1024.

[0019] S3. Pulse leading and trailing edge detection

[0020] S3.1 Detect the envelope starting point n of the filtered signal s1(n0) start and end point n end , the specific method is as follows:

[0021] S3.1.1 Calculate the signal envelope a0(n0) = s1(n0), smooth a0(n0) to obtain the smoothed envelope a(n0), and calculate the average value of the smoothed envelope

[0022] S3.1.2 Setting the signal detection threshold th A , the detection signal envelope exceeds the threshold a(n0)≥th A The starting point index value n corresponding to part A start and the end point index n end . Generally take th A =0.5.

[0023] S3.2 Using n start and n end Intercept the leading and trailing edges of signal s1(n0), that is, take the signal index value n0=n start ,...,n end The corresponding part of the segment is taken as the intercepted signal s(n), where n represents the new signal index, n=1,2,...,N, N=n end -n start +1 indicates the new signal length after truncation.

[0024] S4. Instantaneous frequency calculation

[0025] S4.1 calculates the corresponding differential order L according to the signal length N. Different differential orders are set for signals of different lengths. According to engineering experience, the differential order L can generally be calculated according to the following formula:

[0026]

[0027] S4.2 estimates the instantaneous frequency of the signal s(n) according to the L-fold phase difference method. The specific calculation steps are as follows:

[0028] S4.2.1 Calculate the signal amplitude:

[0029]

[0030] Among them, s I (n), s Q (n) respectively represent the real and imaginary parts of the signal s(n): s(n) = s I (n)+i×s Q (n), i represents the imaginary unit, and Imag(·) represents the operation of taking an imaginary number.

[0031] S4.2.2 Use L-fold phase difference method to find the instantaneous frequency sequence p(n) to improve the adaptability to noise:

[0032]

[0033] S5. Quadratic curve fitting

[0034] The instantaneous frequency of a nonlinear frequency modulation signal can be well fitted with a quadratic curve, so the fitting error can be used as one of the bases for judging whether the signal is a nonlinear frequency modulation signal. The instantaneous frequency sequence p(n) is fitted below. The specific steps are as follows:

[0035] S5.1 Using quadratic curve Fit p(n) and obtain the fitting parameters based on the least squares estimation method

[0036] And the fitted instantaneous frequency series For the least squares estimation method, see "Steven M. Kay, Luo Pengfei. Fundamentals of Statistical Signal Processing [M]. Publishing House of Electronics Industry, 2014."

[0037] S5.2 Calculate the second-order curve fitting error ε:

[0038]

[0039] S5.3 Setting the error threshold th ε , generally set to 0.015~0.1.

[0040] S5.4 Determine the error situation: If the second-order curve fitting error ε is less than the threshold th ε , then proceed to step S7 to calculate the subsequent judgment index; otherwise, perform time-frequency analysis in step S6 to update the fitting result.

[0041] S6. Time-frequency analysis

[0042] Perform time-frequency analysis on the signal s(n), and update the instantaneous frequency sequence p(n) based on the time-frequency analysis results to further reduce the impact of random factors such as noise interference and improve the robustness of the algorithm. The specific steps are as follows:

[0043] S6.1 Perform short-time Fourier transform on the signal s(n) to obtain the time-frequency matrix in Represents N×N FFT dimensional complex set;

[0044] S6.2 calculates the energy of the time-frequency diagram matrix Μ0(n,f), that is, calculates the amplitude value point by point, and obtains Μ(n,f)=Μ0(n,f).

[0045] S6.3 Calculate the mean of Μ(n,f)

[0046] S6.4 Set the time-frequency energy threshold th M , compare M(n,f) at time n with The size of n will satisfy All K f values ​​are expressed as And calculate its mean, we get Indicates that at time n, The kth frequency value, k = 1, 2, K, K is the total number of frequencies that meet the conditions; M It is generally set to 0.7~0.9.

[0047] S6.5 According to the method in step S5, q(n) is fitted to obtain the corresponding fitting parameters and the fitted instantaneous frequency series Then the fitting error ε′ is obtained;

[0048] S6.6 compares the size of ε′ and ε: if ε′<ε, update the fitting result in step S5, update p(n) to q(n), and Updated to Will Updated to Will Updated to Update ε to ε′;

[0049] S7. First-order curve fitting

[0050] In order to avoid misjudgment with the linear frequency modulation signal, it is necessary to fit the instantaneous frequency sequence p(n). The specific steps are as follows:

[0051] S7.1 uses a straight line Fit p(n) and get the fitting slope based on the least squares estimation method Fitting bias value and the fitted instantaneous frequency series For the specific solution process of the least squares estimation method, please refer to "Steven M.Kay, Luo Pengfei. Fundamentals of Statistical Signal Processing [M]. Publishing House of Electronics Industry, 2014."

[0052] S7.2 Calculate the first-order curve fitting error ε LFM :

[0053]

[0054] S8. Time-Bandwidth Product Calculation

[0055] S8.1 estimate the bandwidth BW of the signal s(n) according to the method in step S2.2;

[0056] S8.2 calculates the pulse width PW of the signal s(n) according to the following formula:

[0057] PW=N / f s ;

[0058] S8.3 Combine the pulse width PW of step S8.2 and the bandwidth BW of step S8.1 to calculate the time-bandwidth product TB of the signal:

[0059] TB=PW·BW;

[0060] S9. Histogram center statistics

[0061] The instantaneous frequency of a nonlinear frequency modulation signal is not a straight line. It is generally a sloping curve with fluctuations at the start and end points. In order to avoid misjudgment with phase modulation signals, it is necessary to perform histogram center statistics; the details are as follows:

[0062] S9.1 Overall histogram peak statistics

[0063] S9.1.1 Take the amplitude of the instantaneous frequency sequence p(n) to obtain p(n); divide the value range of p(n) into M1 equal parts, count the frequency of p(n) values ​​in each classification interval, and obtain the corresponding frequency function h(x), x = 1,..., M1. Considering the algorithm complexity and statistical granularity, M1 can be between 80-150;

[0064] S9.1.2 Find the peak of the frequency function h(x) and record the number of peaks with a width greater than 3, expressed as the number of histogram peaks X. h ;

[0065] S9.2 After removing the head and tail parts of p(n) (according to engineering experience, the head and tail N / 20 parts can be removed), divide the remaining part into M2 segments. M2 can generally be taken as 10-20, and record the center of gravity of each segment. The specific steps are as follows:

[0066] S9.2.1 Divide the instantaneous frequency sequence p(n) into M2 segments as follows: Represent M2 different fragments, as follows:

[0067]

[0068] where i h =2,...,M2 represents the corresponding fragment number, ω h =9·N / (10·M2) represents the length of each segment.

[0069] S9.2.2 Calculate the fragments separately The corresponding center:

[0070] The specific calculation method is to remove the maximum and minimum values ​​of each segment, and then record the mean of the remaining values ​​as the center of the segment. The center of each segment is express.

[0071] S9.2.3 Segment trend analysis: If the center of the first segment P1 h To the center of the last segment If the value of shows a monotonically increasing or monotonically decreasing trend, let the fragment center mark F H =1; otherwise, set the fragment center mark F H =0.

[0072] S10. Segmental slope statistics

[0073] In order to avoid confusion with linear frequency modulation signals and misjudgment, it is necessary to perform segmented slope statistics on the instantaneous frequency. The instantaneous frequency sequence p(n) is divided into multiple overlapping segments, and then the least squares estimation method is used to perform a straight line fit on each segment to obtain the corresponding fitting slope, and the distribution of all slopes is counted. The specific steps are as follows:

[0074] S10.1 divides the instantaneous frequency sequence p(n) into M3 segments. According to engineering experience, the performance is slightly better when divided into odd-numbered segments. Generally, M3 can be 5-15. Therefore, the length of each segment is ω k =N / M3. Except for the first segment, move the starting point of segment 2-M3 forward by ω k / 2. Use Represents M3 different fragments, as follows:

[0075] p1(n)=p(n),n=1,....,ω k

[0076]

[0077] where i k =2,...,M3 represents the corresponding fragment number.

[0078] S10.2 Take the starting and ending parts of the instantaneous frequency sequence p(n) as and

[0079]

[0080]

[0081] S10.3 pairs Perform the least squares fitting of step S5 respectively to obtain the corresponding fitting slopes. express;

[0082] S10.4 Statistical slope:

[0083] S10.4.1 Calculate the variance of the fitted slopes for all segments

[0084] S10.4.2 Search The one with the largest absolute value is denoted as The one with the smallest absolute value is denoted as Calculate the maximum slope times the minimum slope

[0085] S11. Overall judgment

[0086] Combine the second-order curve fitting error ε obtained in S5.2 and the first-order curve fitting error ε obtained in S7.2 LFM , the slope multiple T obtained in S10.4.2, the number of histogram peaks X obtained in S9.1.2 h , S9.2.3 obtained fragment center mark F H , S8.3 obtained the time bandwidth product TB and other indicators, according to the following formula to calculate the symbol F NLFM :

[0087] F NLFM =[(ε<ε LFM )∧(ε<0.1·th ε )∧(F H =1)∧(X h ≥5)∧(TB≥8)∧(T≥2)]

[0088] Among them, ∧ represents the "AND" operation, and ∨ represents the "OR" operation.

[0089] If all conditions are met at the same time, that is, F NLFM If it is not zero, the signal is determined to be a NLFM signal; otherwise, the signal is of other types.

[0090] Technical effect:

[0091] The present invention proposes a robust nonlinear frequency modulation signal recognition method under complex conditions to adapt to the accurate recognition of nonlinear frequency modulation signals in actual non-ideal application scenarios. Specifically, it includes the design of a processing flow for nonlinear frequency modulation signal recognition, adaptive signal processing and adaptive parameter setting for complex transmission and reception conditions, and the design of multiple judgment indicators based on the structural characteristics of nonlinear frequency modulation signals in the time domain and frequency domain, which shortens the processing flow of the existing radar intra-pulse analysis system and improves the accuracy and robustness of radar modulation type recognition.

[0092] The technical benefit of the present invention is to directly identify and confirm the type of nonlinear frequency modulation signals under complex conditions, and to support the radar pulse analysis system to quickly and accurately identify radar targets in complex actual scenarios.

[0093] (1) A processing flow for directly identifying nonlinear FM signals under complex conditions is designed, and the second-order curve fitting error ε and the first-order curve fitting error ε are combined in the discrimination. LFM , slope multiple T, number of histogram peaks X h , fragment center mark F H , time-bandwidth product TB and other indicator parameters for comprehensive judgment.

[0094] (2) The present invention designs a method for obtaining the instantaneous frequency domain curve of the signal based on time-frequency analysis, and uses the signal distribution in the time-frequency image to obtain the main trend of the instantaneous frequency of the signal to increase the robustness against noise interference and other situations;

[0095] (3) In order to distinguish it from the linear frequency modulation signal, a segmented slope statistical method was designed. The entire instantaneous frequency was divided into equal parts, and the starting segment and the ending segment were specially extracted. Curve fitting was performed on all sub-segments, and the variance of the fitting slope and the multiples of the maximum and minimum values ​​were statistically calculated.

[0096] (4) In order to distinguish it from phase modulation signals represented by BPSK and QPSK, a histogram center statistical method is designed to calculate the number of frequency peaks and the trend of the main shape (nonlinear frequency modulation signals present monotonically increasing or monotonically decreasing); to increase robustness, the instantaneous phase is cut off and divided into sub-segments when counting the main shape, and the maximum and minimum values ​​are eliminated when counting the center, reducing the impact of abnormal fluctuations caused by noise interference;

[0097] (5) Robust adaptive signal processing and adaptive parameter setting are specially performed for actual complex scenarios, including signal adaptive bandwidth filtering, leading and trailing edge detection, and time-frequency analysis combined with error conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0098] Figure 1 It is a flow chart of the present invention;

[0099] Figure 2 is a flow chart of step S6 time-frequency analysis;

[0100] Figure 3 is a flowchart of the histogram center statistics in step S9;

[0101] Figure 4 is a flow chart of step S10 segmented slope statistics;

[0102] Figure 5 It is the time domain waveform of the ideal nonlinear frequency modulation NLFM signal;

[0103] Figure 6 is the spectrum of the ideal nonlinear frequency modulation NLFM signal;

[0104] Figure 7 It is the time-frequency diagram of the short-time Fourier transform of the ideal nonlinear frequency modulation NLFM signal;

[0105] Figure 8 is the instantaneous frequency of the ideal nonlinear frequency modulation NLFM signal;

[0106] Fig. 9 is the time domain waveform of the NLFM signal when the signal-to-noise ratio is 0dB;

[0107] Fig.10 is the spectrum of the NLFM signal when the signal-to-noise ratio is 0 dB;

[0108] Fig.11 is the instantaneous frequency of the NLFM signal obtained by step S4 when the signal-to-noise ratio is 0 dB;

[0109] Fig.12 It is the instantaneous frequency of the NLFM signal obtained by the first-order difference phase method when the signal-to-noise ratio is 0dB;

[0110] Fig.13 It is the time-frequency diagram obtained by short-time Fourier transform of NLFM signal when the signal-to-noise ratio is 0dB;

[0111] Fig.14 is the time domain waveform of the NLFM signal obtained after step S2 when the signal-to-noise ratio is 0 dB;

[0112] Fig.15is the spectrum of the NLFM signal obtained after step S2 when the signal-to-noise ratio is 0 dB;

[0113] Fig.16 It is the instantaneous frequency of the NLFM signal obtained by the first-order difference phase method when the signal-to-noise ratio is 0dB;

[0114] Fig.17 It is the instantaneous frequency of the NLFM signal obtained through S2 and S4 when the signal-to-noise ratio is 0dB;

[0115] Fig.18 It is the time-frequency diagram obtained by short-time Fourier transform of the filtered NLFM signal when the signal-to-noise ratio is 0dB;

[0116] Fig.19 is the time-frequency distribution of the filtered NLFM signal obtained by step S6.4 when the signal-to-noise ratio is 0 dB;

[0117] Fig. 20 It is the instantaneous frequency of the filtered NLFM signal obtained in step S7 when the signal-to-noise ratio is 0 dB. DETAILED DESCRIPTION

[0118] The specific implementation modes of the present invention will be further described below in conjunction with the accompanying drawings.

[0119] Figure 1 : is a flow chart of the present invention. The present invention proposes a robust nonlinear frequency modulation signal recognition method under complex conditions, which is divided into the following steps:

[0120] S1, signal reception, mainly refers to obtaining the signal to be analyzed;

[0121] S2, adaptive filtering, mainly estimates the frequency and bandwidth of the signal, and adaptively sets the filtering parameters according to the signal frequency and bandwidth to complete the signal filtering;

[0122] S3, pulse leading and trailing edge detection, mainly performs pulse detection on the signal obtained after filtering and intercepts the signal part;

[0123] S4, instantaneous frequency calculation, mainly calculates the instantaneous frequency of the signal based on the phase difference method;

[0124] S5, quadratic curve fitting, mainly uses the quadratic curve to fit the instantaneous frequency of the signal based on the least squares estimation method to obtain the fitting coefficient, fitting error, etc.;

[0125] S6, time-frequency analysis, mainly performs time-frequency analysis on the signal with high error in step S5, and updates the instantaneous frequency and its corresponding least square fitting result in combination with the characteristics of the time-frequency graph to improve the robustness of the algorithm;

[0126] S7, first-order curve fitting, mainly uses the first-order curve to fit the instantaneous frequency based on the least squares estimation method, and obtains the fitting slope, fitting error, etc.;

[0127] S8, histogram center statistics, mainly to avoid misjudgment with phase modulation signals, and to count the instantaneous frequency curve characteristics;

[0128] S9, segmented slope statistics, is mainly to avoid misjudgment as a linear frequency modulation signal, segmented statistics of the instantaneous frequency curve, and calculate indicators such as the center of gravity;

[0129] S10, comprehensive judgment, mainly uses a variety of index parameters to finally confirm the signal type and determine whether it is a nonlinear frequency modulation signal.

[0130] Figure 2 This is a flowchart of step S6 time-frequency analysis. In this step, the signal with a large fitting error in the quadratic curve fitting process in the previous step is further processed to increase the robustness to noise interference and other situations, that is, the corresponding instantaneous frequency characteristics are extracted using the time-frequency image. The specific process is to perform a short-time Fourier transform on the signal, calculate the representative frequency value at each moment based on the time-frequency matrix, combine to form a new instantaneous frequency, and then fit the quadratic curve again, and compare the two fitting errors. If the error corresponding to the time-frequency analysis is small, the fitting instantaneous frequency, fitting parameters and fitting error obtained at this time are used in the subsequent steps.

[0131] Figure 3 This is a flowchart of the histogram center statistics of step S9. This step is mainly to distinguish it from phase modulation signals represented by BPSK and QPSK. Under complex conditions, there are also mutation points and fluctuations in the instantaneous frequency of nonlinear frequency modulation signals, but the main trend of the instantaneous frequency of nonlinear frequency modulation signals is inclined, while the carrier frequency of signals such as BPSK and QPSK is fixed, that is, the main shape of the instantaneous frequency is horizontal, and there are mutation points at the code change. Moreover, due to the constraints of the code element type and code rate, the frequency of occurrence of the distribution position has a certain regularity. In contrast, the fluctuation points of nonlinear frequency modulation signals affected by various factors have obvious randomness. Therefore, this step starts from two parts to calculate the number of frequency peaks and the trend of the main shape (the nonlinear frequency modulation signal presents monotonically increasing or monotonically decreasing). In order to increase robustness, in step S9.2 of the main shape statistics, the instantaneous phase is cut off and divided into sub-segments, and the maximum and minimum values ​​are eliminated when the center is counted, reducing the influence of abnormal fluctuations caused by noise interference.

[0132] Figure 4This is a flowchart of the segmented slope statistics of step S10. This step is mainly to distinguish it from the linear frequency modulation signal. The main shapes of the instantaneous frequency of the linear frequency modulation signal and the nonlinear frequency modulation signal are both inclined lines, but the instantaneous frequency of the linear frequency modulation signal is a straight line with the same slope everywhere; the nonlinear frequency modulation signal is a curve, and the instantaneous frequency changes greatly at the starting point and the ending point, and the slope is a time-varying function. Therefore, this step divides the entire instantaneous frequency into equal parts, and specifically extracts the starting segment and the ending segment, performs curve fitting on all sub-segments, and statistically calculates the variance of the fitting slope and the multiples of the maximum and minimum values. The slope variance and slope multiples of the nonlinear frequency modulation signal are much larger than those of the linear frequency modulation signal, and can be used for judgment.

[0133] Figure 5 It is the time domain waveform of the ideal nonlinear frequency modulation NLFM signal. This figure shows the image of the signal amplitude changing with time in the time domain of the simulated nonlinear frequency modulation radar NLFM signal s0(n0) under ideal conditions. The horizontal axis in the figure is time in seconds; the vertical axis is the amplitude value of the signal. There is a zero point before and after the signal.

[0134] Figure 6 It is the spectrum of the ideal nonlinear frequency modulation NLFM signal. This figure shows the image of the ideal nonlinear frequency modulation NLFM signal s0(n0) in the frequency domain. It can be seen that there is an obvious main peak with multiple low side peaks on the left and right, which shows that the NLFM signal is composed of more continuous frequencies and the energy at different frequency points is different.

[0135] Figure 7 It is the time-frequency diagram of the short-time Fourier transform of the ideal nonlinear frequency modulation NLFM signal. This figure is the time-frequency image obtained after the ideal simulated NLFM signal is short-time Fourier transform. The horizontal axis is time, the unit is seconds, and the vertical axis is the frequency value, the unit is Hz. It can be seen that the signal is an inclined curve in the time-frequency diagram. It should be noted that because the signal is an ideal signal, no adaptive narrowband filtering is performed. This figure is the original received signal directly after step S3 and S6.2 to obtain the short-time Fourier transform corresponding to M (n, f).

[0136] Figure 8 is the instantaneous frequency of the ideal nonlinear frequency modulation NLFM signal. The horizontal axis represents the sample point index of the signal, and the vertical axis is the frequency value. The figure shows the instantaneous frequency curve image of the ideal nonlinear frequency modulation signal calculated by the L-fold phase difference method in step S4. It should be noted that since the signal is an ideal signal, the adaptive filtering processing of step S2 is not required, and the leading and trailing edge detection of step S3 is not performed. Instead, the result obtained by step S4 is directly performed on the received signal. It can be seen that the figure is an inclined curve, corresponding to the signal part, and the horizontal segment at the end of the curve is caused by the continuous zero points after the signal.

[0137] Fig. 9 is the time domain waveform of the NLFM signal when the signal-to-noise ratio is 0dB. The nonlinear frequency modulation signal in this figure is accompanied by additive Gaussian white noise, and the signal-to-noise ratio is 0dB. Figure 5 Compared with the time domain waveform of the ideal signal, it can be seen that the signal edge changes greatly, and the signal and the front and rear zero point boundaries are not obvious, indicating that there is little difference between the signal and the electromagnetic environment noise in the time domain, and it is difficult to directly detect and distinguish the signal.

[0138] Fig.10 This is the spectrum of the NLFM signal when the signal-to-noise ratio is 0dB. This figure shows the spectrum image of the nonlinear frequency modulation signal when the signal-to-noise ratio is 0dB. It can be seen that the signal has a certain bandwidth. Figure 6 Compared with the spectrum of the ideal signal in the image, the noise floor level of the signal has increased significantly. Compared with the signal waveform in the time domain, the signal position can still be clearly located in the frequency domain, and the noise and signal can be distinguished. However, the shape of the spectrum is no longer obvious. Figure 6 The secondary peaks are submerged by noise, making it difficult to determine the signal type through the spectrum.

[0139] Fig.11 is the instantaneous frequency of the NLFM signal obtained by step S4 when the signal-to-noise ratio is 0dB. The figure shows the instantaneous frequency curve image of the NLFM signal when the signal-to-noise ratio is 0dB calculated by the L-phase difference method in step S5. The horizontal axis represents the sample point index of the signal, and the vertical axis is the frequency value. It should be noted that the signal here has not been processed by the adaptive filtering of step S2, nor has the leading and trailing edge detection of step S3 been performed. Instead, the result obtained by step S4 is directly performed on the received signal. It can be seen that due to the influence of noise, there are a lot of large fluctuations on the instantaneous frequency curve, which is different from the Figure 8 Compared with the instantaneous frequency of the ideal signal in the signal-to-noise ratio, the instantaneous frequency has changed significantly under low signal-to-noise ratio and cannot be directly determined as a linear frequency modulation signal, indicating that the signal type cannot be determined directly based on the instantaneous phase under low signal-to-noise ratio.

[0140] Fig.12 is the instantaneous frequency of the NLFM signal obtained by the first-order differential phase method when the signal-to-noise ratio is 0dB. This figure is the instantaneous frequency curve of the nonlinear frequency modulation signal with a signal-to-noise ratio of 0dB obtained by the first-order phase differential method commonly used in the past. The horizontal axis represents the index value of the signal sample point, and the vertical axis represents the normalized signal frequency value. It can be seen that Figure 6 In comparison, affected by noise, the instantaneous frequency at this time no longer has the obvious characteristics of a conventional radar signal. It is difficult to directly determine the signal type based on this result, and it is even more impossible to directly confirm the nonlinear frequency modulation signal.

[0141] Fig.13This is the time-frequency diagram of the NLFM signal obtained by short-time Fourier transform when the signal-to-noise ratio is 0dB. The horizontal axis of the figure is time, in seconds, and the vertical axis is the frequency value, in Hz. It can be seen that due to the high noise level, compared to Figure 7 The time-frequency diagram of the ideal nonlinear frequency modulation NLFM signal in the figure has a large number of randomly scattered noise points, but there is still an obvious inclined curve in the time-frequency diagram, which shows that the time-frequency analysis method has a certain robustness to noise. It should be noted that this figure does not perform adaptive narrowband filtering on the signal, but the original received signal is directly obtained by short-time Fourier transform in steps S3 and S6.2 to obtain M(n,f).

[0142] Fig.14 is the time domain waveform of the NLFM signal obtained after step S2 when the signal-to-noise ratio is 0dB. This figure shows the time domain waveform of the signal after the adaptive filtering in step S2 of the present invention under low signal-to-noise ratio. The horizontal axis is time in seconds, and the vertical axis is the signal amplitude value. It can be seen that after processing, compared with Fig. 9 The unprocessed signal time domain waveform in Fig.14 The fluctuation of the signal amplitude has decreased to a certain extent, but compared with Figure 5 In the ideal signal time domain waveform, the boundary between the low signal-to-noise ratio signal and the noise after being affected by noise is still not obvious.

[0143] Fig.15 It is the spectrum of the NLFM signal obtained after step S2 when the signal-to-noise ratio is 0dB. This figure shows the spectrum waveform of the signal after the adaptive filtering and pulse leading and trailing edge detection of step S2-3 of the present invention under low signal-to-noise ratio. It can be seen that after processing, the noise is significantly suppressed, and compared with the spectrum of the ideal signal, the secondary peak is also suppressed.

[0144] Fig.16 It is the instantaneous frequency of the NLFM signal obtained by the first-order differential phase method when the signal-to-noise ratio is 0dB. This figure shows the instantaneous frequency of the signal after the adaptive filtering and pulse front and rear edge detection in step S2-3 of the present invention under low signal-to-noise ratio and the first-order phase differential processing of the signal. The horizontal axis represents the sampling point, and the vertical axis represents the normalized instantaneous frequency. It can be seen that compared with Fig.12 The instantaneous frequency in the processed signal is Fig.16 The main trend of the instantaneous frequency of the signal, i.e., the inclined curve, can be shown in FIG. 1 , which indicates that the processing of steps S2-S3 of the present invention has a certain effect of adapting to low noise conditions. However, compared with Figure 8 The instantaneous frequency of the ideal signal in Fig.16 The curve in the figure still has a lot of messy lines (or abnormal discrete points) caused by noise.

[0145] Fig.17is the instantaneous frequency of the NLFM signal obtained by S2 and S4 when the signal-to-noise ratio is 0dB. This figure shows the instantaneous frequency of the signal obtained by the adaptive filtering of step S2 of the present invention and the L-fold phase difference processing of S4 under low signal-to-noise ratio. The horizontal axis represents the sampling point and the vertical axis represents the normalized instantaneous frequency. It can be seen that compared with Fig.16 The L-fold phase difference processing designed by the present invention can suppress abnormal points, better extract the instantaneous frequency, and have a better suppression effect on noise. The processed signal is Figure 8 The instantaneous frequency curve of the ideal signal is not much different, with only slight fluctuations. The type of nonlinear frequency modulation signal can be determined by this curve, indicating that the processing of steps S2 and S4 of the present invention has a certain effect of adapting to low noise conditions.

[0146] Fig.18 This is the time-frequency diagram of the NLFM signal after filtering when the signal-to-noise ratio is 0dB, and the signal is transformed by short-time Fourier transform. This figure is the time-frequency image of the signal after short-time Fourier transform after processing in steps S2-S4. The horizontal axis is time, in seconds, and the vertical axis is frequency value, in Hz. It can be seen that after filtering and detection, the original Fig.14 A large number of noise points scattered on the signal are filtered out, leaving only some noise points near the signal. These remaining noise points can be eliminated in step S6.4 to achieve adaptation to the noise environment.

[0147] Fig.19 is the time-frequency distribution of the filtered NLFM signal obtained by step S6.4 when the signal-to-noise ratio is 0dB. Specifically, the figure is a signal with a signal-to-noise ratio of 0dB directly proceeding to step S6 after steps S2 and S3. The corresponding value in the figure is the value that satisfies step S6.4.2 All frequency points of . It can be seen that compared with Fig.18 There are some snowflakes caused by noise left in the image. Fig.19 Only the frequency part corresponding to the signal is retained. The instantaneous frequency extracted on this basis can better suppress noise, thereby achieving a robust effect.

[0148] Fig. 20 is the instantaneous frequency of the filtered NLFM signal obtained by step S7 when the signal-to-noise ratio is 0dB. Fig.19 The instantaneous frequency q(n) is obtained based on the result after step S6.4.3. It can be seen that compared with Fig.11 and Fig.16 The instantaneous frequency image in is Fig. 20 The middle curve is an inclined curve with slight fluctuations and has obvious characteristics. It can be directly determined as a nonlinear frequency modulation signal, indicating that this method has strong signal feature extraction capability and robustness.

Claims

1. A robust nonlinear frequency modulation signal recognition method under complex conditions, characterized in that: The method is divided into the following steps: S1. Signal reception The received signal to be processed is represented by s0(n0), where n0 represents the index value of the sampling point, n0 = 1, 2, ..., N0, N0 represents the initial signal length, and the signal sampling rate is f s ; S2. Adaptive filtering S2.1 uses the real sinusoidal signal frequency estimation method based on DFT to estimate the peak frequency position f0 of the signal s0(n0); S2.2 estimates the bandwidth BW0 of the signal s0(n0), the specific steps are as follows: S2.2.1 According to the non-parametric power spectrum estimation method, the power spectrum S(f) of the signal s0(n0) is obtained, where f represents the frequency index value of the power spectrum, and f = -f s / 2,...,f s / 2; S2.2.2 Find the peak position f of S(f) max , and from f max Search to both sides and record the frequency value f when S(f) drops to 3dB of the peak value l and f r , f l Indicates the frequency value 3dB to the left of the peak, f r Indicates the frequency value 3dB to the right of the peak; S2.2.3 Calculation of f l and f r The distance between them gives the bandwidth of the signal s0(n0) BW0=f r -f l ; S2.3 Adaptively filter the signal using an FFT filter with f0 as the center frequency according to the estimated peak frequency position f0 and bandwidth BW0. The specific steps are as follows: S2.3.1 Set the filter bandwidth factor δ and set the starting frequency of the frequency domain filter to f start =f0-δ·BW0, the cut-off frequency is f end =f0+δ·BW0; S2.3.2 Perform N on s0(n0) FFT Fourier transform of the point, convert it to the frequency domain, and then keep f start and f end The frequency components between them are set to zero, and the remaining frequency components are all set to zero. Finally, an inverse Fourier transform is performed to obtain the filtered signal s1(n0), n0=1,2,...,N0; S3. Pulse leading and trailing edge detection S3.1 Detect the envelope starting point n of the filtered signal s1(n0) start and end point n end , the specific method is as follows: S3.1.1 Calculate the signal envelope a0(n0) = |s1(n0)|, smooth a0(n0) to obtain the smoothed envelope a(n0), and calculate the average value of the smoothed envelope S3.1.2 Setting the signal detection threshold th A , the detection signal envelope exceeds the threshold a(n0)≥th A The starting point index value n corresponding to part A start and the end point index n end ; S3.2 Using n start and n end Intercept the leading and trailing edges of signal s1(n0), that is, take the signal index value n0=n start ,...,n end The corresponding part of the segment is taken as the intercepted signal s(n), where n represents the new signal index, n=1,2,...,N, N=n end -n start +1 indicates the new signal length after interception; S4. Instantaneous frequency calculation S4.1 calculates the corresponding differential order L according to the signal length N. Different differential orders are set for signals of different lengths. S4.2 estimates the instantaneous frequency of the signal s(n) according to the L-fold phase difference method. The specific calculation steps are as follows: S4.2.1 Calculate the signal amplitude: Among them, s I (n), s Q (n) respectively represent the real and imaginary parts of the signal s(n): s(n) = s I (n)+i×s Q (n), i represents the imaginary unit, and Imag(·) represents the operation of taking imaginary numbers; S4.2.2 Use L-fold phase difference method to find the instantaneous frequency sequence p(n) to improve the adaptability to noise: S5. Quadratic curve fitting The instantaneous frequency of the nonlinear frequency modulation signal can be well fitted with a quadratic curve, so the fitting error can be used as one of the bases for judging whether the signal is a nonlinear frequency modulation signal; the instantaneous frequency sequence p(n) is fitted below, and the specific steps are as follows: S5.1 Using quadratic curve Fit p(n) and obtain the fitting parameters based on the least squares estimation method and the fitted instantaneous frequency series S5.2 Calculate the second-order curve fitting error ε: S5.3 Setting the error threshold th ε ; S5.4 Determine the error situation: If the second-order curve fitting error ε is less than the threshold th ε , then proceed to step S7 to calculate the subsequent judgment index; otherwise, perform the time-frequency analysis of step S6 to update the fitting result; S6. Time-frequency analysis Perform time-frequency analysis on the signal s(n), and update the instantaneous frequency sequence p(n) based on the time-frequency analysis results to further reduce the influence of random factors such as noise interference and improve the robustness of the algorithm. The specific steps are as follows: S6.1 Perform short-time Fourier transform on the signal s(n) to obtain the time-frequency matrix in Represents N×N FFT dimensional complex set; S6.2 Calculate the energy of the time-frequency diagram matrix Μ0(n,f), that is, find the amplitude value point by point, and obtain Μ(n,f)=|Μ0(n,f)|; S6.3 Calculate the mean of Μ(n,f) S6.4 Set the time-frequency energy threshold th M , compare M(n,f) at time n with The size of n will satisfy All K f values ​​are expressed as And calculate its mean, we get Indicates that at time n, The kth frequency value of , k = 1, 2, ..., K, K is the total number of frequencies that meet the conditions; S6.5 According to the method in step S5, q(n) is fitted to obtain the corresponding fitting parameters and the fitted instantaneous frequency series Then the fitting error ε′ is obtained; S6.6 compares the size of ε′ and ε: if ε′<ε, update the fitting result in step S5, update p(n) to q(n), and Updated to Will Updated to Will Updated to Update ε to ε′; S7. First-order curve fitting In order to avoid misjudgment with the linear frequency modulation signal, it is necessary to fit the instantaneous frequency sequence p(n); the specific steps are as follows: S7.1 uses a straight line Fit p(n) and get the fitting slope based on the least squares estimation method Fitting bias value and the fitted instantaneous frequency series S7.2 Calculate the first-order curve fitting error ε LFM : S8. Time-Bandwidth Product Calculation S8.1 estimate the bandwidth BW of the signal s(n) according to the method in step S2.2; S8.2 calculates the pulse width PW of the signal s(n) according to the following formula: PW=N / f s ; S8.3 Combine the pulse width PW of step S8.2 and the bandwidth BW of step S8.1 to calculate the time-bandwidth product TB of the signal: TB=PW·BW; S9. Histogram center statistics The instantaneous frequency of a nonlinear frequency modulation signal is not a straight line. It is generally a sloping curve with fluctuations at the start and end points. In order to avoid misjudgment with phase modulation signals, it is necessary to perform histogram center statistics; the details are as follows: S9.1 Overall histogram peak statistics S9.1.1 Take the amplitude of the instantaneous frequency sequence p(n) to obtain |p(n)|; divide the value range of |p(n)| into M1 equal parts, count the frequency of |p(n)| values ​​in each classification interval, and obtain the corresponding frequency function h(x), x=1,...,M1; S9.1.2 Find the peak of the frequency function h(x) and record the number of peaks with a width greater than 3, expressed as the number of histogram peaks X. h ; S9.2 After removing the head and tail parts of p(n), divide the remaining part into M2 segments and record the centroid of each segment; the specific steps are as follows: S9.2.1 Divide the instantaneous frequency sequence p(n) into M2 segments as follows: Represent M2 different fragments, as follows: where i h =2,...,M2 represents the corresponding fragment number, ω h =9·N / (10·M2) represents the length of each segment; S9.2.2 Calculate the fragments separately The corresponding center: The specific calculation method is to remove the maximum and minimum values ​​of each segment, and then record the mean of the remaining values ​​as the center of the segment. The center of each segment is express; S9.2.3 Segment trend analysis: If the center of the first segment To the center of the last segment If the value of shows a monotonically increasing or monotonically decreasing trend, let the fragment center mark F H =1; otherwise, set the fragment center mark F H =0; S10. Segmental slope statistics In order to avoid confusion with linear frequency modulation signals and misjudgment, it is necessary to perform segmented slope statistics on the instantaneous frequency; divide the instantaneous frequency sequence p(n) into multiple overlapping segments, and then use the least squares estimation method to perform linear fitting on each segment to obtain the corresponding fitting slope, and then count the distribution of all slopes; the specific steps are as follows: S10.1 divides the instantaneous frequency sequence p(n) into M3 segments, so the length of each segment is ω k =N / M3; except for the first segment, move the starting point of segment 2-M3 forward ω k / 2; use Represents M3 different fragments, as follows: p1(n)=p(n),n=1,....,ω k where i k =2,...,M3 represents the corresponding fragment number; S10.2 Take the starting and ending parts of the instantaneous frequency sequence p(n) as and S10.3 pairs Perform the least squares fitting of step S5 respectively to obtain the corresponding fitting slopes. express; S10.4 Statistical slope: S10.4.1 Calculate the variance of the fitted slopes for all segments S10.4.2 Search The one with the largest absolute value is denoted as The one with the smallest absolute value is denoted as Calculate the maximum slope times the minimum slope S11. Overall judgment Combine the second-order curve fitting error ε obtained in S5.2 and the first-order curve fitting error ε obtained in S7.2 LFM , the slope multiple T obtained in S10.4.2, the number of histogram peaks X obtained in S9.1.2 h , S9.2.3 obtained fragment center mark F H , S8.3 obtained the time bandwidth product TB and other indicators, according to the following formula to calculate the symbol F NLFM : F NLFM =[(ε<ε LFM )∧(ε<0.1·th ε )∧(F H =1)∧(X h ≥5)∧(TB≥8)∧(T≥2)] Among them, ∧ represents the "and" operation, and ∨ represents the "or" operation; If all conditions are met at the same time, that is, F NLFM If it is not zero, the signal is determined to be a NLFM signal; otherwise, the signal is of other types.

2. A robust nonlinear frequency modulation signal recognition method under complex conditions according to claim 1, characterized in that: In S2.3.1, the filter bandwidth factor δ is set to 0.85-1.

2.

3. A robust nonlinear frequency modulation signal recognition method under complex conditions according to claim 1, characterized in that: In S2.3.2, N FFT Take 1024.

4. A robust nonlinear frequency modulation signal recognition method under complex conditions according to claim 1, characterized in that: In S3.1.2, the signal detection threshold th A =0.

5.

5. A robust nonlinear frequency modulation signal recognition method under complex conditions according to claim 1, characterized in that: In S4.1, the difference order L is calculated according to the following formula:

6. A robust nonlinear frequency modulation signal recognition method under complex conditions according to claim 1, characterized in that: In S5.3, the error threshold th ε Set to 0.015~0.

1.

7. A robust nonlinear frequency modulation signal recognition method under complex conditions according to claim 1, characterized in that: In S6.4, the time-frequency energy threshold th M Set to 0.7~0.

9.

8. A method for identifying robust nonlinear frequency modulation signals under complex conditions according to claim 1, characterized in that: In S9.1.1, M1 is between 80 and 150.

9. A robust nonlinear frequency modulation signal recognition method under complex conditions according to claim 1, characterized in that: In S9.2, after removing the first and last N / 20 parts of p(n), the remaining part is divided into M2 segments, where M2 takes a value between 10 and 20.

10. A method for identifying robust nonlinear frequency modulation signals under complex conditions according to claim 1, characterized in that: In S10.1, M3 is an odd number between 5 and 15.

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