Robustness linear 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 linear frequency modulation signal identification method under complex conditions. Through multi-index joint constraint and hierarchical discrimination processing, adaptive parameter setting and adaptive preprocessing are carried out in combination with signal time-frequency structure characteristics, direct identification of linear frequency modulation signal robustness is realized, radar signal in-pulse processing flow is greatly shortened, and the method is not influenced by acquisition conditions, signal parameters, random interference and the like, and has a wide application prospect. 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 linear frequency modulation signal recognition method under complex conditions. Background Art

[0002] Due to the rapid development of modern radar systems, in order to improve the working performance of radars and achieve low probability of interception and anti-interference, new systems and new purpose radars are constantly put into use. Radar signals no longer use simple single parameter radar modulation types, signal forms are becoming more complex, and modulation parameters are also becoming more agile and diverse. Under this circumstance, the recognition of radar signal intra-pulse modulation types can no longer adapt to the increasingly diverse signal types and increasingly complex signal environments, and it can no longer meet the needs of robust and accurate recognition 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] The idea of ​​existing radar signal modulation recognition methods is to calculate the value of one or more index parameters, and then judge from a number of set alternative types in turn according to the preset rules and parameter conditions. Moreover, the existing methods are generally targeted at certain selected signal types, that is, the signal types in the alternative set are limited and cannot include all types. For example, the literature [Tang Yan. Radar signal parameter detection and intra-pulse identification [D]. University of Electronic Science and Technology of China, 2021] mainly targets 12 types of radar signals, including LFM, SFM, FSK, BPSK, QPSK, Frank, P1, P2, P3, P4, LFM-BPSK and FSK-BPSK. The literature [Shi Hanyu, Si Weijian, Xia Xinfan. Identification of typical radar signal modulation types under low signal-to-noise ratio [J]. Guidance and Fuze, 2023, 44(4):9-16] mainly targets linear frequency modulation (LFM) signals, nonlinear frequency modulation (NLFM) signals and phase shift keying (PSK) signals in frequency modulation signals. Therefore, when the signal type is unknown, the recognition results are often not completely reliable and cannot be directly extended to practical applications. For example, if the actual situation contains signal types other than those in the above alternative set, the credibility of the recognition results of LFM signals will be greatly reduced. Moreover, each type of algorithm often has its own advantages and disadvantages and cannot be adapted to all signal types. In addition, since the experimental settings in existing research are relatively ideal, it is difficult to directly promote and apply them under complex actual conditions.

[0004] If we adjust the processing ideas, set up a special processing flow for a certain type of signal, and directly confirm the signal type based on the essential characteristics of the signal, we can greatly shorten the processing flow and save processing time. Among many signal types, linear frequency modulation signal (LFM) is the most classic pulse compression signal, which has a large time-bandwidth product, is insensitive to Doppler frequency shift, and can simultaneously improve the radar's effective range and range resolution. It is widely used in practice. In the actual radar signal intra-pulse modulation type identification, if the linear frequency modulation signal can be accurately identified at the first time, that is, the LFM signal can be directly confirmed under complex conditions, then for the entire signal analysis and identification system, the amount of calculation can be greatly reduced and the robustness can be improved.

[0005] Ideally, the instantaneous frequency of the LFM signal is a smooth and inclined straight line. However, in actual applications, the phase and frequency will change to a certain extent after being affected by noise and interference. The instantaneous frequency has random fluctuations and glitches, which makes it difficult to confirm directly. In previous studies on linear frequency modulation signals, only a single indicator or a single characteristic is often used to identify linear frequency modulation signals at one time, such as the signal analysis method based on the quadratic phase function (QPF) (Wang Yong, Jiang Yicheng. A new LFM signal parameter estimation algorithm [J]. Signal Processing, 2008 (01): 132-134), and some studies use the peak order of fractional Fourier transform (Tang Yan. Radar signal parameter detection and intra-pulse identification [D]. University of Electronic Science and Technology of China, 2021, Shi Hanyu, Si Weijian, Xia Xinfan. Identification of typical radar signal modulation types under low signal-to-noise ratio [J]. Guidance and Fuze, 2023, 44 (4): 9-16). A single indicator or a single characteristic cannot adapt to complex environments. To obtain accurate linear frequency modulation signal information and quickly and accurately determine the signal type, it is necessary to perform more comprehensive, robust and targeted processing based on the signal modulation characteristics. Summary of the invention

[0006] In order to realize accurate recognition of linear frequency modulation signals in practical application scenarios, the present invention designs a robust linear frequency modulation signal recognition method under complex conditions in combination with the structural characteristics of LFM signals in the time and frequency domains. Direct recognition of the robustness of LFM signals is achieved through multi-index joint constraints, hierarchical discrimination processing, and adaptive parameter setting and adaptive preprocessing in combination with the time-frequency structure characteristics of the signal, which greatly shortens the radar signal pulse processing process, is not affected by acquisition conditions, signal parameters, random interference, etc., 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 linear 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 0.55-0.85.

[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 remaining frequency components are all set to zero, and finally the 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 . Signal detection threshold th A 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 corresponding to signals of different lengths can generally be adaptively set according to the following formula:

[0026]

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

[0028] S4.2.1 Calculate the signal amplitude, expressed as p0(n):

[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 the L-fold phase difference method to find the instantaneous frequency sequence p(n) to improve the adaptability to noise:

[0032]

[0033] S5. Characteristic curve fitting

[0034] S5.1 Use straight line Fit p(n) and use the least squares estimation method to get the fitting slope Fitting bias value 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."

[0035] S5.2 Calculate the fitting error:

[0036]

[0037] S5.3 Setting the error threshold th ε , generally set to 0.015~0.1.

[0038] S5.4 Determine the error situation: If the fitting error 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.

[0039] S6. Time-frequency analysis

[0040] 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:

[0041] S6.1 Perform short-time Fourier transform on the signal s(n) to obtain the time-frequency matrix in Represents N×N FFT A collection of dimensional complex matrices;

[0042] 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)|.

[0043] S6.3 Calculate the mean of Μ(n,f)

[0044] S6.4 extracts the time-frequency distribution. The specific steps are as follows:

[0045] S6.4.1 Setting the time-frequency energy threshold th M , generally set to 0.7~0.9;

[0046] S6.4.2 Compare M(n,f) at time n with The size of n will satisfy The total f-value is expressed as 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;

[0047] S6.5 According to the method in step S5, the curve q(n) is fitted to obtain the corresponding fitting slope Fitting bias value and fitting error ε′;

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

[0049] S7. Time-Bandwidth Product Calculation

[0050] S7.1 estimate the bandwidth BW of the signal s(n) according to the method in step S2.2;

[0051] S7.2 calculates the pulse width PW of the signal s(n) according to the following formula:

[0052] PW=N / f s ;

[0053] S7.3 combines the pulse width PW of step S7.1 and the bandwidth BW of step S7.2 to calculate the time-bandwidth product TB of the signal:

[0054] TB=PW·BW;

[0055] S8. Instantaneous frequency variance characteristics

[0056] Calculate the variance characteristics of the instantaneous frequency to prevent misjudgment as a phase modulation signal or a frequency modulation signal. The specific steps are as follows:

[0057] S8.1 Calculate the mean of the instantaneous frequency sequence p(n) Then calculate the variance σ1 of the instantaneous frequency p(n):

[0058]

[0059] S8.2 Combine the instantaneous frequency sequence in step S5.1 Calculate the linear variance σ2 of the instantaneous frequency p(n):

[0060]

[0061] S8.3 Calculate the absolute value LV of the difference between the variance σ1 and the linear variance σ2:

[0062] LV = |σ1-σ2|;

[0063] S9. Basic characteristics judgment

[0064] S9.1 Calculate the signal normalized modulation slope

[0065] S9.2 uses the time-bandwidth product TB, fitting error ε, and normalized modulation slope Calculate the discrimination flag F1:

[0066]

[0067] Wherein, ∧ represents an "AND" operation. If the above requirement is met, that is, F1=1, it is preliminarily determined to be a linear frequency modulation signal, and the process proceeds to step S10; if the requirement is not met, the process proceeds to step S9.3.

[0068] S9.3 Calculate the discrimination flag F2 according to the following formula:

[0069] F2=[(ε<0.01·th ε )∧(LV>3)∧(TB≥8)]

[0070] If the requirement is met, that is, F2=1, it is preliminarily determined to be a linear frequency modulation signal, and the process continues to step S10; if the requirement is not met, it is identified as other types, and the process ends.

[0071] S10. Segmental slope statistics

[0072] In order to avoid confusion with nonlinear frequency modulation signals and misjudgment, the instantaneous frequency sequence p(n) is segmented, 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 statistically analyzed. The specific steps are as follows:

[0073] S10.1 Divide the instantaneous frequency sequence p(n) into M segments, each segment length is ω = N / M, and M can be 5-15 in general. Except for the first segment, move the starting point of the 2nd to Mth segment forward by ω / 2, and the length is 3·ω / 2. M (n) represent M different fragments, as follows:

[0074] p1(n)=p(n),n=1,....,ω,

[0075] p i (n)=p(n),n=ω·(i-1)-ω / 2+1,....,i·ω,i=2,...,M;

[0076] S10.2 for p1(n)~p M (n) Perform characteristic curve fitting based on the least squares estimation method in step S5 to obtain the corresponding fitting slopes, and use express;

[0077] S10.3 Statistical slope:

[0078] S10.3.1 Calculate the variance of the fitted slopes for all segments

[0079] S10.3.2 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

[0080] S11. Nonlinear curve fitting

[0081] S11.1 Using quadratic curve Fit p(n) and use the least squares estimation method to solve the fitting parameters And the fitted instantaneous frequency series

[0082] S11.2 Calculate the nonlinear curve fitting error ε NLFM :

[0083]

[0084] S12. Hierarchical Decision

[0085] S12.1 Calculate the flag F3 according to the following formula:

[0086] F3=(V k >0.2)∨[(V k >0.1)∧(T>5)]

[0087] Where ∨ represents an "or" operation. If the condition is met, that is, F3 = 1, the signal is not a linear frequency modulation signal, and other types are output, and the process ends; otherwise, step S12.2 is performed.

[0088] S12.2 Calculate the flag F4 according to the following formula:

[0089] F4=[(V k >0.08)∧(T>1.9)]∧[(ε NLFM <0.1·th ε +0.005)∧(ε NLFM <ε)]

[0090] If the condition is met, that is, F4 = 1, the signal is not a linear frequency modulation signal, and other types are output, and the process ends; otherwise, proceed to step S12.3;

[0091] S12.3 Calculate the flag F5 according to the following formula:

[0092] F5=(ε<0.005·th ε )

[0093] If the condition is met, ie, F5=1, the signal is a linear frequency modulation signal; otherwise, the signal is determined to be other types.

[0094] Technical effect:

[0095] The present invention proposes a robust linear frequency modulation signal recognition method under complex conditions to adapt to the accurate recognition of linear frequency modulation signals in actual non-ideal application scenarios. Specifically, it includes the design of a processing flow for linear frequency modulation signal recognition, adaptive signal processing and adaptive parameter setting for complex transmission and reception conditions, multiple judgment indicators based on the structural characteristics of the linear frequency modulation signal in the time domain and frequency domain and their calculation methods, and a multi-indicator hierarchical judgment method. It can adapt to complex application scenarios to realize direct recognition of linear frequency modulation signals, shorten the processing flow of the existing radar intra-pulse analysis system, and improve the accuracy and robustness of radar modulation type recognition.

[0096] The technical benefit of the present invention is to directly identify and confirm the type of linear frequency modulation signal under complex conditions, and support the radar pulse analysis system to quickly and accurately identify radar targets in complex actual scenarios. It is mainly reflected in:

[0097] (1) A processing flow for directly identifying linear frequency modulation signals under complex conditions is designed. A hierarchical discrimination method is used to combine multiple domain indicators such as modulation slope estimation, characteristic curve fitting error, instantaneous frequency variance characteristics, time-bandwidth product, nonlinear curve fitting error, segmented slope distribution variance, and segmented slope multiples for comprehensive judgment. In order to further shorten the processing flow, the time-bandwidth product, fitting error, normalized modulation slope and other indicators are combined in practice to determine whether the signal has the basic characteristics of linear frequency modulation signals. In this link, conventional radar signals, phase modulation signals, dual linear frequency modulation signals, and frequency shift keying signals can be excluded, eliminating the subsequent calculation links, and then focusing on distinguishing similar types.

[0098] (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;

[0099] (3) To avoid misjudging the signal as a nonlinear frequency modulation signal, a segmented slope statistical method and a nonlinear curve fitting method were designed. Indicators such as the nonlinear curve fitting error, the segmented slope distribution variance, and the segmented slope multiple were designed to accurately distinguish the two types of signals.

[0100] (4) To avoid misjudging the signals as FSK or PSK modulation signals, the variance characteristics of the instantaneous frequency are used for differentiation;

[0101] (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. In terms of threshold setting, adaptive threshold values ​​are set based on signal conditions, such as the signal modulation slope threshold th K ;

[0102] (6) A hierarchical decision process is designed to gradually remove abnormal situations according to various situations and achieve accurate distinction of linear frequency modulation signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0103] Figure 1 It is a flow chart of the present invention;

[0104] Figure 2 is a flow chart of the time-frequency analysis step of step S6;

[0105] Figure 3 is a flowchart of basic characteristic determination in step S9;

[0106] Figure 4 is a flowchart of the hierarchical discrimination of step S12;

[0107] Figure 5It is the time domain waveform of the ideal linear frequency modulation LFM signal;

[0108] Figure 6 It is the spectrum waveform of the ideal linear frequency modulation LFM signal;

[0109] Figure 7 It is the time-frequency image obtained by short-time Fourier transform of the ideal linear frequency modulation LFM signal;

[0110] Figure 8 is the instantaneous frequency of the ideal linear frequency modulation LFM signal obtained in step S4;

[0111] Fig. 9 It is the instantaneous frequency fitting result of the ideal linear frequency modulation LFM signal;

[0112] Fig.10 It is the time domain waveform of the linear frequency modulation LFM signal when the signal-to-noise ratio is -5dB;

[0113] Fig.11 It is the spectrum diagram of linear frequency modulation LFM signal when the signal-to-noise ratio is -5dB;

[0114] Fig.12 is the instantaneous frequency of the linear frequency modulation LFM signal obtained by step S4 when the signal-to-noise ratio is -5dB;

[0115] Fig.13 It is the instantaneous frequency of the linear frequency modulation LFM signal obtained by first-order phase difference when the signal-to-noise ratio is -5dB;

[0116] Fig.14 It is the time-frequency image obtained by short-time Fourier transform of linear frequency modulation LFM signal when the signal-to-noise ratio is -5dB;

[0117] Fig.15 is the time domain waveform of the linear frequency modulation LFM signal obtained after steps S2 and S3 when the signal-to-noise ratio is -5dB;

[0118] Fig.16 is the frequency domain waveform of the linear frequency modulation LFM signal obtained after steps S2 and S3 when the signal-to-noise ratio is -5dB;

[0119] Fig.17 is the first-order phase difference of the LFM signal after steps S2 and S3 when the signal-to-noise ratio is -5dB;

[0120] Fig.18 is the instantaneous frequency of the LFM signal after steps S2-S4 when the signal-to-noise ratio is -5dB;

[0121] Fig.19 is the short-time Fourier transform time-frequency diagram of the LFM signal after steps S2-S3 when the signal-to-noise ratio is -5dB;

[0122] Fig. 20 is the time-frequency distribution of the LFM signal obtained in step S6.4 when the signal-to-noise ratio is -5dB;

[0123] Fig.21 is the instantaneous frequency of the LFM signal after steps S2-S4 when the signal-to-noise ratio is -5dB;

[0124] Fig. 22 It is the instantaneous frequency fitting result of the linear frequency modulation LFM signal obtained by time-frequency analysis when the signal-to-noise ratio is -5dB. DETAILED DESCRIPTION

[0125] The specific implementation modes of the present invention will be further described below in conjunction with the accompanying drawings.

[0126] Figure 1 : is a flow chart of the present invention. The present invention proposes a robust linear frequency modulation signal recognition method under complex conditions, which is divided into the following steps:

[0127] S1, signal reception, mainly refers to obtaining the signal to be analyzed;

[0128] 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;

[0129] S3, pulse leading and trailing edge detection, mainly performs pulse detection on the signal obtained after filtering and intercepts the signal part;

[0130] S4, instantaneous frequency estimation, mainly calculates the instantaneous frequency of the signal based on the phase difference method;

[0131] S5, characteristic curve fitting, mainly fits the instantaneous frequency of the signal based on the least squares estimation method to obtain the fitting slope, fitting error, etc.;

[0132] S6, time-frequency analysis, mainly performs time-frequency analysis on the signal with high fitting 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;

[0133] S7, time-bandwidth product calculation, mainly estimates the signal bandwidth and calculates the time-bandwidth product;

[0134] S8, instantaneous frequency variance characteristic, mainly calculates the variance characteristic of the instantaneous frequency to prevent misjudgment as a phase modulation signal or a frequency modulation signal;

[0135] S9, basic characteristic determination, mainly combines fitting error, fitting slope, time-bandwidth product and other conditions to determine whether the signal basically meets the linear frequency modulation signal characteristics;

[0136] S10, segmented slope statistics, is mainly to avoid misjudgment as a nonlinear frequency modulation signal, and to check whether the segmented instantaneous frequency curve is consistent;

[0137] S11, nonlinear curve fitting, mainly performs quadratic curve fitting on the instantaneous frequency of the signal based on the least squares estimation method to obtain the fitting slope, fitting error, etc., to support the subsequent judgment of whether the signal may be a nonlinear frequency modulation signal;

[0138] S12, hierarchical judgment, mainly performs final confirmation on the signal type in a hierarchical manner to determine whether it is a linear frequency modulation signal.

[0139] Figure 2 This is a flowchart of the time-frequency analysis step of step S6. In this step, the signal with a large fitting error in the previous characteristic curve fitting process 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 characteristic 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.

[0140] Figure 3 This is a flowchart of the basic characteristic determination in step S9. The time-bandwidth product, fitting error, normalized modulation slope and other indicators are used to determine whether the signal has the basic characteristics of a linear frequency modulation signal. In this link, conventional radar signals, phase modulation signals, dual linear frequency modulation signals, and frequency shift keying signals can be excluded. Moreover, setting a basic characteristic determination link before the final decision can directly eliminate signals that do not meet the basic conditions, end the processing flow in advance, and shorten the processing time.

[0141] Figure 4 This is a flowchart of hierarchical discrimination of step S12. It is mainly to determine whether the signal is a linear frequency modulation signal, but the key point is to prevent the nonlinear frequency modulation signal that basically meets the conditions in the previous steps from being misjudged as a linear frequency modulation signal. Since the instantaneous frequency of the nonlinear frequency modulation signal is not a straight line, the signal with large instantaneous frequency fluctuations is first eliminated, and then the signal with more nonlinear curve characteristics of the radiation source is eliminated, and finally the error of the linear frequency modulation characteristic curve fitting is combined to make a judgment, and finally a linear frequency modulation signal that meets the conditions is obtained.

[0142] Figure 5 It is the time domain waveform of the ideal linear frequency modulation LFM signal. This figure shows the image of the signal amplitude changing with time in the time domain of the simulated linear frequency modulation LFM 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.

[0143] Figure 6 It is the spectrum waveform of the ideal linear frequency modulation LFM signal. This figure shows the image of the ideal linear frequency modulation LFM signal s0(n0) in the frequency domain. It can be seen that the values ​​at multiple frequency points in the figure are not zero and are basically equal, forming a rectangle, that is, the LFM signal has a wide bandwidth, has multiple frequency components, and the energy of each component is basically equal.

[0144] Figure 7 It is the time-frequency image obtained by short-time Fourier transform of the ideal linear frequency modulation LFM signal. This figure is the time-frequency image obtained by short-time Fourier transform of the ideal simulated LFM signal. 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 straight line 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 steps S3 and S6.2 to obtain the short-time Fourier transform corresponding to M (n, f).

[0145] Figure 8 It is the instantaneous frequency of the ideal linear frequency modulation LFM signal obtained by step S4. 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 linear frequency modulation signal calculated by the L-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 straight line, corresponding to the signal part, and the inclination slope of the straight line is the modulation slope. The horizontal segment at the end of the straight line is caused by the continuous zero points after the signal.

[0146] Fig. 9 is the instantaneous frequency fitting result of the ideal linear frequency modulation LFM signal. Figure 8 The instantaneous frequency in is the result of fitting p(n) in step S5 based on the least squares algorithm. The long and short alternating curved lines in the figure represent the original instantaneous frequency p(n), and the dotted line composed of continuous single short lines represents the fitting result of the least squares algorithm. It can be seen that the least squares algorithm can better fit the overall trend of the original instantaneous frequency curve, and is not affected by the horizontal segment at the end of the curve, and has good robustness.

[0147] Fig.10 This is the time domain waveform of the linear frequency modulation LFM signal when the signal-to-noise ratio is -5dB. The linear frequency modulation signal in this figure is accompanied by additive white Gaussian noise, and the signal-to-noise ratio is -5dB. Figure 5Compared 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.

[0148] Fig.11 This is the spectrum of the linear frequency modulation LFM signal when the signal-to-noise ratio is -5dB. This figure shows the spectrum image of the linear frequency modulation signal when the signal-to-noise ratio is -5dB. It can be seen that the signal has a certain bandwidth. Figure 6 Compared with the spectrum of the ideal signal in the frequency domain, 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 spectrum of the signal is no longer a rectangle with basically equal frequency components, so it is difficult to determine the signal type through the spectrum.

[0149] Fig.12 It is the instantaneous frequency of the linear frequency modulation LFM signal obtained by step S4 when the signal-to-noise ratio is -5dB. The figure shows the instantaneous frequency curve image of the linear frequency modulation LFM signal when the signal-to-noise ratio is -5dB, which is 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 undergone the adaptive filtering processing of step S2, nor the leading and trailing edge detection of step S3, but the result obtained by directly performing step S4 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 consistent with 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 no longer presents an inclined straight line. Therefore, it 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.

[0150] Fig.13 It is the instantaneous frequency of the linear frequency modulation LFM signal obtained by first-order phase difference when the signal-to-noise ratio is -5dB. This figure is the instantaneous frequency curve of the linear frequency modulation signal with a signal-to-noise ratio of -5dB obtained by the first-order phase difference 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, due to the influence of 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 linear frequency modulation signal.

[0151] Fig.14 This is the time-frequency image obtained by short-time Fourier transform of the linear frequency modulation LFM signal when the signal-to-noise ratio is -5dB. 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 with Figure 7The time-frequency diagram of the ideal signal in the figure has a large number of randomly scattered noise points, but there is still an obvious inclined straight line 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).

[0152] Fig.15 It is the time domain waveform of the linear frequency modulation LFM signal after steps S2 and S3 when the signal-to-noise ratio is -5dB. This figure shows the time domain waveform of the signal after the adaptive filtering and pulse leading and trailing edge detection of steps S2-3 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.10 The unprocessed signal time domain waveform in Fig.15 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.

[0153] Fig.16 It is the frequency domain waveform of the linear frequency modulation LFM signal after steps S2 and S3 when the signal-to-noise ratio is -5dB. This figure shows the spectrum waveform of the signal after the adaptive filtering and pulse leading and trailing edge detection of steps S2-3 of the present invention under low signal-to-noise ratio. It can be seen that after processing, the noise is significantly suppressed.

[0154] Fig.17 It is the instantaneous frequency of the LFM signal after the first-order phase difference processing after the steps S2 and S3 when the signal-to-noise ratio is -5dB. This figure shows the instantaneous frequency of the signal after the first-order phase difference processing after the adaptive filtering and pulse leading and trailing edge detection of the steps S2-3 of the present invention at a 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.13 The instantaneous frequency in the processed signal is Fig.17 The main trend of the instantaneous frequency of the signal, i.e., the inclined straight line, 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.17 The curve in the figure still has a lot of messy lines (or abnormal discrete points) caused by noise.

[0155] Fig.18is the instantaneous frequency of the LFM signal after steps S2-S4 at a signal-to-noise ratio of -5dB. The figure shows the instantaneous frequency of the signal obtained after the adaptive filtering and pulse leading and trailing edge detection of steps S2-4 of the present invention under low signal-to-noise ratio, and after L-phase differential processing. The horizontal axis represents the sampling point, and the vertical axis represents the normalized instantaneous frequency. It can be seen that compared with Fig.17 The L-fold differential phase 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 linear frequency modulation signal can be determined by this curve, indicating that the processing of steps S2-S4 of the present invention has a certain effect of adapting to low noise conditions.

[0156] Fig.19 This is the short-time Fourier transform time-frequency diagram of the LFM signal after steps S2-S3 when the signal-to-noise ratio is -5dB. This figure is the time-frequency image obtained by the short-time Fourier transform of the signal after steps S2-S3. 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.

[0157] Fig. 20 is the time-frequency distribution of the LFM signal obtained by step S6.4 when the signal-to-noise ratio is -5dB. 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 Μ(n,f)≥th in step S6.4.2 M All frequency points of M. It can be seen that compared with Fig.19 There are some snowflakes caused by noise left in the image. Fig. 20 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.

[0158] Fig.21 is the instantaneous frequency of the LFM signal obtained after step S6 when the signal-to-noise ratio is -5dB. Fig. 20 The instantaneous frequency q(n) is obtained based on the result after step S6.4.3. It can be seen that compared with Fig.12 and Fig.18 The instantaneous frequency image in Fig.21 The middle curve is an inclined straight line with slight fluctuations, which has obvious characteristics and can be directly determined as a linear frequency modulation signal, indicating that this method has strong signal feature extraction capability and robustness.

[0159] Fig. 22 This is the instantaneous frequency fitting result of the linear frequency modulation LFM signal obtained by time-frequency analysis when the signal-to-noise ratio is -5dB. Fig.21 The instantaneous frequency in is used as p(n) in step S5, and the fitting result is based on the least squares algorithm. The long and short alternating curved lines in the figure represent the original instantaneous frequency p(n), and the dotted line composed of continuous single short lines represents the fitting result of the least squares algorithm. It can be seen that the least squares algorithm can better fit the overall trend of the original instantaneous frequency curve, and is not affected by the horizontal segment at the end of the curve, and has good robustness. Fig. 9 Compared with the fitting result of the ideal signal in the example, the fitting result processed by the present invention at a signal-to-noise ratio of -5dB is close to the ideal case, indicating the effectiveness of the present invention.

Claims

1. A robust linear frequency modulation signal recognition method under complex conditions, It is characterized in that The method is divided into the following steps: S1. Signal reception The received signal to be processed is used as s 0 (n 0 ) indicates that n 0 Indicates the index value of the sampling point, n 0 =1,2,...,N 0 , N 0 Indicates the initial signal length, the signal sampling rate is f s ; S2. Adaptive filtering S2.1 Use the real sinusoidal signal frequency estimation method based on DFT to estimate the signal s 0 (n 0 )’s peak frequency position f 0 ; S2.2 Estimation of signal s 0 (n 0 ) bandwidth BW 0 , the specific steps are as follows: S2.2.1 According to the non-parametric power spectrum estimation method, the signal s is obtained 0 (n 0 ), where f represents the frequency index value of the power spectrum, 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, the signal s 0 (n 0 ) bandwidth BW 0 =f r -f l ; S2.3 According to the estimated peak frequency position f 0 and bandwidth BW 0 , using FFT filter with f 0 The signal is adaptively filtered for the center frequency. 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 =f 0 -δ·BW 0 , the cut-off frequency is f end =f 0 +δ·BW 0 ; S2.3.2 for s 0 (n 0 ) FFT Fourier transform of the point, convert it to the frequency domain, and then keep f start and f end The remaining frequency components are all set to zero, and finally an inverse Fourier transform is performed to obtain the filtered signal s 1 (n 0 ),n 0 =1,2,...,N 0 ; S3. Pulse leading and trailing edge detection S3.1 Detection of filtered signal s 1 (n 0 ) of the envelope starting point n start and end point n end , the specific method is as follows: S3.1.1 Calculate signal envelope a 0 (n 0 )=|s 1 (n 0 )|, and for a 0 (n 0 ) is smoothed to obtain the smoothed envelope a(n 0 ), 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(n 0 )≥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 For signal s 1 (n 0 ) to intercept the front and back edges, that is, take the signal index value n 0 =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 phase difference method. The specific calculation steps are as follows: S4.2.1 Calculate the signal amplitude using p 0 (n) means: 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 the L-fold phase difference method to find the instantaneous frequency sequence p(n) to improve the adaptability to noise: S5. Characteristic curve fitting S5.1 with straight line Fit p(n) and use the least squares estimation method to get the fitting slope Fitting bias value And the fitted instantaneous frequency series S5.2 Calculate the fitting error: S5.3 Setting the error threshold th ε ; S5.4 Determine the error situation: If the fitting error 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 A collection of dimensional complex matrices; S6.2 Calculation of the time-frequency matrix M 0 (n,f) energy, that is, find the amplitude value point by point, and get Μ(n,f)=|Μ 0 (n,f)|; S6.3 Calculate the mean of Μ(n,f) S6.4 extracts the time-frequency distribution. The specific steps are as follows: S6.4.1 Setting the time-frequency energy threshold th M ; S6.4.2 Compare M(n,f) at time n with The size of n will satisfy The total f-value is expressed as 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, the curve q(n) is fitted to obtain the corresponding fitting slope Fitting bias value and fitting error ε′; S6.6 compares the size of ε′ and ε: if ε′<ε, update the fitting result in step S5, that is, update p(n) to q(n), and Updated to Will Updated to Update ε to ε′; S7. Time-Bandwidth Product Calculation S7.1 estimate the bandwidth BW of the signal s(n) according to the method in step S2.2; S7.2 calculates the pulse width PW of the signal s(n) according to the following formula: PW=N / f s ; S7.3 combines the pulse width PW of step S7.1 and the bandwidth BW of step S7.2 to calculate the time-bandwidth product TB of the signal: TB=PW·BW; S8. Instantaneous frequency variance characteristics Calculate the variance characteristics of the instantaneous frequency to prevent misjudgment as a phase modulation signal or a frequency modulation signal; the specific steps are as follows: S8.1 Calculate the mean of the instantaneous frequency sequence p(n) Then calculate the variance σ of the instantaneous frequency p(n) 1 : S8.2 Combine the instantaneous frequency sequence in step S5.1 Calculate the linear variance σ of the instantaneous frequency p(n) 2 : S8.3 Calculation of variance σ 1 With linear variance σ 2 The absolute value of the difference LV: LV=|σ 1 -s 2 |; S9. Basic characteristics judgment S9.1 Calculate the signal normalized modulation slope S9.2 uses the time-bandwidth product TB, fitting error ε, and normalized modulation slope Calculate the discrimination flag F1: Wherein, ∧ represents an "AND" operation; if the above requirements are met, that is, F1=1, it is preliminarily determined to be a linear frequency modulation signal, and the step S10 is continued; if the requirements are not met, the step S9.3 is performed; S9.3 Calculate the discrimination flag F2 according to the following formula: F2=[(ε<0.01·th ε )∧(LV>3)∧(TB≥8)] If the requirement is met, that is, F2=1, it is preliminarily determined to be a linear frequency modulation signal, and the process continues to step S10; if the requirement is not met, it is identified as other types, and the process ends; S10. Segmental slope statistics In order to avoid confusion with nonlinear frequency modulation signals and misjudgment, the instantaneous frequency sequence p(n) is segmented, and then a linear fit is performed on each segment using the least squares estimation method to obtain the corresponding fitting slope, and the distribution of all slopes is statistically analyzed; the specific steps are as follows: S10.1 Divide the instantaneous frequency sequence p(n) into M segments, each segment is ω=N / M in length; except for the first segment, move the starting point of the 2nd to Mth segment forward by ω / 2, and the length is 3·ω / 2; use p 1 (n)~p M (n) represent M different fragments, as follows: p 1 (n)=p(n),n=1,....,ω, p i (n)=p(n),n=ω·(i-1)-ω / 2+1,....,i·ω,i=2,...,M; S10.2 for p 1 (n)~p M (n) Perform characteristic curve fitting based on the least squares estimation method in step S5 to obtain the corresponding fitting slopes, and use express; S10.3 Statistical slope: S10.3.1 Calculate the variance of the fitted slopes for all segments S10.3.2 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. Nonlinear curve fitting S11.1 Using quadratic curve Fit p(n) and use the least squares estimation method to solve the fitting parameters And the fitted instantaneous frequency series S11.2 Calculate the nonlinear curve fitting error ε NLFM : S12. Hierarchical Decision S12.1 Calculate the flag F3 according to the following formula: F3=(V k >0.2)∨[(V k [0.1)∧(T>5)] Where ∨ represents an "or" operation; if the condition is met, that is, F3 = 1, the signal is not a linear frequency modulation signal, and other types are output, and the process ends; otherwise, step S12.2 is performed; S12.2 Calculate the flag F4 according to the following formula: F4=[(V k >0.08)∧(T>1.9)]∧[(ε NLFM <0.1·th ε +0.005)∧(ε NLFM <ε)] If the condition is met, that is, F4 = 1, the signal is not a linear frequency modulation signal, and other types are output, and the process ends; otherwise, proceed to step S12.3; S12.3 Calculate the flag F5 according to the following formula: F5=(ε<0.005·th ε ) If the condition is met, ie, F5=1, the signal is a linear frequency modulation signal; otherwise, the signal is determined to be other types.

2. A robust linear frequency modulation signal recognition method under complex conditions according to claim 1, Features: In S2.3.1, the filter bandwidth factor δ is set to 0.55-0.

85.

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

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

5.

5. A robust linear frequency modulation signal recognition method under complex conditions according to claim 1, Features: In S4.1, the differential order L corresponding to signals of different lengths is adaptively set:

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

1.

7. A robust linear frequency modulation signal recognition method under complex conditions according to claim 1, Features: In S6.4.1, the time-frequency energy threshold th M Set to 0.7~0.

9.

8. A robust linear frequency modulation signal recognition method under complex conditions according to claim 1, Features: In S10.1, M is 5-15.

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