Intermittent sampling forwarding interference identification method

Abstract

The invention relates to an intermittent sampling forwarding interference identification method, and belongs to the technical field of electronic countermeasures. The emission waveform design mainly comprises phase coding waveform identification code design, intra-pulse orthogonal waveform optimization and signal splicing; the receiving time-frequency processing mainly comprises pulse compression processing and time-frequency transformation analysis on echo signals. The intermittent sampling and forwarding interference identification method provided by the invention has the main advantages that the radar interference identification emission waveform based on the identification code has advanced interference identification performance, and at least two types of intermittent sampling and forwarding interference can be identified more accurately.

Description

Technical Field

[0001] This invention belongs to the field of electronic countermeasures technology, specifically relating to a method for identifying intermittent sampling and forwarding interference. Background Technology

[0002] Active radar jamming refers to signals generated by jamming equipment. These active signals can enter the radar receiver and have the ability to interfere with or disrupt the radar's acquisition of target information. Faced with the complex and harsh electromagnetic environment of radar, radar jamming identification has always been a research hotspot in the field of radar electronic countermeasures. Existing jamming identification methods typically employ echo signal feature extraction and classifier-based approaches. First, one or more signal features that help distinguish jamming patterns are extracted. Then, a classifier is designed based on these echo signal features to complete the jamming pattern identification. However, most existing radar transmission signals are linear frequency modulated (LFM) signals. When subjected to intermittent sampling and relay jamming, their echo signals can form a group of one or more false targets resembling real targets. When the jamming sampling pulse width is small, the real target is buried among the false targets. Jamming identification methods based solely on echo signal feature extraction then exhibit low identification performance, affecting subsequent anti-jamming and target identification effectiveness. Summary of the Invention

[0003] The technical problem solved by this invention is to overcome the shortcomings of the prior art. This invention provides an intermittent sampling and forwarding interference identification method, which offers a new approach to improving the performance of radar active interference identification.

[0004] The solution to the technical problem of this invention is: an intermittent sampling and forwarding interference identification method, which includes the following steps:

[0005] S1. Send a radar interference identification transmission signal based on the identification code. The radar interference identification transmission waveform based on the identification code is composed of a phase-coded waveform and a linear frequency modulated waveform. The phase-coded waveform and the linear frequency modulated waveform are optimized for intra-pulse orthogonality.

[0006] S2. Receive interference echo signal, wherein the interference echo signal includes radar interference identification transmission signal based on identification code that is subject to intermittent sampling and forwarding interference;

[0007] S3. Using radar interference to identify the phase coding part and the linear frequency modulation part of the transmitted signal, matching functions are designed for each part, and pulse compression processing is performed on the interference echo signal to separate the phase coding structure and the linear frequency modulation structure.

[0008] S4. For the pulse compression results obtained by the phase coding matching function, the number of peaks and the peak positions in the statistical results are used to identify the target echo and intermittent sampling forwarding interference.

[0009] S5. For the pulse compression result obtained by the linear frequency modulation matching function, perform time-frequency transformation processing, count the peak 3dB width and the number of distance gates with peak values ​​in the time-frequency transformation result, and identify the target echo and intermittent sampling forwarding interference.

[0010] S6. The target echo and interference identification results from steps S4 and S5 are fused to obtain the final identification result.

[0011] Preferably, in step S6, if the recognition results of steps S4 and S5 are the same, then the recognition result of step S4 or step S5 shall be taken as the final recognition result; if steps S4 and S5 are different, then the recognition result of step S4 shall be taken as the final recognition result.

[0012] Preferably, the phase-coded signal waveform contains N sub-pulses, and the phase-coded waveform is represented as follows:

[0013] {s(n)=exp(jφ(n)),n=1,2,…,N}

[0014] Where φ(n), 0≤φ(n)<2π is the phase of the nth sub-pulse in the phase-coded signal waveform.

[0015] Preferably, the number of sub-pulses N does not exceed 10% of the entire length of the radar jamming identification transmission waveform based on the identification code.

[0016] Preferably, the selectable range of phase values ​​for the nth sub-pulse in the phase-encoded signal waveform is: M is a positive even number not exceeding N.

[0017] Preferably, the radar interference identification transmission signal based on the identification code uses minimizing the autocorrelation sidelobe energy of the phase-coded waveform set and the cross-correlation energy within the radar interference identification transmission waveform based on the identification code as the cost function. The simulated annealing algorithm is used to optimize and solve these functions to determine the phase arrangement of the final phase-coded waveform. The phase-coded waveform and the linear frequency modulated waveform are then spliced ​​together to obtain the signal.

[0018] Preferably, the specific steps of step S4 are as follows:

[0019] For the pulse compression processing results corresponding to the phase-coded matching function, count the number N of spikes except for the position t=0. F If N F =0, then the interference echo signal is determined to be the target echo; if N F =1, then the interference echo signal is determined to be intermittent sampling direct forwarding interference, and the sampling pulse width of intermittent sampling direct forwarding interference is the time corresponding to the spike; if N FIf the value is greater than 1, the interference echo signal is determined to be intermittent sampling and repetitive forwarding interference. The sampling pulse width of intermittent sampling and direct forwarding interference is the time interval between spikes, and the number of repetitions is N. F .

[0020] Preferably, the specific steps of step S5 are as follows:

[0021] The pulse compression result corresponding to the linear frequency modulation matched function is subjected to time-frequency transformation to obtain a time-frequency distribution map. The 3dB width ΔF of the peak in the time-frequency distribution map and the number of distance gates N containing the peak are then statistically analyzed. p If the 3dB width of the peak in the time-frequency distribution graph is equal to the pulse width of the transmitted signal, then the interference echo signal is determined to be the target echo; if the 3dB width of the peak in the time-frequency distribution graph is less than the pulse width of the transmitted signal, and N p When N = 1, the interference echo signal is determined to be intermittent sampling direct forwarding interference; if N p If the value is greater than 1, the interference echo signal is determined to be intermittent sampling and repeated forwarding interference.

[0022] Preferably, the 3dB width ΔF of the peak value in the time-frequency distribution plot is related to the transmitted signal pulse width T. p If the following condition is met: then |ΔF-T p |≤10 -8 Therefore, it is assumed that the 3dB width of the peak value in the time-frequency distribution plot is related to the transmitted signal pulse width T. p equal.

[0023] The advantages of this invention compared to the prior art are:

[0024] (1) The present invention has advanced interference identification performance through the interference identification method of transmitting waveform design and receiving time and frequency processing. It realizes the rapid and accurate identification of at least two types of intermittent sampling and forwarding interference. Compared with the interference identification method in the prior art that only extracts features from the echo signal, it improves the accuracy and flexibility of interference identification.

[0025] (2) In the design of the interference identification transmission waveform, the present invention fully combines the characteristic advantages of the two signals by orthogonally optimizing the phase-coded waveform and the linear frequency modulated waveform, thus ensuring the performance of interference identification. Attached Figure Description

[0026] Figure 1 This is a schematic diagram of the radar jamming transmission waveform design result based on the identification code in an embodiment of the present invention;

[0027] Figure 2 This is a schematic diagram of the autocorrelation of the phase-encoded waveform portion in the waveform designed according to an embodiment of the present invention;

[0028] Figure 3This is a schematic diagram of phase-encoded waveform pulse compression in the waveform designed according to an embodiment of the present invention;

[0029] Figure 4 In the waveforms designed for embodiments of the present invention, the phase-coded waveform and the linear frequency-modulated waveform are mutually correlated;

[0030] Figure 5 This is a flowchart illustrating the interference mode type identification based on time-frequency transformation analysis according to an embodiment of the present invention.

[0031] Figure 6 In this embodiment of the invention, the designed interference identification waveform is intermittently sampled and directly forwarded as interference.

[0032] Figure 7 In this embodiment of the invention, the designed interference identification waveform is intermittently sampled and repeatedly forwarded as interference.

[0033] Figure 8(a) shows the pulse compression processing result of the intermittently sampled direct interference echo signal based on the linear frequency modulation matching function in an embodiment of the present invention;

[0034] Figure 8(b) shows the pulse compression processing result of the intermittently sampled direct interference echo signal based on the phase coding matching function in an embodiment of the present invention;

[0035] Figure 9(a) shows the pulse compression processing result of the intermittently sampled repetitive interference echo signal based on the linear frequency modulation matching function in an embodiment of the present invention;

[0036] Figure 9(b) shows the pulse compression processing result of the intermittently sampled repetitive interference echo signal based on the phase coding matching function in an embodiment of the present invention;

[0037] Figure 10 This invention demonstrates the target recognition effect based on the transmission waveform design and time-frequency processing in an embodiment of the invention.

[0038] Figure 11 This invention demonstrates the effectiveness of intermittent sampling direct interference identification based on transmitted waveform design and time-frequency processing in an embodiment of the invention.

[0039] Figure 12 This invention demonstrates the intermittent sampling repetitive interference identification effect based on transmission waveform design and time-frequency processing in an embodiment of the invention. Detailed Implementation

[0040] The present invention will be further described below with reference to the embodiments.

[0041] To better understand the above-described objectives, features, and advantages of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other. Furthermore, the present invention can be implemented in other ways different from those described herein; therefore, the scope of protection of the present invention is not limited to the specific embodiments disclosed below.

[0042] like Figure 5 As shown, this invention provides an intermittent sampling and forwarding interference identification method, employing orthogonal decomposition and time-frequency transformation analysis of the received signal to improve interference pattern identification performance. The method includes the following steps:

[0043] S1. Send a radar interference identification transmission signal based on the identification code. The radar interference identification transmission waveform based on the identification code is composed of a phase-coded waveform and a linear frequency modulated waveform. The phase-coded waveform and the linear frequency modulated waveform are optimized for intra-pulse orthogonality.

[0044] A specific embodiment of the present invention, such as Figure 1 As shown, a radar jamming identification transmission waveform with a length of 1024 was designed, in which the identification code length of the phase-coded waveform is 40. The phase-coded signal in the designed waveform uses a 16-bit random phase, and the bandwidth of the linear frequency modulated waveform is 100MHz, with a modulation frequency of 1014Hz / s. Using minimizing the autocorrelation sidelobe energy of the phase-coded waveform set and the cross-correlation energy within the identification code-based radar jamming identification transmission waveform as the cost function, the simulated annealing algorithm is used for optimization and solution to determine the phase arrangement of the final phase-coded waveform. The phase-coded waveform and the linear frequency modulated waveform are then concatenated to obtain the designed identification code-based radar jamming identification transmission waveform.

[0045] Radar jamming identification based on identification code transmit waveform x = [sh], where s is the identification code of the phase-coded waveform and h is the linear frequency modulated waveform.

[0046] Assuming the phase-coded waveform contains N sub-pulses, the phase-coded waveform s can be represented as s = {s(1)....s(n)....s(N)};

[0047] s(n)=exp(jφ(n)),n=1,2,…,N (1)

[0048] Where φ(n), 0≤φ(n)<2π is the phase of the nth sub-pulse in the phase-coded signal waveform.

[0049] The number of sub-pulses N does not exceed 10% of the entire transmitted waveform length for radar jamming identification based on identification codes.

[0050] The phase-coded signal waveform has multiple discrete random phases, and the selectable range of phase values ​​for the nth sub-pulse in the phase-coded signal waveform is as follows:

[0051]

[0052] Where M is a positive even number not exceeding N;

[0053] The phase of a phase-encoded waveform can be represented in the following matrix form:

[0054] [φ(1),φ(2),.........φ(N)] (3)

[0055] To ensure that the radar jamming identification transmitted waveform based on the identification code can simultaneously utilize the processing characteristics of the identification code and the linear frequency modulated waveform for intermittent sampling and forwarding jamming, it is necessary to avoid mutual interference between the phase-coded waveform and the linear frequency modulated waveform. That is, the phase-coded waveform set and the linear frequency modulated waveform should have good cross-correlation performance. At the same time, the phase-coded waveform should have good autocorrelation performance to avoid the autocorrelation sidelobes affecting the jamming pattern identification.

[0056] The autocorrelation function A(φ,k) of the phase-encoded waveform is expressed as follows:

[0057]

[0058] The cost function E is defined as minimizing the autocorrelation sidelobe energy of the phase-coded waveform and the cross-correlation energy within the transmitted waveform for radar interference identification based on the identification code. The expression for this cost function is:

[0059]

[0060] Where λ1 and λ2 are weighting factors, the sum of λ1 and λ2 is 1, and E is the cost function. The symbol represents convolution, and * represents conjugate.

[0061] Preferably, the radar interference identification transmission signal based on the identification code uses minimizing the autocorrelation sidelobe energy of the phase-coded waveform set and the cross-correlation energy within the radar interference identification transmission waveform based on the identification code as the cost function. The simulated annealing algorithm is used to optimize and solve these functions to determine the phase arrangement of the final phase-coded waveform. The phase-coded waveform and the linear frequency modulated waveform are then spliced ​​together to obtain the signal.

[0062] S2. Receive interference echo signal, wherein the interference echo signal includes radar interference identification transmission signal based on identification code that is subject to intermittent sampling and forwarding interference;

[0063] Orthogonal decomposition and time-frequency transformation analysis are performed on the interference echo signal to enable the identification of the target echo and at least two types of intermittent sampling and forwarding interference modes.

[0064] S3. Using radar interference to identify the phase coding part and the linear frequency modulation part of the transmitted signal, matching functions are designed for each part, and pulse compression processing is performed on the interference echo signal to separate the phase coding structure and the linear frequency modulation structure.

[0065] Since the transmitted waveform is designed to be orthogonal within the pulse between the phase-coded waveform and the linear frequency modulated waveform, pulse compression and time-frequency processing are performed on the echo signal to identify the target echo and intermittent sampling and forwarding interference. First, the phase-coded and linear frequency modulated parts of the transmitted signal are identified using interference detection. Matching functions are designed for each part, and pulse compression processing is performed on the interference echo signal to separate the phase-coded structure and the linear frequency modulated structure.

[0066] For a linear frequency modulated waveform, the waveform model expression corresponding to intermittent sampling direct forwarding interference is:

[0067]

[0068] Where rect(·) is the rectangular gate function, L is the number of interference slices, and T J To interfere with the slice width, K r Let τ be the frequency of the transmitted signal, τ be the time delay introduced by the distance between the jammer and the radar, and t be the time.

[0069] Its amplitude response after pulse compression is expressed as:

[0070]

[0071] Where φ=πK r T J (tT J ).

[0072] It is generated by superimposing multiple slices, when t = k / K r T J When k∈Z, it can obtain a maximum value; sinc(K) r T J (tT J It is generated by pulse compression of a single slice, with a main lobe width of 2 / K. r T J .

[0073] Therefore, for intermittent sampling direct relay jamming, its pulse compression result appears as a group of false targets. For intermittent sampling repeated relay jamming, its pulse compression result is equivalent to multiple time shifts of equation (8), appearing as multiple groups of false targets in the range direction.

[0074] Setting L=1 yields the pulse compression result S of an interference slice. c :

[0075] S c =T J exp(j2πK r T J (tT J )-jπK r t 2 sincK r T J (tT J (10)

[0076] Short-time Fourier transform representation of an interfering slice signal TF(τ) s f) is:

[0077]

[0078] Where, τ s For the sliding window delay of the short-time Fourier transform, T w is the width of the sliding window. f is the frequency.

[0079] An approximate result is given using the stationary phase theorem. By differentiating the phase of the integrated signal and setting the derivative to zero, the relationship between time and frequency can be obtained:

[0080]

[0081] (12) Substituting into equation (10), we can obtain the amplitude response of the time-frequency distribution as follows:

[0082] |TF(t, f)|=|T J sinc(K r T J (tT J ))sinc(T J f)| (13)

[0083] Equation (13) shows that the short-time Fourier transform of the pulse compression result of an interference slice is a sinc function in both the time and frequency domains, and the main lobe width in the time dimension is ΔT = 1 / K. r T J The main lobe width in the frequency dimension is ΔB = 1 / T J .

[0084] Since the transmitted waveform is designed to be orthogonal within the pulse between the phase-coded waveform and the linear frequency modulated waveform, the echo signal is presented as a phase-coded structure and a linear frequency modulated structure after pulse compression processing. Pulse compression processing and time-frequency processing are performed in sequence.

[0085] S4. For the pulse compression results obtained by the phase coding matching function, the number of peaks and the peak positions in the statistical results are used to identify the target echo and intermittent sampling forwarding interference.

[0086] For the pulse compression processing results corresponding to the phase-coded matching function, count the number N of spikes except for the position t=0. F If N F =0, then the interference echo signal is determined to be the target echo; if N F =1, then the interference echo signal is determined to be intermittent sampling direct forwarding interference, and its sampling pulse width is the time corresponding to the spike; if N F If the value is greater than 1, the interference echo signal is determined to be intermittent sampling and repeated relay interference, with the sampling pulse width being the time interval between spikes and the number of repetitions being N. F .

[0087] S5. For the pulse compression result obtained by the linear frequency modulation matching function, perform time-frequency transformation processing, count the peak 3dB width and the number of distance gates with peak values ​​in the time-frequency transformation result, and identify the target echo and intermittent sampling forwarding interference.

[0088] The pulse compression result corresponding to the linear frequency modulation matched function is subjected to time-frequency transformation to obtain a time-frequency distribution map. The 3dB width ΔF of the peak in the time-frequency distribution map and the number of distance gates N containing the peak are then statistically analyzed. p If the 3dB width of the peak in the time-frequency distribution graph is equal to the pulse width of the transmitted signal, then the interference echo signal is determined to be the target echo; if the 3dB width of the peak in the time-frequency distribution graph is less than the pulse width of the transmitted signal, and N p When N = 1, the interference echo signal is determined to be intermittent sampling direct forwarding interference; if N p If the value is greater than 1, the interference echo signal is determined to be intermittent sampling and repeated forwarding interference.

[0089] S6. The target echo and interference identification results from steps S4 and S5 are fused to obtain the final identification result.

[0090] If the recognition results of steps S4 and S5 are the same, then the recognition result of step S4 or step S5 shall be taken as the final recognition result; if steps S4 and S5 are different, then the recognition result of step S4 shall be taken as the final recognition result.

[0091] Example:

[0092] The waveform designed in a specific embodiment of the present invention is as follows: Figure 1 As shown;

[0093] The autocorrelation function and pulse compression results of the phase-encoded waveform portion in the example design waveform are listed below. Figures 2-3 The cross-correlation results of the phase-coded waveform and the linear frequency modulated waveform in the design waveform are listed below. Figure 4 .

[0094] The interference identification results for the examples are listed below. Figures 6-12 .

[0095] Depend on Figure 6 and Figure 7 As shown, the radar interference based on identification codes identifies the transmitted waveform through intermittent sampling direct forwarding and intermittent sampling repeated forwarding interference with a repetition count of 4, both of which include phase coding structure and linear frequency modulation structure.

[0096] As shown in Figures 8(a), 8(b), 9(a), and 9(b), pulse compression processing is performed on the interference echo signal generated by the radar interference identification transmitted waveform based on the identification code to separate the phase coding structure and the linear frequency modulation structure. A threshold is set to remove the influence of the low-amplitude repetitive structure, and the interference mode can then be directly identified based on the separated phase coding structure. In Figures 8(a) and 8(b), a single peak value deviates from the t=0 position, indicating intermittent sampling direct forwarding interference with a sampling pulse width of 5µs. In Figures 9(a) and 9(b), four peak values ​​deviate from the t=0 position, indicating intermittent sampling repeated forwarding interference with a sampling pulse width of 4µs and 4 repetitions.

[0097] Depend on Figures 10-12 As shown, the linear frequency modulated structure signal after pulse compression of the radar interference identification transmitted waveform is subjected to time-frequency transformation processing. The interference mode is then identified based on the number of peaks in the time-frequency transformation result. Figure 10 A peak appears at t=0, which is identified as the target echo. Figure 11 A peak appears in the data and deviates from the position t=0, which is judged to be intermittent sampling direct forwarding interference; Figure 12 The presence of four peaks that deviate from the t=0 position indicates intermittent sampling and repeated forwarding interference.

[0098] The above embodiments are only for illustrating the technical concept and features of the present invention. Their purpose is to enable those skilled in the art to understand the content of the present invention and implement it. They should not be used to limit the scope of protection of the present invention. All equivalent changes or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A method for identifying intermittent sampling and forwarding interference, characterized in that... Includes the following steps: S1. Send a radar interference identification transmission signal based on the identification code. The radar interference identification transmission waveform based on the identification code is composed of a phase-coded waveform and a linear frequency modulated waveform. The phase-coded waveform and the linear frequency modulated waveform are optimized for intra-pulse orthogonality. S2. Receive interference echo signal, wherein the interference echo signal includes radar interference identification transmission signal based on identification code that is subject to intermittent sampling and forwarding interference; S3. Using radar interference to identify the phase coding part and the linear frequency modulation part of the transmitted signal, matching functions are designed for each part, and pulse compression processing is performed on the interference echo signal to separate the phase coding structure and the linear frequency modulation structure. S4. For the pulse compression results obtained by the phase coding matching function, the number of peaks and the peak positions in the statistical results are used to identify the target echo and intermittent sampling forwarding interference. S5. For the pulse compression result obtained by the linear frequency modulation matching function, perform time-frequency transformation processing, count the peak 3dB width and the number of distance gates with peak values ​​in the time-frequency transformation result, and identify the target echo and intermittent sampling forwarding interference. S6. The target echo and interference identification results from steps S4 and S5 are fused to obtain the final identification result.

2. The intermittent sampling forwarding interference identification method according to claim 1, characterized in that, In step S6, if the recognition results of steps S4 and S5 are the same, then the recognition result of step S4 or step S5 shall be taken as the final recognition result; if steps S4 and S5 are different, then the recognition result of step S4 shall be taken as the final recognition result.

3. The intermittent sampling forwarding interference identification method according to claim 1, characterized in that, The phase-coded signal waveform contains N sub-pulses, and the phase-coded waveform is represented as follows: {s(n)=exp(jφ(n)),n=1,2,...,N} Where φ(n), 0≤φ(n)<2π is the phase of the nth sub-pulse in the phase-coded signal waveform.

4. The intermittent sampling forwarding interference identification method according to claim 3, characterized in that, The number of sub-pulses N does not exceed 10% of the entire transmitted waveform length for radar jamming identification based on identification codes.

5. The intermittent sampling forwarding interference identification method according to claim 4, characterized in that, The selectable range of phase values ​​for the nth sub-pulse in the phase-encoded signal waveform is as follows: M is a positive even number not exceeding N.

6. The intermittent sampling forwarding interference identification method according to claim 1, characterized in that, The radar interference identification transmission signal based on the identification code uses minimizing the autocorrelation sidelobe energy of the phase-coded waveform set and the cross-correlation energy within the radar interference identification transmission waveform based on the identification code as the cost function. It is optimized and solved by the simulated annealing algorithm to determine the phase arrangement of the final phase-coded waveform. The phase-coded waveform and the linear frequency modulated waveform are then spliced ​​together to obtain the signal.

7. The intermittent sampling forwarding interference identification method according to claim 1, characterized in that, The specific steps of step S4 are as follows: For the pulse compression processing results corresponding to the phase-coded matching function, count the number N of spikes except for the position t=0. F If N F =0, then the interference echo signal is determined to be the target echo; if N F =1, then the interference echo signal is determined to be intermittent sampling direct forwarding interference, and the sampling pulse width of intermittent sampling direct forwarding interference is the time corresponding to the spike; if N F If the value is greater than 1, the interference echo signal is determined to be intermittent sampling and repetitive forwarding interference. The sampling pulse width of intermittent sampling and direct forwarding interference is the time interval between spikes, and the number of repetitions is N. F .

8. The intermittent sampling forwarding interference identification method according to claim 1, characterized in that, The specific steps of step S5 are as follows: The pulse compression result corresponding to the linear frequency modulation matched function is subjected to time-frequency transformation to obtain a time-frequency distribution map. The 3dB width ΔF of the peak in the time-frequency distribution map and the number of distance gates N containing the peak are then statistically analyzed. p If the 3dB width of the peak in the time-frequency distribution graph is equal to the pulse width of the transmitted signal, then the interference echo signal is determined to be the target echo; if the 3dB width of the peak in the time-frequency distribution graph is less than the pulse width of the transmitted signal, and N p When N = 1, the interference echo signal is determined to be intermittent sampling direct forwarding interference; if N p If the value is greater than 1, the interference echo signal is determined to be intermittent sampling and repeated forwarding interference.

9. The intermittent sampling forwarding interference identification method according to claim 1, characterized in that, The 3dB width ΔF of the peak value in the time-frequency distribution plot is related to the transmitted signal pulse width T. p If the following condition is met: then |ΔF-T p |≤10 -8 Therefore, it is assumed that the 3dB width of the peak value in the time-frequency distribution plot is related to the transmitted signal pulse width T. p equal.

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