CN110048741A - A kind of method for parameter estimation of the Frequency Hopping Signal based on Short-Time Fractional Fourier Transform - Google Patents
A kind of method for parameter estimation of the Frequency Hopping Signal based on Short-Time Fractional Fourier Transform Download PDFInfo
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- CN110048741A CN110048741A CN201910322997.5A CN201910322997A CN110048741A CN 110048741 A CN110048741 A CN 110048741A CN 201910322997 A CN201910322997 A CN 201910322997A CN 110048741 A CN110048741 A CN 110048741A
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
- H04B1/69—Spread spectrum techniques
- H04B1/713—Spread spectrum techniques using frequency hopping
- H04B1/715—Interference-related aspects
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B1/00—Details of transmission systems, not covered by a single one of groups H04B3/00 - H04B13/00; Details of transmission systems not characterised by the medium used for transmission
- H04B1/69—Spread spectrum techniques
- H04B1/7163—Spread spectrum techniques using impulse radio
- H04B1/719—Interference-related aspects
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B2201/00—Indexing scheme relating to details of transmission systems not covered by a single group of H04B3/00 - H04B13/00
- H04B2201/69—Orthogonal indexing scheme relating to spread spectrum techniques in general
- H04B2201/713—Frequency hopping
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B2201/00—Indexing scheme relating to details of transmission systems not covered by a single group of H04B3/00 - H04B13/00
- H04B2201/69—Orthogonal indexing scheme relating to spread spectrum techniques in general
- H04B2201/713—Frequency hopping
- H04B2201/71376—Threshold
Abstract
The invention discloses a kind of method for parameter estimation of Frequency Hopping Signal based on Short-Time Fractional Fourier Transform, characterized in that includes the following steps: 1) to collected Frequency Hopping SignalMake Short-Time Fractional Fourier Transform；2) vector is obtained；3) wavelet transformation；4) it calculatesMean value, seek its amplitude；5) hop period is obtained；6) time-frequency crestal line is found out；7) difference is asked to time-frequency crestal line；8) pulse train is obtained；9) estimated value of jumping moment is obtained；10) jump frequency is obtained.This method energy suppressing crossterms interference, can improve the time frequency analysis precision of frequency parameter estimation.
Description
Technical field
The present invention relates to field of signal processing, specifically a kind of Frequency Hopping Signal based on Short-Time Fractional Fourier Transform
Method for parameter estimation.
Background technique
A kind of communication technology of the frequency hopping communications as spread spectrum communication, because it is excellent with low intercepting and capturing rate, strong anti-interference performance etc.
Gesture is widely used in the communications field.With the development of technology, in terms of frequency hopping communications has also gradually penetrated into civil field,
If unmanned plane flies control signal communication, Bluetooth communication etc. is communicated using Frequency Hopping Signal.Therefore, for receiving end,
The parameter Estimation of accurate estimation Frequency Hopping Signal is of great significance.When being mainly based upon at present about the estimation of frequency parameter
The method of frequency analysis, most common frequency parameter estimation method are that the method for frequency parameter is estimated using Short Time Fourier Transform,
Operand is low, realizes simply, but time frequency resolution precision is not high enough, is based on the method for parameter estimation of Wigner (WVD) transformation,
Though improving time frequency resolution, there are serious cross term interferences.
Summary of the invention
The purpose of the present invention is in view of the shortcomings of the prior art, and providing a kind of jump based on Short-Time Fractional Fourier Transform
The method for parameter estimation of frequency signal.This method energy suppressing crossterms interference can improve the time frequency analysis essence of frequency parameter estimation
Degree.
Realizing the technical solution of the object of the invention is:
A kind of method for parameter estimation of the Frequency Hopping Signal based on Short-Time Fractional Fourier Transform, unlike the prior art
It is to include the following steps:
1) Short-Time Fractional Fourier Transform is made to collected Frequency Hopping Signal x (n): to collected Frequency Hopping Signal x (n)
Make Short-Time Fractional Fourier Transform, similar with Short Time Fourier Transform, Short-Time Fractional Fourier Transform is also a kind of adding window
Transformation, p rank Short-Time Fractional Fourier Transform STFRFTx,p(n, u) is represented by formula (1):
Kernel function Kp(τ, u) is formula (2):
Wherein, g (τ) is window function,
2) it obtains maximum value vector y (n): calculating STFRFTx,p(n, u) goes up the maximum value of each moment n along the time axis,
Obtaining vector y (n) is formula (3):
3) wavelet transformation: making wavelet transformation to vector y (n), the time-domain signal CWT (n, u) after obtaining wavelet transformation；
4) it calculates the mean value of CWT (n, u), seek its amplitude: calculating the mean value of CWT (n, u), remove DC component, and ask it
Amplitude obtains y1(n) it is formula (4):
y1(n)=abs { CWT (n, u)-mean (CWT (n, u)) } (4)；
5) hop period is obtained: to amplitude sequences y1(n) make Fourier transformation, can estimate to obtain hop rate fh, thus may be used
Estimation obtains hop period
6) it finds out time-frequency crestal line: finding out the position loc (n) where the maximum value vector y (n) that step 2) obtains, i.e. time-frequency
Crestal line is formula (5):
Wherein, fsFor sample frequency, NfFor frequency point number；
7) difference is asked to time-frequency crestal line: first difference is asked to time-frequency crestal line loc (n), obtain difference sequence d1It (n) is formula
(6):
d1(n)=abs (diff (loc (n))) (6)；
8) pulse train is obtained: to difference sequence d1(n) denoising is carried out, pulse train d is obtained2(n), i.e. peak value position
It sets, due to affected by noise, needs to handle peak position, the process of processing are as follows: one threshold noise thresholding of setting is low
In the value of the thresholding, then it is assumed that it is noise, is otherwise useful signal, it is at this moment still affected by noise, there can be multiple peak points,
Need therefrom to obtain the pulse train of useful signal, herein mainly by being averaged to a certain range of peak point,
The peak point closest to the average is taken, as the peak point of this section, search range is to difference sequence d1(n) first difference is sought
The distance of each consecutive points afterwards is not more than the half of hop period point, obtains qualified pulse train d3(n)；
9) obtain the estimated value of jumping moment: the corresponding strigula being approximately equal in length in time-frequency crestal line is Hopping frequencies
Duration, according to difference sequence d1(n) the estimated value fh_tiao for acquiring jumping moment is formula (7):
Fh_tiao=[d3(n)+1]/fs(7)；
10) it obtains jump frequency: having estimated to obtain hop period according to step 5)In each jump range, along when
Between axis by the STFRFT in each frequencyx,p(n, u) value is cumulative, the corresponding frequency coordinate of maximizing, then the available section
The normalized frequency of signal, being converted into the corresponding actual frequency of the hop cycle is formula (8):
The technical program makees Fourier Transform of Fractional Order on the basis of Short Time Fourier Transform, to signal, in score field
Upper analysis signal.
When the technical program makees Short-Time Fractional Fourier Transform to signal, the selection of fractional order order p is to pass through searching
So that FRFT modulus value maximum coordinate points p is determined on two-dimensional surface (p, u).
This method energy suppressing crossterms interference, can improve the time frequency analysis precision of frequency parameter estimation.
Detailed description of the invention
Fig. 1 is the flow diagram of embodiment method；
Fig. 2 is the time-frequency crestal line figure in embodiment；
Fig. 3 is embodiment method and hop period estimation method based on Short Time Fourier Transform frequency hopping under the same conditions
The estimation curve comparison diagram that the relative variance of phase estimate changes with signal-to-noise ratio.
Specific embodiment
The content of present invention is further elaborated with reference to the accompanying drawings and examples, but is not limitation of the invention.
Embodiment:
Referring to Fig.1, a kind of method for parameter estimation of the Frequency Hopping Signal based on Short-Time Fractional Fourier Transform, including it is as follows
Step:
1) Short-Time Fractional Fourier Transform is made to collected Frequency Hopping Signal x (n): to collected Frequency Hopping Signal x (n)
Make Short-Time Fractional Fourier Transform, similar with Short Time Fourier Transform, Short-Time Fractional Fourier Transform is also a kind of adding window
Transformation, p rank Short-Time Fractional Fourier Transform STFRFTx,p(n, u) is represented by formula (1):
Kernel function Kp(τ, u) is formula (2):
Wherein, g (τ) is window function, The essence of Short-Time Fractional Fourier Transform is by signal x (n) multiplied by the adjustable window letter of a window width
Number, namely Short Time Fourier Transform is made to signal x (n), then Fourier Transform of Fractional Order is made to signal, about fractional order order p
Selection, this example be by set p range and step-length, in parameter (p, u) plane search so that FRFT modulus value is maximum
Most it is worth point, the corresponding p value of maximum value is exactly the fractional order order that experiment is chosen at this time；
2) it obtains maximum value vector y (n): calculating STFRFTx,p(n, u) goes up the maximum value of each moment n along the time axis,
Obtaining vector y (n) is formula (3):
3) wavelet transformation: making wavelet transformation to vector y (n), the time-domain signal CWT (n, u) after obtaining wavelet transformation；
4) it calculates the mean value of CWT (n, u), seek its amplitude: calculating the mean value of CWT (n, u), remove DC component, and ask it
Amplitude obtains y1(n) it is formula (4):
y1(n)=abs { CWT (n, u)-mean (CWT (n, u)) } (12)；
5) hop period is obtained: to amplitude sequences y1(n) make Fourier transformation, can estimate to obtain hop rate fh, thus may be used
Estimation obtains hop period
6) it finds out time-frequency crestal line: finding out the position loc (n) where the maximum value vector y (n) that step 2) obtains, i.e. time-frequency
Crestal line is formula (5):
Wherein, fsFor sample frequency, NfFor frequency point number；
7) difference is asked to time-frequency crestal line: first difference is asked to time-frequency crestal line loc (n), obtain difference sequence d1It (n) is formula
(6):
d1(n)=abs (diff (loc (n))) (14)；
8) pulse train is obtained: to difference sequence d1(n) denoising is carried out, pulse train d is obtained2(n), i.e. peak value position
It sets, due to affected by noise, needs to handle peak position, the process of processing are as follows: one threshold noise thresholding of setting is low
In the value of the thresholding, then it is assumed that it is noise, is otherwise useful signal, it is at this moment still affected by noise, there can be multiple peak points,
Need therefrom to obtain the pulse train of useful signal, herein mainly by being averaged to a certain range of peak point,
The peak point closest to the average is taken, as the peak point of this section, search range is to difference sequence d1(n) first difference is sought
The distance of each consecutive points afterwards is not more than the half of hop period point, obtains qualified pulse train d3(n)；
9) estimated value of jumping moment: comparative diagram 2 is obtained, figure it is seen that be approximately equal in length in time-frequency crestal line
Corresponding strigula is Hopping frequencies duration, according to difference sequence d3(n) the estimated value fh_tiao of jumping moment is acquired
For formula (7):
Fh_tiao=[d3(n)+1]/fs(15)；
10) it obtains jump frequency: having estimated to obtain hop period according to step 5)In each jump range, along when
Between axis by the STFRFT in each frequencyx,p(n, u) value is cumulative, the corresponding frequency coordinate of maximizing, then the available section
The normalized frequency of signal, being converted into the corresponding actual frequency of the hop cycle is formula (8):
This example validity can be verified by following emulation:
1. simulated conditions and method:
Using relative mean square error as the technical indicator of measure algorithm precision in emulation experiment, relative mean square error mathematics is fixed
Justice are as follows:
Wherein,To recycle the value that estimation obtains every time, M is the cycle-index under each signal to noise ratio, ThFor parameter Estimation
Actual value,
Simulation parameter is provided that under the conditions of white Gaussian noise, uses Hopping frequencies collection for { 98 76 52 38 78
48 44 36 40 50 } MHz, hop cycle 0.0014ms, sample frequency 200MHz, the sampling number of every jump are 280.
2. analysis of simulation result:
As shown in figure 3, the example method and the estimation method based on Short Time Fourier Transform, under the same conditions, signal-to-noise ratio
Range is in [- 10:10] dB, and hop period estimation relative mean square error compares, and simulation result shows in low signal-to-noise ratio situation
Under, the estimated accuracy of the example method is better than the estimated accuracy based on Short Time Fourier Transform method, and performance, which is substantially better than, to be based on
Short Time Fourier Transform method.
Claims (1)
1. a kind of method for parameter estimation of the Frequency Hopping Signal based on Short-Time Fractional Fourier Transform, characterized in that including as follows
Step:
1) Short-Time Fractional Fourier Transform is made to collected Frequency Hopping Signal x (n):
Short-Time Fractional Fourier Transform, p rank Short-Time Fractional Fourier Transform are made to collected Frequency Hopping Signal x (n)
STFRFTx,p(n, u) is represented by formula (1):
Kernel function Kp(τ, u) is formula (2):
Wherein, g (τ) is window function,
2) it obtains vector y (n): calculating STFRFTx,p(n, u) goes up the maximum value of each moment n along the time axis, obtains vector y
(n) it is formula (3):
3) wavelet transformation: making wavelet transformation to vector y (n), the time-domain signal CWT (n, u) after obtaining wavelet transformation；
4) it calculates the mean value of CWT (n, u), seek its amplitude: calculating the mean value of CWT (n, u), remove DC component, and seek its amplitude,
Obtain y1(n) it is formula (4):
y1(n)=abs { CWT (n, u)-mean (CWT (n, u)) } (4)；
5) hop period is obtained: to amplitude sequences y1(n) make Fourier transformation, can estimate to obtain hop rate fh, thus can estimate
To hop period
6) it finds out time-frequency crestal line: finding out the position loc (n) where the maximum value vector y (n) that step 2) obtains, i.e. time-frequency crestal line
For formula (5):
Wherein, fsFor sample frequency, NfFor frequency point number；
7) difference is asked to time-frequency crestal line: first difference is asked to time-frequency crestal line loc (n), obtain difference sequence d1(n) it is formula (6):
d1(n)=abs (diff (loc (n))) (6)；
8) pulse train is obtained: to difference sequence d1(n) denoising is carried out, pulse train d is obtained2(n), i.e. peak position, obtains
To qualified pulse train d3(n)；
9) obtain the estimated value of jumping moment: the corresponding strigula being approximately equal in length in time-frequency crestal line is that Hopping frequencies continue
Time, according to difference sequence d3(n) the estimated value fh_tiao for acquiring jumping moment is formula (7):
Fh_tiao=[d3(n)+1]/fs(7)；
10) it obtains jump frequency: having estimated to obtain hop period according to step 5)In each jump range, along the time axis
By the STFRFT in each frequencyx,p(n, u) value is cumulative, the corresponding frequency coordinate of maximizing, then the available segment signal
Normalized frequency, be converted into the corresponding actual frequency of the hop cycle be formula (8):
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| CN112929053A (en) * | 2021-03-10 | 2021-06-08 | 吉林大学 | Frequency hopping signal feature extraction and parameter estimation method |
| CN113824468A (en) * | 2021-08-18 | 2021-12-21 | 华南理工大学 | Chirp spread spectrum human body communication method based on active carrier label modulation |
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| CN112327052A (en) * | 2020-11-02 | 2021-02-05 | 清源智翔(重庆)科技有限公司 | Rapid high-precision frequency measurement method and system |
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| CN112929053A (en) * | 2021-03-10 | 2021-06-08 | 吉林大学 | Frequency hopping signal feature extraction and parameter estimation method |
| CN113824468A (en) * | 2021-08-18 | 2021-12-21 | 华南理工大学 | Chirp spread spectrum human body communication method based on active carrier label modulation |
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