CN110048741A - A kind of method for parameter estimation of the Frequency Hopping Signal based on Short-Time Fractional Fourier Transform - Google Patents

Abstract

The invention discloses a parameter estimation method for a frequency hopping signal based on short-time fractional Fourier transform, which is characterized in that the method includes the following steps: 1) for the collected frequency hopping signal Do short-time fractional Fourier transform; 2) get the vector ; 3) wavelet transform; 4) calculation 5) Obtain the frequency hopping period; 6) Find the time-frequency ridge; 7) Differentiate the time-frequency ridge; 8) Obtain the pulse sequence; 9) Obtain the estimated value of the hopping moment; 10) Get the hopping frequency. This method can suppress cross-term interference, and can improve the time-frequency analysis accuracy of frequency hopping parameter estimation.

Description

A Parameter Estimation Method of Frequency Hopping Signal Based on Short-time Fractional Fourier Transform

technical field

The invention relates to the field of signal processing, in particular to a parameter estimation method of a frequency hopping signal based on short-time fractional Fourier transform.

Background technique

As a communication technology of spread spectrum communication, frequency hopping communication is widely used in the field of communication because of its advantages of low interception rate and strong anti-interference performance. With the development of technology, frequency hopping communication has gradually penetrated into the civilian field, such as UAV flight control signal communication, Bluetooth communication, etc., all use frequency hopping signals for communication. Therefore, for the receiving end, it is of great significance to accurately estimate the parameter estimation of the frequency hopping signal. At present, the estimation of frequency hopping parameters is mainly based on time-frequency analysis. The most commonly used method for estimating frequency hopping parameters is to use short-time Fourier transform to estimate frequency hopping parameters. Although the time-frequency resolution is improved, the parameter estimation method based on Wegener (WVD) transform has serious cross-term interference.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a parameter estimation method for a frequency hopping signal based on short-time fractional Fourier transform in view of the deficiencies of the prior art. This method can suppress cross-term interference, and can improve the time-frequency analysis accuracy of frequency hopping parameter estimation.

The technical scheme that realizes the object of the present invention is:

A method for parameter estimation of a frequency hopping signal based on short-time fractional Fourier transform, which is different from the prior art, includes the following steps:

1) Perform short-time fractional Fourier transform on the collected frequency hopping signal x(n): perform short-time fractional Fourier transform on the collected frequency hopping signal x(n), and the short-time Fourier transform Similar to the transformation, the short-time fractional Fourier transform is also a windowed transform. The p-order short-time fractional Fourier transform STFRFT _x,p (n,u) can be expressed as formula (1):

The kernel function K _p (τ, u) is formula (2):

Among them, g(τ) is the window function,

2) Obtain the maximum value vector y(n): Calculate the maximum value of STFRFT _x,p (n,u) at each time n along the time axis, and obtain the vector y(n) as formula (3):

3) Wavelet transform: perform wavelet transform on the vector y(n) to obtain the time domain signal CWT(n, u) after wavelet transform;

4) Calculate the mean value of CWT(n,u) and find its amplitude: Calculate the mean value of CWT(n,u), remove the DC component, and find its amplitude, and obtain y ₁ (n) as formula (4):

y ₁ (n)=abs{CWT(n,u)-mean(CWT(n,u))}(4);

5) Obtaining the frequency hopping period: Fourier transform is performed on the amplitude sequence y ₁ (n), the hopping speed fh can be estimated, and the frequency hopping period can be estimated from this

6) Find the time-frequency ridge: find the position loc(n) where the maximum vector y(n) obtained in step 2) is located, and the instant-frequency ridge is formula (5):

Among them, f _s is the sampling frequency, and N _f is the number of frequency points;

7) Differentiate the time-frequency ridge line: Calculate the first-order difference of the time-frequency ridge line loc(n), and obtain the difference sequence d ₁ (n) as formula (6):

d ₁ (n)=abs(diff(loc(n))) (6);

8) Obtaining the pulse sequence: perform denoising processing on the difference sequence d ₁ (n) to obtain the pulse sequence d ₂ (n), that is, the peak position. Due to the influence of noise, the peak position needs to be processed. The processing process is: set Set a threshold noise threshold, the value below the threshold is considered to be noise, otherwise it is a useful signal, and it is still affected by noise at this time, there will be multiple peak points, and the pulse sequence of the useful signal needs to be obtained. By averaging the peak points within _a certain range, the peak point closest to the average is taken as the peak point of the segment. Not more than half of the frequency hopping period point, obtain the qualified pulse sequence d ₃ (n);

9) Obtain the estimated value of the hopping moment: the short horizontal lines with approximately equal lengths on the time-frequency ridge line correspond to the duration of the frequency hopping frequency. According to the difference sequence d ₁ (n), the estimated value fh_tiao of the hopping moment is obtained as Formula (7):

fh_tiao=[d ₃ (n)+1]/f _s (7);

10) Obtain the hopping frequency: According to step 5), the frequency hopping period has been estimated In each hop range, the STFRFT _x,p (n,u) values at each frequency are accumulated along the time axis, and the frequency coordinate corresponding to the maximum value is found, then the normalized frequency of the signal can be obtained, and the conversion The actual frequency corresponding to this jump period is formula (8):

The technical scheme performs fractional Fourier transform on the signal on the basis of the short-time Fourier transform, and analyzes the signal in the fractional domain.

When this technical solution performs short-time fractional Fourier transform on the signal, the selection of the fractional order p is determined by finding the coordinate point p that maximizes the FRFT modulus value on the two-dimensional plane (p, u).

This method can suppress cross-term interference, and can improve the time-frequency analysis accuracy of frequency hopping parameter estimation.

Description of drawings

1 is a schematic flowchart of an embodiment method;

2 is a time-frequency ridge diagram in an embodiment;

FIG. 3 is a comparison diagram of estimation curves of the relative variance of the frequency hopping period estimation with the signal-to-noise ratio of the embodiment method and the short-time Fourier transform-based frequency hopping period estimation method under the same conditions.

Detailed ways

The content of the present invention will be further described below with reference to the accompanying drawings and embodiments, but it is not intended to limit the present invention.

Example:

1 , a method for estimating parameters of a frequency hopping signal based on short-time fractional Fourier transform includes the following steps:

1) Perform short-time fractional Fourier transform on the collected frequency hopping signal x(n): perform short-time fractional Fourier transform on the collected frequency hopping signal x(n), and the short-time Fourier transform Similar to the transformation, the short-time fractional Fourier transform is also a windowed transform. The p-order short-time fractional Fourier transform STFRFT _x,p (n,u) can be expressed as formula (1):

The kernel function K _p (τ, u) is formula (2):

Among them, g(τ) is the window function, The essence of the short-time fractional Fourier transform is to multiply the signal x(n) by a window function with an adjustable window width, that is, perform short-time Fourier transform on the signal x(n), and then perform fractional order on the signal. Fourier transform, regarding the selection of fractional order p, in this example, by setting the range and step size of p, the maximum value point that maximizes the FRFT modulus is searched on the parameter (p, u) plane. The p value corresponding to the value is the fractional order selected in the experiment;

2) Obtain the maximum value vector y(n): Calculate the maximum value of STFRFT _x,p (n,u) at each time n along the time axis, and obtain the vector y(n) as formula (3):

3) Wavelet transform: perform wavelet transform on the vector y(n) to obtain the time domain signal CWT(n, u) after wavelet transform;

4) Calculate the mean value of CWT(n,u) and find its amplitude: Calculate the mean value of CWT(n,u), remove the DC component, and find its amplitude, and obtain y ₁ (n) as formula (4):

y ₁ (n)=abs{CWT(n,u)-mean(CWT(n,u))}(12);

5) Obtaining the frequency hopping period: Fourier transform is performed on the amplitude sequence y ₁ (n), the hopping speed fh can be estimated, and the frequency hopping period can be estimated from this

6) Find the time-frequency ridge: find the position loc(n) where the maximum vector y(n) obtained in step 2) is located, and the instant-frequency ridge is formula (5):

Among them, f _s is the sampling frequency, and N _f is the number of frequency points;

7) Differentiate the time-frequency ridge line: Calculate the first-order difference of the time-frequency ridge line loc(n), and obtain the difference sequence d ₁ (n) as formula (6):

d ₁ (n)=abs(diff(loc(n)))(14);

8) Obtaining the pulse sequence: perform denoising processing on the difference sequence d ₁ (n) to obtain the pulse sequence d ₂ (n), that is, the peak position. Due to the influence of noise, the peak position needs to be processed. The processing process is as follows: set Set a threshold noise threshold, the value below the threshold is considered to be noise, otherwise it is a useful signal, and it is still affected by noise at this time, there will be multiple peak points, and the pulse sequence of the useful signal needs to be obtained. By averaging the peak points within _a certain range, the peak point closest to the average is taken as the peak point of this segment. Not more than half of the frequency hopping period point, obtain the qualified pulse sequence d ₃ (n);

9) Obtain the estimated value of the hopping moment: with reference to Figure 2, it can be seen from Figure 2 that the short horizontal lines with approximately equal lengths on the time-frequency ridge line correspond to the duration of the frequency hopping frequency, according to the difference sequence d ₃ (n ) to obtain the estimated value fh_tiao of the jump moment as formula (7):

fh_tiao=[d ₃ (n)+1]/f _s (15);

10) Obtain the hopping frequency: According to step 5), the frequency hopping period has been estimated In each hop range, the STFRFT _x,p (n,u) values at each frequency are accumulated along the time axis, and the frequency coordinate corresponding to the maximum value is found, then the normalized frequency of the signal can be obtained, and the conversion The actual frequency corresponding to this jump period is formula (8):

The validity of this example can be verified by the following simulation:

1. Simulation conditions and methods:

In the simulation experiment, the relative mean square error is used as a technical indicator to measure the accuracy of the algorithm, and the relative mean square error is mathematically defined as:

in, is the estimated value for each cycle, M is the number of cycles under each signal-to-noise ratio, _Th is the actual value of parameter estimation,

The simulation parameters are set as follows: under the condition of Gaussian white noise, the frequency hopping frequency set is {98 76 52 38 7848 44 36 40 50}MHz, the hopping period is 0.0014ms, the sampling frequency is 200MHz, and the number of sampling points per hop is 280.

2. Analysis of simulation results:

As shown in Figure 3, the method in this example and the estimation method based on short-time Fourier transform, under the same conditions, the signal-to-noise ratio range is within [-10:10]dB, and the relative mean square error of the frequency hopping period estimation is compared, The simulation results show that under the condition of low signal-to-noise ratio, the estimation accuracy of the method in this example is better than the estimation accuracy of the method based on the short-time Fourier transform, and the performance is obviously better than that of the method based on the short-time Fourier transform.

Claims (1)

1. A method for estimating parameters of a frequency hopping signal based on short-time fractional Fourier transform is characterized by comprising the following steps:

1) performing short-time fractional Fourier transform on the acquired frequency hopping signal x (n):

performing short-time fractional Fourier transform on the acquired frequency hopping signal x (n), and performing p-order short-time fractional Fourier transform STFRFT_x,p(n, u) can be expressed as formula (1):

kernel function K_p(τ, u) is formula (2):

wherein g (τ) is a window function,

2) obtain vector y (n): calculating STFRFT_x,p(n, u) along the maximum value of each time n on the time axis, a vector y (n) is obtained as formula (3):

3) wavelet transformation: performing wavelet transformation on the vector y (n) to obtain a time domain signal CWT (n, u) after the wavelet transformation;

4) calculating the mean value of CWT (n, u), and calculating the amplitude: calculating the mean value of CWT (n, u), removing DC component, and calculating its amplitude to obtain y₁(n) is formula (4):

y₁(n)＝abs{CWT(n,u)-mean(CWT(n,u))} (4)；

5) obtaining a frequency hopping period: for amplitude sequence y₁(n) Fourier transform, the hopping speed fh can be estimated, and the hopping period can be estimated

6) Finding out time-frequency ridge lines: finding out the position loc (n) of the maximum vector y (n) obtained in step 2), i.e. the frequency ridge line is formula (5):

wherein f is_sIs the sampling frequency, N_fCounting the number of frequency points;

7) and (3) carrying out difference calculation on time-frequency ridge lines: computing time-frequency ridge loc (n)Difference is carried out once to obtain a difference sequence d₁(n) is formula (6):

d₁(n)＝abs(diff(loc(n))) (6)；

8) obtaining a pulse sequence: for difference sequence d₁(n) carrying out denoising treatment to obtain a pulse sequence d₂(n), i.e. the peak position, to obtain a qualified pulse sequence d₃(n)；

9) Obtaining an estimated value of a jump moment: the short transverse lines with approximately equal length on the time-frequency ridge line correspond to the continuous time of the frequency hopping frequency according to the difference sequence d₃(n) obtaining an estimated value fh _ tiao at the jump time as formula (7):

fh_tiao＝[d₃(n)+1]/f_s(7)；

10) obtaining a hopping frequency: according to step 5) estimated frequency hopping periodWithin each hop range, the STFRFT at each frequency is measured along the time axis_x,pThe (n, u) values are accumulated, and the frequency coordinate corresponding to the maximum value is found, so that the normalized frequency of the signal of the segment can be obtained, and the actual frequency corresponding to the hop period is converted into the formula (8):