Method for generating non-Gaussian white noise by MATLAB (matrix laboratory)

Abstract

The invention relates to the technical field of low-frequency communication, in particular to a method for generating non-Gaussian white noise through MATLAB, and the method comprises the steps: analyzing the distribution characteristics of the low-frequency non-Gaussian white noise, and obtaining the distribution characteristics; fitting the distribution features by using distribution function fitting to obtain fitting features; according to the method, based on the fitting feature and the probability density distribution graph of the non-Gaussian white noise, noise distribution in an existing material is compared, the non-Gaussian white noise generated by software is comprehensively compared, and by means of the feature function of noise distribution, the distribution characteristics of the low-frequency noise after whitening processing can be highly fitted, and the noise distribution accuracy is improved. Compared with the prior art, the method has the advantages that noise feature distribution function fitting is adopted, and the method is highly similar to actually measured data in feature; by adjusting noise parameters, different non-Gaussian noise conditions can be fitted, and the method is suitable for simulation requirements under various conditions.

Description

Technical Field

[0001] The invention relates to the technical field of low-frequency communication, and in particular to a method for generating non-Gaussian white noise by using MATLAB. Background Art

[0002] Low-frequency communication usually refers to communication in the 3-300kHz frequency band, which has important applications in underwater communication, earthquake monitoring, and deep-sea resource monitoring. Due to the particularity of its application scenarios, the study of low-frequency communication has important strategic significance. As the main interference source of low-frequency communication, low-frequency noise has seriously damaged the quality and reliability of low-frequency communication. How to remove low-frequency noise has become a key factor in determining the quality of low-frequency communication.

[0003] Research shows that low-frequency noise is non-Gaussian noise, which mainly comes from various interferences in the natural environment, such as the mains electricity and lightning weather in the atmosphere, among which lightning is the main factor causing low-frequency noise. However, if ordinary people want to collect noise in such a complex environment, they need to use professional equipment and antennas. In particular, noise data in special environments may be confidential and cannot be publicly collected and tested, let alone used in general algorithm simulation research. Summary of the invention

[0004] The purpose of the present invention is to provide a method for generating non-Gaussian white noise using MATLAB, which is intended to be added to a simulation system as a simulation reference value to verify the quality of a communication algorithm when there is no measured data.

[0005] To achieve the above object, the present invention provides a method for generating non-Gaussian white noise using MATLAB, comprising the following steps:

[0006] Analyze the distribution characteristics of low-frequency non-Gaussian white noise to obtain distribution features;

[0007] Fitting the distribution feature using distribution function fitting to obtain a fitting feature;

[0008] Based on the fitting characteristics combined with the probability density distribution graph of non-Gaussian white noise, the noise distribution in the existing materials is compared to conduct a comprehensive comparison of the non-Gaussian white noise generated by the software.

[0009] The non-Gaussian white noise model includes an α noise distribution model and a Class A noise distribution model.

[0010] The generation of the noise requires a number of samples, that is, the actual length of the simulated noise. It is necessary to set a data length parameter, and the length of the noise is selected by controlling the input parameter.

[0011] The probability density function of the α distribution of the α noise distribution model can be obtained by performing inverse Fourier transform on the characteristic function.

[0012] The probability density function of the Class A distribution of the Class A noise distribution model is the cumulative sum of infinite kernel functions and has no closed expression.

[0013] The invention discloses a method for generating non-Gaussian white noise by using MATLAB. The method comprises the following steps: analyzing the distribution characteristics of low-frequency non-Gaussian white noise to obtain distribution characteristics; fitting the distribution characteristics by using distribution function fitting to obtain fitting characteristics; comparing the noise distribution in existing materials based on the fitting characteristics and the probability density distribution graph of non-Gaussian white noise, and comprehensively comparing the non-Gaussian white noise generated by software. The method can highly fit the distribution characteristics of low-frequency noise after whitening processing by means of the characteristic function of noise distribution, and has high practical value for program simulation. Compared with the prior art, the method adopts noise characteristic distribution function fitting, which is highly similar to the characteristics of measured data; different non-Gaussian noise situations can be fitted by adjusting noise parameters, and is suitable for simulation requirements in various situations. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0015] Figure 1 This is a schematic diagram of the process of generating non-Gaussian white noise.

[0016] Figure 2 It is a common non-Gaussian noise distribution diagram (KDE estimation method).

[0017] Figure 3 It is the tailing plot of non-Gaussian noise.

[0018] Figure 4 It is the SaS simulated noise data and its estimated PDF graph.

[0019] Figure 5 This is the estimation diagram of SaS simulated noise data using the ClassA model.

[0020] Figure 6 is the Class A noise model and its estimation graph.

[0021] Figure 7 This is the estimation diagram of Class A simulated noise data using the SaS model.

[0022] Figure 8 The present invention provides a flow chart of a method for generating non-Gaussian white noise using MATLAB. DETAILED DESCRIPTION

[0023] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to be used to explain the present invention, and should not be construed as limiting the present invention.

[0024] See also Figures 1 to 8 , the present invention provides a method for generating non-Gaussian white noise using MATLAB, comprising the following steps;

[0025] S1 analyzes the distribution characteristics of low-frequency non-Gaussian white noise to obtain distribution features;

[0026] S2 uses distribution function fitting to fit the distribution feature to obtain a fitting feature;

[0027] S3 compares the noise distribution in the existing materials based on the fitting features combined with the probability density distribution graph of the non-Gaussian white noise, and performs a comprehensive comparison of the non-Gaussian white noise generated by the software.

[0028] In the embodiment of the present invention, there are many description models of non-Gaussian noise, such as α noise distribution model, Class A noise distribution model, mixed Gaussian noise distribution model, etc. This method is mainly designed for α noise and Class A noise, which are the most commonly used models among many models.

[0029] Design 1: Overall program design

[0030] Due to the different noise models, it is necessary to set control parameters. By setting different parameter values, specific noise types are generated. Usually, there are two situations for setting parameters. When the parameter value is 1, the program will generate non-Gaussian noise data that meets the Class A noise model. When the parameter value is not 1 (any value other than 1), the program will generate non-Gaussian noise data that meets the α noise model. For this reason, the following will be divided into two situations to introduce different noise model generation methods. The generation of noise requires the number of samples, that is, the actual length of the simulated noise. The data length parameter needs to be set. The length of the noise can be selected by controlling the input parameters.

[0031] Design 2: Generate alpha noise model

[0032] The α-stable distribution is a non-Gaussian noise that fits the pulse form with a probability density function similar to the Gaussian distribution. The α-stable distribution satisfies the generalized central limit theorem and has a more general meaning than the Gaussian distribution. It can accurately describe the characteristics of actual data. The α-stable distribution can be described by the characteristic function

[0033] Φ α (ω)=exp{jδω-γ|ω| α [1+jβsgn(ω)Ω(ω,α)]}

[0034] in

[0035]

[0036] sgn(ω) represents the sign function, α∈(0,2] is called the characteristic index, which determines the degree of pulse distribution characteristics; γ is called the dispersion coefficient, which is used to examine the degree of dispersion of samples relative to the mean; β is called the symmetry parameter, if β = 0, the α stable distribution is called SαS distribution; δ is called the location parameter, for SαS distribution, if α∈(0,1], δ represents the median, and if α∈(1,2], it represents the mean. Note that the probability density function of the α distribution can be obtained by performing an inverse Fourier transform on the characteristic function, that is,

[0037] f SαS (x) = F -1 [Φ α (ω)]

[0038] Among them, F -1 is the inverse Fourier transform.

[0039] When the generated noise conforms to the α noise model, it is necessary to set the model parameters, mainly including the characteristic exponential parameter α, symmetry parameter β and dispersion coefficient parameter σ appearing in the above formula; to generate the α noise model, it is necessary to first generate a uniform distribution U between [-π / 2, π / 2], and then generate an exponential distribution W with a mean of 1; it is necessary to generate the Ω function based on the characteristic exponential parameter α. When α is 1, the distribution model satisfies the Cauchy distribution. Multiply the exponential distribution W by π / 2 and then by the cosine value of the uniform distribution, divide by π / 2 plus the product of the symmetry parameter β, then take the logarithm of the above calculation result, and then multiply by the symmetry parameter β to obtain the result 1; add π / 2 to the product of the symmetry parameter β and the uniform distribution U, and then multiply by the tangent value of the uniform distribution U to obtain the result 2; subtract the result 1 from the result 2, and then multiply it by 2 / π and the dispersion coefficient γ, and then add π / 2 to the symmetry parameter β, the dispersion coefficient γ, and the dispersion coefficient Take the product of the logarithm of γ to get the noise model when α is 1; when the input α is not 1, take the tangent of the product of π / 2 and α, multiply it by the symmetry parameter β, and finally square the product and add 1 to get result 3; take result 3 to the power of twice α to get result 4; take the tangent of the product of π / 2 and α, multiply it by the symmetry parameter β, then take the inverse tangent, and finally divide it by α to get result 5; add result 5 to uniform distribution U and multiply it by α, and then take the sine value to get result 6; divide result 6 by the 1 / α power of the cosine value of uniform distribution U to get result 7; take the cosine value of the difference between uniform distribution U and parameter α, multiply it by the uniform distribution and result 5, and then divide it by the knowledge distribution W, and finally take the difference between 1 / α and 1 to get result 8; multiply result 4 by result 7 and result 8, and then multiply it by the dispersion coefficient γ, and add the location parameter δ to get the final distribution when α is not 1.

[0040] Design 3: Generating Class A Noise Model

[0041] The characteristic of ClassA distribution is good applicability. After superimposing Gaussian noise, it still maintains ClassA distribution, but the parameters will change. The probability density function of ClassA distribution is the cumulative sum of infinite kernel functions. There is no closed expression. It is generally expressed as

[0042]

[0043] Where a is the pulse index, Γ is the Gaussian pulse power ratio, and m represents the number of pulses in the noise.

[0044] Programming

[0045] When the generated noise meets the ClassA noise model, it is necessary to set the model parameters, mainly including the pulse index α, Gaussian pulse power ratio Γ and noise average power σ, as well as the number of pulse data m in the noise; the pulse index α is calculated as the e-power to obtain result 9; the result 9 is compared with a random number in [0, 1]. If the result 9 is small, the result 9 is multiplied by the pulse index α and then divided by the number of pulses m+1, and finally the result 9 is added to obtain result 10. If the result 9 is large, the result 9 is not processed; the result of dividing the number of pulses m by the pulse index α plus the Gaussian pulse power ratio Γ, and then divided by the sum of 1 and the Gaussian pulse power ratio Γ, and the square root is multiplied by the acoustic average power σ to obtain result 11; the result 11 is multiplied by the random normal distribution to obtain the final output ClassA noise model.

[0046] Design 4: Verification of the accuracy of the results of simulated noise data

[0047] Whether the program design is correct often needs to be verified by setting the control parameter to 1, selecting the noise model that generates the α distribution, and then generating the simulation data of the α distribution according to Design 2;

[0048] Given the parameters α is 1.5, β is 0, σ is 1, N is 819200, and run the generator;

[0049] Analyze the graphics generated by the program, estimate the probability density distribution of the simulation data according to the kernel density estimation method (a known common estimation method); use the known SαS model to estimate the simulation noise data; the estimation results are shown in Figure 4 The curves of the two estimation results are obviously different from the Gaussian distribution graph generated directly by the mean and variance of the noise. The overall noise shows a trend of being high in the middle and low at both ends, and there are obvious tails at both ends of the noise. Figure 2 The typical non-Gaussian noise distribution characteristics in the data are consistent, which proves that the data generated by the software is valid, and also proves that the KDE estimation method is accurate and effective; the ClassA distribution model method is used to estimate the simulated noise data; the estimation results are shown in Figure 5 It can be seen that the noise distribution characteristics modeled by the ClassA noise model are obviously inconsistent with the results obtained by KDE estimation. This is not difficult to understand, because SαS noise and ClassA noise are two different types of non-Gaussian noise, and their common feature is that they both have obvious tails.

[0050] According to the overall design of Design 1, by setting the control parameter to 2, the noise model for generating Class A distribution is selected, and then the simulation data of Class A distribution is generated according to Design 3; the parameters α are given as 0.35, Γ is 0.1, σ is 1, and N is 819200 and the generation program is run; the graphics generated by the program are analyzed, and the probability density distribution of the simulation data is estimated according to the kernel density estimation method (a known common estimation method); the simulation noise data is estimated using the Class A distribution model method; the estimation results are shown in Figure 6 The KDE estimation results are basically consistent with the ClassA model estimation results, especially the estimation of the noise tail part is completely consistent. There are obvious tails at both ends of the noise. Figure 2 The typical non-Gaussian noise distribution characteristics in the data are consistent, proving that the data generated by the software is valid; the known SαS model is used to estimate the simulated noise data; the estimation results are shown in Figure 7 The distribution curve obtained by the SαS distribution model completely coincides with the KDE estimation result, and is closer to the Class A model curve in the central axis. Therefore, the SαS distribution model can achieve a high degree of fit for the Class A noise model. Compared with the previous fit when the Class A model was used to estimate α noise, it can be seen that the SαS distribution model is more accurate in describing the noise distribution.

[0051] The above disclosure is only a preferred embodiment of the method of generating non-Gaussian white noise using MATLAB of the present invention. Of course, it cannot be used to limit the scope of rights of the present invention. Ordinary technicians in this field can understand that all or part of the processes of the above embodiment are implemented, and equivalent changes made according to the claims of the present invention still fall within the scope of the invention.

Claims

1. A method for generating non-Gaussian white noise using MATLAB, characterized in that: The steps include: Analyze the distribution characteristics of low-frequency non-Gaussian white noise to obtain distribution features; Fitting the distribution feature using distribution function fitting to obtain a fitting feature; Based on the fitting characteristics combined with the probability density distribution graph of non-Gaussian white noise, the noise distribution in the existing materials is compared to conduct a comprehensive comparison of the non-Gaussian white noise generated by the software.

2. The method for generating non-Gaussian white noise using MATLAB as claimed in claim 1, wherein ； The non-Gaussian white noise model includes an α noise distribution model and a Class A noise distribution model.

3. The method for generating non-Gaussian white noise using MATLAB as claimed in claim 1, It is characterized by: The generation of the noise requires a number of samples, that is, the actual length of the simulated noise. It is necessary to set a data length parameter, and the length of the noise is selected by controlling the input parameter.

4. The method for generating non-Gaussian white noise using MATLAB as claimed in claim 2, It is characterized by: The probability density function of the α distribution of the α noise distribution model can be obtained by performing inverse Fourier transform on the characteristic function.

5. The method for generating non-Gaussian white noise using MATLAB as claimed in claim 2, It is characterized by: The probability density function of the Class A distribution of the Class A noise distribution model is the cumulative sum of infinite kernel functions and has no closed expression.

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