Parameter Estimation Of LFM Signals In Alpha Stable Noise

Linear frequency modulation(LFM)signals are a class of typical non-stationary signals.Due to their advantages of low interception probability,long range,and large time-bandwidth product,they are widely used in radar,sonar,communications,seismic detection and other fields.Traditional LFM signal detection and parameter estimation methods are mostly carried out under Gaussian noise environment,but in recent years,research has found that most of the noise in practical applications is non-Gaussian,which is more suitable to be described by the alpha stable distribution model.Signal processing methods based on Gaussian noise model are no longer applicable to this kind of situation.Therefore,it is of great significance to carry out research on the detection and parameter estimation methods of linear frequency modulation signals under alpha stable distributed noise.The traditional parameter estimation methods degrade or even become invalid under the alpha stable distribution noise.In this regard,the thesis proposes a new compressing transform function based method for LFM signal parameter estimation under alpha stable distribution noise.A new compressing transform function is constructed and compared with the fractional low-order function.The derivation proves that this function has better impulse noise suppression capability than the fractional lower-order function.The thesis analyzes the approximate linearity of the function near the zero point,derives that the second-order moments are bounded after the proposed transformation for any random variable,and proves that the initial frequency and frequency modulation slope information of an LFM signal are unchanged after the transformation.Then the function-transformed noisy signal is subjected to the fractional Fourier transform.According to the relationship between the peak coordinates and the signal parameters in the Fr FT domain,the peak point in the transform domain is located and the signal parameter estimates can be obtained.Simulation experiments show that the proposed method can effectively suppress the impulse noise and accurately estimate the parameter information of the signal.This method is simple and robust.Moreover,it does not require the prior information of the impulsive noise.Under the environment of alpha stable distribution noise,the traditional time-frequency analysis methods are no longer applicable.To solve this problem,this thesis constructs a Cauchy-type transform function that can suppress large scale impulse noise,and proposes a new short time Cauchy Fourier transform time-frequency analysis method based on this function.A short-term Cauchy Fourier transform of the signal can be obtained using the short-term stationarity of the LFM signals through adding a sliding window to the time-domain observation signal and analyzing the signal in the window based on the Cauchy-type transform function.This method can effectively suppress impulse noise and the time-frequency distribution of the signal can be obtained.Then,using the characteristic that the LFM signal is a straight line in the time-frequency domain,the Hough line detection method is used to analyze the time-frequency distribution of the LFM signal,and the parameter estimation of the signal is obtained.Simulation experiments show that this method can effectively estimate signal parameters under alpha stable distribution noise,and has good performance under impulse noises of different intensities.Correlation entropy is a new signal processing theory proposed and rapidly developed in recent years.Correlation entropy is essentially a correlation function.Impulse noise can be suppressed by choosing different kernel functions.The traditional correlation entropy mostly employs Gaussian kernel function,and uses the exponential decay characteristic of Gaussian function to suppress impulse noise.However,due to the randomness and unmeasurability of impulse noise,a single correlation entropy kernel function has weak processing ability when facing such complex data.In addition,there is also the problem of not being able to suppress continuous similar impulse noise.To deal with this,the thesis constructs a mixed correlation entropy function,which enhances the ability to process complex data,and then weights the mixed correlation entropy function to obtain the weighted mixed correlation entropy function.The WMCF can avoid the problem of not being able to suppress the continuous similar amplitude noise.The WMCF function maintains the characteristic of suppressing impulse noise.Compared with the correlation entropy,the series expansion of the WMCF function contains all the order moment information of the signal.The derivation proves the existence of WMCF under the alpha stable distribution.Combining the WMCF and the STFT time-frequency analysis the SWMFT time-frequency distribution of the signal under impulse noise can be obtained.Utilizing the characteristic that the time-frequency distribution of the LFM signal is a straight line,the parameter estimation of the LFM signal can be gained by Hough transform.This method can perform time-frequency analysis of the LFM signal under the alpha stable noise,and can also suppress the impulse noise very well in the environment with high impulse intensity.