Research On The Performance Of LMP Algorithm In Non-Gaussian Noise Environment

Adaptive filter is an effective tool in the field of adaptive signal processing.It can automatically adjust parameters according to certain criteria without any relevant statistical prior knowledge,so that the system can achieve optimal performance.Among them,the core of the adaptive filter is the adaptive filter algorithm,and the performance of the adaptive filter algorithm directly affects the quality of the filter performance,which has certain theoretical value and practical significance for the performance research of the adaptive filter algorithm.In the process of adaptive filtering algorithm performance research,people usually consider two aspects.On the one hand,the steady-state behavior and instantaneous behavior of the adaptive filter in a stable environment are considered;the former can obtain the mean square error of the adaptive filter after reaching the steady state.The latter can obtain information about the stability and convergence of the adaptive filter;on the other hand,the tracking performance of the adaptive filter in a non-stationary environment is considered.At present,in the performance research process of traditional adaptive filtering algorithms,the noise is usually assumed to be Gaussian distribution and signal processing methods based on second-order statistics are paid much attention.Many scholars have analyzed the performance of the LMP adaptive filtering algorithm under Gaussian noise,but there are a lot of impulsive non-Gaussian noise in the real application environment.This article mainly analyzes the steady-state performance,tracking performance and transient performance of the LMP adaptive filtering algorithm in a non-Gaussian noise environment.The specific work of this thesis is as follows:(1)The characteristics of non-Gaussian noise in real life environment are studied,and three common non-Gaussian noise statistical models are established: Alpha stable distribution noise model,Middleton Class A noise model and Bernoulli-Gaussian impulse noise model.The mathematical expressions and some parameters of various noise models are explained in detail,and the statistical distribution of noise models and random sequences of various noises are simulated by MATLAB,and the research results of various noise models are applied to the performance of MATLAB simulation platform Analyzing simulation work.(2)Based on the foundation of energy conservation in stationary and non-stationary environments,the estimated error function of the LMP algorithm under Alpha stable distribution noise is expanded by Taylor series,and the separation assumption conditions are used to analyze the performance of the LMP algorithm in stationary and non-stationary environments.Steady-state performance,derive the steady-state excess mean square error expression in a stable environment and the steady-state tracking excess mean square error,the optimal step size and the smallest steady-state excess mean square error expression in a nonstationary environment,and Analyze the range of stable convergence step of LMP algorithm.In addition,the transient performance of the LMP algorithm under Alpha stable distributed noise is analyzed,and the transient mean square deviation expression under the white input signal and the relevant input signal is derived.Finally,the correctness of the theoretical results is verified by MATLAB simulation experiment.(3)Based on the performance analysis method of the LMP algorithm under Alpha stable distributed noise,the steady-state excess mean square error of the LMP algorithm under Middleton Class A noise and Bernoulli-Gaussian impulsive noise and the steady-state tracking excess under non-stationary environment are also averaged.The theoretical formulas of square error,optimal step size and minimum steady-state excess mean square error are derived.Finally,the transient performance of the LMP algorithm under Middleton Class A noise and BernoulliGaussian impulse noise is analyzed.The simulation experiment results show that the derived theoretical expression is consistent with the simulation experiment value.