Research On Adaptive Filtering Algorithm Under Alpha Stable Distribution Noise

Adaptive filtering has been widely used in system identification,prediction,channel equalization and interference cancellation.Research of adaptive filtering algorithm under non-Gaussian noise is a hot topic in signal processing.According to the ratio of zero or near zero value to non-zero value of unit impulse response,the system can be divided into the sparse system and the non-sparse system.This thesis mainly researches the application of adaptive filtering algorithm in sparse and non-sparse system identification,respectively.First of all,the basic theories of adaptive filtering model in the system identification,parameters affecting the performance of adaptive filtering algorithms,and Alpha stable distribution are briefly introduced.Then,two kinds of adaptive filtering algorithms with good anti-impulse noise performance for sparse system identification are proposed.Under the background of Alpha stable distribution noise,weighted zero attraction is applied to the LMP algorithm,and the weighted zero-attractive least mean P-norm(RZA-LMP)algorithm is proposed.The RZA-LMP algorithm is able to distinguish between zero and non-zero coefficients of unit impulse response.In order to alleviate the contradiction between the convergence speed and steady-state error of the RZA-LMP algorithm,a variable step size weighted zero attracting least mean P-norm(VSS-RZA-LMP)algorithm is proposed.The simulation results show that the VSS-RZA-LMP algorithm is the best,the RZA-LMP is better than the ZA-LMP algorithm.The VSS-RZA-LMP algorithm effectively alleviates the contradiction between convergence speed and steady-state error under different sparsity degrees,and has the fastest convergence speed and the smallest steady-state error.Thirdly,two kinds of kernel adaptive filtering algorithms with good anti-impulse noise performance for non-sparse system identification are proposed.In non-sparse system,to reduce the computational complexity and storage capacity of the kernel adaptive filtering(KAF)algorithm,clustering and transfer learning are applied to the kernel least mean P-norm(KLMP)algorithm and the quantized kernel least mean P-norm(QKLMP)algorithm,and the nearest-instance-centroid-estimation kernel least mean P-norm algorithm(NICE-KLMP)algorithm and the nearest-instance-centroid-estimation quantization kernel least mean P-norm algorithm(NICE-QKLMP)algorithm are obtained.The simulation results show that the complexity of the NICE-KLMP and NICE-QKLMP algorithms is lower than that of the QKLMP algorithm,and the anti-impulse noise performances of the three algorithms is the same well almostly.Finally,a Gaussian kernel explicit mapping method and the kernel filtering algorithms with low complexity are proposed.By using the explicit mapping method,the kernel least mean P-norm algorithm based on Gaussian kernel explicit mapping(KLMP-GKEM)is obtained.At the same time,the method and normalized decorrelation are applied to KAPP algorithm,and a normalized decorrelation KAPP algorithm based on Gaussian kernel explicit mapping(KNDAPP-GKEM)is proposed.Normalized decorrelation can effectively solve the problem of slow convergence speed caused by high correlation of input data.The simulation results show that compared with the KLMP-GKEM and KAPP algorithms,KNDAPP-GKEM algorithm has the fastest convergence speed and the best performance of system identification,its training time is slightly longer than the KLMP-GKEM algorithm,but it is much shorter than KAPP algorithm.