Research On The Robust Proportionate-type Sparse Adaptive Filtering Algorithms Against Non-gaussian Impulsive Interference

The traditional adaptive algorithms mainly include least mean square(LMS)algorithm and recursive least square(RLS)algorithm.Compared with the RLS algorithm,LMS has been widely used because of its simple structure and easy implementation.As an improved algorithm of LMS algorithm,normalized least mean square(NLMS)algorithm is faster than LMS algorithm in terms of the convergence speed.However,when the system is a sparse system,LMS and NLMS algorithms converge slowly.The proportionate-type adaptive algorithms,such as proportionate normalized least mean square(PNLMS),improved proportionate normalized least mean square(IPNLMS)and so on,improved the convergence speed of NLMS algorithm for utilizing the prior knowledge of system sparseness.When the system is sparse,compared with the LMS algorithm and the NLMS algorithm,the PNLMS algorithm has a faster convergence speed.However,under the non-Gaussian impulsive noise environment,the performance of the traditional proportional-type algorithms deteriorates severely;even does not converge.Simultaneously,when the input is high eigenvalue spread,the convergence speeds of the traditional proportionate-type adaptive algorithms become slower.To solve those problems,this paper gives the following solutions:First,the use of maximum correntropy criterion(MCC)and normalized least mean square algorithm based on arc-tangent function(Arc-NLMS)combine the proportionate gain matrix of traditional PNLMS algorithm into the cost function,respectively.And propose proportionate maximum correntropy criterion(PMCC)algorithm and proportionate arc-tangent normalized least mean square(P-Arc-NLMS).And then,the convergence performances of the proposed algorithms are proved by the convergence condition analysis,the computational complexity analysis and the computer simulation experiment.Second,based on the study of leaky least mean square(LLMS),the PLLMS-MCC algorithm is proposed by introducing the leaky factor in the improved cost function.The improvements make the traditional proportionate-type algorithms can keep good convergence performances when the input is eigenvalue spread under non-Gaussian impulse interference.In addition,for relatively large complexity of the proposed algorithm,this paper proposes sparse adaptive algorithms based on sign function-type,and carries on the simulation and the result analysis.