Research On Set-Membership Sparse Adaptive Filtering Algorithm Against Non-gaussian Impulsive Interference

In the adaptive filtering algorithm,Set Membership Filtering(SMF)algorithms represent a class of recursive algorithms based on predefined error bound.They allow the algorithms not to update the tap coefficients when the estimated error was less than the preset bound.Therefore,the SMF algorithms have lower computational complexity than the Least Mean Squares algorithms.Adaptive algorithms were more often used in non-sparse systems in the early stage of research.With the development of signal processing technology,researchers have found that there was a distinctive system in the reality.Most of the tap coefficients of system were close to zero or zero,and only a few tap coefficients were larger in value.This characteristic is sparse,and systems with such characteristic are sparse.In recent years,researchers have proposed algorithms for sparse systems based on LMS algorithm and SMF algorithm to improve the performance of the algorithm in sparse systems,but most of researches were done under Gaussian noise.However,there were non-Gaussian interferences in practical applications,which seriously degrades the performance of sparse algorithms,and even no longer converges and Some sparse adaptive algorithms with anti-impulse capability whose computational complexity are very massive.For these two problems,this paper proposes the following solutions:(1)In order to solve the problem of performance degradation of adaptive algorithms in non-Gaussian noise environment.Step-size gain matrix of Proportionate Normalized Least Mean Squares algorithm and cost function of Arc-tangent Normalized Least Mean Squares algorithm were introduced into the cost function of Set-Membership Normalized Least Mean Squares with Adaptive Error Bound algorithm.Set-Membership Arc-tangent Proportionate Normalized Least Mean Squares algorithm was proposed.The step-size gain matrix of the PNLMS algorithm improved the convergence speed of the proposed algorithm in sparse system.The cost function of Arc-NLMS algorithm was introduced to make the algorithm get anti-impulse capability.Simulation experiments showed that the proposed algorithm has better convergence performance and steady-state error performance than other anti-impulse sparse adaptive algorithms under non-Gaussian impulse noise interference.(2)In order to solve the problem of massive computational complexity in the antiimpulse sparse adaptive algorithm.Sparse norm constraint was introduced into cost function of Set-Membership Normmalized Least Mean Square Algorithm with Robust Error Bound,Zero Attracting Set-Membership Normalized Least Mean Squares with Robust Error Bound and Reweighted Zero Attracting Set-Membership Normalized Least Mean Squares with Robust Error Bound algorithm were proposed.The sparse norm constraint algorithm has lower computational complexity than the proportionate algorithm.The error bound of the SM algorithm itself is robust and does not require additional antiimpluse techniques.Therefore,the computational complexity of the algorithm can be reduced.Simulation experiments showed that the actual computation of the proposed algorithms were lower when they keep similar performance with other anti-impulse sparse algorithms.