Research On Sparse Adaptive Filter Algorithms Based On The Constraint Of Norm Penalty

Adaptive filtering is an important branch of signal processing theory,and its ability of self-adaptive learning has been favored by domestic and foreign researchers.For several decades,after the effort of scholars to study and improve,the adaptive filtering technology has been widely used in many fields,such as echo cancellation,system identification,channel equalization,and it also plays an important role in the industrial areas,such as biomedical engineering,communication engineering,radar systems,automatic control systems.Adaptive algorithm is the basis of adaptive filtering theory.The adaptive algorithms commonly used include Least Mean Square?LMS?,Affine Projection?AP?,Recursive Least Squares?RLS?,and so on.In practice,there are many sparse systems and the number of zero or near zero tap coefficients of these systems is much higher than the non-zero tap coefficients.Due to the particularity of the system structure,the algorithms applied to the sparse system should take into account the sparse characteristic to improve the performance of the algorithm.While the calculation process of the traditional adaptive algorithm didn't use the characteristic of sparseness,thus it is difficult to identify the sparse system with good approximation.First of all,this paper briefly introduces the principle of adaptive filter structure,system identification model,and the parameters that affect the performance of the filter.Secondly,the existing zero-attracting sparse penalty algorithms based on l₁ norm,l₀ norm and l_p norm constraint are reviewed and analyzed.In this paper,a variable step-size Reweighted Zero-Attracting LMS?RZA-LMS?algorithm based on the error function is proposed to solve the contradiction between the steady-state performance and the convergence rate caused by the fixed step-size RZA-LMS.The step size of proposed algorithm is updated by the non-linear relationship between the step size and the power of the noise-free priori estimation error.The simulation results show that the initial convergence speed and the steady state performance of the proposed variable step-size algorithm are improved,thus the global performance of the algorithm is improved.Finally,aiming at the logarithmic function penalty constraint term of RZA-LMS algorithm,we propose an improved sparse algorithm based on error function penalty.The improved algorithm increases the zero attractivity of the smaller tap coefficients and further reduces the attracting of the larger tap coefficients.In order to improve the performance against impulsive noise,a sparse algorithm based on error function penalty constraint under the maximum correntropy criterion is proposed.