Research On Robust Adaptive Filtering Algorithm Based On Norm Constraint

The adaptive filtering algorithm automatically adjusts the filter parameters according to the environment,and is widely used in many fields such as speech prediction,radar systems,and network echo.In these practical applications,many systems to be estimated have sparse characteristics,that is,the number of zero weight coefficients in the system impulse response is far more than the number of non-zero weight coefficients.The Zero Attracting Least Mean Square Algorithm(ZA-LMS)fully considers the sparse characteristics of the system itself,and is a very typical sparse adaptive filtering algorithm.However,the traditional ZA-LMS algorithm imposes the same magnitude of attraction to the ownership coefficient,and the attraction does not change with the weight coefficient,which leads to the problem of insufficient attraction when the weight coefficient is zero,and the algorithm's convergence speed is slow.At the same time,the fixed step size and regularization parameters also limit the balance between the algorithm's convergence performance and steady-state performance.Therefore,this thesis conducts in-depth research on ZA-LMS algorithms and proposes improved algorithms.First of all,in view of the lack of attractiveness of the ZA-LMS algorithm,which leads to the slow convergence of the algorithm,the penalty term of the cost function of the ZA-LMS algorithm is improved,and a new weight coefficient update equation is derived.The algorithm can update the attractiveness in real time according to the change of the weight coefficient during the update iteration process.When the weight coefficient is zero,the attractiveness of the weight coefficient is increased.Since the weight coefficient of zero takes up a larger proportion in the sparse system,Increasing the attraction to the zero weight coefficient can speed up the overall convergence speed of the algorithm.Secondly,fixed values are selected for the step size and regularization parameters of the ZA-LMS algorithm,which leads to contradictory problems in the convergence performance and steady-state performance of the algorithm.The idea of variable parameters is introduced,that is,the method of minimizing the mean square deviation is used to derive with variable step length and regularization parameters,a variable parameter and logarithmic function of ZA-LMS(VP-LZA-LMS)is proposed.This algorithm solves the problem that fixed step size and fixed regularization parameters reduce the performance of the algorithm,thereby significantly improving its robustness in sparse systems.Finally,the theoretical analysis of the convergence performance and steady-state performance in the mean square sense of the algorithm is carried out,and simulation experiments are carried out to verify.The simulation results show that when the input signal is white signal and related signal,compared with some existing sparse adaptive filtering algorithms,the new algorithm proposed in this thesis can be applied to sparse systems with different sparseness,and the convergence performance,steady-state performance,robustness,and tracking performance perform well.