Research On Variable Step-size Adaptive Filtering Algorithms In Certain Scenarios

Adaptive filtering algorithm play an important role in the fields of system identification,noise cancellation,channel equalization,echo cancellation and distributed estimation.After the structure of the adaptive filter has been selected,its performance depends on the adaptive filtering algorithm used by it.Convergence rate and steady-state misalignment are two significant performance metrics.However,for a fixed step-size adaptive filter,the larger the step-size is,the faster its convergence rate is,but the larger its misalignment is;on the contrary,the smaller the step-size,the smaller its misalignment is,but the slower its convergence rate is.Therefore,fast convergence rate and small steady-state misalignment are a conflicted set of demands and a tradeoff between them is required.This thesis focuses on the topics of adaptive filtering algorithms suited for the scenarios of Gaussian noise,impulsive interference and noisy inputs to the filter and mainly studies how to use variable step-size method to address the tradeoff problem existing in the above algorithms.For Gaussian noise environments,this thesis proposes a variable step-size affine projection-like(APL)algorithm,which can not only accelerate the convergence rate for correlated input signal,but also reduce the steady-state misalignment of the APL algorithm.Sparse systems are one of the most common system types in the real world.To overcome the problem that sparse adaptive filtering algorithms cannot suppress the impulse noise interference,the idea of robust adaptive filtering is applied to sparse system identification and derive a weighted zero-attracting sign algorithm,based on which a variable step-size parameter is developed to further reduce steady-state misalignment.In some applications the input of the adaptive filter will be interfered by noise,which may make it produce biased estimation.Research has shown that bias-compensated sign algorithm can reduce the estimation bias of the adaptive filter with noisy inputs.This thesis incorporates variable step-size method into bias-compensated sign algorithm to further reduce its steady-state misalignment.Different experimental environments are used to simulate the proposed algorithms,and the simulation results verify their correctness and effectiveness.