Research On The Variable Step Size Affine Projection Sign Algorithms

In recent years,with the advancement of signal processing technology and the expansion of communication applications,sensors for acquiring signals have gradually evolved into spatially distributed,networked and so on.Therefore,researches on distributed adaptive algorithms have been caused widespread attention.The Affine Projection Algorithm(APA)can achieve fast convergence rate,especially when the input signals are highly correlated,but it suffers from severe tracking performance degeneration under impulsive noise.The Sign Algorithm(SA)can achieve good tracking performance under impulsive noise,but it converges slowly.The Affine Projection Sign Algorithm(APSA)combines both fast convergence rate of APA and robustness against impulsive noise of SA,therefore,it is used to replace APA to enhance the robustness of the algorithms.However,whether single-node or distributed APSA,it is difficult to balance the contradiction between convergence rate and steady-state error caused by fixed step size.This thesis mainly studies this defect.First of all,this thesis briefly introduces the structure and principle of adaptive filters,then summarizes the basic theoretical knowledge of distributed adaptive network,and simply summarizes the derivation processes of the Least Mean Square(LMS)algorithm and its typical improved algorithms.Secondly,aiming at the problem of tracking performance degradation of the existing variable step size APSA algorithms in an unstable environment,this thesis proposes a new variable step size APSA based on the modified error function.The proposed algorithm substitutes the power of the noise-free prior error as an independent variable into the modified error function,and uses the calculated result as a step function to update the weight vector.In addition,the convergence condition,steady-state error and computational complexity of the proposed algorithm are analyzed.The results show that compared with the existing variable step size APSA algorithms,the proposed algorithm can achieve faster convergence rate,lower steady-state error and better stability.The above conclusions are verified by simulation experiments.Finally,to solve the problem between convergence rate and steady-state error caused by fixed step size in distributed APSA,this thesis proposes a distributed maximum correntropy variable step size APSA.The proposed algorithm substitutes the error of the previous moment as the independent variable into the correntropy function,and uses the calculated result as a step function to update the weight vector.The simulation results show that compared with the existing distributed APSA,the proposed algorithm effectively alleviates the contradiction between convergence rate and steady-state error caused by fixed step size,and improves the performance of algorithms.