Study On Steady-State Performance Of Adaptive Filters Based On Sign Function

With the rapid development of the current mobile communication network,the digital signal processing technology has been an unprecedented development opportunities,and adaptive filter as a key part of signal processing technology,makes adaptive filter development has entered a new era.Adaptive filters have become a key part of many modern communication and control systems,which can be used for system identification,adaptive equalization,echo cancellation,beam forming and so on.There are many adaptive filtering algorithms,The Least Mean Square(LMS)algorithm is the most popular adaptive filtering algorithm,and it is so popular because of its simplicity and robustness.In recent years,Related literature have proposed a number of improved algorithms for LMS to overcome some of the limitations of the LMS algorithm by changing the estimation error function from linear to non-linear,such as the normalized LMS(NLMS)algorithm,the minimum mixing norm(Least Mean Mixed Norm,LMMN)algorithm,affine projection(AP)algorithm and so on,However,for the algorithms of the estimation error signal contains sign function,the relevant literature is not a lot,so it is necessary to study this kind of algorithm.The main work of this thesis from the following aspects:(1)Analyze and review the history of the adaptive filter,and then analyze the LMS algorithm,the NLMS algorithm and the AP algorithm in detail,so as to carry on the deeper step study later.(2)The steady-state tracking excess mean square error(TEMSE)performance and the steady-state mean square error(MSE)performance with the estimated error signal f(e)= g(e)sgn(e)are studied in detail,of course,includes both real and complex cases.The derivation process is based on the Taylor series expansion and Price theory,and gives the analytical expressions of the steady state MSE and the steady state TEMSE for the real value case and the complex value case.Finally,a lot of simulations is carried out on its theoretical and simulation values.(3)The non-linear estimation error signal with sign function sgn(e)is applied to the NLMS algorithm and the AP algorithm,The updated expression of the weight vector is deduced and the steady-state MSE of the two new algorithms is deduced.The simulation results show that the theoretical value agrees well with the simulated value.