Study Of Sparse Adaptive Filtering Algorithms Based On Mmse

Adaptive filter can dynamically adjust its parameters without knowing the systemcharacteristics in advance, and has a wide range of applications in system identification,voice prediction, echo cancellation and many other aspects.This paper discusses the system identification model based on adaptive filteringalgorithms, and learns more on sparse impulse response problems, mainly on thecharacteristics of the acoustic echo path is sparse. Sparsity refers to most of the weightcoefficients are very small or0, only a small part of the weight coefficient are relativelylarge.LMS(Least Mean Square) algorithm, based on MMSE, has the advantages of simplestructure, fast convergence and low computational complexity among many adaptivefiltering algorithms. But along with the improvement of people’s demands forcommunication quality, and no consideration on sparsity in the sparse pulse responsesystem, the traditional LMS algorithm has been unable to achieve the best filtering effect.In this paper, the sparse adaptive filtering algorithms are studied and compared, andthe two main kinds of algorithms are discussed based on the research of LMS algorithm,and considering sparse characteristics of acoustic echo path. One kind is proportionateadaptive filtering algorithm based on MMSE, including Proportionate Normalized LeastMean Square (PNLMS), PNLMS based on Mu-law (MPNLMS), IPNLMS based onl1Norm and Improved MPNLMS (MIPNLMS). In this paper, the proportionate adaptivefiltering algorithm have been studied, and the simulation experiment have been done,computational complexity, convergence speed and steady-state misadjustment and otheraspects of the performance evaluation are used to analyze their advantages anddisadvantages.Another kind is zero-attracting least mean square algorithm, including zero attractingLMS and zero attracting NLMS. From the simulation, the two zero-attracting least meansquare algorithms and their corresponding basic algorithms have been compared andanalyzed, then the standard PNLMS algorithm and the ZA-NLMS algorithm have been compared，the results show that the ZA-LMS algorithm has better performance than thePNLMS algorithm when the impulse is sparse.