Research And Application Of The Sparse Penalized Adaptive Filter Algorithm

As one of the important area of signal processing, generally, the adaptive filter theoryautomatically adjust the weights of the filter coefficients to achieve optimal filtering throughself-learning method, and is widely used in the field of system identification, noisecancellation. The design of adaptive filter algorithm is an important part within the design ofadaptive filter. The performance of the adaptive algorithm decides the performance of theadaptive filter. Adaptive filter algorithms partially include least mean square, recursive leastsquare and affine projection algorithm. Least mean square, based on the development ofWinner filter theory, is one of the most classical adaptive algorithms which has simplestructure, low computational complexity, and easily implemented in hardware. As the NLMSalgorithms generalization, APA has the advantages of fast convergence rate. However, in thepractical application of system identification, many pended identification systems are oftensparse, that is, most of the taps are zeros. LMS algorithm does not make full use of the priorinformation that the impulse response is usually sparse, so least mean square algorithm is notideal in solving the problem of the sparse system.Based on the sparsity of the impulse response and the analysis of the adaptive filter andLMS algorithm, this paper completes the following work.First, because the disadvantage of the zero-attracting least mean square (ZA-LMS)algorithm gives the same zero-attracting to the coefficient values of the filters, the paperproposes p (0<p <1) norm and the reweighted p (0<p <1) norm penalty LMS algorithm afterthe reviews of the zero-attracting least mean square (ZA-LMS) algorithm and the weightedzero-attracting least mean square (RZA-LMS) algorithm. These algorithms succeed in theapplication of the model of sparse system identification. The results show that the reweightedp-norm penalty LMS algorithm is the best improved least mean square algorithm in solvingthe sparse system identification.Second, although the improved sparse-penalty LMS algorithms consider and resolve theproblem of sparse impulse response, but the slow convergence rate is still a problems to besolved. The thinking of sparse-penalty LMS algorithm to be extended to the APA, the papersproposes three improvements APA: the zero attract affine projection algorithm (ZA-APA),the reweighted zero attract affine projection algorithm (RZA-APA) and p (0<p <1) normpenalty affine projection algorithm (l p-APA).Experiments demonstrate the feasibility ofimproved the algorithm.Experiments demonstrate the advantages of the proposed algorithms of the filters in both convergence rate and steady-state behaviors about the sparse system identification. Thesealgorithms lay the foundation in practical applications.