Research On Sparse Adaptive Filtering Algorithm In Implusive Noise Environments

Adaptive filtering algorithms,which dedices directly the performance of filtering, hasbeen the hot topic in the field of signal and information processing.With the development ofinformation technology and communications, the traditional adaptive filtering algorithm isfacing new challenges, The impulse response of channel in some communication systems isvery long and sparse, noise existing in reality often obey Gauss distribution, at the sametime, there are still some strong impulsive non Gauss distribution. This paper studies theimpulsive noise and sparse adaptive filtering algorithm in detail.The main works can be summarized as follows:Firstly, three definitions of-stable distributions are discussed, different effects of thefour characteristic parameters for-stable distributions are explained. Some properties of-stable distributions, fractional lower order moments and the smallest deviation criteria arediscussed, the problem of generation of-stable random variables subject to arbitrary fourparameters is discussed. Finally, the pulse characteristics of-stable distribution are shownby simulations.Then,the adaptive filtering principle is explained, two classical adaptive filteringalgorithm based on the minimum mean square error criterion in Gaussian noise condition areintroduced, that is the least mean square (LMS) algorithm and the normalized LMS algorithm.On this basis, this paper introduces the least averagel pnorm (LMP) algorithm and thenormalized LMP algorithm-stable impulsive noise conditions, instead of the twoalgorithms with minimal deviation criterion minimum mean square error criterion, which isthe promotion of adaptive algorithms in Gaussian noise condition.The convergence of LMSalgorithm, NLMS algorithm, LMP algorithm and NLMP algorithm are analyzed via computersimulation, pointed out that LMP algorithm and NLMP algorithm has good convergenceperformance under impulse noise conditions, while under Gaussian noise conditions alsoshowed good filtering effect.At last, sparse impulsive response adaptive filtering algorithm,namely, zero attractingminimum mean square (ZA-LMS) algorithm and ZA-NLMS algorithm are introduced. Thealgorithm introducedl1norm with sparse features are closely related to LMS algorithm cost function, makes the dominant zero coefficients in sparse system accelerate convergence,thereby significantly improve the convergence performance of the adaptive algorithm.Inspired by this idea, this paper presents a zero to attract the minimum averagel pnorm(ZA-LMP) algorithm and normalized ZA-NLMP algorithm, the algorithm introduced thel1norm to LMP algorithm cost function. Through computer simulations, compared to theconvergence rate and steady-state error of several algorithms, proved that the new algorithmhas better convergence performance than several other algorithms under the strong impulsivenoise and sparse response conditions,while has a good filtering effect in Gaussian noise.