Study On The Adaptive Filtering Algorithm In Non-Gaussian Alpha-Stable Distribution Environments

Among many non-Gaussian noise models, the symmetric alpha-stable (SαS) probability density functions can accurately model large classes of impulsive noises. Theα-stable distribution with 0 <α< 2 does not exist finite second order statistics. Consequently, many standard signal processing tools (e.g. power spectrum and the least-square techniques) which are based on assumption of finite variance will be considerably weakened and may in fact give misleading results. The pth ordermoment (p <α) forα-stable distribution is finite and it can be used in adaptivefiltering.LMP, NLMP, RLMP algorithm is three kinds of classic algorithms using pth order moment forα-stable distribution.Forever, LMP algorithm have too low convergence rate , and RLMP have too large calculation. How to find better performance algorithm with little calculation between convergence rate and stable error?A novel variable step size (NLMP) algorithm is proposed in where the gradient of the filter weights is used to adjust the step size. During convergence,a decrease in the gradient of the filter weights cause a step size decrease. The computer simulations show very good convergence ability and tracing ability. Compared with other variable step size algorithms, the proposed algorithm uses little additional memory and computations relative to the original NLMP and the additional work is independent of the filter length.The other advantage is that the coefficients of the proposed algorithm are insensitive to the additive noise energy so that even if the noise energy changes, the algorithm can still work well without re-adjusting the coefficients.In the end ,we consider further how to improve the rate of LMP algorithm, and give the study anticipation on it.