An Adaptive Filtering Algorithm for Non-Gaussian Signals in Alpha-Stable Distribution

Received: 8 September 2019 Accepted: 14 December 2019 Currently, many adaptive filtering algorithms are available for the non-Gaussian environment, namely, least mean square (LMS) algorithm, recursive least square (RLS) algorithm, least mean fourth (LMF) algorithm, and subspace minimum norm (SMN) algorithm. Most of them can converge to the steady-state, but face various constraints in the presence of alpha (α)-stable noises. To solve the problem, this paper aims to develop an adaptive filtering algorithm for non-Gaussian signals in α-stable distribution, drawing on the merits of existing adaptive filtering algorithms. Firstly, the authors introduced the theory of α-stable distribution, the central limit theorem and fractional lower-order statistics (FLOS). Next, two classic adaptive filtering algorithms, RLS and LMS, were summarized, and compared through tests. On this basis, the FLOS-SMN algorithm was designed in the light of the features of the LMS and the SMN, which applies to the filtering of non-Gaussian signals in αstable distribution. Finally, the proposed algorithm was proved as faster, more stable and more adaptable than the traditional method.