Robust adaptive filtering algorithms for α-stable random processes

A new class of algorithms based on the fractional lower order statistics is proposed for finite impulse response adaptive filtering in the presence of a stable processes. It is shown that the normalized least mean p-norm (NLMP) and Douglas´ family of normalized least mean square algorithms are special cases of the proposed class of algorithms. A convergence proof for the new algorithm is given by showing that it performs a descent-type update of the NLMP cost function. Simulation studies indicate that the proposed algorithms provide superior performance in impulsive noise environments compared to the existing approaches