Adaptive filtering algoritm for time-variant symmetric α-stable signals

Abstract

The existence of non-Gaussian distributed impulsive signals has roots in the generalized central theorem. In particular, the symmetric α-stable (SαS) distribution has been used to model heavy-tailed phenomena encountered in communication, underwater acoustics, and radar. Most previous work in the field of active control uses some of the numerous variants of LMS algorithm extended with the filtered-x scheme. The stable processes, however, do not possess finite second-order moments. Hence, the filter should be based on lp-norm optimization. The p-norm enters the expression for the tap-weight update [p(t)<α̂(t)]. In this work a new adaptive algorithm referred to as regularized normalized least−mean p−norm algorithm [εNLMp(t)] is presented. A running estimate α̂(t) of the time−variant characteristic exponent of the stable signal is obtained. Hence, by adaptively tuning the filter p−norm a more optimal filter performance results in time−variant situations. Simulation analysis provides insight into the adaptive filter performance for various time−invariant and time−variant noisy signals for 1<α(t)≤2. Moreover, it is demonstrated that the filter performance is only marginally degraded compared with LMS algorithm for ordinary time−invariant Gaussian noise signals. Performance of an active control system exposed to time−varying heavy−tailed noise signals is presented.