Fractional‐order complex correntropy algorithm for adaptive filtering in α‐stable environment

Abstract

In adaptive filtering applications, the Gaussian distribution cannot be used to model the signal/noise with frequent spikes accurately. In fact, the rational model to simulate the behaviour of such signal/noise is the α-stable distribution process. In this letter, a fractional-order complex correntropy algorithm is proposed to deal with the case that both signal and noise processes are modelled as complex-valued α-stable signals. Compared with the classical approaches, the proposed fractional-order complex correntropy extends the Gaussian assumption of signal/noise in the complex domain to the assumption of α-stable distributions without second-order and higher order statistical moments. Benefitting from the fractional-order calculus and correntropy criterion, fractional-order complex correntropy shows great robustness to the jittery behaviour of complex-valued α-stable signal/noise. In addition, a convergence analysis for fractional-order complex correntropy has been carried out. Simulations on system identification revealed that the filtering performance is significantly improved by using fractional-order complex correntropy.