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

Abstract

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.

Keywords

• Other topics in statistics
• Filtering methods in signal processing
• Other topics in statistics
• Signal processing theory