An adaptive convex combination of CLMK and ACLMK algorithms for processing complex-valued signals

Abstract

This paper introduces a novel adaptive convex combination (ACC) of the complex-valued least mean kurtosis (CLMK) and augmented CLMK (ACLMK) algorithms by inspiring their individual advantages to effectively process circular and noncircular complex-valued signals. For this purpose, the negated kurtosis-based cost function of the overall error signal in the complex domain is primarily defined and then it is minimized to obtain the update rule of the mixing parameter for the proposed ACC. The proposed ACC offers a significant opportunity for the CLMK and ACLMK algorithms to work collaboratively. By iteratively updating the mixing parameter based on the mentioned kurtosis cost function, the proposed ACC adaptively dominates the CLMK or ACLMK at its overall output according to the requirements of the filter operating environments to improve the overall filtering performance in terms of the convergence rate and steady-state error. The evolution of the mixing parameter in the proposed ACC also gives information about the characteristic behaviour of the considered signal or system. Moreover, for the first time in this paper, the stability of the mixing parameter update rule of the proposed ACC is theoretically analysed in the sense of Lyapunov to derive its step size bounds. On the other h and, since the analyses of the CLMK and ACLMK algorithms in the sense of Lyapunov are still missing in the literature, in the scope of this work, their Lyapunov analyses are also provided in detail. The comprehensive simulations on system identification and one-step ahead prediction scenarios in the complex domain support both the mentioned elegant properties of the proposed ACC and its superior performance over the existing ACC.