An adaptive approach for the identification of improper complex signals

A real-time approach for the identification of second-order noncircularity (improperness) of complex valued signals is introduced. This is achieved based on a convex combination of a standard and widely linear complex adaptive filter, trained by the corresponding complex least mean square (CLMS) and augmented CLMS (ACLMS) algorithms. By providing a rigorous account of widely linear autoregressive modelling the analysis shows that the monitoring of the evolution of the adaptive convex mixing parameter within this structure makes it possible to both detect and track the complex improperness in real time, unlike current methods which are block based and static. The existence and uniqueness of the solution are illustrated through the analysis of the convergence of the convex mixing parameter. The analysis is supported by simulations on representative datasets, for a range of both proper and improper inputs.