An augmented affine projection algorithm for the filtering of noncircular complex signals

An augmented affine projection adaptive filtering algorithm (AAPA), utilising the full second order statistical information in the complex domain is proposed. This is achieved based on the widely linear model and the joint optimisation of the direct and conjugate data channel parameters. The analysis illustrates that the use of augmented complex statistics and widely linear modelling makes the AAPA suitable for the processing of both second order complex circular (proper) and noncircular (improper) signals. The derivation is supported by the analysis of convergence in the energy conservation setting. Simulations on both benchmark and real-world noncircular wind signals support the analysis.