Adaptive IIR Filtering of Noncircular Complex Signals

A recursive learning algorithm for the training of widely linear infinite impulse response complex valued adaptive filters is proposed. The use of so called augmented complex statistics makes this algorithm suitable for the processing of both second order circular (proper) and noncircular (improper) signals. A closed form solution for the bound on the stepsize is provided, and the small stepsize assumption in the derivation is used to reduce the computational complexity. Simulations for both synthetic and real-world circular and noncircular signals are provided in the prediction setting, illustrating the benefits of the proposed algorithm when modelling general complex signals.