Reduced-complexity widely linear adaptive estimation

Widely linear filters play an important role in signal processing applications where the circularity properties on the complex data do not hold. They are able to achieve smaller mean-square error (MSE) than linear complex filters, but at a significantly higher computational cost. In this paper, we propose a modified version of widely linear filters with a reduced computational complexity. In the proposed version, the data vector is real, being constituted by the real and imaginary parts of the complex data separately. We prove that the new scheme achieves the same minimum MSE of standard widely linear estimators. We exemplify this idea for the least-mean squares (LMS) algorithm and also for the recursive least-squares (RLS) algorithm.