Second-order analysis of the RC-WL-QLMS algorithm

In this paper we develop a second-order analysis of the widely-linear reduced-complexity quaternion LMS algorithm (RC-WL-QLMS), proposed. We use an approach based on writing the quaternion vectors and matrices as extended real entities, in order to make the analysis similar to the real LMS algorithm analysis. As a result, we obtain a second-order model of the RC-WL-QLMS for small step-sizes. We present simple equations for the steady-state EMSE and MSD, and a second-order criterion to choose the step-size.