Steady-state performance analysis of quaternion-valued least mean square adaptive algorithm

Abstract

The quaternion-valued least mean squares (QvLMS) adaptive algorithm has been proved valid for the adaptive filtering in quaternion domain. However, there have been few researches on its performance. This paper firstly deduces the energy conservation relation in quaternion domain and then analyzes the steady-state performance of QvLMS algorithm in stationary and non-stationary environment by using the quaternion energy conservation relation. The relevant expressions are deduced and then the step-size range which can guarantee the algorithm convergence is obtained. Simulation results demonstrate the rationality of the analysis.