A zero-attracting quaternion-valued least mean square algorithm for sparse system identification

Recently, quaternion-valued signal processing has received more and more attention. In this paper, the quaternion-valued sparse system identification problem is studied for the first time and a zero-attracting quaternion-valued least mean square (LMS) algorithm is derived by considering the l₁ norm of the quaternion-valued adaptive weight vector. By incorporating the sparsity information of the system into the update process, a faster convergence speed is achieved, as verified by simulation results.