A complex-valued adaptive filter algorithm for system identification problem

In this study, a complex-valued adaptive filter algorithm based on Lyapunov stability theory is presented to solve a system identification problem in the complex domain. The performance of the proposed complex-valued Lyapunov adaptive filter (CLAF) algorithm is improved for the complex-valued system identification problem by integrating the LST into the filter optimization cost. The performance of the proposed algorithm is tested on a complex-valued moving average (MA) system identification problem and compared with the conventional complex-valued least mean square (CLMS) and complex-valued normalized least mean square (CNLMS) algorithms. The simulation results show that the proposed CLAF algorithm has achieved a faster convergence rate and a lower steady-state MSE performance when compared to the other algorithms.