Fixed order implementation of kernel RLS-DCD adaptive filters

In this paper, we propose an efficient structure of the kernel recursive least squares (KRLS) adaptive filters for implementing with low and fixed amount of computational complexity. The concept of kernel adaptive filters is derived by applying the kernel method to the linear adaptive filters for achieving the autonomous learning of non-linear environments. It is expected to provide a better noise reduction performance in non-linear environments than the conventional linear adaptive filters. One of the problems of the kernel adaptive filters is the required amount of calculation. Besides, they increase as the adaptation time advances as opposed to the linear case. In this paper, we propose an efficient implementation method of the KRLS dichotomous coordinate descent (DCD) adaptive algorithm. The proposed method enables us to implement at a constant amount of computation by fixing the order of the filter and the dictionary maintaining the fast rate of convergence of the KRLS-DCD algorithm. The effectiveness of the proposed method is confirmed by computer simulations.