Design of optimum error nonlinearity for channel estimation in the presence of class-A impulsive noise

In this work an optimum error nonlinearity is derived for the channel estimation in the existence of class-A impulsive noise. The main idea of the design is based on minimizing the steady-state error to reach the limit dictated by the Cramer-Rao Lower Bound (CRLB) of the implicit estimation process. By using the proposed method, optimum error nonlinearity is devised for long adaptive filters without employing any assumption on the distribution input regressor constituents and on the noise distribution, independence input regressor assumption and any kind of linearization. Moreover, to implement the proposed design, two different methods for estimating the variance of a priori estimation error are developed. Furthermore, an intelligent switching mechanism is also introduced to efficiently utilize the designed optimum error non-linearity for the impulsive noise. The theoretical results are testify through simulations, to show the superiority of the designed optimum error nonlinearity.