An Adaptive Algorithm Based On The Sigmoidal Function

In this work, we show the development of an adaptive algorithm based on the Ln(cosh varepsilon) as cost function applied upon the error, called Sigmoidal Algorithm (SA). That function generates a surface which yields fast convergence along with lower misadjustment. It is similar to the family of algorithms proposed by Walach and Widrow [1]. The later ones were shown to behave poorer than the LMS algorithm [2], when the noise was Gaussian. We study the SA algorithm convergence behavior and find equations for the misadjustment and the learning time. Results showed that the SA had a better performance than the LMS when the noise had a Gaussian distribution.