Generalized normalized gradient descent algorithm based on estimated a posteriori error

A Normalized-Least-Mean-Square (NLMS) algorithm is used to adapt to an unknown system by minimizing the error between the desired signal and the signal resulting from the adaptive filter. A small positive constant value is used to ameliorate the problem of its diverging when the input power is small. Moreover, it can be a variable, where Generalized Normalized Gradient Descent (GNGD) algorithm can be used to update the value based on the a priori error. The Steady-State Mean Square Error (SSMSE) performance of the algorithm is expected to improve by using a posteriori error instead of the a priori error. In this paper, a GNGD algorithm based on estimated a posteriori error is derived for use in coefficient update using NLMS algorithm. With simulation results, it is shown that using a posteriori error for updating the small constant value within channel equalizer coefficient update process decreases the algorithm's SSMSE performance sensitivity to varying initial step size.