A Generalized Normalized Gradient Descent Algorithm

A generalized normalized gradient descent (GNGD) algorithm for linear finite-impulse response (FIR) adaptive filters is introduced. The GNGD represents an extension of the normalized least mean square (NLMS) algorithm by means of an additional gradient adaptive term in the denominator of the learning rate of NLMS. This way, GNGD adapts its learning rate according to the dynamics of the input signal, with the additional adaptive term compensating for the simplifications in the derivation of NLMS. The performance of GNGD is bounded from below by the performance of the NLMS, whereas it converges in environments where NLMS diverges. The GNGD is shown to be robust to significant variations of initial values of its parameters. Simulations in the prediction setting support the analysis.