An efficient least mean squares algorithm based on q-gradient

In this work, we propose a novel LMS type algorithm by utilizing the q-gradient. The concept of q-gradient is derived from the definition of Jacksons derivative which is also called as the q-derivative. The q-gradient based LMS algorithm results in faster convergence for q > 1 because of the fact that the q-derivative, unlike the conventional derivative which evaluates tangent, computes the secant of the cost function and hence takes larger steps towards the optimum solution. We show an important application of the proposed q-LMS algorithm in which it acts like a whitening filter. Convergence analysis of the proposed algorithm is also presented. Simulation results are presented to support our theoretical findings.