  A novel adaptive filtering method called $q$-Volterra least mean square
($q$-VLMS) is presented in this paper. The $q$-VLMS is a nonlinear extension of
conventional LMS and it is based on Jackson's derivative also known as
$q$-calculus. In Volterra LMS, due to large variance of input signal the
convergence speed is very low. With proper manipulation we successfully
improved the convergence performance of the Volterra LMS. The proposed
algorithm is analyzed for the step-size bounds and results of analysis are
verified through computer simulations for nonlinear channel estimation problem.
