Improved convergence analysis of stochastic gradient adaptive filters using the sign algorithm

Convergence analysis of stochastic gradient adaptive filters using the sign algorithm is presented in this paper. The methods of analysis currently available in literature assume that the input signals to the filter are white. This restriction is removed for Gaussian signals in the analysis. Expressions for the second moment of the coefficient vector and the steady-state error power are also derived. Simulation results are presented, and the theoretical and empirical curves show a very good match.