Comparison of the convergence of two algorithms for adaptive FIR digital filters

The convergence properties of two different algorithms for the updating of the coefficients of an adaptive FIR digital filter are investigated and compared with one another. These algorithms are the stochastic iteration algorithm and the sign algorithm. In this latter algorithm a one-bit gradient estimation is used which makes its implementation very simple. The convergence is characterized by the residual echo variance after convergence, and a parameter that indicates the speed of the convergence. It is shown that the convergence of the sign algorithm can always be assured but is much slower than that of the stochastic iteration algorithm if the same variance of the residual echo is to be obtained.