Stability conditions for adaptive algorithms with non-quadratic error criteria

In this paper, stability conditions in terms of the upper bounds of the step size and of the initial value of the Mean Squared Error (MSE) are derived for FIR adaptive filters with non-quadratic error criteria, where "rth power" of the error is used in the correlation multiplier for tap weight adaptation. Simple formulae of the upper bounds for the Least Mean Fourth Algorithm (LMFA) (r = 3) are given, and simulations with some examples verify the stability conditions derived.