Using non-linear even functions for error minimization in adaptive filters

In this work, we analyze algorithms for adaptive filtering based on non-linear cost function of the error, which we named non-linear even moment (NEM) algorithms. We assume that this non-linear function can be generally described in a Taylor series as a linear combination of the even moments of the error. NEM is a generalization of the well-known least mean square (LMS). We study the NEM convergence behavior and derive equations for misadjustment and convergence. We found a good approximation for the theoretical results and we show that there are various combinations of the even moments which yields better results than the LMS as well as other algorithms proposed in the literature.