Title: Random Euler Complex-Valued Nonlinear Filters,
Abstract: Over the last decade, both the neural network and kernel adaptive filter have
successfully been used for nonlinear signal processing. However, they suffer
from high computational cost caused by their complex/growing network
structures. In this paper, we propose two random Euler filters for
complex-valued nonlinear filtering problem, i.e., linear random Euler
complex-valued filter (LRECF) and its widely-linear version (WLRECF), which
possess a simple and fixed network structure. The transient and steady-state
performances are studied in a non-stationary environment. The analytical
minimum mean square error (MSE) and optimum step-size are derived. Finally,
numerical simulations on complex-valued nonlinear system identification and
nonlinear channel equalization are presented to show the effectiveness of the
proposed methods.