On the LMS algorithm with constant and variable leakage factor in a nonlinear environment

This paper studies the application of the linear least-mean-square (LMS) algorithm with leakage to a system having a memoryless saturation-type nonlinearity. This approach represents an interesting alternative to the nonlinear LMS (NLLMS) algorithm. The major drawback to implement the latter is that the model parameters of the system nonlinearity must be known. In contrast, the linear LMS algorithm with leakage does not require such knowledge. It permits to approximate the performance of the NLLMS by properly selecting a constant leakage factor value. To cope with an eventual change of the environment, a strategy for a variable leakage is also proposed. Several numerical simulations are presented with the aim of ratifying the feasibility of the proposed approach