  In most practical adaptive signal processing systems, e.g., active noise
control, active vibration control, and acoustic echo cancellation, substantial
nonlinearities that cannot be neglected exist. In this paper, we analyze the
behaviors of an adaptive system in which the output of the adaptive filter has
the clipping saturation-type nonlinearity by a statistical-mechanical method.
We discuss the dynamical and steady-state behaviors of the adaptive system by
asymptotic analysis, steady-state analysis, and numerical calculation. As a
result, it has become clear that the saturation value has the critical point at
which the system's mean-square stability and instability switch. The obtained
theory well explains the strange behaviors around the critical point observed
in the computer simulation. Finally, the exact value of the critical point is
also derived.
