Adaptive Nonlinearity Identification in a Hammerstein System using a Pseudo Coherence Function

A Hammerstein system consists of a memoryless nonlinear block followed by a linear time-invariant subsystem. We propose to model or to approximate the memoryless nonlinear block using a linear combination of nonlinear basis functions. We formulate a novel nonlinearity parameter estimation algorithm using a pseudo magnitude squared coherence (MSC) function based criterion. The proposed method carries out nonlinearity identification without knowing the linear block in the Hammerstein system. A low complexity adaptive algorithm is proposed to update the parameter estimates of the nonlinear block. Numerical examples are provided to illustrate the performance of the proposed method.