Series-cascade nonlinear adaptive filters

It is known that certain classes of nonlinear systems can be represented by one of three cascade models: i) a linear filter followed by a memoryless nonlinearity (Wiener model), ii) a memoryless nonlinearity followed by a linear filter (Hammerstein model), or iii) a linear filter, a memoryless nonlinearity, and a second linear filter (LNL model). In this paper we consider LNL adaptive systems with an FIR linear system at the input stage and a FIR linear system at the output stage. Then combining the linear input stage and the memoryless nonlinear stage of the LNL model is considered, resulting in the series-cascade of a Wiener system with a linear output stage. Adaptive algorithms are derived for these structures and experimental examples are shown to illustrate their performance.