Conjugate gradient algorithm for series cascade nonlinear adaptive filters

This paper considers series-cascade nonlinear filter architectures consisting of a linear FIR input filter, a memoryless polynomial nonlinearity, and a linear FIR/IIR output filter (LNL). Earlier publications reported on the development of the LMS and RLS backpropagation algorithms for training this same adaptive filter structure. In this paper the conjugate gradient backpropagation algorithm is derived for the joint adaptation of the LNL structure. An echo cancellation example is considered to study the algorithm in terms of its learning characteristics and computational complexity.