Nonlinear adaptive prediction of complex-valued signals by complex-valued PRNN

A complex-valued pipelined recurrent neural network (CPRNN) for nonlinear adaptive prediction of complex nonlinear and nonstationary signals is introduced. This architecture represents an extension of the recently proposed real-valued PRNN of Haykin and Li in 1995. To train the CPRNN, a complex-valued real time recurrent learning (CRTRL) algorithm is first derived for a single recurrent neural network (RNN). This algorithm is shown to be generic and applicable to general signals that have complex domain representations. The CRTRL is then extended to suit the modularity of the CPRNN architecture. Further, to cater to the possibly large dynamics of the input signals, a gradient adaptive amplitude of the nonlinearity within the neurons is introduced to give the adaptive amplitude CRTRL (AACRTRL). A comprehensive analysis of the architecture and associated learning algorithms is undertaken, including the role of the number of nested modules, number of neurons within the modules, and input memory of the CPRNN. Simulations on real-world and synthetic complex data support the proposed architecture and algorithms.