A normalised complex backpropagation algorithm

A backpropagation based algorithm for training nonlinear complex valued feed-forward neural networks employed as nonlinear adaptive filters is derived. The proposed normalised complex backpropagation (NCBP) algorithm is an improvement on the complex backpropagation (CBP) algorithm by including an adaptive normalised learning rate. This is achieved by performing a minisation of the complex-valued instantaneous output error that has been expanded via a Taylor series expansion. The proposed algorithm is applicable to any complex-valued nonlinear architecture. Experiments on complex coloured and nonlinear signals confirm that the NCBP algorithm outperforms the standard CBP algorithm.