Summary: FULLY COMPLEX MULTI-LAYER PERCEPTRON NETWORK
FOR NONLINEAR SIGNAL PROCESSING
and Tülay Adali
Information Technology Laboratory
Department of Computer Science and Electrical Engineering
University of Maryland Baltimore County, Baltimore, Maryland 21250 U.S.A.
Center for Advanced Aviation System Development
The MITRE Corporation
McLean, Virginia 22102 U.S.A.
Designing a neural network (NN) to process complex-valued signals is a challenging task since a complex
nonlinear activation function (AF) cannot be both analytic and bounded everywhere in the complex plane . To
avoid this difficulty, 'splitting', i.e., using a pair of real sigmoidal functions for the real and imaginary components
has been the traditional approach. However, this `ad hoc' compromise to avoid the unbounded nature of nonlinear
complex functions results in a nowhere analytic AF that performs the error back-propagation (BP) using the split
derivatives of the real and imaginary components instead of relying on well-defined fully complex derivatives. In
this paper, a fully complex multi-layer perceptron (MLP) structure that yields a simplified complex-valued back-