Complex-valued function approximation using an improved BP learning algorithm for feed-forward networks

In a fully complex-valued feed-forward network, the convergence of the complex-valued back-propagation learning algorithm depends on the choice of the activation function, minimization criterion, initial weights and the learning rate. The minimization criteria used in the existing learning algorithms do not approximate the phase well in complex-valued function approximation problems. This aspect is very important in telecommunication and medical imaging applications. In this paper, we propose an improved complex-valued back propagation algorithm using an exponential activation function and a logarithmic minimization criterion, which approximates both the magnitude and phase well. Performance of the proposed scheme is evaluated using the complex XOR problem and a synthetic complex-valued function approximation problem. Also, a comparative analysis on the convergence of the existing fully complex and split complex networks is presented.