A fast learning Fully Complex-valued Relaxation Network (FCRN)

This paper presents a fast learning algorithm for a single hidden layer complex-valued neural network named as the “Fully Complex-valued Relaxation Network (FCRN)”. FCRN employs a fully complex-valued Gaussian like activation function (sech) in the hidden layer and an exponential activation function in the output layer. FCRN estimates the minimum energy state of a logarithmic error function which represents both the magnitude and phase errors explicitly to compute the optimum output weights for randomly chosen hidden layer parameters. As the weights are computed by the inversion of a nonsingular matrix, FCRN requires lesser computational effort during training. Performance studies using a synthetic function approximation problem and a QAM equalization problem show improved approximation ability of the proposed FCRN network.