On the Application of Multi-Layered Perceptrons to Nonlinear Equalization for Frequency Selective Fading Channels and Nonlinear Prediction for Time Selective Rayleigh Fading Channels

Abstract

<p>We show that in the additive white Gaussian noise channel that a single neuron using the standard sigmodial nonlinearity function is effectively a Bayesian estimator for a binary (±1) level signal and establish a link between the weight(s) of the neuron and the noise variance associated with the signal. This relationship is then extended to neurons where the sigmodial nonlinearity function incorporates a gain term. By extending these results to multi-level signalling we develop a new nonlinearity function that incorporates a gain α which simplifies the structure of the neural network. We show that this gain term in linked to the noise variance much like the gain term in a neuron using sigmodial nonlinearity for binary signalling.</p> <p>In applying neural networks to the channel equalization problem for frequency selective fading we make use of complex neurons in the neutral network. We look at both binary signalling in two dimensions, and higher level signaling as well. Our results show that while neural nets provide a significant performance increase in the case of binary signalling in two dimensions this performance is not reflected in the results for the higher level signalling schemes. In this case the neural net equalizer performance tends to parallel that of the linear transversal equalizer.</p> <p>Under the Rayleigh fading channel, we demonstrate the feasibility of using a simple neural network as a phase predictor to significantly reduce the error rate for quadrature phase shift keying signalling in this channel. With this network it is possible to remove the error floor that is normally encountered in this channel for average signal to noise ratios of less than 60dB.</p>