BLIND EQUALIZATION AND SOURCE SEPARATION USING NEURAL NETWORKS

Abstract

Neural networks provide a powerful tool for many signal processing applications, including blind signal processing. The task of blind equalization is concerned with retrieval of unknown transmitted sequence, from the output of a channel, while the problem of blind source separation consists of recovering the unknown sources from their observed mixtures. In both cases, neither the knowledge of transmitted signals nor any information about the channel or mixing medium is used. The present study focuses on the application of neural networks in blind equalization and source separation. The objective is to obtain better performance in terms of lower mean square error (MSE), symbol error rate (SER) and inter-symbol interference in case of blind equalization and to study some new algorithms concerning the problem of source separation. The multi-layer feedforward neural networks are used for the symbol spaced and fractionally spaced blind equalization of complex channels and the performance is compared with that obtained with linear FIR filters. The nonlinear complex activation functions used in the networks are found to be suitable for M-ary phase shift keying (PSK) and quadrature amplitude modulation (QAM) signals. The learning rules based on constant modulus algorithm (CMA) cost functions are obtained for updating the complex valued weights of the networks. To improve the rate of convergence of the neural blind equalizers, a new cost function, which is a modified version of the CMA cost function, is proposed. This cost function enables the application of recursive least squares technique to achieve fast blind equalization. Performance of these neural blind equalizers is examined in nonstationary environment and a modified activation function is proposed for better performance. Applicability of nonlinear activation functions for multi-input/multi-output blind equalization is also studied. Application of RBF network as a nonlinear estimator is presented for a Bussgang blind equalizationtechnique using zero-memory nonlinear estimator. Next, the performance of recurrent structures for blind equalization is examined. For a channel with distant echoes, the application of two different complex-valued recurrent structures, namely, a recurrent neural network (RNN) and a multi-layer perceptron (MLP) network with feedback of previously detected symbols in the output layer, is studied. To reduce the computational complexity, a simplified learning rule is suggested for the MLPbased recurrent structure. The concept of feedback is then extended to MIMO blind equalization in order to achieve lower MSE and symbol error rate. Nonlinear structures of the neural networks can effectively deal with the situations where the nonlinearity is explicitly present in the form of nonlinear channels. For the equalization of nonlinear channels different neural structures viz. MLP, RBF and Functional Link Artificial Neural Network (FLANN) are used and their performances are compared. A modification in the FLANN, namely, making the activation function of the FLANN adaptable, leads to faster convergence of equalizer. Simulations are performed using CMA and statistical moments-based cost functions for channels with two different nonlinearities. For blind source separation problem, neural network approaches are, generally, based on higher order statistics (HOS). HOS enters into the model, through nonlinear functions used in the learning rules. For separation of sub-Gaussian and super-Gaussian signals, different nonlinear functions are required. When the observed mixture contains both, sub- Gaussian as well as super-Gaussian source signals, the choice of nonlinear function becomes difficult in absence of any knowledge of statistical nature of source signals. To overcome this problem, a kurtosis-based scheme is suggested for the selection of nonlinear functions. An 11 algorithm to obtain the output signals according to the statistical properties of source signals is also considered. Finally the application of blind source separation in adaptive beamforming is considered where the linear nodes of BSS networks are appropriately replaced by nonlinear nodes. Performance in terms of signal to interference and noise ratio (SINR) of these beamformers is compared with linear network beamformers.