In this study, a fourth-order cumulants based iterative algorithm for blind channel equalization is introduced, which is robust with respect to the existence of heavy Gaussian noise in a channel and does not require the minimum phase characteristic of the channel. The transmitted signals at the receiver are over-sampled to ensure the channel described by a full-column rank matrix. It changes a single-input/single-output (SISO) finite-impulse response (FIR) channel to a single-input/multi-output (SIMO) channel. Based on the properties of the fourth-order cumulants of the over-sampled channel inputs, the iterative algorithm is derived to estimate the deconvolution matrix which makes the overall transfer matrix transparent, i.e., it can be reduced to the identity matrix by simple reordering and scaling. In simulation studies, both a closed-form and a stochastic version of the proposed algorithm are tested with three-ray multi-path channels, and their performances are compared with the methods based on conventional second-order statistics and higher-order statistics (HOS) as well. Relatively good results with fast convergence speed are achieved, even when the transmitted symbols are significantly corrupted with Gaussian noise.

This paper discusses the application of a fuzzy-ARTMAP neural network to digital communications channel equalization. This approach provides new solutions for solving the problems, such as complexity and long training, which found when implementing the previously developed neural-basis equalizers. The proposed fuzzy-ARTMAP equalizer is fast and easy to train and includes capabilities not found in other neural network approaches; a small number of parameters, no requirements for the choice of initial weights, automatic increase of hidden units, no risk of getting trapped in local minima, and the capability of adding new data without retraining previously trained data. In simulation studies, binary signals were generated at random in a linear channel with Gaussian noise. The performance of the proposed equalizer is compared with other neural net basis equalizers, specifically MLP and RBF equalizers.