Abstruct-The paper investigates the application of a radial basis function network to digital communications channel equalization. It is shown that the radial basis function network has an identical structure to the optimal Bayesian symbol-decision equalizer solution and, therefore, can be employed to implement the Bayesian equalizer. The training of a radial basis function network to realize the Bayesian equalization solution can be achieved efficiently using a simple and robust supervised clustering algorithm. During data transmission a decision-directed version of the clustering algorithm enables the radial basis function network to track a slowly time-varying environment. Moreover, the clustering scheme provides an automatic compensation for nonlinear channel and equipment distortion. This represents a radically new approach to the adaptive equalizer design. Computer simulations are included to illustrate the analytical results.

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Abstract-A Bayesian solution is derived for digital communication channel equalization with decision feedback. This is an extension to the maximum a posteriori probability symbol-decision equalizer to include decision feedback. A novel scheme of utilizing decision feedback is proposed which not only improves equalization performance but also reduces computational complexity dramatically. It is shown that the Bayesian equalizer has an equivalent structure to the radial basis function network, the latter being a one-hidden-layer artificial neural network widely used in pattern classification and many other areas of signal processing. Two adaptive approaches are developed to realize the Bayesian solution. The maximum likelihood Viterbi algorithm and the conventional decision feedback equalizer are used as two benchmarks to assess the performance of the Bayesian decision feedback equalizer.

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A multi-stage blind clustering algorithm is proposed for equalisation of multi-level quadrature amplitute modulation (M-$AM) channels. A hierarchical decomposition divides the task of equalising a high-order QAM channel into much simpler sub-tasks. Each sub-task can be accomplished fast and reliably using a blind clustering algorithm derived originally for 4-QAM signals. The constant modulus algorithm (CMA) is used as a benchmark to assess this multi-stage blind equaliser. It is demonstrated that the new blind algorithm achieves much faster convergence and is very robust when input symbols are not sufficiently white. This multi-stage clustering equaliser only requires slightly more computations than the CMA and, like the latter, its computational complexity does not increase as the levels of digital symbols increase. Paper approved by Jack H. Winters, the Editor for Equalization of the IEEE Communications Society. Manuscript

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We present a method of modifying the structure of radial basis function (RBF) network to work with nonstationary series that exhibit homogeneous nonstationary behavior. In the original RBF network, the hidden node's function is to sense the trajectory of the time series and to respond when there is a strong correlation between the input pattern and the hidden node's center. This type of response, however, is highly sensitive to changes in the level and trend of the time series. To counter these effects, the hidden node's function is modified to one which detects and reacts to the gradient of the series. We call this new network the gradient RBF (GRBF) model. Single and multistep predictive performance for the Mackey-Glass chaotic time series were evaluated using the classical RBF and GRBF models. The simulation results for the series without and with a tine-varying mean confirm the superior performance of the GRBF predictor over the RBF predictor.