A radial basis function (RBF) equalizer design process has been developed in which the number of basis function centers used is substantially fewer than conventionally required. The reduction of centers is accomplished in two-steps. First an algorithm is used to select a reduced set of centers that lie close to the decision boundary. Then the centers in this reduced set are grouped, and an average position is chosen to represent each group. Channel order and delay, which are determining factors in setting the initial number of centers, are estimated from regression analysis. In simulation studies, an RBF equalizer with more than 2000-to-1 reduction in centers performed as well as the RBF equalizer without reduction in centers, and better than a conventional linear equalizer.

We discuss the application of a radial basis function (RBF) network to the channel equalization problem. In particular, the purpose of the paper is to improve the previously developed RBF equalizer with training using K-means and LMS methods; reducing the RBF network size by considering a lesser number of RBF centers, and developing new techniques for determining channel order which is required to specify the structure of an RBF equalizer. A linear regression model was used for estimating the channel order. The basic idea of reducing the network size is to select the centers, based on the channel lag. This work includes the comparison of the limits of mean square error (MSE) convergence of both a linear equalizer and an RBF equalizer.

Frequency-domain filtering is effective both for realizing asymptotically orthogonalized designs which can rapidly acquire a signal with a large eigenvalue spread and for realizing efficient block implementations. However, most previous work in this area has assumed a stationary input signal. The authors further define the extensions necessary to accommodate the cyclostationary signal seen by a fractionally spaced equalizer. When the cyclostationary nature of the signal is exploited, the asymptotically exact Wiener solution can be realized by two equivalent architectures. The first architecture results from demultiplexing the input data into parallel, decimated, stationary signals which are individually transformed. Postprocessing then coherently combines corresponding frequency bins. The second, equivalent, architecture results from direct transformation of the input cyclostationary signal. Postprocessing coherently combines frequency bins, which exhibit spectral correlation. Special periodic noise spectra are identified which expedite collapsing to half the number of spectral bins.>

The noniterative method of adaptive channel equalization proposed by Butler and Cantoni [1] is investigated. Its start-up time is improved remarkably by choosing the period of the training sequence judiciously and performing the estimation of channel parameters exactly over one period. The resulting version of the algorithm is as fast as the fastest known iterative algorithms, such as Godard's Kaiman algorithm [2].

When a vestigial sideband (VSB) modulated signal, with carrier present, is demodulated with an envelope detector it suffers an unavoidable distortion. The optimum VSB filter which minimizes this distortion is obtained, and it is shown that the filter transfer function should be flat around the carrier frequency ω0and should not be designed with a large slope at ω0as has heretofore been done.