Optimal equalization of wideband coaxial cable channels using “bump” equalizers

Abstract

Two methods are described for the optimal equalization of a channel with “Bump” Equalizers composed of several adjustable-gain Bode Networks. The first method is a general one and applies a steepest descent algorithm which minimizes the total mean-squared error (MSE) of the equalized channel. It requires continuous gradient information on the error-gain relationship in order to determine exactly the optimum equalizer adjustments and involves a relatively complicated procedure to calculate the gradient. However, the second method, which also applies a steepest descent algorithm, develops the necessary gradient information with knowledge of the error signal only at selected frequencies across the bandwidth occupied by the channel. Under idealized assumptions, it is shown that the gradients obtained by the second method are exact. When the assumptions do not apply exactly, it is shown by computer simulation that the difference between the gradients obtained by the two methods is very small. A significant potential advantage of the second method lies in the hardware realization which only requires the measurement of the channel error at 2M — 1 frequencies at the equalizing station (where M is the number of Bode Networks in the equalizer). From these frequency domain errors, the gradients can be generated as real-time signals and applied to the appropriate adjustable elements to obtain the optimum gain settings for minimum MSE.