Joint Optimization of Automatic Equalization and Carrier Acquisition for Digital Communication

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Abstract
In this paper, we analyze single-sideband amplitude-modulation digital communication systems to develop a method for jointly and optimally setting the carrier phase and the automatic transversal equalizer of such systems. Mean-square equalization error is used as the performance criterion. We develop a simple receiver structure and study the convergence of the method. Exact locations of the stationary points in the parameter space are determined and the classifications of the stationary points are obtained. We show that the mean-square equalization error has only global minima and saddlepoints, but not local minima and maxima. Thus, the mean-square equalization error will converge to the absolute minimum by the proposed method, regardless of the initial settings of the parameters. A simple condition on the step sizes of the adjustments is also obtained which ensures the convergence of the process. Explicit formulas of the joint optimum parameter settings and of the corresponding minimum mean-square error are obtained. For illustration purposes, a single-sideband digital communication system using a five- or nine-tap transversal equalizer is simulated on a computer. Both theory and simulation show that the equalization error depends critically on the carrier phase when the number of equalizer taps is not large, and that the minimum equalization error can be obtained by using the proposed method.

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