Abstract
Optimal control techniques are used to derive necessary conditions for designing optimum waveforms for pulse-position modulation communication systems. Nonlinear modulation threshold effects are incorporated directly into the design by introducing constraints on the side-lobe peaks of the autocorrelation function. The search is performed over the class of signals satisfying constraints on the average power, peak power, and bandwidth. The optimum signal in this class is the one whose autocorrelation function has the sharpest central peak while the side-lobe peaks are below the specified constraint level. The necessary conditions are obtained by treating the correlation constraints as functional constraints on the state-variables and applying Neustadt's abstract variational theory. The conditions are in the form of differential-difference equations of the advanced and retarded type which appear to be extremely difficult to solve analytically.
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