Numerical optimization techniques applied to PPM signal design

A computer-oriented algorithm is developed for designing optimum waveforms for a pulse-position-modulation communication system. Nonlinear modulation threshold effects are incorporated directly into the design by introducing constraints on the sidelobe peaks of the autocorrelation function. The search is performed over the class of signals satisfying constraints on 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 sidelobe peaks are below the specified constraint level. Numerical results for a realistic problem are presented, and the effect of introducing the correlation and peak power constraints is studied. It is shown that a large reduction in the sidelobe peaks is possible with relatively little loss in the sharpness of the central peak.