Arrival Times of Satellite-Broadened Laser Pulses

A method for measuring the time of arrival of very narrow laser pulses which have been reflected and randomly broadened by a target is examined. It is known that these return pulses from the target have very small rise times. A threshold detection algorithm that detects the rising edge of the pulse is used for obtaining the pulse arrival times. The errors of the scheme are evaluated numerically for different pulse shapes, and a loose bound on the errors of detecting a typical pulse is obtained. Finally, a gamma-density model is used to characterize the random gain processes of the optical receiver, and the effect of such random gains on the errors of threshold detection is analyzed.