An investigation is reported of an acquisition system for digital communication over fading dispersive channels that is optimum in the maximum-likelihood sense. A performance measure for the synchronizer in the acquisition mode is defined. Upper and lower bounds on the performance measure are derived. The effective bounds on parameters, such as signal-to-noise ratio, pulse width and modulation, number of pulses, spread of the channel, and the size of the resolution cell, on the performance of the synchronizer is investigated. >