Timing Acquisition of Wideband PPM Systems over Multipath

The acquisition, or synchronization, of a multipath channel profile for ultra-wideband pulse position modulation (PPM) communication systems is considered. The rate of increase of the number of paths as the bandwidth grows determines whether acquisition can occur. If the number of independent Gaussian paths increases without bound, but slower than the bandwidth, then the system cannot acquire in the limit. Acquisition is not possible on multipath channels with deterministic path amplitudes, if the number of paths diverges but not too fast. These results hold for exponential or uniform power delay profiles