Synchronization of PPM over Wideband Multipath Channels

The acquisition, or synchronization, of the multipath 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 synchronization can occur. It is shown that if the number of paths increases without bound, but slower than the square root of the bandwidth, then the system cannot synchronize in the limit. This result holds for an exponential or a uniform power delay profile, for IID Gaussian paths or deterministic paths