  The acquisition, or synchronization, of the multipath profile for an
ultrawideband pulse position modulation (PPM) communication systems is
considered. Synchronization is critical for the proper operation of PPM based
For the multipath channel, it is assumed that channel gains are known, but path
delays are unknown. In the limit of large bandwidth, W, it is assumed that the
number of paths, L, grows. The delay spread of the channel, M, is proportional
to the bandwidth. The rate of growth of L versus M determines whether
synchronization can occur. It is shown that if L/sqrt(M) --> 0, then the
maximum likelihood synchronizer cannot acquire any of the paths and
alternatively if L/M --> 0, the maximum likelihood synchronizer is guaranteed
to miss at least one path.
