Performance of PPM Multipath Synchronization in the Limit of Large Bandwidth

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.