Performance of PPM Multipath Synchronization in the Limit of Large Bandwidth

TL;DR

This paper analyzes the limits of multipath synchronization in ultrawideband PPM systems as bandwidth increases, showing conditions under which synchronization fails due to increasing path complexity.

Contribution

It introduces theoretical conditions for synchronization success or failure in large bandwidth regimes with growing multipath components.

Findings

Synchronization fails if number of paths grows faster than the square root of bandwidth.

Maximum likelihood synchronizer misses paths if paths grow faster than bandwidth.

Conditions for guaranteed synchronization success are identified.

Abstract

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.