Multipath Delay Profile Acquisition for Ultra-Wideband PPM Systems

The acquisition of a multipath channel profile (including the leading delay) for ultra-wideband pulse position modulation (PPM) communication systems is considered in the limit of large bandwidth. Optimal acquisition is defined by the maximum likelihood detector whose performance can be assessed via order statistics. Four channel scenarios are examined: deterministic or Gaussian channel taps, uniform or exponential power delay profiles. For these four channels, the rate of growth of the multipath as a function of bandwidth which leads to acquisition failure is determined. Acquisition is not even partially possible on multipath channels with deterministic path amplitudes, if the number of paths diverges too fast. Furthermore, if the number of independent Gaussian paths increases without bound, but slower than the bandwidth, then the system cannot even partially acquire in the limit. These negative results are shown for somewhat idealized environments, implying that multipath delay profile acquisition will fail under more realistic conditions.