For an ultra-wideband (UWB) system, since the signal bandwidth and the sampling rate are high, there are only a small number of paths that contribute to a resolvable tap/bin. So central limit theorem does not hold and we do not see uniformly distributed phase. It is observed in actual measurements that the phase only takes values of 0 or \pi.
Measurement results show that the amplitudes can be modeled as lognormal-distributed r.v.'s. The reason why the amplitude does not follow a Rayleigh distribution, is that central limit theorem does not hold due to a small number of paths associated with a resolvable bin. Two Poisson models are employed in the modeling of the arrival times of resolvable paths. The first Poisson model is for the first path of each path-cluster and the second Poisson model is for the paths (or rays) within each cluster. The power delay profile is modeled by a double exponential decay model; i.e., the average powers of the first paths of path-clusters follow an exponential-decaying law, and the average powers of the paths within each cluster also follow an exponential-decaying law.
Since lognormal distribution is statistically better than Rayleigh
distribution for the same SNR, i.e., lognormal has a larger tail than Rayleigh,
we need fewer taps in the RAKE receiver to achieve the same BER performance. Applications