Modeling and statistical analysis of ultra-wideband (UWB) channels and systems: A point-process approach

Ultra-wideband (UWB) communications has generated intense interest because it may provide very high bit rate, low-cost, low-power wireless communication for a wide variety of systems. Another factor that enhances interest in UWB is that the Federal Communications Commission has recently allocated 7.5 GHz of spectrum for unlicensed commercial UWB communication systems.;To aid in the understanding of UWB channels, the IEEE 802.15.3a standards body has developed a modification of the Saleh-Valenzuela (SV) model as the accepted channel model for UWB investigations. Although this model is straightforward to simulate, it is not directly amenable to theoretical analysis. To address this difficulty, this dissertation develops the SV/IEEE 802.15.3a channel model as a two-dimensional augmented cluster process. It is shown that many relevant quantities of UWB wireless channels such as bit-error probability (BEP) and capacity can be expressed in terms of shot-noise random variables. By expressing these shot-noise random variables as counting integrals, it is then possible to derive formulas for their statistics.;Based on this framework, the probability density function of the channel coefficients of the tapped-delay-line and virtual-channel models can be evaluated and are shown to be non-Gaussian. It is shown that the capacity of the IEEE 802.15.3a channel model can be expressed as a function of a matrix whose elements are shot-noise random variables. These elements can actually be highly non-Gaussian and correlated. For this reason, direct computation of the capacity is difficult except for the case when the matrix is scalar. We also derive the characteristic functions of the elements of the matrix to allow us to compute their statistics. Furthermore, this framework shows that explicit formulas can be obtained for estimation techniques that require the correlation function and the correlation matrix of the channel process.;UWB signals not only suffer significant time spread, but also angular spread. This framework is extended to UWB space-time channel models. The UWB space-time channel model can be analyzed as a three-dimensional point process. Using the formulas derived at the beginning of the dissertation, it is shown that statistics of the UWB space-time channel model can be derived.