A Parametric Analytical Diffusion Model for Indoor Ultra-Wideband Received Signal

A parametric model for indoor ultra-wideband (UWB) impulse response at the receiver is derived analytically based on diffusion phenomenon and stochastic differential equations (SDE). This novel approach considers the channel in continuous space instead of characterizing the discrete multipath components. It was hypothesized that the multiple wave reflections in the rich scatter indoor environment cause diffusion-like behavior in the received signal. Our analysis suggested a geometric Brownian motion with exponential decaying factor as the channel stochastic impulse response. The simple closed form of the model has parameters that can be adjusted for different indoor channel behaviors, i.e., match the power delay profile and channel statistics. The model parameters were estimated for an office building, and its statistics were compared to the statistics of a set of data from experiment. The IEEE channel model (CM3) was used for comparison purposes. The results have shown that our proposed model closely resembles experimentally collected data for dense multipath channels