6533b82cfe1ef96bd1290108

RESEARCH PRODUCT

A Highly Flexible Trajectory Model Based on the Primitives of Brownian Fields—Part II: Analysis of the Statistical Properties

subject

description

In the first part of our paper, we have proposed a highly flexible trajectory model based on the primitives of Brownian fields (BFs). In this second part, we study the statistical properties of that trajectory model in depth. These properties include the autocorrelation function (ACF), mean, and the variance of the path along each axis. We also derive the distribution of the angle-of-motion (AOM) process, the incremental traveling length process, and the overall traveling length. It is shown that the path process is in general non-stationary. We show that the AOM and the incremental traveling length processes can be modeled by the phase and the envelope of a complex Gaussian process with nonidentical means and variances of the quadrature components. In accordance with empirical studies, we prove that the AOM process does not follow the uniform distribution. As special cases, we show that the incremental traveling length process follows the Rice and Nakagami-q distributions, whereas the overall traveling path can be modeled by a random variable following either the Gaussian or the lognormal distribution. The flexibility of the results is demonstrated and discussed extensively. It is shown that the results are in line with those of real-world user tracings. The results can be used in many areas of wireless communications.