  In this paper, we derive closed-form expressions for significant statistical
properties of the link signal-to-noise ratio (SNR) and the separation distance
in mobile ad hoc networks subject to Ornstein-Uhlenbeck (OU) mobility and
Rayleigh fading. In these systems, the SNR is a critical parameter as it
directly influences link performance. In the absence of signal fading, the
distribution of the link SNR depends exclusively on the squared distance
between nodes, which is governed by the mobility model. In our analysis, nodes
move randomly according to an Ornstein-Uhlenbeck process, using one tuning
parameter to control the temporal dependency in the mobility pattern. We derive
a complete statistical description of the squared distance and show that it
forms a stationary Markov process. Then, we compute closed-form expressions for
the probability density function (pdf), the cumulative distribution function
(cdf), the bivariate pdf, and the bivariate cdf of the link SNR. Next, we
introduce small-scale fading, modelled by a Rayleigh random variable, and
evaluate the pdf of the link SNR for rational path loss exponents. The validity
of our theoretical analysis is verified by extensive simulation studies. The
results presented in this work can be used to quantify link uncertainty and
evaluate stability in mobile ad hoc wireless systems.
