Statistical Properties of Transmissions Subject to Rayleigh Fading and Ornstein-Uhlenbeck Mobility


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 that are subject to Ornstein-Uhlenbeck (OU) mobility and Rayleigh fading. These expressions are applicable in mobile ad hoc networks subject to Ornstein-Uhlenbeck (OU) mobility and Rayleigh fading. The signal-to-noise ratio (SNR) is an important parameter in these systems because it has a direct impact on the performance of the links. In the absence of signal fading, the distribution of the link SNR is entirely dependent on the squared distance between nodes, which is controlled by the mobility model. This is the case even in the absence of signal degradation. In our investigation, nodes move in a haphazard manner in accordance with an Ornstein-Uhlenbeck process. We make use of one tuning parameter to control the temporal dependency in the mobility pattern. We demonstrate that the squared distance can be modeled as a stationary Markov process and derive a comprehensive statistical description of it. 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. These expressions are used to model the distribution of the link SNR. Next, we evaluate the probability density function (pdf) of the link SNR for rational path loss exponents. This is followed by the introduction of small-scale fading, which is modeled by a Rayleigh random variable. The correctness of our theoretical analysis has been demonstrated by means of exhaustive simulation research. The findings that were presented in this work can be implemented into mobile ad hoc wireless systems in order to quantify link uncertainty and evaluate system stability.

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