Characterizing time-dependent variance and coefficient of variation of SIR in D2D connectivity

Attempting to build a uniform theory of mobility-dependent characterization of wireless communications systems, in this paper, we address time-dependent analysis of the signal-to-interference ratio (SIR) in device-to-device (D2D) communications scenario. We first introduce a general kinetic-based mobility model capable of representing the movement process of users with a wide range of mobility characteristics including conventional, fractal and even non-stationary ones. We then derive the time-dependent evolution of mean, variance and coefficient of variation of SIR metric. We demonstrate that under non-stationary mobility behavior of communicating entities the SIR may surprisingly exhibit stationary behavior. © 2017, Springer International Publishing AG.