On the Simulation of Correlated Mobile-to-Mobile Fading Channels for Time-Varying Velocities

In this paper, we study two models to simulate mobile-to-mobile channels for arbitrary velocities variations of the transmitter and/or the receiver. The first one that has been proposed in the literature and referred here to as naive is proved not to work. The second, called effective model introduced very recently provides expected results in terms of time-varying Doppler shift. We introduce the notions of deterministic and probabilistic consistencies in order to check the validity of the models. We prove that the deterministic consistency of the effective model implies its probabilistic consistency, whatever the statistical distributions of the angle of arrivals and angles of departures and whatever the velocities variations. This result generalizes previous ones from the literature. We also develop a simple procedure to simulate both the Rayleigh and the Rician channels with arbitrary changes in the velocity.