Two-Hop Connectivity to the Roadside in a VANET Under the Random Connection Model

We compute the expected number of cars that have at least one two-hop path to a fixed roadside unit in a one-dimensional vehicular ad hoc network in which other cars can be used as relays to reach a roadside unit when they do not have a reliable direct link. The pairwise channels between cars experience Rayleigh fading in the random connection model, and so exist, with probability function of the mutual distance between the cars, or between the cars and the roadside unit. We derive exact equivalents for this expected number of cars when the car density $\rho$ tends to zero and to infinity, and determine its behaviour using an infinite oscillating power series in $\rho$, which is accurate for all regimes. We also corroborate those findings to a realistic situation, using snapshots of actual traffic data. Finally, a normal approximation is discussed for the probability mass function of the number of cars with a two-hop connection to the origin. The probability mass function appears to be well fitted by a Gaussian approximation with mean equal to the expected number of cars with two hops to the origin.Comment: 21 pages, 7 figure

On the Temporal Effects of Mobile Blockers in Urban Millimeter-Wave Cellular Scenarios

Millimeter-wave (mmWave) propagation is known to be severely affected by the blockage of the line-of-sight (LoS) path. In contrast to microwave systems, at shorter mmWave wavelengths such blockage can be caused by human bodies, where their mobility within environment makes wireless channel alternate between the blocked and non-blocked LoS states. Following the recent 3GPP requirements on modeling the dynamic blockage as well as the temporal consistency of the channel at mmWave frequencies, in this paper a new model for predicting the state of a user in the presence of mobile blockers for representative 3GPP scenarios is developed: urban micro cell (UMi) street canyon and park/stadium/square. It is demonstrated that the blockage effects produce an alternating renewal process with exponentially distributed non-blocked intervals, and blocked durations that follow the general distribution. The following metrics are derived (i) the mean and the fraction of time spent in blocked/non-blocked state, (ii) the residual blocked/non-blocked time, and (iii) the time-dependent conditional probability of having blockage/no blockage at time t1 given that there was blockage/no blockage at time t0. The latter is a function of the arrival rate (intensity), width, and height of moving blockers, distance to the mmWave access point (AP), as well as the heights of the AP and the user device. The proposed model can be used for system-level characterization of mmWave cellular communication systems. For example, the optimal height and the maximum coverage radius of the mmWave APs are derived, while satisfying the required mean data rate constraint. The system-level simulations corroborate that the use of the proposed method considerably reduces the modeling complexity.Comment: Accepted, IEEE Transactions on Vehicular Technolog