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Section: New Results

Models for wireless networks

Interference and SINR coverage in spatial non-slotted Aloha networks

Participants : Bartek Blaszczyszyn, Paul Muhlethaler.

We propose two analytically tractable stochastic-geometric models of interference in adhoc networks using pure (non-slotted) Aloha as the medium access. In contrast the slotted model, the interference in pure Aloha may vary during the transmission of a tagged packet. We develop closed form expressions for the Laplace transform of the empirical average of the interference experienced during the transmission of a typical packet. Both models assume a power-law path-loss function with arbitrarily distributed fading and feature configurations of transmitters randomly located in the Euclidean plane according to a Poisson point process. Depending on the model, these configurations vary over time or are static. We apply our analysis of the interference to study the Signal-to- Interference-and-Noise Ratio (SINR) outage probability for a typical transmission in pure Aloha. The results are used to compare the performance of non-slotted Aloha to the slotted one, which has almost exclusively been previously studied in context of wired ad-hoc networks.

Random linear multihop relaying in a general field of interferers using spatial Aloha

Participants : Bartek Blaszczyszyn, Paul Muhlethaler.

We study a stationary Poisson pattern of nodes on a line embedded in an independent planar Poisson field of interfering nodes. Assuming slotted Aloha and the signal-to-interference-and-noise ratio capture condition, with the usual power-law path loss model and Rayleigh fading, we explicitly evaluate several local and end-to-end performance characteristics related to the nearest-neighbor packet relaying on this line, and study their dependence on the model parameters (the density of relaying and interfering nodes, Aloha tuning and the external noise power). Our model can be applied in two cases: the first use is for vehicular ad-hoc networks, where vehicles are randomly located on a straight road. The second use is to study a “typical” route traced in a (general) planar ad-hoc network by some routing mechanism. The approach we have chosen allows us to quantify the non-efficiency of long-distance routing in “pure ad-hoc” networks and evaluate a possible remedy for it in the form of additional “fixed” relaying nodes, called road-side units in a vehicular network. It also allows us to consider a more general field of interfering nodes and study the impact of the clustering of its nodes on the routing performance. As a special case of a field with more clustering than the Poison field, we consider a Poisson-line field of interfering nodes, in which all the nodes are randomly located on random straight lines. In this case our analysis rigorously (in the sense of Palm theory) corresponds to the typical route of this network. The comparison to our basic model reveals a paradox: clustering of interfering nodes decreases the outage probability of a single (typical) transmission on the route, but increases the mean end-to-end delay