Interference and Outage in Clustered Wireless Ad Hoc Networks

In the analysis of large random wireless networks, the underlying node distribution is almost ubiquitously assumed to be the homogeneous Poisson point process. In this paper, the node locations are assumed to form a Poisson clustered process on the plane. We derive the distributional properties of the interference and provide upper and lower bounds for its CCDF. We consider the probability of successful transmission in an interference limited channel when fading is modeled as Rayleigh. We provide a numerically integrable expression for the outage probability and closed-form upper and lower bounds.We show that when the transmitter-receiver distance is large, the success probability is greater than that of a Poisson arrangement. These results characterize the performance of the system under geographical or MAC-induced clustering. We obtain the maximum intensity of transmitting nodes for a given outage constraint, i.e., the transmission capacity (of this spatial arrangement) and show that it is equal to that of a Poisson arrangement of nodes. For the analysis, techniques from stochastic geometry are used, in particular the probability generating functional of Poisson cluster processes, the Palm characterization of Poisson cluster processes and the Campbell-Mecke theorem.Comment: Submitted to IEEE Transactions on Information Theor

Evaluation of the Accuracy of a Bounded Physical Interference Model for Multi-Hop Wireless Networks

In this paper, we consider the accuracy of bounded physical interference models for use in multi-hop wireless networks. In these models, physical interference is accounted for but only for a subset of nodes around each receiver, and interference from farther transmitters is ignored. These models are very often used, both in theoretical analyses and simulations, with an "interference range" that defines the distance from a receiver beyond which interference is ignored. In this paper, we prove that, if the interference range is chosen as any unbounded increasing function of the number of nodes in the network, the total ignored interference converges to zero as the number of nodes approaches infinity. This result is proven under both constant node density and uniform random node distribution assumptions. We also prove that, if the interference range is considered to be a constant, e.g. a multiple of the transmission range, the total ignored interference does not converge to zero and, in fact, can be several orders of magnitude greater than the noise for networks of moderate size. The theoretical results are enhanced by simulations, which evaluate the bounded models relative to the true physical interference model and demonstrate, empirically, that slowly increasing interference ranges are necessary and sufficient to achieve good accuracy. Our results also demonstrate that a scheduling algorithm that considers a fixed interference range will produce schedules with a very high percentage of failing transmissions, which would have substantial negative impacts on performance and fairness in such networks