Mathematical Modeling and Analysis of Computer Networks
"A Statistical Physics Approach to
Information Flow in Wireless Networks"
UC San Diego
We review scaling results for the per-node throughput capacity of wireless networks under the following model: nodes are distributed in a square of area n according to a Poisson point process of unit density, source-destination pairs are selected uniformly at random and need to communicate information at rate R(n), each node radiates a signal x(t) subject to power constraint x2(t) and propagation loss that is an increasing function of the Euclidian distance. The objective is to characterize the almost sure behaviour of R(n) as n tends to infinity.
Constructive lower bounds and information theoretic upper bounds are reviewed for this model. Specifically, a lower bound based on percolation theoretic arguments is presented, and an information theoretic upper bound is obtained using a geometric variation of the cut-set argument of Leveque and Telatar (2005).
The gap between upper and lower bounds under different propagation models is discussed, as long as extensions of the model to fading, and issues in decentralized MAC and routing protocols design.