Publications and Preprints

This paper presents results on the typical number of simultaneous point-to-point transmissions above a minimum rate that can be sustained in a network with $n$ nodes when all nodes can interfere with each other. In particular we obtain a scaling law when the channel gains between the transmitter and receiver are independent Rayleigh distributed random variables. We show that asymptotically with probability 1 the number of simultaneous transmissions is of the order of $C(\log n)^{\alpha(n)}$ where $1 < \alpha(n) \leq 2 $ and $\alpha(n) \to 2$ as $n\to \infty$. We show that this asymptotic matches the results obtained from simulations.