Theoretical Statistics and Mathematics Unit, ISI Delhi

On the Typical Number of Links Supporting a Minimum Rate in Wireless Ad-Hoc Networks

by Hengameh Keshavarz, Ravi R. Mazumdar, and Rahul Roy

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.

isid/ms/2012/01 [fulltext]

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