On the number of active links in random wireless networks
Abstract
This paper presents results on the typical number of simultaneous pointtopoint transmissions above a minimum rate that can be sustained in a network with $n$ transmitterreceiver node pairs when all transmitting nodes can potentially interfere with all receivers. In particular we obtain a scaling law when the fading gains are independent Rayleigh distributed random variables and the transmitters over different realizations are located at the points of a stationary Poisson field in the plane. We show that asymptotically with probability approaching 1, the number of simultaneous transmissions (links that can transmit at greater than a minimum rate) is of the order of $O(n^{\frac{1}{4}})$. These asymptotic results are confirmed from simulations.
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 arXiv:
 arXiv:1412.3098
 Bibcode:
 2014arXiv1412.3098K
 Keywords:

 Computer Science  Information Theory;
 Primary 94A40;
 Secondary 60G60;
 94A17