On the connectivity of cooperative and non cooperative wireless communication networks

In a seminal work, Gupta and Kumar derived the conditions for the asymptotic connectivity of a network composed of nodes uniformly distributed over a disc of unit area, as the number of nodes goes to infinity. In this work, we incorporate the channel fading and we provide the conditions for the network connectivity, in case of single or multi-antenna transceivers. In particular, we derive closed form, albeit approximate, expressions for the spatial density with which the nodes must be deployed in order to insure the network connectivity with a desired probability. Finally, we show how to improve the connectivity by allowing nearby nodes to transmit in a cooperative manner, using a distributed space-time coding strategy, in order to get spatial diversity gain.