Percolation and Connectivity on the Signal to Interference Ratio Graph

Seminar
Thursday, March 22, 2012
7:00 PM
Free and open to the public

Open to all WNCG students and faculty

A wireless communication network is considered where any two nodes are connected if the signal-to-interference ratio (SIR) between them is greater than a threshold. Assuming that the nodes of the wireless network are distributed as a Poisson point process (PPP), percolation (formation of an unbounded connected cluster) on the resulting SIR graph is studied as a function of the density of the PPP. It is shown that for a small enough threshold, there exists a closed interval of densities for which percolation happens with non-zero probability. Conversely,it is shown that for a large enough threshold, there exists a closed interval of densities for which the probability of percolation is zero. Connectivity properties of the SIR graph are also studied by restricting all the nodes to lie in a bounded area.Assigning separate frequency bands or time-slots proportional to the logarithm of the number of nodes to different nodes for transmission/reception is shown to be necessary and sufficient for guaranteeing connectivity in the SIR graph.

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Speaker

Rahul Vaze

Tata Institute of Fundamental Research