Prof. Srikanth Iyer (Indian Institute of Science, Bangalore, currently visiting Statistics and Probability Dept, UCSB)

Title: Extended Random Signal-to-Interference-and-Noise-Ratio Graphs with Fading

Abstract: The asymptotic properties of a random geometric graph (SINR-F) on uniform points in which a directed link exists between two nodes if the signal-to-interference-noise-ratio is above a certain threshold will be discussed.

The first step is to study such a graph in the presence of fading effects alone (RGG-F). For this graph an almost sure limit for the critical power required to ensure that the graph does not possess isolated nodes and a criterion under which the number of isolated nodes converges in distribution to a Poisson distribution is proved. A sufficient condition under which the graph will be connected with high probability will be presented as well as almost sure bounds on the maximum and minimum vertex degrees.

Finally an almost sure upper bound on the maximum received interference is obtained. This enables one to choose an asymptotic spread parameter so as to bound the maximum received interference. With this choice of spread parameter the results obtained for RGG-F can be extended to SINR-F.