Poisson-Poisson Cluster SINR Coverage Process

In [1], a new coverage process was defined. It was motivated by the various SINR(Signal to Interference Noise Ratio) models in wireless communications. The underlying point process was assumed to be a Poisson process. In this report, we extend the theory to the case when the underlying point process is a Poisson-Poisson cluster process. Firstly, we define the stochastic geometric model. We give sufficient conditions similar to [1] for the model to be well-defined. Finally, certain results analogous to the cited paper are derived. The reader can also refer to [2] for some more results on such a model and [3] for percolation in such a model. The necessity of this extension arises mainly because in certain models of wireless communications the antennae are clustered or bunched together. And cluster processes model such cases better than Poisson process. Our main goal in this direction is comparison of the two models. In SINR models one would expect the clustering to have a negative impact on the connectivity of the network. The report is organized as follows: Section 2 describes the model in generality and various assumptions for the model to be well-defined. The concluding remark describes the specific model we shall analyse in lot more detail. The sufficient conditions for the assumptions on the model to be satisfied are given in Section 3. Finally, in Section 4 we derive formulae for the coverage probability.