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The percolation of a broadcast in a multihop radio network modeled by a spatial Poisson process is studied. The effect of station density and transmission radius on the extent of broadcast percolation is examined. For broadcast percolation in one spatial dimension, analytical expressions for the average extent of percolation are derived. A model for two-dimensional spatial percolation is presented along with related simulation results. The results suggest that in optimizing transmission radius as a function of communication performance measures, the choice of radius may be bounded from below by the need to maintain a desired network connectivity. The connectivity constraint can be relaxed to some extent in certain non-Poisson spatial models.>
Cheng et al. (Sat,) studied this question.