The Impact of Realistic Footprint Shapes on the Connectivity of Wireless Sensor Networks

Radio channel fluctuations affecting links of Wireless Sensor Networks (WSNs) show an evident spatial correlation, besides the random behavior caused by obstacles and fading effects. This makes node footprints (i.e. the area covered by the radio transmitter of a node) irregular. Nonetheless, the vast majority of models used in the literature to assess the performance of WSNs in terms of network connectivity, neglect this evidence. They usually consider either the deterministic disk model (with circular footprints) or some random connection model assuming i.i.d. channel fluctuations when different links are realized at the same node with different neighbors. We show in this paper that in realistic settings the spatial correlations of the random fluctuations play a relevant role; we support this statement with an analysis starting from real measurements performed on-field. However, we also show that the i.i.d model provides results which can be close enough to reality in some cases. More precisely, assuming a constant average number of neighbors, we study the percolating properties of realistic and theoretical footprints on random graphs by computing the relative size of the largest component of the graph. Our results show that the presence of correlation may be beneficial or detrimental, depending of whether one considers undirected or directed graphs, i.e., ultimately, on the application.