The Impact of Correlated Channel Fluctuations on the Connectivity of Wireless Ad-Hoc Networks

Channel fluctuations affecting links of ad-hoc and sensor networks show an evident spatial correlation, besides the random behavior. Nonetheless, the vast majority of models used in the literature assign edges between pairs of vertices of a graph according to either the deterministic disk model or some random connection model assuming i.i.d. fluctuations. We believe none of the approaches reflects the reality. In this paper we introduce a Correlated Random Connection Model (CRCM) which accounts for angular correlation, by means of a tunable parameter, in the fluctuations that affect two links sharing one of the endpoints. Assuming a constant average number of neighbors, we study the percolating properties of correlated footprints on random graphs by computing the relative size of the two largest components of the graph and the probability of the event of (almost) connectivity. We also compare it to the case of some non-probabilistic shapes of both theoretical and practical flavor. 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.