Probability of k-Hop Connection under Random Connection Model

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Journal Article
IEEE Communications Letters, 2010, 14 (11), pp. 1023 - 1025
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Consider a wireless sensor network with Ltd. sensors following a homogeneous Poisson distribution in a given area A in R2. A sensor located at x2 ? A is directly connected to a sensor located at x1 ? A with probability g (x2 - x1), independent of any other distinct pair of sensors. In this letter, we provide a recursive formula for computing Pr (k|x), the probability that a node x ? A apart from another node is connected to that node at exactly k hops, for a generic random connection function g : R2 ? . The recursive formula is accurate for k = 1, 2 and provides an approximation for Pr (k|x) for k > 2. The exact and approximate analytical results are validated by simulations. The knowledge of Pr (k|x) can be used in a number of areas in sensor networks.
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