On the Probability of K-hop Connection in Wireless Sensor Networks

Considering a wireless sensor network whose sensors are randomly and independently distributed in a bounded area according to a homogeneous Poisson process with intensity p and each sensor has a uniform transmission radius of r
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, an important problem is to obtain the probability that two random sensors separated by a known distance x are k hop neighbors for some positive integer k. In this letter, we give a recursive analytical equation for computing this probability. The analytical solution is validated by simulations.