K-hop Statistics in Wireless Sensor Networks

In WSNs (Wireless Sensor Networks), a source node sends its packets via multi-hop relays to a destination node if the source node cannot communicate with the destination node directly. A destination's hop-count with respect to a source is the least number of multi-hop relays required for the source to reach it. Given a WSN whose nodes are distributed randomly according to a homogeneous Poisson point process, we propose a method termed CSP (Convolution of Successive Progress) to compute the conditional probability that a destination node has hop-count h with respect to a source node given that the the distance between the source and the destination is d. We also extend the CSP method into three-dimensional networks. Simulation studies show that the proposed method is able to achieve significant error reduction in computing the conditional probability compared with existing methods.