Energy optimal neighbor discovery for single-radio single-channel wireless sensor networks

Neighbor discovery is a fundamental procedure that needs to be carried out in every wireless sensor network in order to enable communication capabilities. If nodes are mobile or multiple channels are used in the network, the same algorithm may be needed to be carried out several times during the network lifetime, consuming precious energy. In this paper we propose a way for optimizing a neighbor discovery procedure suitable for a single-radio single-channel scenario. Assuming a realistic energy model which accounts for energy required for transmitting discovery queries and listening for acknowledgements and explicitly accounting for collisions we exploit power control and the use of a contention window of variable size to minimize sensors¿ energy consumption while both transmitting and receiving. We formulate the neighbor discovery problem as a Markov decision process and through dynamic programming we compute an optimal policy defining the power level and the contention window size that must be used while broadcasting queries. This policy minimizes the energy cost of the discovery procedure for a given constraint on the maximum probability of having collisions. We further provide guidelines useful for implementing sub-optimal policies which perform asymptotically optimal for high node densities and can be computed on-line by motes with low capabilities.