Optimal relay placement for lifetime maximization in wireless underground sensor networks

Because of highly lossy underground channels and the difficulty in recharging the buried sensor nodes (SNs), power conservation is a primary objective in the design of wireless underground sensor networks (WUSNs). One promising approach to prolonging the lifetimes of WUSNs is to deploy aboveground relay nodes (RNs) to relay the traffic. However, there are several challenges. First, the candidate locations of RNs are affected by the terrestrial environment. Second, signal attenuation is complex because of the multimedium propagation. Third, the optimal placement problem has to be considered in a three-dimensional space. Finally, load balancing among RNs is required to ensure that there is no overloading or exhausting of a single node. In this paper, the RN placement problem in WUSNs is modeled and formulated for the first time; the goal is to deploy a limited number of RNs to maximize the lifetimes of WUSNs under system constraints, such as locations, load balancing, network topology, and a practical channel model. Furthermore, the problem is reformulated by introducing an extra decision vector to transform the original constraints into linear constraints, and then, a two-phase method is presented to solve the problem efficiently. Extensive simulations are carried out to evaluate the performance of the proposed method.