Joint power optimization and connectivity control problem over underwater random sensor networks

In this paper, the problem of power optimization and connectivity control for an underwater random sensor network is investigated. The weighted edge connectivity is proposed as a metric to evaluate the connectivity of the weighted expected graph of a random sensor network where the elements of the weight matrix represent the operational probability of their corresponding communication links. The introduced connectivity measure is described as an explicit function of the transmission power of the sensors and the statistical parameters of the communication channels. An optimization problem is then presented to minimize the total power consumption of the network while a lower bound on the global weighted edge connectivity of the network is satisfied. An analytical solution to the optimization problem is obtained by considering a directed cycle topology for the expected communication graph. The efficacy of the obtained results is confirmed for log-normal distribution of the power gain of acoustic communication channels.