Joint optimal placement and energy allocation of underwater sensors in a tree topology

By using the Karush-Kuhn-Tucker (KKT) conditions in a multi-hop hierarchical tree structure we obtained the optimal placement of the underwater acoustic sensor nodes with respect to the capacity of the wireless links between the nodes. We assumed that the energy consumption of each sensor node is constant. We were able to calculate the vertical and horizontal distances between each sensor nodes and also between any levels of interest. On the same tree topology we focused on the energy efficient transmission in underwater sensor networks by providing the optimal transmitting energies for the nodes with fixed locations.