Frequency Selection and Relay Placement for Energy Efficiency in Underwater Acoustic Networks

When planning the deployment of an underwater network, the frequency-dependent nature of the underwater acoustic channel has a significant impact on network performance. The quality of acoustic communication in the underwater medium is heavily dependent on the choice of frequency and link length. In this paper, we consider the problems of choosing the proper frequency and node locations for minimizing energy consumption in the network. First, we look at the single frequency that minimizes the transmission power for a network with links of varying lengths. We propose approximate models for this frequency for cases when the link lengths are known exactly and when only probabilistic knowledge of the link lengths is available. Second, to better understand the importance of the actual locations of nodes, we study the problem of relay placement in a multihop line network. We demonstrate that utilizing different frequencies has an impact on the optimal relay placement, and we provide conditions for which the optimal placement is equidistant on the line. Finally, we solve the problem of jointly optimizing the relay placement and the single-frequency choice for a line network. To validate our results, we test our models using simulations of network deployment, and we test our optimal relay placement strategy for a variety of underwater channel settings.