Underwater communication is a challenging topic due to its singular channel characteristics. Most protocols used in terrestrial wireless communication can not be directly applied in the underwater world. In this paper, we focus on the issue of energy efficient transmission in underwater sensor networks (UWSNs) and analyze this problem in a rigorous and theoretical way. We formalize an optimization problem which aims to minimize energy consumption and simultaneously accounts for other performance metrics such as the data reliability and the communication delay. With the help of Karush-Kuhn-Tucker conditions (KKT conditions), we derive a simple and explicit, but nevertheless accurate, approximate solution under reasonable assumptions. This approximate solution provides theoretical guidelines for designing durable and reliable UWSNs. Our result also shows that reliability and communication delay are crucial factors to the energy consumption for transmission.
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