As wireless sensor networks utilize battery-operated nodes, energy efficiency is of paramount importance at all levels of system design. In order to save energy in the transfer of data from the sensor nodes to one or more sinks, the data may be routed through other nodes rather than transmitting it directly to the sink(s). In this paper, we investigate the problem of energy-efficient transmission of data over a noisy channel, focusing on the setting of physical layer parameters. We derive a metric called the energy per successfully received bit, which specifies the expected energy required to transmit a bit successfully over a particular distance given a channel noise model. By minimizing this metric, we can find, for different modulation schemes, the energyoptimal relay distance and the optimal transmit energy as a function of channel noise level and path loss exponent. These results enable network designers to select the hop distance, transmit power and/or modulation scheme that maximize network lifetime.

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