On Energy-Efficient Time Synchronization for Wireless Sensors under Large-Scale and Small-Scale Fading Effects

In this work, the existing trade-off between time synchronization quality and energy is studied for both large-scale and small-scale fading wireless channels. We analyze the clock offset estimation problem using one-way, two-way and N-way message exchange mechanisms affected by Gaussian and exponentially distributed impairments. Our main contribution is a general relationship between the total energy required for synchronizing a wireless sensor network and the clock offset estimation error by means of the transmit power, number of transmitted messages and average message delay, deriving the energy optimal lower bound as a function of the time synchronization quality and the number of hops in a multi-hop network.