Optimizing the Bit Transmission Power for Link Layer Energy Efficiency Under Imperfect CSI

In this paper, we study the issue of selecting the transmission power (energy per symbol) to minimize the expected energy required to successfully deliver a link-layer packet to the destination node in a wireless link performing the automatic repeat request. We consider the system that has a slow-fading channel and employs a minimum mean square error-based channel estimation scheme for a pilot symbol-assisted modulation. We derive a closed-form expression for the packet error probability (PkEP) in the presence of channel estimation error, and we use this expression for minimizing the PkEP in allocating the transmission energy among the pilot and data symbols. We also derive the expected energy required to successfully deliver a link-layer packet as a function of the transmission power and present an optimization method based on the properties of this function.