Duplexing and synchronism for energy efficient communication over a relay channel

This paper investigates the impact of usual practical constraints for the relay channel in the energy efficient regime. Specifically, we take into account constraints on the transmission/reception duplexing and on the synchronization between the source and the relay. New and already known bounds for the maximum rate-per-energy that depend on the constraints considered, are presented in a unified manner. Lower bounds are with decode-and-forward and upper-bounds with the cut-set bound. It is shown that while synchronism provides gains on the maximum RPE, duplexing does not. To see the gain by duplexing the slope of the spectral efficiency with respect the energy-per-bit is also derived.