This SpringerBrief explores the advantage of relaying techniques in addressing the increasing demand for high data rates and reliable services over the air. It demonstrates how to design cost-effective relay systems that provide high spectral efficiency and fully exploit the diversity of the relay channel. The brief covers advances in achievable rates, power allocation schemes, and error performance for half-duplex (HD) and full-duplex (FD) amplify-and-forward (AF) single-relay systems. The authors discuss the capacity and respective optimal power allocation for a wide range of HD protocols...