Energy Efficient Relaying in Multiantenna Two-Hop Channels With Imperfect CSI

In this letter, we investigate robust beamforming to improve the energy efficiency (EE) of a relaying system where only imperfect channel state information (CSI) is available at the relay. Specifically, from the perspective of worst-case robustness, we focus on the robust energy efficient relay beamforming optimization under the norm bounded channel error model. We equivalently transform the complicated primal robust fractional optimization problem into a one-dimensional search, which admits a unique globally optimal solution. In particular, based on this optimal solution, we further obtain explicit asymptotic closed-form results under various specific scenarios of interest.