In this paper, we focus on the energy efficiency (EE) optimization for an amplify-and-forward (AF) relay network, where the energy-constrained relay harvests energy from a transmitter using power splitting (PS) scheme. We aim to maximize the EE of the network via jointly optimizing the transmit precoding, relay beamforming, and PS ratio, under the constraints of transmit power and the spectral efficiency. To solve the formulated fractional programming, we approximate the problem via two layer optimization, where the outer problem is handled by the Dinkelbach method, and the inner problem is solved by penalized difference-of-convex (DC) and constrained concave-convex procedure (CCCP). Finally, an iterative method is proposed. Simulation results demonstrate the performance of the proposed design.
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