To improve the energy efficiency of amplify-and-forward multi-antenna relay networks

an energyefficient beamforming algorithm is proposed.The proposed algorithm maximize normalized signal-to-noise ratio（ PNSNR） of system while satisfying constraints of relay power. The resultant optimization problem is a non-convex optimization problem

which can be simplify as a one-dimensional optimization problem and can be solved by derivation method. Simulation results show that the proposed approach can significantly improve the energy efficiency of the network

which is much better than that of the optimal SNR-based beamforming algorithm and amplify-and-forward mode without beamforming.