Energy-Efficient Power Allocation for Fixed-Gain Amplify-and-Forward Relay Networks with Partial Channel State Information

In this letter, energy-efficient transmission and power allocation for fixed-gain amplify-and-forward relay networks with partial channel state information (CSI) are studied. In the energy-efficiency problem, the total power consumed is minimized while keeping the signal-to-noise-ratio (SNR) above a certain threshold. In the dual problem of power allocation, the end-to-end SNR is maximized under individual and global power constraints. Closed-form expressions for the optimal source and relay powers and the Lagrangian multiplier are obtained. Numerical results show that the optimal power allocation with partial CSI provides comparable performance as optimal power allocation with full CSI at low SNR.