Optimal energy efficient joint power allocation for two-hop single-antenna relaying systems

In this paper, the joint source-relay power allocation issue in green dual-hop single-antenna relaying systems is investigated from the energy efficiency point of view. By considering a practical power consumption model, the optimal transmit power of the source and that of the relay are derived in the form of analytical expressions based on the maximisation of energy efficiency with a guarantee of the required spectral efficiency. The novelty of the work lies in that the highly complicated optimisation problem is solved by deliberately manipulating the Lagrangian function using the properties of the Lambert function. It is shown that the optimal relay-to-source power ratio is adaptive to the ratio of the instantaneous two-hop channel gains. Numerical simulations have illustrated the effectiveness of our proposed scheme. Copyright (C) 2014 John Wiley & Sons, Ltd.