Lagrange multiplier based power minimization algorithm with relay selection in cooperative system

In this paper, we propose a power allocation scheme to minimize the total power consumption in a decode-and-forward (DF) multi-relay cooperative system considering the required data rate. Based on the minimal transmit power of the source and the instantaneous channel state information (CSI) between the source and the relays, the optimal relays will be selected to reduce the total system power consumption. With the application of Lagrange multiplier technique together with relay selection, the power minimization problem can be solved. Simulation results show that the total power consumption of the proposed scheme is significantly reduced compared with that of the direct transmission and the best relay scheme in opportunistic relay selection (ORS).