Energy minimization in cooperative relay networks with sleep modes

We consider a cooperative relay network where a source node communicates to a destination node with the help of multiple relay nodes (RNs). RNs are assumed to be able to work in either active mode or sleep mode. To minimize the total energy consumption, working modes of RNs and power allocation need to be optimized. Based on the time scales of mode transition, we formulate two different energy minimization problems. In the case of fast transition, where the transition can be applied in each frame, the problem is shown to be a supermodular minimization problem. We propose a relaxation based algorithm with a provable performance bound. In the case of slow transition, where the working modes of RNs are fixed, the problem is proven to be NP-hard even for the single relay selection case. Approximation algorithms are proposed based on the supermodular structure of the problem. Simulation results show that the proposed algorithms perform close to optimal, and significant energy saving can be achieved. The effect of the transition cost and the comparison between fast transition and slow transition are also presented.