On the Energy Efficiency in Multi-user Multi-relay Coded Network

In this paper, the energy efficiency (EE) of a cooperative diversity system with maximum diversity network coding (MDNC) is studied. In the considered system, channel state information (CSI) is only available at the receivers for all the channels. We formulate the problem of maximizing the EE under the constraint on the outage probability. The problem is NP-hard due to the non-convexity of the outage probability function and the nonlinear fractional structure of the introduced EE. To solve the optimization problem efficiently, first, the outage probability function is tightly approximated as a log-convex form in the high signal-to-noise ratio (SNR) region. Further, based on the fractional programming, we transform the introduced EE into a subtractive-form, which is proved to be a convex form. The tradeoff between outage probability and EE is given. The results show that our power allocation (PA) policy can substantially increase the EE. We show that EE can be increased if more relays forward the messages. Additionally, we also investigate the effect of the relay locations on the EE and demonstrate that the increase in the transmission distance in the first hop causes the loss of the EE. The loss can be reduced by our PA policy.