  The energy efficiency (EE) of a multi-user multi-relay system with the
maximum diversity network coding (MDNC) is studied. We explicitly find the
connection among the outage probability, energy consumption and EE and
formulate the maximizing EE problem under the outage probability constraints.
Relay scheduling (RS) and power allocation (PA) are applied to schedule the
relay states (transmitting, sleeping, \emph{etc}) and optimize the transmitting
power under the practical channel and power consumption models. Since the
optimization problem is NP-hard, to reduce computational complexity, the outage
probability is first tightly approximated to a log-convex form. Further, the EE
is converted into a subtractive form based on the fractional programming. Then
a convex mixed-integer nonlinear problem (MINLP) is eventually obtained. With a
generalized outer approximation (GOA) algorithm, RS and PA are solved in an
iterative manner. The Pareto-optimal curves between the EE and the target
outage probability show the EE gains from PA and RS. Moreover, by comparing
with the no network coding (NoNC) scenario, we conclude that with the same
number of relays, MDNC can lead to EE gains. However, if RS is implemented,
NoNC can outperform MDNC in terms of the EE when more relays are needed in the
MDNC scheme.
