  This paper investigates the energy efficiency (EE) in multiple relay aided
OFDM system, where decode-and-forward (DF) relay beamforming is employed to
help the information transmission. In order to explore the EE performance with
user fairness for such a system, we formulate an optimization problem to
maximize the EE by jointly considering several factors, the transmission mode
selection (DF relay beamforming or direct-link transmission), the helping relay
set selection, the subcarrier assignment and the power allocation at the source
and relays on subcarriers, under nonlinear proportional rate fairness
constraints, where both transmit power consumption and linearly rate-dependent
circuit power consumption are taken into account. To solve the non-convex
optimization problem, we propose a low-complexity scheme to approximate it.
Simulation results demonstrate its effectiveness. We also investigate the
effects of the circuit power consumption on system performances and observe
that with both the constant and the linearly rate-dependent circuit power
consumption, system EE grows with the increment of system average channel-to
noise ratio (CNR), but the growth rates show different behaviors. For the
constant circuit power consumption, system EE increasing rate is an increasing
function of the system average CNR, while for the linearly rate-dependent one,
system EE increasing rate is a decreasing function of the system average CNR.
This observation is very important which indicates that by deducing the circuit
dynamic power consumption per unit data rate, system EE can be greatly
enhanced. Besides, we also discuss the effects of the number of users and
subcarriers on the system EE performance.
