  This article is on the energy efficient precoder design in multi-user
multiple-input-multiple-output (MU-MIMO) systems which is also robust with
respect to the imperfect channel state information (CSI) at the transmitters.
In other words, we design the precoder matrix associated with each transmitter
to maximize the general energy efficiency of the network. We investigate the
problem in two conventional cases. The first case considers the statistical
characterization for the channel estimation error that leads to a quadratically
constrained quadratic program (QCQP) with a semi-closed-form solution. Then, we
turn our attention to the case which considers only the uncertainty region for
the channel estimation error; this case eventually results in a semi-definite
program (SDP).
