  Assume that a multi-user multiple-input multiple-output (MIMO) system is
designed from scratch to uniformly cover a given area with maximal energy
efficiency (EE). What are the optimal number of antennas, active users, and
transmit power? The aim of this paper is to answer this fundamental question.
We consider jointly the uplink and downlink with different processing schemes
at the base station and propose a new realistic power consumption model that
reveals how the above parameters affect the EE. Closed-form expressions for the
EE-optimal value of each parameter, when the other two are fixed, are provided
for zero-forcing (ZF) processing in single-cell scenarios. These expressions
prove how the parameters interact. For example, in sharp contrast to common
belief, the transmit power is found to increase (not to decrease) with the
number of antennas. This implies that energy-efficient systems can operate in
high signal-to-noise ratio regimes in which interference-suppressing signal
processing is mandatory. Numerical and analytical results show that the maximal
EE is achieved by a massive MIMO setup wherein hundreds of antennas are
deployed to serve a relatively large number of users using ZF processing. The
numerical results show the same behavior under imperfect channel state
information and in symmetric multi-cell scenarios.
