  In this paper, we examine the maximization of energy efficiency (EE) in
next-generation multi-user MIMO-OFDM networks that evolve dynamically over time
- e.g. due to user mobility, fluctuations in the wireless medium, modulations
in the users' load, etc. Contrary to the static/stationary regime, the system
may evolve in an arbitrary manner so, targeting a fixed optimum state (either
static or in the mean) becomes obsolete; instead, users must adjust to changes
in the system "on the fly", without being able to predict the state of the
system in advance. To tackle these issues, we propose a simple and distributed
online optimization policy that leads to no regret, i.e. it allows users to
match (and typically outperform) even the best fixed transmit policy in
hindsight, irrespective of how the system varies with time. Moreover, to
account for the scarcity of perfect channel state information (CSI) in massive
MIMO systems, we also study the algorithm's robustness in the presence of
measurement errors and observation noise. Importantly, the proposed policy
retains its no-regret properties under very mild assumptions on the error
statistics and, on average, it enjoys the same performance guarantees as in the
noiseless, deterministic case. Our analysis is supplemented by extensive
numerical simulations which show that, in realistic network environments, users
track their individually optimum transmit profile even under rapidly changing
channel conditions, achieving gains of up to 600% in energy efficiency over
uniform power allocation policies.
