  The main objective of this work is to improve the energy-efficiency (EE) of a
multiple access channel (MAC) system, through power control, in a distributed
manner. In contrast with many existing works on energy-efficient power control,
which ignore the possible presence of a queue at the transmitter, we consider a
new generalized cross-layer EE metric. This approach is relevant when the
transmitters have a non-zero energy cost even when the radiated power is zero
and takes into account the presence of a finite packet buffer and packet
arrival at the transmitter. As the Nash equilibrium (NE) is an
energy-inefficient solution, the present work aims at overcoming this deficit
by improving the global energy-efficiency. Indeed, as the considered system has
multiple agencies each with their own interest, the performance metric
reflecting the individual interest of each decision maker is the global
energy-efficiency defined then as the sum over individual energy-efficiencies.
Repeated games (RG) are investigated through the study of two dynamic games
(finite RG and discounted RG), whose equilibrium is defined when introducing a
new operating point (OP), Pareto-dominating the NE and relying only on
individual channel state information (CSI). Accordingly, closed-form
expressions of the minimum number of stages of the game for finite RG (FRG) and
the maximum discount factor of the discounted RG (DRG) were established. The
cross-layer model in the RG formulation leads to achieving a shorter minimum
number of stages in the FRG even for higher number of users. In addition, the
social welfare (sum of utilities) in the DRG decreases slightly with the
cross-layer model when the number of users increases while it is reduced
considerably with the Goodman model. Finally, we show that in real systems with
random packet arrivals, the cross-layer power control algorithm outperforms the
Goodman algorithm.
