  A game-theoretic framework is used to study the effect of constellation size
on the energy efficiency of wireless networks for M-QAM modulation. A
non-cooperative game is proposed in which each user seeks to choose its
transmit power (and possibly transmit symbol rate) as well as the constellation
size in order to maximize its own utility while satisfying its delay
quality-of-service (QoS) constraint. The utility function used here measures
the number of reliable bits transmitted per joule of energy consumed, and is
particularly suitable for energy-constrained networks. The best-response
strategies and Nash equilibrium solution for the proposed game are derived. It
is shown that in order to maximize its utility (in bits per joule), a user must
choose the lowest constellation size that can accommodate the user's delay
constraint. Using this framework, the tradeoffs among energy efficiency, delay,
throughput and constellation size are also studied and quantified. The effect
of trellis-coded modulation on energy efficiency is also discussed.
