  In this work, a non-cooperative power control game for multi-carrier CDMA
systems is proposed. In the proposed game, each user needs to decide how much
power to transmit over each carrier to maximize its overall utility. The
utility function considered here measures the number of reliable bits
transmitted per joule of energy consumed. It is shown that the user's utility
is maximized when the user transmits only on the carrier with the best
"effective channel". The existence and uniqueness of Nash equilibrium for the
proposed game are investigated and the properties of equilibrium are studied.
Also, an iterative and distributed algorithm for reaching the equilibrium (if
it exists) is presented. It is shown that the proposed approach results in a
significant improvement in the total utility achieved at equilibrium compared
to the case in which each user maximizes its utility over each carrier
independently.
