A game-theoretic approach for studying energy efficiency-delay tradeoffs in multiple-access networks is proposed. Focusing on the uplink of a code-division multiple-access (CDMA) network, a noncooperative game is considered in which each user seeks to choose a transmit power that maximizes its own utility while satisfying its (transmission) delay requirements. The utility function measures the number of reliable bits transmitted per joule of energy and the user's delay constraint is modeled as an upper bound on the delay outage probability. The Nash equilibrium for the proposed game is derived, and its existence and uniqueness are proved. Using a large-system analysis, explicit expressions for the utilities achieved at equilibrium are obtained for the matched filter, decorrelating and (linear) minimum-mean-square-error (MMSE) multiuser detectors. The effects of delay quality-of-service (QoS) constraints on the users' utilities (in bits per joule) and network capacity (i.e., the maximum number of users that can be supported) are quantified. Using the proposed framework, the tradeoffs between energy efficiency and delay are quantified in a competitive multiuser setting.
