Energy-Aware Competitive Power Allocation for Heterogeneous Networks Under QoS Constraints

This work proposes a distributed power allocation scheme for maximizing energy efficiency in the uplink of orthogonal frequency-division multiple access (OFDMA)-based heterogeneous networks (HetNets). The user equipment (UEs) in the network are modeled as rational agents that engage in a non-cooperative game where each UE allocates its available transmit power over the set of assigned subcarriers so as to maximize its individual utility (defined as the user's throughput per Watt of transmit power) subject to minimum-rate constraints. In this framework, the relevant solution concept is that of Debreu equilibrium, a generalization of Nash equilibrium which accounts for the case where an agent's set of possible actions depends on the actions of its opponents. Since the problem at hand might not be feasible, Debreu equilibria do not always exist. However, using techniques from fractional programming, we provide a characterization of equilibrial power allocation profiles when they do exist. In particular, Debreu equilibria are found to be the fixed points of a water-filling best response operator whose water level is a function of minimum rate constraints and circuit power. Moreover, we also describe a set of sufficient conditions for the existence and uniqueness of Debreu equilibria exploiting the contraction properties of the best response operator. This analysis provides the necessary tools to derive a power allocation scheme that steers the network to equilibrium in an iterative and distributed manner without the need for any centralized processing. Numerical simulations are then used to validate the analysis and assess the performance of the proposed algorithm as a function of the system parameters.Comment: 37 pages, 12 figures, to appear IEEE Trans. Wireless Commu

A Repeated Game Formulation of Energy-Efficient Decentralized Power Control

Decentralized multiple access channels where each transmitter wants to selfishly maximize his transmission energy-efficiency are considered. Transmitters are assumed to choose freely their power control policy and interact (through multiuser interference) several times. It is shown that the corresponding conflict of interest can have a predictable outcome, namely a finitely or discounted repeated game equilibrium. Remarkably, it is shown that this equilibrium is Pareto-efficient under reasonable sufficient conditions and the corresponding decentralized power control policies can be implemented under realistic information assumptions: only individual channel state information and a public signal are required to implement the equilibrium strategies. Explicit equilibrium conditions are derived in terms of minimum number of game stages or maximum discount factor. Both analytical and simulation results are provided to compare the performance of the proposed power control policies with those already existing and exploiting the same information assumptions namely, those derived for the one-shot and Stackelberg games.Comment: 25 pages, 5 figures, accepted for publication in IEEE Transaction on Wireless Communicatio

A Game-Theoretic Approach to Energy-Efficient Modulation in CDMA Networks with Delay Constraints

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.Comment: Appeared in the Proceedings of the 2007 IEEE Radio and Wireless Symposium, Long Beach, CA, January 9-11, 200