A game-theoretic approach to energy-efficient power control in multicarrier CDMA systems

Abstract

Abstract-A game-theoretic model for studying power control in multicarrier code-division multiple-access systems is proposed. Power control is modeled as a noncooperative game in which each user decides how much power to transmit over each carrier to maximize its own utility. The utility function considered here measures the number of reliable bits transmitted over all the carriers per joule of energy consumed and is particularly suitable for networks where energy efficiency is important. The multidimensional nature of users' strategies and the nonquasi-concavity of the utility function make the multicarrier problem much more challenging than the single-carrier or throughput-based-utility case. It is shown that, for all linear receivers including the matched filter, the decorrelator, and the minimum-mean-square-error detector, a user's utility is maximized when the user transmits only on its "best" carrier. This is the carrier that requires the least amount of power to achieve a particular target signal-to-interference-plus-noise ratio at the output of the receiver. The existence and uniqueness of Nash equilibrium for the proposed power control game are studied. In particular, conditions are given that must be satisfied by the channel gains for a Nash equilibrium to exist, and the distribution of the users among the carriers at equilibrium is characterized. In addition, an iterative and distributed algorithm for reaching the equilibrium (when it exists) is presented. It is shown that the proposed approach results in significant improvements in the total utility achieved at equilibrium compared with a single-carrier system and also to a multicarrier system in which each user maximizes its utility over each carrier independently.

Wardrop Equilibrium for CDMA Systems

“…This work is an extension of [4] in the case of frequency-selective fading, in the framework of asymptotic CDMA with a cyclic prefix. We do not consider multiple carriers, as in [5], and the results are very different to those obtained in this work. The extension is not trivial and involves advanced results on random matrices with non-equal variances due to Girko [6] whereas classical results rely on the work of Silverstein [7].…”

“…In [4], defining the utility as the ratio of the throughput to the transmission power, the authors obtain results of existence and unicity of a Nash equilibrium in this hypothesis. As far as the attenuation is concerned, only flat fading is considered in [4] and in [5], in the case of multiple carriers (each one being flat fading). However, wireless transmissions generally suffer from the effect of multiple paths, thus becoming frequency-selective.…”

Energy Efficient Power Control in Impulse Radio UWB Wireless Networks

“…4 shows the utility as a function of the channel gain when the processing gain N is constant, but the ratio N c /N f is variable. 7 The results have been obtained for a network with K = 16 users, L = 100 channel paths and processing gain N = 1000, using ARake receivers at the base station. The solid line corresponds to N c /N f = 40, the dotted line represents N c /N f = 2.5, and the dashed line shows N c /N f = 0.1.…”

“…Joint network-centric and user-centric power control are discussed in [6]. In [7], the authors propose a power control game for multicarrier CDMA (MC-CDMA) systems, while in [8] the effects of the receiver have been considered, particularly extending the study to multiuser detectors and multiantenna receivers.…”

Game‐theoretic beamforming techniques for multiuser multi‐cell networks under mixed quality of service constraints

“…The utility function was modelled as the number of information bits received per Joule of energy expended which captures the trade-off between quality of service (QoS) requirements and energy consumption. The latter work was extended to a multi-carrier data network in [6]. Noncooperative games were used in [7][8][9][10] to develop distributed algorithms.…”