Energy-Efficient Resource Allocation in Multiuser MIMO Systems: A Game-Theoretic Framework

arXiv:0807.3094v1 [cs.IT] 19 Jul 2008 ENERGY-EFFICIENT RESOURCE ALLOCATION IN MULTIUSER MIMO SYSTEMS: A GAME-THEORETIC FRAMEWORK Stefano Buzzi1, H. Vincent Poor2, and Daniela Saturnino1 1University of Cassino, DAEIMI 03043 Cassino (FR) - Italy; {buzzi, d.saturnino}@unicas.it 2Princeton University, School of Engineering and Applied Science Princeton, NJ, 08544 - USA; poor@princeton.edu ABSTRACT This paper focuses on the cross-layer issue of resource al- location for energy efficiency in the uplink of a multiuser MIMO wireless communication system. Assuming that all of the transmitters and the uplink receiver are equipped with multiple antennas, the situation considered is that in which each terminal is allowed to vary its transmit power, beam- forming vector, and uplink receiver in order to maximize its own utility, which is defined as the ratio of data throughput to transmit power; the case in which non-linear interference cancellation is used at the receiver is also investigated. Ap- plying a game-theoretic formulation, several non-cooperative games for utility maximization are thus formulated, and their performance is compared in terms of achieved average util- ity, achieved average SINR and average transmit power at the Nash equilibrium. Numerical results show that the use of the proposed cross-layer resource allocation policies brings remarkable advantages to the network performance. 1. INTRODUCTION The increasing demand for new wireless applications, and the tremendous progress in the development of smartphones and handheld devices with exceptional computing capabili- ties requires wireless communication infrastructures capable of delivering data at higher and higher data-rates. The use of multiple antennas at both ends of a wireless link has proved to be a key technology to improve the spectral efficiency of wireless networks [1]. Likewise, intelligent resource allo- cation procedures also will play a prominent role to ensure reliability and efficiency in future wireless data networks. This paper focuses on the uplink of a multiuser multiple-input multiple-output (MIMO) communication sys- tem, wherein both the mobile terminals and the common ac- cess point (AP) are equipped with multiple antennas. We are interested in the design of non-cooperative resource al- location policies aimed at energy efficiency maximization, which is defined here as the number of reliably delivered in- formation symbols per unit-energy taken from the battery. Energy-efficiency maximization is indeed a crucial problem in mobile wireless communications, wherein mobile users are interested in making a careful and smart use of the en- ergy stored in their battery. Following a recent trend, we use game theory tools [2] in order to obtain non-cooperative re- source allocation procedures, maximizing each user’s energy This research was supported in part by the U. S. National Science Foun- dation under Grants ANI-03-38807 and CNS-06-25637. efficiency with respect to its own transmit power, beamform- ing vector and uplink receiver. A game-theoretic framework for non-cooperative energy efficiency maximization has been widely applied in the re- cent past to design resource allocation policies for code divi- sion multiple access (CDMA) systems [3, 4, 5] and for ultra- wideband (UWB) systems [6]. On the other hand, MIMO communication systems have received a great deal of at- tention in the last decade (see, for instance, the references in the recent textbook [1]). Among the studies addressing joint transmitter and receiver adaptation for improved perfor- mance, we cite the papers [7, 8], which consider transceiver optimization for multiuser MIMO systems in cooperative en- vironments, i.e. assuming that a central processor allocates resources among active users, and neglecting the issue of power control. In this paper, we extend the game-theoretic framework, surveyed in [9], to multiuser MIMO wireless systems. We consider the case in which energy efficiency is to be maxi- mized with respect to a. the transmit power of each user, assuming matched filter- ing at the receiver; b. the transmit power and the choice of the uplink linear re- ceiver for each user; c. the transmit power, the beamforming vector and the choice of the uplink linear receiver for each user; and d. the transmit power and the choice of the non-linear serial interference cancellation (SIC) uplink receiver for each user. Note that consideration of these games is not a trivial exten- sion of the results reported in authors’ previous studies, since the analysis of the Nash equilibrium (NE) points for some of the above games, and in particular for the cases c. and d. poses new mathematical challenges. More precisely, we will see that problems a. and b. are somewhat equivalent to those treated in [3] and [4] for a CDMA system, while, instead proof of the existence of a NE for problem c. requires a new and different approach. Finally, the consideration of problem d., which assumes the u

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