1862 IEEE TRANSACTIONS ONVEHICULAR TECHNOLOGY, VOL. 55, NO. 6, NOVEMBER 2006 A Distributed Power-Allocation and Signal-Shaping Game for the Competitively Optimal Throughput-Maximization of Multiple-Antenna “ad hoc” Networks Enzo Baccarelli, Mauro Biagi, Member, IEEE, and Cristian Pelizzoni Abstract—This paper focuses on the competitively optimal power control and signal shaping for “ad hoc” networks composed by multiple-antenna noncooperative transmit/receive terminals af- fected by spatially colored multiple-access interference (MAI). The target is the competitive maximization of the information through- put sustained by each link that is active over the network. For this purpose, the MAI-impaired network is modeled as a noncoopera- tive strategic game, and sufficient conditions for the existence and uniqueness of the Nash equilibrium (NE) are provided. Further- more, iterative power-control and signal-shaping algorithms are presented to efficiently achieve the NE under both best-effort and “contracted QoS” policies. The presented algorithms also account for the effect of (possibly) imperfect channel estimates available at the transmit/receive units active over the network, they are fully scalable, and they may be implemented in a fully distributed and asynchronous way. The presented numerical results support the conclusion that the proposed distributed algorithms may be able to outperform the conventional centralized orthogonal MAC strategies (as time division multiple access, frequency division multiple access, and code division multiple access) in terms of a sustained network throughput, especially in operating scenarios affected by a strong MAI. Index Terms—Competitive optimality, game theory, multiple- access interference (MAI), multiple antennas, power allocation, spatial signal shaping. I. STATE OF ART AND GOALS OF THE WORK D UE TO THE increasing demand for pervasive high- throughput personal communication services (PCSs), the requirement for “always-on” mobile access based on uncoor- dinated “ad hoc”-type networking architectures is expected to dramatically increase within the next few years [9]. To satisfy the resulting demand for a large network throughput, the spatial dimension provided by wireless multiantenna terminals may be exploited [10]. As a consequence, an increasing attention has been paid to the development of next-generation array- equipped transceivers for wireless PCSs [10]. Manuscript received September 15, 2004; revised July 23, 2005 and Decem- ber 31, 2005. This work was supported in part by the National project Wireless 8O2.16 Multi-antenna mEsh Networks (WOMEN) under Grant 2005093248. The review of this paper was coordinated by Prof. Z. Wang. The authors are with the INFO-COM Department, University of Rome “La Sapienza,” 00184 Rome, Italy (e-mail: enzobac@infocom.uniroma1.it; biagi@infocom.uniroma1.it; pelcris@infocom.uniroma1.it). Color versions of Figs. 1 and 3–7 are available at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TVT.2006.878565 A. Related Works and Proposed Contributions Power control and spatial signal shaping are central issues for the optimized design of multiple-access interference (MAI)- limited “ad hoc” networks. In fact, in these networks, the information throughput (measured in bits/slot), which is con- veyed by each link, depends on the power allocation and signal shaping carried out by all the other transmitters active over the network. Thus, the optimized design of the overall network involves a performance tradeoff among all active transmitters. Such a tradeoff is the subject of the present work. Specifically, the power-control and signal-shaping algorithms, which we propose, aim to maximize the information throughput conveyed by each link active over the network and are based on the modeling of the “ad hoc” network as a noncooperative strategic game. A game theoretic approach has been followed in several recent contributions dealing with power control in wireless networks [1], [4], [5], [18]. In addition, a game theory is also employed in [19] to solve the problem of the power allocation in single-user multiple-input multiple-output (MIMO) systems with imperfect channel estimation. However, all these works focus on scenarios characterized by either single-antenna ter- minals, where the spatial dimension of the system is fully neglected, or single user multiantenna terminals. Thus, the problem of the power allocation in MIMO systems, which is impaired by multiuser interference, still appears to be an open problem. On the contrary, in emerging next-generation “ad hoc” networks employing multiantenna transceivers, the spatial dimension of the overall system is crucial and must be explicitly taken into account in order to optimize the network throughput. The main result of this contribution is that, under suitable conditions, the multiantenna MAI channel game has a unique Nash equilibrium (NE) under both best-effort and “contracted QoS” access policies. This result leads to iterative fully scalable power-control and signal-shaping algorithms that are able to achieve the equilibrium point in a fully distributed and asynchronous way (see the Proposition 3). Specifically, the presented power-control and signal-shaping algorithms ex- hibit the following advantages over conventional centralized orthogonal access methods as time division multiple access (TDMA)/frequency division multiple access (FDMA)/code di- vision multiple access (CDMA). 1) The proposed algorithms are fully scalable and may be implemented without any centralized controller. 0018-9545/$20.00 © 2006 IEEE