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86
Competitive design of multiuser MIMO systems based on game theory: A unified view
- IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS
, 2008
"... This paper considers the noncooperative maximization of mutual information in the Gaussian interference channel in a fully distributed fashion via game theory. This problem has been studied in a number of papers during the past decade for the case of frequency-selective channels. A variety of condi ..."
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Cited by 62 (4 self)
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This paper considers the noncooperative maximization of mutual information in the Gaussian interference channel in a fully distributed fashion via game theory. This problem has been studied in a number of papers during the past decade for the case of frequency-selective channels. A variety of conditions guaranteeing the uniqueness of the Nash Equilibrium (NE) and convergence of many different distributed algorithms have been derived. In this paper we provide a unified view of the state-ofthe-art results, showing that most of the techniques proposed in the literature to study the game, even though apparently different, can be unified using our recent interpretation of the waterfilling operator as a projection onto a proper polyhedral set. Based on this interpretation, we then provide a mathematical framework, useful to derive a unified set of sufficient conditions guaranteeing the uniqueness of the NE and the global convergence of waterfilling based asynchronous distributed algorithms. The proposed mathematical framework is also instrumental to study the extension of the game to the more general MIMO case, for which only few results are available in the current literature. The resulting algorithm is, similarly to the frequency-selective case, an iterative asynchronous MIMO waterfilling algorithm. The proof of convergence hinges again on the interpretation of the MIMO waterfilling as a matrix projection, which is the natural generalization of our results obtained for the waterfilling mapping in the frequency-selective case.
Optimal resource allocation for MIMO ad hoc cognitive radio networks
- in Proc. 46th Annu. Allerton Conf. Commun., Control, Comput
, 2008
"... Abstract—Maximization of the weighted sum-rate of secondary users (SUs) possibly equipped with multiantenna transmitters and receivers is considered in the context of cognitive radio (CR) net-works with coexisting primary users (PUs). The total interference power received at the primary receiver is ..."
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Cited by 39 (0 self)
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Abstract—Maximization of the weighted sum-rate of secondary users (SUs) possibly equipped with multiantenna transmitters and receivers is considered in the context of cognitive radio (CR) net-works with coexisting primary users (PUs). The total interference power received at the primary receiver is constrained to main-tain reliable communication for the PU. An interference channel configuration is considered for ad hoc networking, where the re-ceivers treat the interference from undesired transmitters as noise. Without the CR constraint, a convergent distributed algorithm is developed to obtain (at least) a locally optimal solution. With the CR constraint, a semidistributed algorithm is introduced. An al-ternative centralized algorithm based on geometric programming and network duality is also developed. Numerical results show the efficacy of the proposed algorithms. The novel approach is flexible to accommodate modifications aiming at interference alignment. However, the stand-alone weighted sum-rate optimal schemes pro-posed here have merits over interference-alignment alternatives es-pecially for practical SNR values. Index Terms—Ad hoc network, cognitive radio, interference net-work, MIMO, optimization. I.
The MIMO Iterative Waterfilling Algorithm
- IEEE TRANSACTIONS ON SIGNAL PROCESSING (ACCEPTED)
, 2008
"... This paper considers the non-cooperative maximization of mutual information in the vector Gaussian interference channel in a fully distributed fashion via game theory. This problem has been widely studied in a number of works during the past decade for frequency-selective channels, and recently for ..."
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Cited by 30 (2 self)
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This paper considers the non-cooperative maximization of mutual information in the vector Gaussian interference channel in a fully distributed fashion via game theory. This problem has been widely studied in a number of works during the past decade for frequency-selective channels, and recently for the more general MIMO case, for which the state-of-the art results are valid only for nonsingular square channel matrices. Surprisingly, these results do not hold true when the channel matrices are rectangular and/or rank deficient matrices. The goal of this paper is to provide a complete characterization of the MIMO game for arbitrary channel matrices, in terms of conditions guaranteeing both the uniqueness of the Nash equilibrium and the convergence of asynchronous distributed iterative waterfilling algorithms. Our analysis hinges on new technical intermediate results, such as a new expression for the MIMO waterfilling projection valid (also) for singular matrices, a mean-value theorem for complex matrix-valued functions, and a general contraction theorem for the multiuser MIMO watefilling mapping valid for arbitrary channel matrices. The quite surprising result is that uniqueness/convergence conditions in the case of tall (possibly singular) channel matrices are more restrictive than those required in the case of (full rank) fat channel matrices. We also propose a modified game and algorithm with milder conditions for the uniqueness of the equilibrium and convergence, and virtually the same performance (in terms of Nash equilibria) of the original game.
MIMO cognitive radio: A game theoretical approach
, 2010
"... The concept of cognitive radio (CR) has recently received great attention from the research community as a promising paradigm to achieve efficient use of the frequency resource by allowing the coexistence of licensed (primary) and unlicensed (secondary) users in the same bandwidth. In this paper we ..."
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Cited by 26 (3 self)
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The concept of cognitive radio (CR) has recently received great attention from the research community as a promising paradigm to achieve efficient use of the frequency resource by allowing the coexistence of licensed (primary) and unlicensed (secondary) users in the same bandwidth. In this paper we propose and analyze a totally decentralized approach, based on game theory, to design cognitive MIMO transceivers, who compete with each other to maximize their information rate. The formulation incorporates constraints on the transmit power as well as null and/or soft shaping constraints on the transmit covariance matrix, so that the interference generated by secondary users be confined within the temperature-interference limit required by the primary users. We provide a unified set of conditions that guarantee the unique-ness and global asymptotic stability of the Nash equilibrium of all the proposed games through totally distributed and asynchronous algorithms. Interestingly, the proposed algorithms overcome the main drawback of classical waterfilling based algorithms—the violation of the temperature-interference limit—and they have the desired features required for CR applications, such as low-complexity, distributed implementation, robustness against missing or outdated updates of the users, and fast convergence behavior.
Decomposition by partial linearization: Parallel optimization of multiuser systems
- IEEE Trans. on Signal Processing
, 2014
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Distributed Dynamic Pricing for MIMO Interfering Multiuser Systems: A Unified Approach
"... Abstract—Wireless networks are composed of many users that usually have conflicting objectives and generate interference to each other. The system design is typically formulated as the optimization of the weighted sum of the users ’ utility functions. In an attempt to obtain distributed algorithms i ..."
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Cited by 17 (5 self)
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Abstract—Wireless networks are composed of many users that usually have conflicting objectives and generate interference to each other. The system design is typically formulated as the optimization of the weighted sum of the users ’ utility functions. In an attempt to obtain distributed algorithms in the case this sum is nonconvex, researchers have proposed pricing mechanisms which however are based on heuristics and valid only for a restricted class of problems. In this paper we propose a general framework for the distributed optimization of the nonconvex sum-utility function. Our main contributions are: i) the derivation for the first time of a general dynamic pricing mechanism, ii) a framework that can be easily particularized to well-known applications, giving rise to very efficient practical algorithms that outperform existing methods; and iii) the solution to the currently open problem of social optimization for MIMO multiuser systems. I.
On the Nash equilibria in decentralized parallel interference channels
- in IEEE Workshop on Game Theory and Resource Allocation for 4G
, 2011
"... Abstract—In this paper, the 2-dimensional decentralized parallel interference channel (IC) with 2 transmitter-receiver pairs is modelled as a non-cooperative static game. Each transmitter is assumed to be a fully rational entity with complete information on the game, aiming to maximize its own indiv ..."
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Cited by 15 (11 self)
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Abstract—In this paper, the 2-dimensional decentralized parallel interference channel (IC) with 2 transmitter-receiver pairs is modelled as a non-cooperative static game. Each transmitter is assumed to be a fully rational entity with complete information on the game, aiming to maximize its own individual spectral efficiency by tuning its own power allocation (PA) vector. Two scenarios are analysed. First, we consider that transmitters can split their transmit power between both dimensions (PA game). Second, we consider that each transmitter is limited to use only one dimension (channel selection CS game). In the first scenario, the game might have either one or three NE in pure strategies (PS). However, two or infinitely many NE in PS might also be observed with zero probability. In the second scenario, there always exists either one or two NE in PS. Using Monte-Carlo simulations, we show that in both games there always exists a non-zero probability of observing more than one NE. More interestingly, we show that the highest and lowest network spectral efficiency at any of the NE in the CS game are always higher than the ones in the PA.
Joint sensing and power allocation in nonconvex cognitive radio games: Quasi-nash equilibria
- in Proc. of the 17th International Conference on Digital Signal Processing (DSP2011), Corfu
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