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MultiUser MISO interference channels with SingleUser detection: Optimality of beamforming and the achievable rate region
 IEEE TRANS. INFORM. TH
, 2009
"... For a multiuser interference channel with multiantenna transmitters and singleantenna receivers, by restricting each transmitter to Gaussian input and each receiver to a singleuser detector, computing the largest achievable rate region amounts to solving a family of nonconvex optimization probl ..."
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Cited by 29 (1 self)
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For a multiuser interference channel with multiantenna transmitters and singleantenna receivers, by restricting each transmitter to Gaussian input and each receiver to a singleuser detector, computing the largest achievable rate region amounts to solving a family of nonconvex optimization problems. Recognizing the intrinsic connection between the signal power at the intended receiver and the interference power at the unintended receiver, the original family of nonconvex optimization problems is converted into a new family of convex optimization problems. It is shown that, for such interference channels with each receiver implementing singleuser detection, transmitter beamforming can achieve all boundary points of the achievable rate region.
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 temperatureinterference limit required by the primary users. We provide a unified set of conditions that guarantee the uniqueness 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 temperatureinterference limit—and they have the desired features required for CR applications, such as lowcomplexity, distributed implementation, robustness against missing or outdated updates of the users, and fast convergence behavior.
Game theory and the frequency selective interference channel  A tutorial
, 2009
"... This paper provides a tutorial overview of game theoretic techniques used for communication over frequency selective interference channels. We discuss both competitive and cooperative techniques. ..."
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Cited by 18 (2 self)
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This paper provides a tutorial overview of game theoretic techniques used for communication over frequency selective interference channels. We discuss both competitive and cooperative techniques.
Distributed Resource Allocation Schemes: Pricing Algorithms for Power Control and Beamformer Design in Interference Networks
"... Achieving high spectral efficiencies in wireless networks requires the ability to mitigate and manage the associated interference. This becomes especially important in networks where many transmitters and receivers are randomly placed, so that in the absence of coordination a particular receiver is ..."
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Cited by 16 (0 self)
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Achieving high spectral efficiencies in wireless networks requires the ability to mitigate and manage the associated interference. This becomes especially important in networks where many transmitters and receivers are randomly placed, so that in the absence of coordination a particular receiver is likely to encounter significant interference from a neighboring transmitter. A challenge is then to provide a means
Restricted generalized Nash equilibria and controlled penalty algorithm
, 2008
"... The generalized Nash equilibrium problem (GNEP) is a generalization of the standard Nash equilibrium problem (NEP), in which each player’s strategy set may depend on the rival players ’ strategies. The GNEP has recently drawn much attention because of its capability of modeling a number of interesti ..."
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Cited by 11 (2 self)
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The generalized Nash equilibrium problem (GNEP) is a generalization of the standard Nash equilibrium problem (NEP), in which each player’s strategy set may depend on the rival players ’ strategies. The GNEP has recently drawn much attention because of its capability of modeling a number of interesting conflict situations in, for example, an electricity market and an international pollution control. However, a GNEP usually has multiple or even infinitely many solutions, and it is not a trivial matter to choose a meaningful solution from those equilibria. The purpose of this paper is twofold. First we present an incremental penalty method for the broad class of GNEPs and show that it can find a GNE under suitable conditions. Next, we formally define the restricted GNE for the GNEPs with shared constraints and propose a controlled penalty method, which includes the incremental penalty method as a subprocedure, to compute a restricted GNE. Numerical examples are provided to illustrate the proposed approach. Key words. Generalized Nash equilibrium, shared constraints, shadow price, penalty method, restricted GNE. 1
Distributed power allocation with sinr constraints using trial and error learning
 in Military Communications and Information Systems Conference, MCC, Gdańsk
, 2012
"... Abstract—In this paper, we address the problem of global transmit power minimization in a selfconfiguring network where radio devices are subject to operate at a minimum signal to interference plus noise ratio (SINR) level. We model the network as a parallel Gaussian interference channel and we int ..."
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Cited by 8 (7 self)
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Abstract—In this paper, we address the problem of global transmit power minimization in a selfconfiguring network where radio devices are subject to operate at a minimum signal to interference plus noise ratio (SINR) level. We model the network as a parallel Gaussian interference channel and we introduce a fully decentralized algorithm (based on trial and error) able to statistically achieve a configuration where the performance demands are met. Contrary to existing solutions, our algorithm requires only local information and can learn stable and efficient working points by using only one bit feedback. We model the network under two different game theoretical frameworks: normal form and satisfaction form. We show that the converging points correspond to equilibrium points, namely Nash and satisfaction equilibrium. Similarly, we provide sufficient conditions for the algorithm to converge in both formulations. Moreover, we provide analytical results to estimate the algorithm’s performance, as a function of the network parameters. Finally, numerical results are provided to validate our theoretical conclusions.
QualityOfService Provisioning in Decentralized Networks: A Satisfaction Equilibrium Approach
, 2012
"... This paper introduces a particular game formulation and its corresponding notion of equilibrium, namely the satisfaction form (SF) and the satisfaction equilibrium (SE). A game in SF models the case where players are uniquely interested in the satisfaction of some individual performance constraints ..."
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Cited by 6 (3 self)
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This paper introduces a particular game formulation and its corresponding notion of equilibrium, namely the satisfaction form (SF) and the satisfaction equilibrium (SE). A game in SF models the case where players are uniquely interested in the satisfaction of some individual performance constraints, instead of individual performance optimization. Under this formulation, the notion of equilibrium corresponds to the situation where all players can simultaneously satisfy their individual constraints. The notion of SE, models the problem of QoS provisioning in decentralized selfconfiguring networks. Here, radio devices are satisfied if they are able to provide the requested QoS. Within this framework, the concept of SE is formalized for both pure and mixed strategies considering finite sets of players and actions. In both cases, sufficient conditions for the existence and uniqueness of the SE are presented. When multiple SE exist, we introduce the idea of effort or cost of satisfaction and we propose a refinement of the SE, namely the efficient SE (ESE). At the ESE, all players adopt the action which requires the lowest effort for satisfaction. A learning method that allows radio devices to achieve a SE in pure strategies in finite time and requiring only onebit feedback is also presented. Finally, a power control game in the interference channel is used to highlight the advantages of modeling QoS problems following the notion of SE rather than other equilibrium concepts, e.g., generalized Nash equilibrium.
1 Equilibrium Pricing of Interference in Cognitive Radio Networks
"... In this paper we address the problem of spectrum allocation in cognitive radio networks in which licensed users allow unlicensed users to make use of their allocated capacity, provided a set of interference constraints on the receivers of licensed users are satisfied. In this scenario, the tradition ..."
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Cited by 6 (4 self)
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In this paper we address the problem of spectrum allocation in cognitive radio networks in which licensed users allow unlicensed users to make use of their allocated capacity, provided a set of interference constraints on the receivers of licensed users are satisfied. In this scenario, the traditional distributed dynamical spectrum allocation approach is unable to enforce such interference constraints. To address this problem, we propose to allocate the spectrum to unlicensed users by pricing the interference constraints. In such a scheme, a total charge for each unlicensed user will be determined based upon their contribution to the total interference as measured by each licensed user. We also formulate the notion of interference equilibrium, which is a state of the network where i) all interference constraints are satisfied and ii) no unlicensed user has an incentive to alter its own transmission power levels. We propose a distributed algorithm and apply it to two cognitive radio network configurations. For each configuration we give sufficient conditions to guarantee convergence of the unlicensed users ’ power profiles and ensure interference prices converge to an interference equilibrium. I.
1 Satisfaction Equilibrium: A General Framework for QoS Provisioning in SelfConfiguring Networks
"... Abstract—This paper is concerned with the concept of equilibrium and quality of service (QoS) provisioning in selfconfiguring wireless networks with noncooperative radio devices (RD). In contrast with the Nash equilibrium (NE), where RDs are interested in selfishly maximizing its QoS, we present a ..."
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Cited by 5 (3 self)
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Abstract—This paper is concerned with the concept of equilibrium and quality of service (QoS) provisioning in selfconfiguring wireless networks with noncooperative radio devices (RD). In contrast with the Nash equilibrium (NE), where RDs are interested in selfishly maximizing its QoS, we present a concept of equilibrium, named satisfaction equilibrium (SE), where RDs are interested only in guaranteing a minimum QoS. We provide the conditions for the existence and the uniqueness of the SE. Later, in order to provide an equilibrium selection framework for the SE, we introduce the concept of effort or cost of satisfaction, for instance, in terms of transmit power levels, constellation sizes, etc. Using the idea of effort, the set of efficient SE (ESE) is defined. At the ESE, transmitters satisfy their minimum QoS incurring in the lowest effort. We prove that contrary to the (generalized) NE, at least one ESE always exists whenever the network is able to simultaneously support the individual QoS requests. Finally, we provide a fully decentralized algorithm to allow selfconfiguring networks to converge to one of the SE relying only on local information. I.
A Generalized Iterative Waterfilling Algorithm for Distributed Power Control in the Presence
, 2008
"... Consider a scenario in which K users and a jammer share a common spectrum of N orthogonal tones. Both the users and the jammer have limited power budgets. The goal of each user is to allocate its power across the N tones in such a way that maximizes the total sum rate that he/she can achieve, while ..."
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Cited by 4 (1 self)
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Consider a scenario in which K users and a jammer share a common spectrum of N orthogonal tones. Both the users and the jammer have limited power budgets. The goal of each user is to allocate its power across the N tones in such a way that maximizes the total sum rate that he/she can achieve, while treating the interference of other users and the jammer’s signal as additive Gaussian noise. The jammer, on the other hand, wishes to allocate its power in such a way that minimizes the utility of the whole system; that being the total sum of the rates communicated over the network. For this noncooperative game, we propose a generalized version of the existing iterative waterfilling algorithm whereby the users and the jammer update their power allocations in a greedy manner. We study the existence of a Nash equilibrium of this noncooperative game as well as conditions under which the generalized iterative waterfilling algorithm converges to a Nash equilibrium of the game. The conditions that we derive in this paper depend only on the system parameters, and hence can be checked a priori. Simulations show that when the convergence conditions are violated, the presence of a jammer can cause the, otherwise convergent, iterative waterfilling algorithm to oscillate.