Convergence Theorem for a General Class of Power-Control Algorithms

Leung, Kin K.; Sung, Chi Wan; Wong, Wing Shing; Lok, Tat-Ming

doi:10.1109/tcomm.2004.833140

Cited by 67 publications

(50 citation statements)

References 16 publications

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“…In the case of convex power sets (continuous sets of powers), this simplifies (as in [5] and [11]) to finding a fixed point of p = I(p). We assume here that Si is unbounded (there are no maximum power restrictions, although we shall show below that one can restrict indeed to compact (bounded) sets S i .…”

Section: Convergence Of Power Control Algorithmsmentioning

confidence: 99%

“…i) Another reference that pursued the direction of [11] is [5]. It presents a "canonical" algorithm that converges to a feasible desired power region rather than to a given global min as in Yate's paper.…”

Section: Remarkmentioning

confidence: 99%

“…In particular, the problem of stabilization of linear systems only with amplitude saturation has been exhaustively addressed in the literature (see, among others, [1]- [3] and the references therein). On the other hand, the rate saturation problem has first received a special interest in the aeronautic field, where the tradeoff between high performance requirements and the use of hydraulic servos presenting rate limitations is always present (see, for instance, [4], [5], and the references therein).…”

Section: Introductionmentioning

confidence: 99%

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S-modular games and power control in wireless networks

Altman

Altman²

2003

IEEE Trans. Automat. Contr.

197

147

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Abstract-This note shows how centralized or distributed power control algorithms in wireless communications can be viewed as S-modular games coupled policy sets (coupling is due to the fact that the set of powers of a mobile that satisfy the signal-to-interference ratio constraints depends on powers used by other mobiles). This sheds a new light on convergence properties of existing synchronous and asynchronous algorithms, and allows us to establish new convergence results of power control algorithms. Furthermore, known properties of power control algorithms allow us to extend the theory of S-modular games and obtain conditions for the uniqueness of the equilibrium and convergence of best response algorithms independently of the initial state.

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Section: Convergence Of Power Control Algorithmsmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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S-modular games and power control in wireless networks

Altman

Altman²

2003

IEEE Trans. Automat. Contr.

197

147

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“…Give the advantages mentioned above, there is a number of studies in the literature where radio power control algorithms have been proposed by considering iterations similar to (4) [8][9][10][11][12][13]. In these approaches, the interference functions are not necessarily standard, and the focus has been in studying the convergence of iteration (4) to a fixed point rather than the meaning of the fixed point in terms of optimality for problem (3).…”

Section: 2018 Draftmentioning

confidence: 99%

Optimality of Radio Power Control Via Fast-Lipschitz Optimization

Fischione

2016

IEEE Trans. Commun.

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Fixed point algorithms play an important role to compute feasible solutions to the radio power control problems in wireless networks. Although these algorithms are shown to converge to the fixed points that give feasible problem solutions, the solutions often lack notion of problem optimality. This paper reconsiders well known fixed point algorithms such as those with standard and type-II standard interference functions, and investigates the conditions under which they give optimal power control solutions by the recently proposed Fast-Lipschitz optimization framework. When the qualifying conditions of Fast-Lipschitz optimization apply, it is established that the fixed points are the optimal solutions of radio power optimization problems. The analysis is performed by a logarithmic transformation of variables that gives problems treatable within the Fast-Lipschitz framework. It is shown how the logarithmic problem constraints are contractive by the standard or type-II standard assumptions on the original power control problem, and how a set of cost functions fulfill the Fast-Lipschitz qualifying conditions. The analysis on non monotonic interference function allows to establish a new qualifying condition for Fast-Lipschitz optimization. The results are illustrated by considering power control problems with standard interference function, problems with type-II standard interference functions, and a case of sub-homogeneous power control problems. It is concluded that Fast-Lipschitz optimization may play an important role in many resource allocation problems in wireless networks.

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“…Actually, it has been proved [45] that positivity is implied by monotonicity and scalability, x being positive.…”

Section: Uniqueness Of the Gnementioning

confidence: 99%

Modeling the Power Allocation in Dynamic Spectrum Access for Cognitive Radios as a Generalized Nash Equilibrium Problem

Prati¹

2014

Int. J. of Pure and Appl. Math.

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The demand of radio resources like mobile phones and Internet services is dramatically increasing and inefficiency in the traditional allocation of electromagnetic spectrum is apparent. A novel paradigm for allocating resources is the Dynamic Spectrum Access, where primary and secondary users share the same frequency band.In this paper, in a Cognitive Radio context, we model the power allocation for secondary users coexisting in the same frequency band with primary ones as a Generalized Nash Equilibrium Problem. We develop a theoretic analysis showing existence and uniqueness of the Generalized Nash Equilibrium and convergence of the Best Response Algorithm to it. In practical implementations, the conditions we propose are natural (a lower and an upper bound for the Signal-to-Interference-plus-Noise-Ratio of the radio devices are involved) and easy to be locally verified by users, which just need the knowledge of the total interference they experience near their own receiver.

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Convergence Theorem for a General Class of Power-Control Algorithms

Cited by 67 publications

References 16 publications

S-modular games and power control in wireless networks

S-modular games and power control in wireless networks

Optimality of Radio Power Control Via Fast-Lipschitz Optimization

Modeling the Power Allocation in Dynamic Spectrum Access for Cognitive Radios as a Generalized Nash Equilibrium Problem

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