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28
Dynamic Spectrum Management: Complexity and Duality
, 2007
"... Consider a communication system whereby multiple users share a common frequency band and must choose their transmit power spectral densities dynamically in response to physical channel conditions. Due to cochannel interference, the achievable data rate of each user depends on not only the power spe ..."
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Cited by 129 (8 self)
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Consider a communication system whereby multiple users share a common frequency band and must choose their transmit power spectral densities dynamically in response to physical channel conditions. Due to cochannel interference, the achievable data rate of each user depends on not only the power spectral density of its own, but also those of others in the system. Given any channel condition and assuming Gaussian signaling, we consider the problem to jointly determine all users ’ power spectral densities so as to maximize a systemwide utility function (e.g., weighted sumrate of all users), subject to individual power constraints. For the discretized version of this nonconvex problem, we characterize its computational complexity by establishing the NPhardness under various practical settings, and identify subclasses of the problem that are solvable in polynomial time. Moreover, we consider the Lagrangian dual relaxation of this nonconvex problem. Using the Lyapunov theorem in functional analysis, we rigorously prove a result first discovered by Yu and Lui (2006) that there is a zero duality gap for the continuous (Lebesgue integral) formulation. Moreover, we show that the duality gap for the discrete formulation vanishes asymptotically as the size of discretization decreases to zero.
Dynamic resource allocation in cognitive radio networks
 IEEE Signal Process. Mag
, 2010
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Distributed Power Allocation with Rate Constraints in Gaussian FrequencySelective Interference Channels
, 2007
"... This paper considers the minimization of transmit power in Gaussian frequencyselective interference channels, subject to a rate constraint for each user. To derive decentralized solutions that do not require any cooperation among the users, we formulate this power control problem as a (generalized) ..."
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Cited by 50 (3 self)
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This paper considers the minimization of transmit power in Gaussian frequencyselective interference channels, subject to a rate constraint for each user. To derive decentralized solutions that do not require any cooperation among the users, we formulate this power control problem as a (generalized) Nash equilibrium game. We obtain sufficient conditions that guarantee the existence and nonemptiness of the solution set to our problem. Then, to compute the solutions of the game, we propose two distributed algorithms based on the single user waterfilling solution: The sequential and the simultaneous iterative waterfilling algorithms, wherein the users update their own strategies sequentially and simultaneously, respectively. We derive a unified set of sufficient conditions that guarantee the uniqueness of the solution and global convergence of both algorithms. Our results are applicable to all practical distributed multipointtomultipoint systems, either wired or wireless, where a quality of service in terms of information rate must be guaranteed for each link. Index Terms: Gaussian frequencyselective interference channel, mutual information, game theory,
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.
Duality Gap Estimation and Polynomial Time Approximation for Optimal Spectrum Management
, 2008
"... Consider a communication system whereby multiple users share a common frequency band and must choose their transmit power spectra jointly in response to physical channel conditions including the effects of interference. The goal of the users is to maximize a systemwide utility function (e.g., weigh ..."
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Cited by 11 (1 self)
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Consider a communication system whereby multiple users share a common frequency band and must choose their transmit power spectra jointly in response to physical channel conditions including the effects of interference. The goal of the users is to maximize a systemwide utility function (e.g., weighted sumrate of all users), subject to individual power constraints. A popular approach to solve the discretized version of this nonconvex problem is by Lagrangian dual relaxation. Unfortunately the discretized spectrum management problem is NPhard and its Lagrangian dual is in general not equivalent to the primal formulation due to a positive duality gap. In this paper, we use a convexity result of Lyapunov to estimate the size of duality gap for the discretized spectrum management problem and show that the duality gap vanishes asymptotically at the rate O(1= p N), where N is the size of the uniform discretization of the shared spectrum. If the channels are frequency at, the duality gap estimate improves to O(1=N). Moreover, when restricted to the FDMA spectrum sharing strategies, we show that the Lagrangian dual relaxation, combined with a linear programming scheme, can generate an optimal solution for the continuous formulation of the spectrum management problem in polynomial time for any > 0.
Dynamic Power Allocation Under Arbitrary Varying Channels – An Online Approach
"... Abstract—A major problem in wireless networks is coping with limited resources, such as bandwidth and energy. These issues become a major algorithmic challenge in view of the dynamic nature of the wireless domain. We consider in this paper the singletransmitter power assignment problem under timev ..."
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Cited by 9 (0 self)
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Abstract—A major problem in wireless networks is coping with limited resources, such as bandwidth and energy. These issues become a major algorithmic challenge in view of the dynamic nature of the wireless domain. We consider in this paper the singletransmitter power assignment problem under timevarying channels, with the objective of maximizing the data throughput. It is assumed that the transmitter has a limited power budget, to be sequentially divided during the lifetime of the battery. We deviate from the classic work in this area, which leads to explicit “waterfilling ” solutions, by considering a realistic scenario where the channel state quality changes arbitrarily from one transmission to the other. The problem is accordingly tackled within the framework of competitive analysis, which allows for worst case performance guarantees in setups with arbitrarily varying channel conditions. We address both a “discrete ” case, where the transmitter can transmit only at a fixed power level, and a “continuous” case, where the transmitter can choose any power level out of a bounded interval. For both cases, we propose online powerallocation algorithms with proven worstcase performance bounds. In addition, we establish lower bounds on the worstcase performance of any online algorithm, and show that our proposed algorithms are optimal. I.
Distributed Throughput Maximization in Wireless Networks via Random Power Allocation
"... Abstract—We consider throughputoptimal power allocation in multihop wireless networks. The study of this problem has been limited due to the nonconvexity of the underlying optimization problems, that prohibits an efficient solution even in a centralized setting. We take a randomization approach t ..."
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Cited by 9 (1 self)
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Abstract—We consider throughputoptimal power allocation in multihop wireless networks. The study of this problem has been limited due to the nonconvexity of the underlying optimization problems, that prohibits an efficient solution even in a centralized setting. We take a randomization approach to deal with this difficulty. To this end, we generalize the randomization framework originally proposed for input queued switches to an SINR ratebased interference model. Further, we develop distributed power allocation and comparison algorithms that satisfy these conditions, thereby achieving (nearly) 100% throughput. We illustrate the performance of our proposed power allocation solution through numerical investigation and present several extensions for the considered problem. Index Terms—Power allocation, wireless scheduling, capacity region, graphbased interference model, SINR interference model. I.
NearOptimal Power Control in Wireless Networks: A Potential Game Approach
"... We study power control in a multicell CDMA wireless system whereby selfinterested users share a common spectrum and interfere with each other. Our objective is to design a power control scheme that achieves a (near) optimal power allocation with respect to any predetermined network objective (suc ..."
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Cited by 8 (3 self)
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We study power control in a multicell CDMA wireless system whereby selfinterested users share a common spectrum and interfere with each other. Our objective is to design a power control scheme that achieves a (near) optimal power allocation with respect to any predetermined network objective (such as the maximization of sumrate, or some fairness criterion). To obtain this, we introduce the potentialgame approach that relies on approximating the underlying noncooperative game with a “close ” potential game, for which prices that induce an optimal power allocation can be derived. We use the proximity of the original game with the approximate game to establish through Lyapunovbased analysis that natural userupdate schemes (applied to the original game) converge within a neighborhood of the desired operating point, thereby inducing nearoptimal performance in a dynamical sense. Additionally, we demonstrate through simulations that the actual performance can in practice be very close to optimal, even when the approximation is inaccurate. As a concrete example, we focus on the sumrate objective, and evaluate our approach both theoretically and empirically.
Maximizing Sum Rates in Cognitive Radio Networks: Convex Relaxation and Global Optimization Algorithms
"... Abstract—A key challenge in wireless cognitive radio networks is to maximize the total throughput also known as the sum rates of all the users while avoiding the interference of unlicensed band secondary users from overwhelming the licensed band primary users. We study the weighted sum rate maximiza ..."
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Cited by 6 (3 self)
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Abstract—A key challenge in wireless cognitive radio networks is to maximize the total throughput also known as the sum rates of all the users while avoiding the interference of unlicensed band secondary users from overwhelming the licensed band primary users. We study the weighted sum rate maximization problem with both power budget and interference temperature constraints in a cognitive radio network. This problem is nonconvex and generally hard to solve. We propose a reformulationrelaxation technique that leverages nonnegative matrix theory to first obtain a relaxed problem with nonnegative matrix spectral radius constraints. A useful upper bound on the sum rates is then obtained by solving a convex optimization problem over a closed bounded convex set. It also enables the sumrate optimality to be quantified analytically through the spectrum of speciallycrafted nonnegative matrices. Furthermore, we obtain polynomialtime verifiable sufficient conditions that can identify polynomialtime solvable problem instances, which can be solved by a fixedpoint algorithm. As a byproduct, an interesting optimality equivalence between the nonconvex sum rate problem and the convex maxmin rate problem is established. In the general case, we propose a global optimization algorithm by utilizing our convex relaxation and branchandbound to compute an optimal solution. Our technique exploits the nonnegativity of the physical quantities, e.g., channel parameters, powers and rates, that enables key tools in nonnegative matrix theory such as the (linear and nonlinear) PerronFrobenius theorem, quasiinvertibility, FriedlandKarlin inequalities to be employed naturally. Numerical results are presented to show that our proposed algorithms are theoretically sound and have relatively fast convergence time even for largescale problems. Index Terms—Optimization, convex relaxation, cognitive radio networks, nonnegative matrix theory. I.
Cognitive MIMO Radio: Incorporating Dynamic Spectrum Access
 in Multiuser MIMO Network”, in Proc. IEEE GLOBECOM
"... Abstract—In this paper, we develop a general mathematical framework to incorporate dynamic spectrum access in a multiuser MIMO network. This framework is particularly helpful in computing the maximum achievable system capacity of a resulting multipleband multiuser MIMO network. The mathematical f ..."
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Abstract—In this paper, we develop a general mathematical framework to incorporate dynamic spectrum access in a multiuser MIMO network. This framework is particularly helpful in computing the maximum achievable system capacity of a resulting multipleband multiuser MIMO network. The mathematical formulation to maximize the system capacity is shown to be quite similar to that of a well studied singleband multiuser MIMO network. It is further shown that the capacity maximization problem is equivalent to finding the optimal eigenvalues of the input symbol covariance matrices of the users in each frequency band. Due to the dependence of the eigenvalues on the physical characteristics of the system, such as orientation of the antennas and the channel conditions, it is difficult to achieve their optimal values in general. Because of this difficulty in achieving the optimal capacity, we also consider the suboptimal MIMO techniques (specifically beamforming) and study their capacity performance in a multipleband multiuser MIMO system. Index Terms—Cognitive radio, dynamic spectrum access, dynamic spectrum allocation, multiuser MIMO network, beamforming, nonconvex nonlinear programming. I.