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28
Fast algorithms and performance bounds for sum rate maximization in wireless networks
 in Proceedings of IEEE INFOCOM
, 2009
"... Abstract — Sum rate maximization by power control is an important, challenging, and extensively studied problem in wireless networks. It is a nonconvex optimization problem and achieves a rate region that is in general nonconvex. We derive approximation ratios to the sum rate objective by studying t ..."
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Cited by 28 (10 self)
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Abstract — Sum rate maximization by power control is an important, challenging, and extensively studied problem in wireless networks. It is a nonconvex optimization problem and achieves a rate region that is in general nonconvex. We derive approximation ratios to the sum rate objective by studying the solutions to two related problems, sum rate maximization using an SIR approximation and maxmin weighted SIR optimization. We also show that these two problems can be solved very efficiently, using much faster algorithms than the existing ones in the literature. Furthermore, using a new parameterization of the sum rate maximization problem, we obtain a characterization of the power controlled rate region and its convexity property in various asymptotic regimes. Engineering implications are discussed for IEEE 802.11 networks. Index Terms — Duality, Distributed algorithm, Power control, Weighted sum rate maximization, Nonnegative matrices and applications,
Nonnegative matrix inequalities and their application to nonconvex power control optimization
 SIAM Journal on Matrix Analysis and Applications
"... Abstract. Maximizing the sum rates in a multiuser Gaussian channel by power control is a nonconvex NPhard problem that finds engineering application in code division multiple access (CDMA) wireless communication network. In this paper, we extend and apply several fundamental nonnegative matrix ine ..."
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Cited by 9 (7 self)
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Abstract. Maximizing the sum rates in a multiuser Gaussian channel by power control is a nonconvex NPhard problem that finds engineering application in code division multiple access (CDMA) wireless communication network. In this paper, we extend and apply several fundamental nonnegative matrix inequalities initiated by Friedland and Karlin in a 1975 paper to solve this nonconvex power control optimization problem. Leveraging tools such as the Perron–Frobenius theorem in nonnegative matrix theory, we (1) show that this problem in the power domain can be reformulated as an equivalent convex maximization problem over a closed unbounded convex set in the logarithmic signaltointerferencenoise ratio domain, (2) propose two relaxation techniques that utilize the reformulation problem structure and convexification by Lagrange dual relaxation to compute progressively tight bounds, and (3) propose a global optimization algorithm with ϵsuboptimality to compute the optimal power control allocation. A byproduct of our analysis is the application of Friedland– Karlin inequalities to inverse problems in nonnegative matrix theory.
Cognitive Radio Network Duality and Algorithms for Utility Maximization
"... Abstract—We study a utility maximization framework for spectrum sharing among cognitive secondary users and licensed primary users in cognitive radio networks. All the users maximize the network utility by adapting their signaltointerferenceplusnoise ratio (SINR) assignment and transmit power su ..."
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Cited by 8 (5 self)
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Abstract—We study a utility maximization framework for spectrum sharing among cognitive secondary users and licensed primary users in cognitive radio networks. All the users maximize the network utility by adapting their signaltointerferenceplusnoise ratio (SINR) assignment and transmit power subject to power budget constraints and additional interference temperature constraint for the secondary users. The utility maximization problem is challenging to solve optimally in a distributed manner due to the nonconvexity and the tight coupling between the power budget and interference temperature constraint sets. We first study a special case where egalitarian SINR fairness is the utility, and a tuningfree distributed algorithm with a geometric convergence rate is developed to solve it optimally. Then, we answer the general utility maximization question by developing a cognitive radio network duality to decouple the SINR assignment, the transmit power and the interference temperature allocation. This leads to a utility maximization algorithm that leverages the egalitarian fairness power control as a submodule to maintain a desirable separability in the SINR assignment between the secondary and primary users. This algorithm has the advantage that it can be distributively implemented, and the method converges relatively fast. Numerical results are presented to show that our proposed algorithms are theoretically sound and practically implementable. Index Terms—Optimization, network utility maximization, cognitive radio networks, spectrum allocation. I.
Joint beamforming and power control in coordinated multicell: Maxmin duality, effective network and large system transition
 IEEE TRANS. WIRELESS COMMUN
, 2013
"... This paper studies joint beamforming and power control in a coordinated multicell downlink system that serves multiple users per cell to maximize the minimum weighted signaltointerferenceplusnoise ratio. The optimal solution and distributed algorithm with geometrically fast convergence rate are ..."
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Cited by 8 (1 self)
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This paper studies joint beamforming and power control in a coordinated multicell downlink system that serves multiple users per cell to maximize the minimum weighted signaltointerferenceplusnoise ratio. The optimal solution and distributed algorithm with geometrically fast convergence rate are derived by employing the nonlinear PerronFrobenius theory and the multicell network duality. The iterative algorithm, though operating in a distributed manner, still requires instantaneous power update within the coordinated cluster through the backhaul. The backhaul information exchange and message passing may become prohibitive with increasing number of transmit antennas and increasing number of users. In order to derive asymptotically optimal solution, random matrix theory is leveraged to design a distributed algorithm that only requires statistical information. The advantage of our approach is that there is no instantaneous power update through backhaul. Moreover, by using nonlinear PerronFrobenius theory and random matrix theory, an effective primal network and an effective dual network are proposed to characterize and interpret the asymptotic solution.
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.
Routing, Scheduling and Power Allocation in Generic OFDMA Wireless Networks: Optimal Design and Efficiently Computable Bounds
"... Abstract—The goal of this paper is to determine the data routes, subchannel schedules, and power allocations that maximize a weightedsum rate of the data communicated over a generic OFDMA wireless network in which the nodes are capable of simultaneously transmitting, receiving and relaying data. T ..."
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Cited by 4 (4 self)
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Abstract—The goal of this paper is to determine the data routes, subchannel schedules, and power allocations that maximize a weightedsum rate of the data communicated over a generic OFDMA wireless network in which the nodes are capable of simultaneously transmitting, receiving and relaying data. Two instances are considered. In the first instance, subchannels are allowed to be timeshared by multiple links, whereas in the second instance, each subchannel is exclusively used by one of the links. Using a change of variables, the first problem is transformed into a convex form. In contrast, the second problem is not amenable to such a transformation and results in a complex mixed integer optimization problem. To develop insight into this problem, we utilize the first instance to obtain efficiently computable lower and upper bounds on the weightedsum rate that can be achieved in the absence of timesharing. Another lower bound is obtained by enforcing the scheduling constraints through additional power constraints and a monomial approximation technique to formulate the design problem as a geometric program. Numerical investigations show that the obtained rates are higher when timesharing is allowed, and that the lower bounds on rates in the absence of timesharing are relatively tight. Index Terms—Crosslayer design, geometric programming, monomial approximation, timesharing, selfconcordance. I.
On the maximum achievable sumrate with successive decoding in interference channels
 IEEE Trans. Inf. Theory
, 2012
"... Abstract—In this paper, we investigate the maximum achievable sumrate of the twouser Gaussian interference channel with Gaussian superposition coding and successive decoding. We first examine an approximate deterministic formulation of the problem, and introduce the complementarity conditions that ..."
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Cited by 4 (1 self)
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Abstract—In this paper, we investigate the maximum achievable sumrate of the twouser Gaussian interference channel with Gaussian superposition coding and successive decoding. We first examine an approximate deterministic formulation of the problem, and introduce the complementarity conditions that capture the use of Gaussian coding and successive decoding. In the deterministic channel problem, we find the constrained sumcapacity and its achievable schemes with the minimum number of messages, first in symmetric channels, and then in general asymmetric channels. We show that the constrained sumcapacity oscillates as a function of the cross link gain parameters between the information theoretic sumcapacity and the sumcapacity with interference treated as noise. Furthermore, we show that if the number of messages of either of the two users is fewer than the minimum number required to achieve the constrained sumcapacity, the maximum
On the SCALE algorithm for multiuser multicarrier power spectrum management
 IEEE Trans. Signal Process
, 2012
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Slow Admission and Power Control for Small Cell Networks via Distributed Optimization
"... Abstract—Although small cell networks are environmentally friendly and can potentially improve the coverage and capacity of cellular layers, it is imperative to control the interference in such networks before overlaying them in a macrocell network on a largescale basis. In recent work, we develope ..."
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Cited by 2 (0 self)
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Abstract—Although small cell networks are environmentally friendly and can potentially improve the coverage and capacity of cellular layers, it is imperative to control the interference in such networks before overlaying them in a macrocell network on a largescale basis. In recent work, we developed the joint admission and power control algorithm for twotier small cell networks in which the number of small cell users that can be admitted at their qualityofservice (QoS) constraints is maximized without violating the macrocell users ’ QoS constraints. The QoS metric adopted is outage probability. In this paper, we investigate the distributed implementation of the joint admission and power control problem where the small cells can determine jointly their admissibility and transmit powers autonomously. I.
EnergyInfeasibility Tradeoff in Cognitive Radio Networks: PriceDriven Spectrum Access Algorithms
"... Abstract—We study the feasibility of the total power minimization problem subject to power budget and SignaltoInterferenceplusNoise Ratio (SINR) constraints in cognitive radio networks. As both the primary and the secondary users are allowed to transmit simultaneously on a shared spectrum, unco ..."
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Cited by 1 (1 self)
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Abstract—We study the feasibility of the total power minimization problem subject to power budget and SignaltoInterferenceplusNoise Ratio (SINR) constraints in cognitive radio networks. As both the primary and the secondary users are allowed to transmit simultaneously on a shared spectrum, uncontrolled access of secondary users degrades the performance of primary users and can even lead to system infeasibility. To find the largest feasible set of secondary users (i.e., the system capacity) that can be supported in the network, we formulate a vectorcardinality optimization problem. This nonconvex problem is however hard to solve, and we propose a convex relaxation heuristic based on the sumofinfeasibilities in optimization theory. Our methodology leads to the notion of admission price for spectrum access that can characterize the tradeoff between the total energy consumption and the system capacity. Pricedriven algorithms for joint power and admission control are then proposed that quantify the benefits of energyinfeasibility balance. Numerical results are presented to show that our algorithms are theoretically sound and practically implementable. Index Terms—Optimization, cognitive radio networks, spectrum access control, power and admission control. I.