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27
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,
Spectrummanagement in multiuser cognitive wireless networks: Optimality and algorithms
 IEEE J. Selected Areas Commun
"... Abstract—Spectrum management is used to improve performance in multiuser communication system, e.g., cognitive radio or femtocell networks, where multiuser interference can lead to data rate degradation. We study the nonconvex NPhard problem of maximizing a weighted sum rate in a multiuser Gaussia ..."
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Cited by 27 (11 self)
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Abstract—Spectrum management is used to improve performance in multiuser communication system, e.g., cognitive radio or femtocell networks, where multiuser interference can lead to data rate degradation. We study the nonconvex NPhard problem of maximizing a weighted sum rate in a multiuser Gaussian interference channel by power control subject to affine power constraints. By exploiting the fact that this problem can be restated as an optimization problem with constraints that are spectral radii of specially crafted nonnegative matrices, we derive necessary and sufficient optimality conditions and propose a global optimization algorithm based on the outer approximation method. Central to our techniques is the use of nonnegative matrix theory, e.g., nonnegative matrix inequalities and the PerronFrobenius theorem. We also study an inner approximation method and a relaxation method that give insights to special cases. Our techniques and algorithm can be extended to a multiple carrier system model, e.g., OFDM system or receivers with interference suppression capability. Index Terms—Optimization, nonnegative matrix theory, dynamic spectrum access, power control, cognitive wireless networks. I.
A unified analysis of maxmin weighted SINR for MIMO downlink system
 IEEE Trans. Signal Process
, 2011
"... Abstract—This paper studies the maxmin weighted signaltointerferenceplusnoise ratio (SINR) problem in the multipleinputmultipleoutput (MIMO) downlink, where multiple users are weighted according to priority and are subject to a weightedsumpower constraint. First, we study the multiplein ..."
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Cited by 13 (4 self)
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Abstract—This paper studies the maxmin weighted signaltointerferenceplusnoise ratio (SINR) problem in the multipleinputmultipleoutput (MIMO) downlink, where multiple users are weighted according to priority and are subject to a weightedsumpower constraint. First, we study the multipleinputsingleoutput (MISO) and singleinputmultipleoutput (SIMO) problems using nonlinear Perron–Frobenius theory. As a byproduct, we solve the open problem of convergence for a previously proposed MISO algorithm by Wiesel, Eldar, and Shamai in 2006. Furthermore, we unify our analysis with respect to the previous alternate optimization algorithm proposed by Tan, Chiang, and Srikant in 2009, by showing that our MISO result can, in fact, be derived from their algorithm. Next, we combine our MISO and SIMO results into an algorithm for the MIMO problem. We show that our proposed algorithm is optimal when the channels are rankone, or when the network is operating in the low signaltonoise ratio (SNR) region. Finally, we prove the parametric continuity of the MIMO problem in the power constraint, and we use this insight to propose a heuristic initialization strategy for improving the performance of our (generally) suboptimal MIMO algorithm. The proposed initialization strategy exhibits improved performance over random initialization. Index Terms—Beamforming, multipleinput–multipleoutput (MIMO), uplink–downlink duality.
Optimal power control in Rayleighfading heterogeneous networks
 in Proc. IEEE INFOCOM
, 2011
"... Abstract—Heterogeneous wireless networks employ varying degrees of network coverage using power control in a multitier configuration, where lowpower femtocells are used to enhance performance, e.g., optimize outage probability. We study the worst outage probability problem under Rayleigh fading. A ..."
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Cited by 13 (5 self)
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Abstract—Heterogeneous wireless networks employ varying degrees of network coverage using power control in a multitier configuration, where lowpower femtocells are used to enhance performance, e.g., optimize outage probability. We study the worst outage probability problem under Rayleigh fading. As a byproduct, we solve an open problem of convergence for a previously proposed algorithm in the interferencelimited case. We then address a total power minimization problem with outage specification constraints and its feasibility condition. We propose a dynamic algorithm that adapts the outage probability specification in a heterogeneous network to minimize the total energy consumption and simultaneously guarantees all the femtocell users a minmax fairness in terms of the worst outage probability. Index Terms — Optimization, nonnegative matrix theory, outage probability, power control, femtocell networks.
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.
Maxmin SINR coordinated multipoint downlink transmission–duality and algorithms
 IEEE Trans. Signal Process
, 2012
"... Abstract—This paper considers the maxmin weighted signaltointerferenceplusnoise ratio (SINR) problem subject to multiple weightedsum power constraints, where the weights can represent relative power costs of serving different users. First, we study the power control problem. We apply nonlinear ..."
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Cited by 8 (3 self)
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Abstract—This paper considers the maxmin weighted signaltointerferenceplusnoise ratio (SINR) problem subject to multiple weightedsum power constraints, where the weights can represent relative power costs of serving different users. First, we study the power control problem. We apply nonlinear PerronFrobenius theory to derive closedform expressions for the optimal value and solution and an iterative algorithm which converges geometrically fast to the optimal solution. Then, we use the structure of the closedform solution to show that the problem can be decoupled into subproblems each involving only one power constraint. Next, we study the multipleinputsingleoutput (MISO) transmit beamforming and power control problem. We use uplinkdownlink duality to show that this problem can be decoupled into subproblems each involving only one power constraint. We apply this decoupling result to derive an iterative subgradient projection algorithm for the problem. Index Terms—Beamforming, multipleinputmultipleoutput (MIMO), uplinkdownlink duality.
Giannakis, “Distributed optimal beamformers for cognitive radios robust to channel uncertainties
 IEEE Trans. Sig. Proc
, 2012
"... Abstract—Through spatial multiplexing and diversity, multiinput multioutput (MIMO) cognitive radio (CR) networks can markedly increase transmission rates and reliability, while controlling the interference inflicted to peer nodes and primary users (PUs) via beamforming. The present paper optimiz ..."
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Cited by 7 (1 self)
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Abstract—Through spatial multiplexing and diversity, multiinput multioutput (MIMO) cognitive radio (CR) networks can markedly increase transmission rates and reliability, while controlling the interference inflicted to peer nodes and primary users (PUs) via beamforming. The present paper optimizes the design of transmit and receivebeamformers for ad hoc CR networks when CRtoCR channels are known, but CRtoPU channels cannot be estimated accurately. Capitalizing on a normbounded channel uncertainty model, the optimal beamforming design is formulated to minimize the overall meansquare error (MSE) from all data streams, while enforcing protection of the PU system when the CRtoPU channels are uncertain. Even though the resultant optimization problem is nonconvex, algorithms with provable convergence to stationary points are developed by resorting to block coordinate ascent iterations, along with suitable convex approximation techniques. Enticingly, the novel schemes also lend themselves naturally to distributed implementations. Numerical tests are reported to corroborate the analytical findings. Index Terms—Beamforming, channel uncertainty, cognitive radios, distributed algorithms, MIMO wireless networks, robust optimization. I.
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.