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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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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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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.
Wireless Network Optimization by PerronFrobenius Theory
"... Abstract—A basic question in wireless networking is how to optimize the wireless network resource allocation for utility maximization and interference management. In this paper, we present an overview of a PerronFrobenius theoretic framework to overcome the notorious nonconvexity barriers in wirel ..."
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Abstract—A basic question in wireless networking is how to optimize the wireless network resource allocation for utility maximization and interference management. In this paper, we present an overview of a PerronFrobenius theoretic framework to overcome the notorious nonconvexity barriers in wireless utility maximization problems. Through this approach, the optimal value and solution of the optimization problems can be analytically characterized by the spectral property of matrices induced by nonlinear positive mappings. It also provides a systematic way to derive distributed and fastconvergent algorithms and to evaluate the fairness of resource allocation. This approach can even solve several previously open problems in the wireless networking literature, e.g., Kandukuri and Boyd (TWC 2002), Wiesel, Eldar and Shamai (TSP 2006), Krishnan and Luss (WCNC 2011). More generally, this approach links fundamental results in nonnegative matrix theory and (linear and nonlinear) PerronFrobenius theory with the solvability of nonconvex problems. In particular, for seemingly nonconvex problems, e.g., maxmin wireless fairness problems, it can solve them optimally; for truly nonconvex problems, e.g., sum rate maximization, it can even be used to identify polynomialtime solvable special cases or to enable convex relaxation for global optimization. To highlight the key aspects, we also present a short survey of our recent efforts in developing the nonlinear PerronFrobenius theoretic framework to solve wireless network optimization problems with applications in MIMO wireless cellular, heterogeneous smallcell and cognitive radio networks. Key implications arising from these work along with several open issues are discussed.
Egalitarian Fairness Framework for Joint Rate and Power Optimization in Wireless Networks
"... ABSTRACT How do we efficiently and fairly allocate the resource in a wireless network? We study a joint rate and power control optimization to achieve egalitarian fairness (maxmin weighted fairness) in multiuser wireless networks. The key challenge to optimizing the fairness of maximizing the data ..."
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ABSTRACT How do we efficiently and fairly allocate the resource in a wireless network? We study a joint rate and power control optimization to achieve egalitarian fairness (maxmin weighted fairness) in multiuser wireless networks. The key challenge to optimizing the fairness of maximizing the data rates for all the users is the nonconvexity and the nonlinearity of the problem. Additionally, an important requirement is the need for lowcomplexity algorithms. We exploit the nonlinear PerronFrobenius theory and nonnegative matrix theory to solve this nonconvex resource control problem. A fixedpoint algorithm that resembles a nonlinear version of the Power Method in linear algebra and converges very fast to the optimal solution is also proposed.
IEEE JOURNAL OF SELECTED AREAS IN COMMUNICATIONS 1 Beamforming Duality and Algorithms for Weighted Sum Rate Maximization in Cognitive Radio Networks
"... In this paper, we investigate the joint design of transmit beamforming and power control to maximize the weighted sum rate in the multipleinput singleoutput (MISO) cognitive radio network constrained by arbitrary power budgets and interference temperatures. The nonnegativity of the physical quanti ..."
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In this paper, we investigate the joint design of transmit beamforming and power control to maximize the weighted sum rate in the multipleinput singleoutput (MISO) cognitive radio network constrained by arbitrary power budgets and interference temperatures. The nonnegativity of the physical quantities, e.g., channel parameters, powers, and rates, is exploited to enable key tools in nonnegative matrix theory, such as the (linear and nonlinear) PerronFrobenius theory, quasiinvertibility, and FriedlandKarlin inequalities, to tackle this nonconvex problem. Under certain (quasiinvertibility) sufficient condition, we propose a tight convex relaxation technique that relaxes multiple constraints to bound the global optimal value in a systematic way. Then, a singleinput multipleoutput (SIMO)MISO duality is established through a virtual dual SIMO network and Lagrange duality. This SIMOMISO duality is equivalent to the zero Lagrange duality gap condition that connects the optimality conditions of the primal MISO network and the virtual dual SIMO network. Moreover, by exploiting the SIMOMISO duality, an algorithm is developed to solve the sum rate maximization problem optimally. Numerical examples demonstrate the computational efficiency of our algorithm when the number of transmit antennas is large. Index Terms Optimization, convex relaxation, cognitive radio network, nonnegative matrix theory, quasiinvertibility, KarushKuhnTucker conditions, PerronFrobenius theorem. I.
A Unified Framework for Wireless MaxMin Utility Optimization with General Monotonic Constraints
"... Abstract—This paper presents a unifying and systematic framework to solve wireless maxmin utility fairness optimization problems in multiuser wireless networks with generalized monotonic constraints. These problems are often challenging to solve due to their nonlinearity and nonconvexity. Our fra ..."
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Abstract—This paper presents a unifying and systematic framework to solve wireless maxmin utility fairness optimization problems in multiuser wireless networks with generalized monotonic constraints. These problems are often challenging to solve due to their nonlinearity and nonconvexity. Our framework leverages a general result in nonlinear PerronFrobenius theory to characterize the global optimal solution of these problems analytically, and to design scalable and fastconvergent algorithms for the computation of the optimal solution. This work advances the stateoftheart in handling wireless utility optimization problems with nonlinear monotonic constraints, which existing methodologies cannot handle, and also unifies previous works in this area. Several representative applications are considered to illustrate the effectiveness of the proposed framework, including maxmin quality of service subject to robust interference temperature constraints in cognitive radio networks, minmax outage subject to outage constraints in heterogeneous networks, and minmax weighted MSE subject to SINR constraints in multiuser downlink system. I.
Distributed Energy Efficient Crosslayer Optimization for Multihop MIMO Cognitive Radio Networks with Primary User Rate Protection
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1Energyefficient Nonstationary Spectrum Sharing
"... We develop a novel design framework for energyefficient spectrum sharing among autonomous users who aim to minimize their energy consumptions subject to minimum throughput requirements. Most existing works proposed stationary spectrum sharing policies, in which users transmit at fixed power levels. ..."
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We develop a novel design framework for energyefficient spectrum sharing among autonomous users who aim to minimize their energy consumptions subject to minimum throughput requirements. Most existing works proposed stationary spectrum sharing policies, in which users transmit at fixed power levels. Since users transmit simultaneously under stationary policies, to fulfill minimum throughput requirements, they need to transmit at high power levels to overcome interference. To improve energy efficiency, we construct nonstationary spectrum sharing policies, in which the users transmit at timevarying power levels. Specifically, we focus on TDMA (timedivision multiple access) policies in which one user transmits at each time (but not in a roundrobin fashion). The proposed policy can be implemented by each user running a lowcomplexity algorithm in a decentralized manner. It achieves high energy efficiency even when the users have erroneous and binary feedback about their interference levels. Moreover, it can adapt to the dynamic entry and exit of users. The proposed policy is also deviationproof, namely autonomous users will find it in their selfinterests to follow it. Compared to existing policies, the proposed policy can achieve an energy saving of up to 90 % when the number of users is high. I.