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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.
Efficient Resource Scheduling for a Secondary Network in Shared Spectrum
"... Abstract—With limited opportunities to open up new unencumbered bands to mobile wireless services, interest in enhancing methods for sharing of spectrum between services is high. For example, the band 16951710 MHz is expected to be made available to 3GPP LongTerm Evolution cellular network uplin ..."
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Abstract—With limited opportunities to open up new unencumbered bands to mobile wireless services, interest in enhancing methods for sharing of spectrum between services is high. For example, the band 16951710 MHz is expected to be made available to 3GPP LongTerm Evolution cellular network uplinks by sharing with incumbent meteorological satellite services already in the band. The LTE networks are to be operated in a manner that ensures no loss of incumbent capability by adhering to protection requirements such as a limit on the aggregate interference power at fixed incumbent earth station locations. In this paper, we consider this specific spectrum sharing scenario as motivation and formulate an optimization framework for power control and timefrequency resource scheduling on the LTE uplink with an aggregate interference constraint. We design and propose a novel algorithm inspired by numerical solution and analysis of the optimization problem. Using theory and simulation, we show that our algorithm significantly outperforms more simplistic approaches, well approximates the optimal solution, and is of sufficient scope and complexity for practical implementation, even in relatively large LTE networks. Algorithms of this kind are necessary for mobile wireless networks to make the most of constrained spectrum resources in shared bands. I.