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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.
Maximizing Sum Rate and Minimizing MSE on Multiuser Downlink: Optimality, Fast Algorithms and Equivalence via Maxmin SIR
"... Maximizing the minimum weighted SIR, minimizing the weighted sum MSE and maximizing the weighted sum rate in a multiuser downlink system are three important performance objectives in joint transceiver and power optimization, where all the users have a total power constraint. We show that, through co ..."
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Cited by 27 (13 self)
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Maximizing the minimum weighted SIR, minimizing the weighted sum MSE and maximizing the weighted sum rate in a multiuser downlink system are three important performance objectives in joint transceiver and power optimization, where all the users have a total power constraint. We show that, through connections with the nonlinear PerronFrobenius theory, jointly optimizing power and beamformers in the maxmin weighted SIR problem can be solved optimally in a distributed fashion. Then, connecting these three performance objectives through the arithmeticgeometric mean inequality and nonnegative matrix theory, we solve the weighted sum MSE minimization and the weighted sum rate maximization in the low to moderate interference regimes using fast algorithms. In the general case, we first establish the optimality conditions to the weighted sum MSE minimization and the weighted sum rate maximization problems and provide their further connection to the maxmin weighted SIR problem. We then propose a distributed weighted proportional SIR algorithm that leverages our fast maxmin weighted SIR algorithm to solve the two nonconvex problems, and give conditions under which global optimality is achieved. Numerical results are provided to complement the analysis.
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.
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.
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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Cited by 1 (1 self)
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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.
1Spectrum Management in Multiuser Cognitive Wireless Networks: Optimality and Algorithm
"... 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 throughput degradation. We study the nonconvex NPhard problem of maximizing a weighted sum rate in a multiuser Gaus ..."
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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 throughput 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.
Link Energy Minimization in IRUWB Based . . .
 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, ACCEPTED FOR PUBLICATION
, 2010
"... Impulse Radio Ultra WideBand (IRUWB) communication has proven to be an important technique for supporting highrate, shortrange, and lowpower communication. In this paper, using detailed models of typical IRUWB transmitter and receiver structures, we model the energy consumption per information ..."
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Impulse Radio Ultra WideBand (IRUWB) communication has proven to be an important technique for supporting highrate, shortrange, and lowpower communication. In this paper, using detailed models of typical IRUWB transmitter and receiver structures, we model the energy consumption per information bit in a single link of an IRUWB system, considering packet overhead, retransmissions, and a Nakagamim fading channel. Using this model, we minimize the energy consumption per information bit by finding the optimum packet length and the optimum number of RAKE fingers at the receiver for different transmission distances, using Differential Phaseshift keying (DBPSK), Differential Pulseposition Modulation (DPPM) and Onoff Keying (OOK), with coherent and noncoherent detection. Symbol repetition schemes with hard decision (HD) combining and soft decision (SD) combining are also compared in this paper. Our results show that at very short distances, it is optimum to use large packets, OOK with noncoherent detection, and HD combining, while at longer distances, it is optimum to use small packets, DBPSK with coherent detection, and SD combining. The optimum number of RAKE fingers are also found for given transmission schemes.
Generalized Perron–Frobenius Theorem for Nonsquare Matrices
, 2014
"... The celebrated Perron–Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of sci ..."
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The celebrated Perron–Frobenius (PF) theorem is stated for irreducible nonnegative square matrices, and provides a simple characterization of their eigenvectors and eigenvalues. The importance of this theorem stems from the fact that eigenvalue problems on such matrices arise in many fields of science and engineering, including dynamical systems theory, economics, statistics and optimization. However, many reallife scenarios give rise to nonsquare matrices. Despite the extensive development of spectral theories for nonnegative matrices, the applicability of such theories to nonconvex optimization problems is not clear. In particular, a natural question is whether the PF Theorem (along with its applications) can be generalized to a nonsquare setting. Our paper provides a generalization of the PF Theorem to nonsquare matrices. The extension can be interpreted as representing clientserver systems with additional degrees of freedom, where each client may choose between multiple servers that can cooperate in serving it (while potentially interfering with other clients). This formulation is motivated by applications to power control in