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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.
Offline Power Allocation and Spectrum Sensing Strategy in EnergyHarvesting Cognitive Radio Networks
"... Energyharvesting cognitive radio network has emerged as a solution to increase energy and spectrum efficiency. In this thesis, we propose shortterm offline optimal power allocation algorithms for multiuser energyharvesting cognitive radio networks considering interference between secondary user ..."
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Energyharvesting cognitive radio network has emerged as a solution to increase energy and spectrum efficiency. In this thesis, we propose shortterm offline optimal power allocation algorithms for multiuser energyharvesting cognitive radio networks considering interference between secondary users. Assuming finite and rechargeable batteries for secondary users and a timeslotted operation model, an offline optimization problem is formulated so as to maximize the network throughput during finite timeperiod. To that aim, the design of a power allocation and the spectrum sensing strategy is required. Together with the inherent constraints imposed by the use of energyharvesting devices, a collision constraint is also required to limit the probability of interference with the primary user and to guarantee the quality of service. Because of the intractability of the power allocation problem in the interference channel, we spilt the optimization task for two different size cognitive radio networks: a) 2user
Subspace Communication
, 2014
"... We are surrounded by electronic devices that take advantage of wireless technologies, from our computer mice, which require little amounts of information, to our cellphones, which demand increasingly higher data rates. Until today, the coexistence of such a variety of services has been guaranteed by ..."
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We are surrounded by electronic devices that take advantage of wireless technologies, from our computer mice, which require little amounts of information, to our cellphones, which demand increasingly higher data rates. Until today, the coexistence of such a variety of services has been guaranteed by a fixed assignment of spectrum resources by regulatory agencies. This has resulted into a blind alley, as current wireless spectrum has become an expensive and a scarce resource. However, recent measurements in dense areas paint a very different picture: there is an actual underutilization of the spectrum by legacy systems. Cognitive radio exhibits a tremendous promise for increasing the spectral efficiency for future wireless systems. Ideally, new secondary users would have a perfect panorama of the spectrum usage, and would opportunistically communicate over the available resources without degrading the primary systems. Yet in practice, monitoring the spectrum resources, detecting available resources for opportunistic communication, and transmitting over the resources are hard tasks. This thesis addresses the tasks of monitoring, de
Spectrum Sharing For DelaySensitive Applications With Continuing QoS Guarantees
"... AbstractWe study a wireless network in which multiple users stream delaysensitive applications such as video conferencing and video streaming. Existing spectrum sharing policies, which determine when users access the spectrum and at what power levels, are either constant (i.e. users transmit simu ..."
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AbstractWe study a wireless network in which multiple users stream delaysensitive applications such as video conferencing and video streaming. Existing spectrum sharing policies, which determine when users access the spectrum and at what power levels, are either constant (i.e. users transmit simultaneously, at constant power levels) or weighted roundrobin timedivision multiple access (TDMA) (i.e. users access the spectrum in turn, one at a time). Due to multiuser interference, constant policies have low spectrum efficiency. We show that roundrobin policies are inefficient for delaysensitive applications because the various "positions" (i.e. transmission opportunities) in a cycle are not created equal: earlier transmission opportunities are more desirable since they enable users to transmit with lower delays. Specifically, we show that (weighted) roundrobin TDMA policies cannot simultaneously achieve high network performance and low transmission delays. This problem is exacerbated when the number of users is large. We propose a novel framework for designing optimal TDMA spectrum sharing policies for delaysensitive applications, which can guarantee their continuing QoS (CQoS), i.e. the desired throughput (and the resulting transmission delay) starting from every moment in time is guaranteed for each user. We prove that the fulfillment of CQoS guarantees provides strict upper bounds on the transmission delays incurred by the users. We construct the optimal TDMA policy that maximizes the desired network performance (e.g. maxmin fairness or social welfare) subject to the users' CQoS guarantees. The key feature of the proposed policy is that it is not cyclic as in (weighted) roundrobin policies. Instead, it adaptively determines which user should transmit next, based on the users' remaining amounts of transmission opportunities needed to achieve the desired performance. We also propose a lowcomplexity algorithm, which is run by each user in a distributed manner, to construct the optimal policy. Simulation results demonstrate that our proposed policy significantly outperforms the optimal constant policy and roundrobin policies by up to 6 dB and 4 dB in peak signaltonoise ratio (PSNR) for video streaming.
Spectrum Optimization in MultiUser MultiCarrier Systems with Iterative Convex and Nonconvex Approximation Methods
, 2013
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Optimization of Perron eigenvectors and applications: From web ranking to chronotherapeutics
, 2012
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Scheduling using Optimization Decomposition in Wireless Network with Time Performance Analysis
"... ABSTRACT: Virtualization is a key technology underlying multi server computing platforms, where applications encapsulated within Virtual Machines are dynamically mapped onto a pool of physical servers. In this paper, we argue that multi server providers can significantly lower operational costs, an ..."
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ABSTRACT: Virtualization is a key technology underlying multi server computing platforms, where applications encapsulated within Virtual Machines are dynamically mapped onto a pool of physical servers. In this paper, we argue that multi server providers can significantly lower operational costs, and improve hosted application performance, by accounting for affinities and conflicts between coplaced Virtual Machines. The estimated Virtual Machine size is the basis for allocating resources commensurate with demand. In contrast to the traditional practice of estimating the size of Virtual Machines individually, we propose a jointvirtual machine provisioning approach in which multiple virtual machines are consolidated and provisioned together, based on an estimate of their aggregate capacity needs. This new approach exploits statistical multiplexing among the workload patterns of multiple virtual machines, i.e., the peaks and valleys in one workload pattern do not necessarily coincide with the others. Thus, the unused resources of a low utilized virtual machine can be borrowed by the other colocated virtual machines with high utilization. Compared to individualvirtual machine based provisioning; jointvirtual machine provisioning could lead to much higher resource utilization. This paper presents three design modules to enable such a concept in practice. Specifically, a performance constraint describing the capacity need of a virtual machine for achieving a certain level of application performance; an algorithm for estimating the aggregate size of multiplexed virtual machines; a virtual machine selection algorithm that seeks to find those virtual machine combinations with complementary workload patterns.
Wideband Cognitive Radio: . . . Subspace Communication
, 2014
"... We are surrounded by electronic devices that take advantage of wireless technologies, from our computer mice, which require little amounts of information, to our cellphones, which demand increasingly higher data rates. Until today, the coexistence of such a variety of services has been guaranteed by ..."
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We are surrounded by electronic devices that take advantage of wireless technologies, from our computer mice, which require little amounts of information, to our cellphones, which demand increasingly higher data rates. Until today, the coexistence of such a variety of services has been guaranteed by a fixed assignment of spectrum resources by regulatory agencies. This has resulted into a blind alley, as current wireless spectrum has become an expensive and a scarce resource. However, recent measurements in dense areas paint a very different picture: there is an actual underutilization of the spectrum by legacy systems. Cognitive radio exhibits a tremendous promise for increasing the spectral efficiency for future wireless systems. Ideally, new secondary users would have a perfect panorama of the spectrum usage, and would opportunistically communicate over the available resources without degrading the primary systems. Yet in practice, monitoring the spectrum resources, detecting available resources for opportunistic communication, and transmitting over the resources are hard tasks. This thesis addresses the tasks of monitoring, de
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.
Secrecy Capacity Scaling of LargeScale Cognitive Networks
"... Increasingly, more spectrum bands are utilized for unlicensed use in wireless cognitive networks. It is important to study how informationtheoretic secrecy capacity is affected in largescale cognitive networks. We consider two scenarios: (1) noncolluding case, where eavesdroppers decode messages ..."
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Increasingly, more spectrum bands are utilized for unlicensed use in wireless cognitive networks. It is important to study how informationtheoretic secrecy capacity is affected in largescale cognitive networks. We consider two scenarios: (1) noncolluding case, where eavesdroppers decode messages individually. In this case, we propose a new secure protocol model to analyze the transmission opportunities of secondary nodes. We show that the secrecy capacity of the primary network is not affected, while the secondary network can achieve the same performance as a standalone network in the order sense. Since our analysis is general as we only make a few relaxed assumptions on both networks, the conclusions hold when both networks are classic static networks, networks with i.i.d mobility, multicast networks etc. (2) colluding case where eavesdroppers can collude to decode a message. In that case, we show that the lower bound of pernode secrecy capacity of the primary network is Ω ( 1√