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QoS and Fairness Constrained Convex Optimization of Resource Allocation for Wireless Cellular and Ad Hoc Networks
 in Proc. IEEE Infocom
, 2002
"... For wireless cellular and ad hoc networks with QoS constraints, we propose a suite of problem formulations that allocate network resources to optimize SIR, maximize throughput and minimize delay. The distinguishing characteristics of these resource allocation formulations is that, by using convex op ..."
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Cited by 68 (10 self)
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For wireless cellular and ad hoc networks with QoS constraints, we propose a suite of problem formulations that allocate network resources to optimize SIR, maximize throughput and minimize delay. The distinguishing characteristics of these resource allocation formulations is that, by using convex optimization, they accommodate a variety of realistic QoS and fairness constraints. Their globally optimal solutions can be computed efficiently through polynomial time interior point methods, even though they use nonlinear objectives and constraints.
Power control by geometric programming
 IEEE Trans. on Wireless Commun
, 2005
"... Abstract — In wireless cellular or ad hoc networks where Quality of Service (QoS) is interferencelimited, a variety of power control problems can be formulated as nonlinear optimization with a systemwide objective, e.g., maximizing the total system throughput or the worst user throughput, subject ..."
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Cited by 40 (5 self)
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Abstract — In wireless cellular or ad hoc networks where Quality of Service (QoS) is interferencelimited, a variety of power control problems can be formulated as nonlinear optimization with a systemwide objective, e.g., maximizing the total system throughput or the worst user throughput, subject to QoS constraints from individual users, e.g., on data rate, delay, and outage probability. We show that in the high SignaltoInterference Ratios (SIR) regime, these nonlinear and apparently difficult, nonconvex optimization problems can be transformed into convex optimization problems in the form of geometric programming; hence they can be very efficiently solved for global optimality even with a large number of users. In the medium to low SIR regime, some of these constrained nonlinear optimization of power control cannot be turned into tractable convex formulations, but a heuristic can be used to compute in most cases the optimal solution by solving a series of geometric programs through the approach of successive convex approximation. While efficient and robust algorithms have been extensively studied for centralized solutions of geometric programs, distributed algorithms have not been explored before. We present a systematic method of distributed algorithms for power control that is geometricprogrammingbased. These techniques for power control, together with their implications to admission control and pricing in wireless networks, are illustrated through several numerical examples. Index Terms — Convex optimization, CDMA power control, Distributed algorithms. I.
the Complexity and Distributed Construction of EnergyEfficient Broadcast Trees
 in Static and Ad Hoc Wireless Networks,” Proc. CISS
, 2002
"... Abstract—This paper addresses the energyefficient broadcasting problem in ad hoc wireless networks. First, we show that finding the minimumenergy broadcast tree is NPcomplete. We then develop a distributed clustering algorithm that computes energyefficient broadcast trees in polynomial time. Our ..."
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Cited by 30 (3 self)
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Abstract—This paper addresses the energyefficient broadcasting problem in ad hoc wireless networks. First, we show that finding the minimumenergy broadcast tree is NPcomplete. We then develop a distributed clustering algorithm that computes energyefficient broadcast trees in polynomial time. Our distributed algorithm computes all N possible broadcast trees simultaneously, while requiring O(N 2) messages to be exchanged between nodes. We compare our algorithm’s performance to the bestknown centralized algorithm, and show that it constructs trees consuming, on average, only 18 % more energy. We also consider the possibility of having multiple source nodes that can be used to broadcast the message and adapt our algorithm to compute energyefficient broadcast trees with multiple source nodes. We observe a reduction in the amount of energy needed to form the broadcast tree that is linear in the number of source nodes. Index Terms—Broadcast, complexity, energy efficiency, wireless networks. I.
Simultaneous routing and power allocation in CDMA wireless data networks
 IEEE Trans. on Communications
, 2003
"... Abstract — The optimal routing of data in a wireless network depends on the link capacities, which, in turn, are determined by the allocation of transmit powers across the network. Thus, the optimal network performance can only be achieved by simultaneous optimization of routing and power allocation ..."
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Cited by 22 (2 self)
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Abstract — The optimal routing of data in a wireless network depends on the link capacities, which, in turn, are determined by the allocation of transmit powers across the network. Thus, the optimal network performance can only be achieved by simultaneous optimization of routing and power allocation. In this paper, we study this joint optimization problem in CDMA data networks using convex optimization techniques. Although link capacity constraints of CDMA systems are not jointly convex in rates and powers, we show that coordinate projections or transformations allow the simultaneous routing and power allocation problem to be formulated as (in systems with interference cancellation) or approximated by (in systems without interference cancellation) a convex optimization problem which can be solved very efficiently. We also propose a heuristic linkremoval procedure based on the convex approximation to further improve the system performance. I.
Resource Allocation for QoS Provisioning in Wireless Ad Hoc Networks
 Proc. IEEE Globecom
, 2001
"... For wireless ad hoc networks with multihop transmissions and Rayleigh fading, this paper maximizes the overall system throughput subject to QoS constraints on power, probability of outage, and data rates. Formulations are also given which minimize delay and optimize network resources in a wireless a ..."
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Cited by 5 (1 self)
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For wireless ad hoc networks with multihop transmissions and Rayleigh fading, this paper maximizes the overall system throughput subject to QoS constraints on power, probability of outage, and data rates. Formulations are also given which minimize delay and optimize network resources in a wireless ad hoc network, where each link is shared by multiple streams of traffic from different QoS classes, and each traffic traverses many links. Although these optimal resource allocation problems are nonlinear, they can be posed as geometric programs, which are transformed into convex optimizations, and can be solved globally and efficiently through interiorpoint methods.
Localized Access Point Association in Wireless LANs with Bounded Approximation Ratio
"... The current access point (AP) association schemes in wireless LANs, such as IEEE 802.11, cause an unbalanced load which reduces the performance of both the entire network and individual users. Intensive studies were motivated to determine efficient methods of balancing loads among APs. Previous work ..."
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Cited by 3 (3 self)
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The current access point (AP) association schemes in wireless LANs, such as IEEE 802.11, cause an unbalanced load which reduces the performance of both the entire network and individual users. Intensive studies were motivated to determine efficient methods of balancing loads among APs. Previous works provided either the heuristics without theoretical analysis on the performance, or algorithms that require a centralized node or the propagation of global information. In this paper, we model the AP association problem as the manytoone matching problem in the bipartite graph. Our objective is to maximize the total load among all APs. We propose a localized algorithm that provides a bounded approximation ratio in terms of total load and does not require the propagation of local information. We also extend the localized algorithm through iterative executions, and allow for adaptation to various environments. Extensive simulations are conducted to verify our results.
On Multicast Beamforming for Minimum Outage
"... Abstract—The multicast beamforming problem is considered from the viewpoint of minimizing outage probability subject to a transmit power constraint. The main difference with the pointtopoint transmit beamforming problem is that in multicast beamforming the channel is naturally modeled as a Gaussia ..."
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Cited by 1 (1 self)
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Abstract—The multicast beamforming problem is considered from the viewpoint of minimizing outage probability subject to a transmit power constraint. The main difference with the pointtopoint transmit beamforming problem is that in multicast beamforming the channel is naturally modeled as a Gaussian mixture, as opposed to a single Gaussian distribution. The Gaussian components in the mixture model user clusters of different means (locations) and variances (spreads). It is shown that minimizing outage probability subject to a transmit power constraint is an NPhard problem when the number of Gaussian kernels, J, is greater than or equal to the number of transmit antennas, N. Through dimensionality reduction, it is also shown that the problem is practically tractable for 2 − 3 Gaussian kernels. An approximate solution based on the Markov inequality is also proposed. This is simple to compute for any J and N, and often works well in practice. Index Terms—Multicast beamforming, outage probability, transmit power constraint. I.
Nonconvex Optimization for Communication Networks
"... Nonlinear convex optimization has provided both an insightful modeling language and a powerful solution tool to the analysis and design of communication systems over the last decade. A main challenge today is on nonconvex problems in these applications. This chapter presents an overview on some of ..."
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Nonlinear convex optimization has provided both an insightful modeling language and a powerful solution tool to the analysis and design of communication systems over the last decade. A main challenge today is on nonconvex problems in these applications. This chapter presents an overview on some of the important nonconvex optimization problems in communication networks. Four typical applications are covered: Internet congestion control through nonconcave network utility maximization, wireless network power control through geometric and sigmoidal programming, DSL spectrum management through distributed nonconvex optimization, and Internet intradomain routing through nonconvex, nonsmooth optimization. A variety of nonconvex optimization techniques are showcased: sumofsquares programming through successive SDP relaxation, signomial programming through successive GP relaxation, leveraging specific structures in these engineering problems for efficient and distributed heuristics, and changing the underlying protocol to enable a different problem formulation in the first place. Collectively, they illustrate three alternatives of tackling nonconvex optimization for communication networks: going “through” nonconvexity, “around” nonconvexity, and “above” nonconvexity.
1 Allocating Resources to Multiple Antenna Mobile Nodes in Fading Wireless AdHoc Networks with Temporally Correlated Loss
"... Abstract — Addressing the tradeoff between the QoS and consumed power is a critical issue for wireless adhoc networks. The loss observed in such networks is often temporally correlated. Multiple antenna systems utilizing spacetime block codes are gaining increasing popularity as the result of bein ..."
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Abstract — Addressing the tradeoff between the QoS and consumed power is a critical issue for wireless adhoc networks. The loss observed in such networks is often temporally correlated. Multiple antenna systems utilizing spacetime block codes are gaining increasing popularity as the result of being adopted by different wireless standards. This paper focuses on optimal resource allocation schemes for wireless adhoc networks with mobile nodes utilizing spacetime block codes. Relying on adaptive modulation techniques for multiple antenna systems, this paper examines optimal schemes of maximizing throughput under power and loss constraints as well as minimizing transmission power under throughput and loss constraints. In order to properly model temporally correlated loss observed in a fading wireless channel, we propose the use of finitestate Markov chains. Details of fading statistics of signaltointerference ratio (SIR), an important indicator of transmission quality, are presented. We also analyze the impacts of enforcing power, blockloss probabilities, and throughput constraints in conjunction with the use of spacetime block codes.
Efficient Optimization of Constrained Nonlinear Resource Allocations ∗ Mung Chiang
"... We present an efficient method to optimize network resource allocations under nonlinear Quality of Service (QoS) constraints. We first propose a suite of generalized proportional allocation schemes that can be obtained by minimizing the informationtheoretic function of relative entropy. We then opt ..."
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We present an efficient method to optimize network resource allocations under nonlinear Quality of Service (QoS) constraints. We first propose a suite of generalized proportional allocation schemes that can be obtained by minimizing the informationtheoretic function of relative entropy. We then optimize over the allocation parameters, which are usually design variables an engineer can directly vary, either for a particular user or for the worstcase user, under constraints that lower bound the allocated resources for all other users. Despite the nonlinearity in the objective and constraints, we show this suite of resource allocation optimization can be efficiently solved for global optimality through a convex optimization technique called geometric programming. This general method and its extensions are applicable to a wide array of resource allocation problems, including processor sharing, congestion control, admission control, and wireless network power control. We focus on several specific formulations and numerical examples for an admission control scheme, and for power control problems of throughput maximization under outage and delay constraints for wireless multihop networks.