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.

Abstract — In wireless cellular or ad hoc networks where Quality of Service (QoS) is interference-limited, a variety of power control problems can be formulated as nonlinear optimization with a system-wide 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 Signal-to-Interference 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 geometric-programming-based. 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.

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 non-linear, they can be posed as geometric programs, which are transformed into convex optimizations, and can be solved globally and efficiently through interior-point methods.

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 many-to-one 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.

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 point-to-point 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 NP-hard 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.

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: sum-of-squares 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.

Abstract — Addressing the tradeoff between the QoS and consumed power is a critical issue for wireless ad-hoc networks. The loss observed in such networks is often temporally correlated. Multiple antenna systems utilizing space-time 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 ad-hoc networks with mobile nodes utilizing space-time 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 finite-state Markov chains. Details of fading statistics of signal-to-interference ratio (SIR), an important indicator of transmission quality, are presented. We also analyze the impacts of enforcing power, block-loss probabilities, and throughput constraints in conjunction with the use of space-time block codes.