Prashanth Hande

Power Control in Wireless Cellular Networks

Transmit power in wireless cellular networks is a key degree of freedom in the management of interference, energy, and connectivity. Power control in both the uplink and downlink of a cellular network has been extensively studied, especially over the last 15 years, and some of the results have enabled the continuous evolution and significant impact of the digital cellular technology. This survey provides a comprehensive discussion of the models, algorithms, analysis, and methodologies in this vast and growing literature. It starts with a taxonomy of the wide range of power control problem formulations, and progresses from the basic formulation to more sophisticated ones. When transmit power is the only set of optimization variables, algorithms for fixed SIR are presented first, before turning to their robust versions and joint SIR and power optimization. This is followed by opportunistic and non-cooperative power control. Then joint control of power together with beamforming pattern, base station assignment, spectrum allocation, and transmit schedule is surveyed\break one-by-one. Throughout the survey, we highlight the use of mathematical language and tools in the study of power control, including optimization theory, control theory, game theory, and linear algebra. Practical implementations of some of the algorithms in operational networks are discussed in the concluding section. As illustrated by the open problems presented at the end of most chapters, in the area of power control in cellular networks, there are still many under-explored directions and unresolved issues that remain theoretically challenging and practically important..

Distributed rate allocation for inelastic flows

A common assumption behind most of the recent research on network rate allocation is that traffic flows are elastic, which means that their utility functions are concave and continuous and that there is no hard limit on the rate allocated to each flow. These critical assumptions lead to the tractability of the analytic models for rate allocation based on network utility maximization, but also limit the applicability of the resulting rate allocation protocols. This paper focuses on inelastic flows and removes these restrictive and often invalid assumptions. First, we consider nonconcave utility functions, which turn utility maximization into difficult, nonconvex optimization problems. We present conditions under which the standard price-based distributed algorithm can still converge to the globally optimal rate allocation despite nonconcavity of utility functions. In particular, continuity of price-based rate allocation at all the optimal prices is a sufficient condition for global convergence of rate allocation by the standard algorithm, and continuity at at least one optimal price is a necessary condition. We then show how to provision link capacity to guarantee convergence of the standard distributed algorithm. Second, we model real-time flow utilities as discontinuous functions. We show how link capacity can be provisioned to allow admission of all real-time flows, then propose a price-based admission control heuristics when such link capacity provisioning is impossible, and finally develop an optimal distributed algorithm to allocate rates between elastic and real-time flows.

Distributed rate allocation for inelastic flows: optimization frameworks, optimality conditions, and optimal algorithms

A common assumption behind most of the recent research on network utility maximization is that traffic flows are elastic, which implies that their utility functions are concave and there are no hard limits on the rate allocated to each flow. These critical assumptions lead to tractability of the analytic models of utility maximization, but also limits applicability of the resulting rate allocation protocols. This paper focuses on inelastic flows and removes these restrictive and often invalid assumptions. We present several optimization frameworks, optimality conditions, and optimal algorithms. First, we consider nonconcave utility functions, which turn utility maximization into nonconvex, constrained optimization problems that are well-known to be difficult. We present conditions under which the current standard price-based distributed algorithm can still converge to the globally optimal rate allocation despite nonconcavity of utility functions. In particular, continuity of price-based rate allocation at all the optimal prices is a sufficient condition for global convergence of rate allocation by the standard algorithm, and continuity at at least one optimal price is a necessary condition. In the second part of the paper, we provide a general problem formulation of rate allocation among time-sensitive flows from real-time and streaming applications, as well as a decomposition into subproblems coordinated by pricing. After simplifying the subproblems by leveraging the optimization structures, we highlight the difficult issues of causality and time-scale, and propose an effective price-based heuristics for admission control and an optimal algorithm for a special case formulation.

Distributed Uplink Power Control for Optimal SIR Assignment in Cellular Data Networks

This paper solves the joint power control and SIR assignment problem through distributed algorithms in the uplink of multi-cellular wireless networks. The 1993 Foschini–Miljanic distributed power control can attain a given fixed and feasible SIR target. In data networks, however, SIR needs to be jointly optimized with transmit powers in wireless data networks. In the vast research literature since the mid-1990s, solutions to this joint optimization problem are either distributed but suboptimal, or optimal but centralized. For convex formulations of this problem, we report a distributed and optimal algorithm. The main issue that has been the research bottleneck is the complicated, coupled constraint set, and we resolve it through a re-parametrization via the left Perron Frobenius eigenvectors, followed by development of a locally computable ascent direction. A key step is a new characterization of the feasible SIR region in terms of the loads on the base stations, and an indication of the potential interference from mobile stations, which we term spillage. Based on this load-spillage characterization, we first develop a distributed algorithm that can achieve any Pareto-optimal SIR assignment, then a distributed algorithm that picks out a particular Pareto-optimal SIR assignment and the associated powers through utility maximization. Extensions to power-constrained and interference-constrained cases are carried out. The algorithms are theoretically sound and practically implementable: we present convergence and optimality proofs as well as simulations using 3GPP network and path loss models.

Distributed Load-Balancing in a Multi-Carrier Wireless System

We consider a cellular network or a wireless local area network (WLAN), deployed with attachment points (APs) capable of transmission and reception in multiple radio-frequency (RF) carriers. A major factor contributing to the efficiency and stability of the network is the mechanism determining the connection of terminals to the appropriate AP and the RF carrier. This paper describes a practical, distributed, network-assisted and terminal-driven mechanism to determine the connections for load-balancing among the available RF carriers. The mechanism is based on a metric that we term as the service level indicating metric (SLIM). We extend the notion of SLIM to cases where Quality-of-Service (QoS) parameters are specified and propose a load-balancing mechanism for such cases. We demonstrate the near-optimality of the proposed mechanisms through 3GPP based simulations.

QoS-revenue tradeoff with time-constrained ISP pricing

Usage-based pricing has been recognized as a network congestion management tool. Internet Service Providers (ISPs), however, have limited ability to set time-adaptive usage-price to manage congestion arising from time-varying consumer utility for data. To achieve the maximum revenue, ISP can set its time-invariant usage-price low enough to aggressively encourage consumers traffic demand. The downside is that ISP has to drop consumers excessive traffic demand through congestion management (i.e., packet dropping), which may degrade Quality of Service (QoS) of consumers traffic. Alternatively, to protect consumers QoS, ISP can set its time-invariant usage-price high enough to reduce consumers traffic demand, thus minimizing the need for congestion management through packet dropping. The downside is that ISP suffers a revenue loss due to the inefficient usage of its network. The tradeoff between ISPs revenue maximization and consumers QoS protection motivates us to study ISPs revenue maximization subject to QoS constraint in terms of the number of packets dropped. We investigate two different QoS measures: short-term per-slot packet dropping constraint and long-term packet dropping constraint. The short-term constraint can be interpreted as a more transparent congestion management practice compared to the long-term constraint. We analyze ISPs optimal time-invariant pricing for both constraints, and develop an upper bound for the optimal revenue by considering the specified packet dropping threshold. We quantify the impact of consumers price elasticity on ISPs optimal revenue and show that ISP should carry out a differentiated QoS protection strategy based on consumers price elasticity in order to mitigate the revenue loss1.

Joint Beamforming and Power Control for Optimal SIR Assignment in Cellular Uplinks

This paper considers the nonconvex and globally coupled problem of joint antenna beamforming and transmit power control, in order to maximize the network-wide utility as a function of attained SIRs. Using a spillage-load characterization for power control [13], we assign utility as a function of attained SIRs and formulate the joint optimization as a utility maximization problem. Despite the highly coupled structure of the problem, we propose an efficient distributed algorithm that is proved to be convergent in general. Despite nonconvexity in the joint optimization, we prove global optimality in the two user case. We find in simulations the algorithm always converges to the global optimal allocation, and the Pareto-optimal tradeoff between power and antenna beamforming in maximizing network utility is illustrated.

Pricing broadband: Survey and open problems

Driven by the emerging directions from the FCC and the broadband market, this paper aims at answering the fundamental question of how to use pricing as a lever to enable universal broadband coverage and effective network management in the United States. We address differential pricing as a network management tool, i.e., what to charge, how to charge, and how much to charge. We also outline research towards multi-platform two-sided pricing focusing on ISP that charges both content and application providers. Open problems are highlghted. As a next step, through collaboration we will combine the access to large-scale empirical data with rigorous modeling and analysis; we will go all the way from data collection through mathematical analysis to practical impact on policy decisions and ISP business decisions, thus closing the loop in the study of network economics for universal broadband coverage.