Mobile-edge cloud computing is a new paradigm to provide cloud computing capabilities at the edge of pervasive radio access networks in close proximity to mobile users. In this paper, we first study the multi-user computation offloading problem for mobile-edge cloud computing in a multi-channel wireless interference environment. We show that it is NP-hard to compute a centralized optimal solution, and hence adopt a game theoretic approach for achieving efficient computation offloading in a distributed manner. We formulate the distributed computation offloading decision making problem among mobile device users as a multi-user computation offloading game. We analyze the structural property of the game and show that the game admits a Nash equilibrium and possesses the finite improvement property. We then design a distributed computation offloading algorithm that can achieve a Nash equilibrium, derive the upper bound of the convergence time, and quantify its efficiency ratio over the centralized optimal solutions in terms of two important performance metrics. We further extend our study to the scenario of multi-user computation offloading in the multi-channel wireless contention environment. Numerical results corroborate that the proposed algorithm can achieve superior computation offloading performance and scale well as the user size increases.

Efficient Multi-User Computation Offloading for Mobile-Edge Cloud Computing

A systematic understanding of the decomposability structures in network utility maximization is key to both resource allocation and functionality allocation. It helps us obtain the most appropriate distributed algorithm for a given network resource allocation problem, and quantifies the comparison across architectural alternatives of modularized network design. Decomposition theory naturally provides the mathematical language to build an analytic foundation for the design of modularized and distributed control of networks. In this tutorial paper, we first review the basics of convexity, Lagrange duality, distributed subgradient method, Jacobi and Gauss-Seidel iterations, and implication of different time scales of variable updates. Then, we introduce primal, dual, indirect, partial, and hierarchical decompositions, focusing on network utility maximization problem formulations and the meanings of primal and dual decompositions in terms of network architectures. Finally, we present recent examples on: systematic search for alternative decompositions; decoupling techniques for coupled objective functions; and decoupling techniques for coupled constraint sets that are not readily decomposable

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A tutorial on decomposition methods for network utility maximization

Network protocols in layered architectures have historically been obtained on an ad hoc basis, and many of the recent cross-layer designs are also conducted through piecemeal approaches. Network protocol stacks may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems. This paper presents a survey of the recent efforts towards a systematic understanding of layering as optimization decomposition, where the overall communication network is modeled by a generalized network utility maximization problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. There can be many alternative decompositions, leading to a choice of different layering architectures. This paper surveys the current status of horizontal decomposition into distributed computation, and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and channel coding. Key messages and methods arising from many recent works are summarized, and open issues discussed. Through case studies, it is illustrated how layering as Optimization Decomposition provides a common language to think about modularization in the face of complex, networked interactions, a unifying, top-down approach to design protocol stacks, and a mathematical theory of network architectures

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Layering as Optimization Decomposition: A Mathematical Theory of Network Architectures

| Network protocols in layered architectures have historically been obtained on an ad hoc basis, and many of the recent cross-layer designs are also conducted through piecemeal approaches. Network protocol stacks may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems. This paper presents a survey of the recent efforts towards a systematic understanding of "layering" as "optimization decomposition," where the overall communication network is modeled by a generalized network utility maximization problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. There can be many alternative decompositions, leading to a choice of different layering architectures. This paper surveys the current status of horizontal decomposition into distributed computation, and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and channel coding. Key messages and methods arising from many recent works are summarized, and open issues discussed. Through case studies, it is illustrated how "Layering as Optimization Decomposition" provides a common language to think about modularization in the face of complex, networked interactions, a unifying, top-down approach to design protocol stacks, and a mathematical theory of network architectures.

Layering as optimization decomposition: A mathematical theory of network architectures : There are various ways that network functionalities can be allocated to different layers and to different network elements, some being more desirable than others. The intellectual goal of the research surveyed by this article is to provide a theoretical foundation for these architectural decisions in networking

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..

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Power Control in Wireless Cellular Networks

Transmit and/or receive diversity is achieved using multiple antennas. In some embodiments, a single transmitter chain within a wireless terminal is coupled over time to a plurality of transmit antennas. At any given time, a controllable switching module couples the single transmitter chain to one the plurality of transmit antennas. Over time, the switching module couples the output signals from the single transmitter chain to different transmit antennas. Switching decisions are based upon predetermined information, dwell information, and/or channel condition feedback information. Switching is performed on some dwell and/or channel estimation boundaries. In some OFDM embodiments, each of multiple transmitter chains is coupled respectively to a different transmit antenna. Information to be transmitted is mapped to a plurality of tones. Different subsets of tones are formed for and transmitted through different transmit chain/antenna sets simultaneously. The balance of tones allocated to the subsets for each antenna are changed as a function of predetermined information, dwell information, and/or channel condition feedback information.

Methods and apparatus of providing transmit and/or receive diversity with multiple antennas in wireless communication systems

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.

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Distributed uplink power control for optimal sir assignment in cellular data networks

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.

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Distributed rate allocation for inelastic flows

Methods and apparatus for collecting, measuring, reporting and/or using information which can be used for interference control purposes. Wireless terminals measure signals transmitted from one or more base stations, e.g., base station sector transmitters. The measured signals may be, e.g., beacon signals and/or pilot signals. From the measured signals, the wireless terminal generates one or more gain ratios which provide information about the relative gain of the communications channels from different base station sectors to the wireless terminal. This information represents interference information since it provides information about the signal interference that will be caused by transmissions from other base station sectors relative to transmissions made by the base station sector to which the wireless terminal is attached. Based on the signal energy measurements and relative gains generated from the energy measures, reports are generated in accordance with the invention and sent to one or more base stations.

Prashanth Hande

Papers

Power Control in Wireless Cellular Networks

Methods and apparatus of providing transmit and/or receive diversity with multiple antennas in wireless communication systems

Distributed uplink power control for optimal sir assignment in cellular data networks

Distributed rate allocation for inelastic flows

Methods and apparatus for determining, communicating and using information which can be used for interference control purposes