Introduction

Discrete optimization is a problem in which the decision variables assume discrete values from a specified set. Combinatorial optimization problems, on the other hand, are problems of choosing the best combination out of all possible combinations. Most combinatorial problems can be formulated as integer programs. In wireless networking and resource allocation, integer/combinatorial optimization problems are investigated with the efficient allocation of limited resources to meet desired objectives when the values of some or all of the variables are restricted to be integral. Constraints on basic resources, such as modulation, channel allocation, and coding rate restrict the possible alternatives that are considered feasible. For example, in 3G cellular networks, discrete processing gains for different codes give users different bandwidths for transmission. In a WLAN, the available time slots are occupied by different users. Consequently the allocation of time is restricted to a discrete nature. InWiMAX or Flash-OFDM, the distinct time-frequency slot is also allocated to the admitted users. Moreover, for practical implementation, the coding rate and adaptive modulation can have only discrete values. Even for the power control, the minimal step for the current cellular system is 1 dB. To design future wireless networks, it is of importance to study these integer optimizations, especially from an industrial implementation point of view.

The versatility of the integer/combinatorial optimization model stems from the fact that, in many practical problems, activities and resources, such as channel, user, and time slot, are indivisible.

Introduction

Rate adaptation is one of the most important resource-allocation issues, because the system can adapt the users' rates so that the limited radio resources can be efficiently utilized. Compared with power control, rate adaptation gives a newdimension of freedom to change the information transmission rate over time, i.e., power control maintains the desired link quality, whereas rate adaptation adjusts this link quality. In this chapter, we give an overview of the rate-adaptation system: where and how the rates can be changed; what the challenges and constraints are; and how rate adaptation can be combined with other techniques.

According to the different ISO (International Organization for Standardization) layers, rate adaptation can be classified into three different types: source rate adaptation in the application layer, rate control for data communication in the network/MAC layer, and channel protection adaptation in the physical layers. They are briefly summarized here:

1. • Source Rate Adaptation

2. This type of adaptation adjusts the quality of transmitting information. For example, the voice encoder can change the information rate according to the talking period and the silence period, as it is useless to have a high data rate for the silence period. For video transmission, the data rate is very bursty over time, because of the different video scenarios and different frames such as I, B, P frames. Because the capacity to deliver the information is limited by the communication systems, the design of the wireless network protocol shall carefully consider the source rate adaptation so that the received information has high quality using the limited system resources.

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Introduction

In mathematics, the term optimization refers to the study of problems that have the following forms:

• given: a function f : A → R from a certain set A to the real numbers;

• sought: an element x0 in Asuch that f (x0) ≤ f (x), ∀x ∈ A(“minimization”) or such that f (x0) ≥ f (x)∀x ∈ A(“maximization”).

Typically, A is a certain subset of the Euclidean space Rn, often specified by a set of constraints, equalities, or inequalities that the members of A have to satisfy. The elements of A are called feasible solutions. The function f is called an objective function, or cost function. A feasible solution that minimizes (or maximizes, if that is the goal) the objective function is called an optimal solution. The domain A of f is called the search space, and the elements of A are called candidate solutions or feasible solutions.

Such a formulation is sometimes called a mathematical program. Many real-world and theoretical problems may be modeled in this general framework. In this chapter, we discuss the following major subfields of the mathematical programming:

1. Linear programming (LP) studies the case in which the objective function f is linear and the set A is specified using only linear equalities and inequalities.

2. Convex programming studies the case in which the constraints and the optimization goals are all convex or linear.

3. Nonlinear programming (NLP) studies the general case in which the objective function or the constraints or both contain nonlinear parts.

4. Dynamic programming studies the case in which the optimization strategy is based on splitting the problem into smaller subproblems or considers the optimization problems over time.

Introduction

“Wireless network” refers to a telecommunications network whose interconnections between nodes is implemented without the use of wires. Wireless networks have seen unprecedent growth during the past few decades and will continuously evolve in the future. Seamless mobility and coverage ensure that various types of wireless connections can be made anytime, anywhere. In this chapter, we introduce some basic types of wireless networks and give the readers some preliminary backgrounds for the current state-of-the-art development.

Wireless networks use electromagnetic waves, such as radio waves, for carrying information. Therefore the performance is greatly influenced by randomly fluctuating wireless channels. To understand the channels, in Section 2.2, we will study the existing wireless channel models used for different network scenarios.

There are many existing wireless standards. We consider them according to the order of coverage area, and start with cellular wireless networks. The third-generation (3G) wireless cellular network standards have been enhanced to offer significantly increased performance for data and broadcast services through the introduction of high-speed downlink packet access, enhanced uplink, and multimedia broadcast multicast services. In Section 2.3, we provide an overviewof the key elements and technologies. Specifically, we discuss WCDMA, CDMA2000, TD/S CDMA, and 4G and beyond.

WiMax, based on the IEEE 802.16 standard for a wireless metropolitan-area network (WMAN), is expected to enable true broadband speeds over wireless networks at a cost that enables mass-market adoption. WiMAX has the ability to deliver true broadband speeds and help make the vision of pervasive connectivity a reality. We discuss some techniques and the standard in Section 2.4.

Over the past decade, there has been a significant advance in the design of wireless networks, ranging from physical-layer algorithm development, medium-access control (MAC) layer protocol design, to network- and system-level optimization. Many wireless standards have been proposed to suit the demands of various applications. Over time, researchers have come to the realization that, for wireless networks, because of fading channels, user mobility, energy/power resources, and many other factors, one cannot optimize wireless communication systems as has been traditionally done in wired networks, in which one can simply focus on and optimize each networking layer without paying much attention to the effects of other layers. For wireless networks, cross-layer optimization is a central issue to ensure overall system performance. Yet resource allocation is one of the most important issues for cross-layer optimization of wireless networks.

For instance, across different layers, one cannot design physical-layer coding, modulation, or equalization algorithms by assuming that the MAC layer issues are completely perfect, and vice versa. There are also user diversities—different users at different times and locations may suffer different channel conditions, and therefore may have different demands and capability. Fixing and allocating bandwidths and resources without considering such user diversity can simply waste system resources, and thus performances. In addition, in wireless networks there are space, time, and frequency diversities as well. Taking advantage of those diversities can significantly improve communication performance. All those factors contribute to the need of careful consideration of resource allocations.

We have witnessed the advance of resource allocation in recent years with tremendous progress.

Introduction

Game theory is a branch of applied mathematics that uses models to study interactions with formalized incentive structures (“games”). It studies the mathematical models of conflict and cooperation among intelligent and rational decision makers. “Rational” means that each individual's decision-making behavior is consistent with the maximization of subjective expected utility. “Intelligent” means that each individual understands everything about the structure of the situation, including the fact that others are intelligent, rational, decision makers. It has applications in a variety of fields, including economics, international relations, evolutionary biology, political science, and military strategy. Game theorists study predicted and actual behavior, as well as optimal strategies, of individuals in games.

For the history of game theory, the basis of modern game theory can be considered an outgrowth of a few seminal works:

• Augustin Cournot, in his 1838 paper Researches into the Mathematical Principles of the Theory of Wealth, gives an intuitive explanation of what would eventually be formalized as the Nash equilibrium, as well as provides an evolutionary or dynamic notion of best responses to the actions of others.

• Francis Ysidro Edgeworth's Mathematical Physics (1881) demonstrated the notion of competitive equilibriums in a two-person (as well as two-type) economy.

• Emile Borel, in Algebre et calcul des probabilites, Comptes Rendus Academie des Sciences, Vol. 184, 1927, provided the first insight into mixed strategies that state that randomization may support a stable outcome.

Although many other contributors hold a place in the history of game theory, it is widely accepted that modern analysis began with John von Neumann's and Oskar Morgenstern's book, Theory of Games and Economic Behavior, which is the analytical base for the works [217] of John Nash.

Introduction

In wireless networks, the available radio resources such as bandwidth are very limited. On the other hand, the demands for wireless services are exponentially increasing. Not only is the number of users booming, but also more bandwidth is required for the new services such as video telephony, TV on demand, wireless Internet, and wireless gaming. How to accommodate all these requirements has become an emergent research issue in wireless networking. Resource allocation and its optimization are general methods to improve the network performances.

The design of wireless networking is usually conducted in two different styles. For physical-layer researchers, the bandwidth is very limited and optimization is critical to approach the optimality, such as the Shannon capacity. On the other hand, for higher-layer researchers, it is mostly impossible to have any analytical solution. Therefore the design criteria is often heuristic. There are trade-offs between these two types of approaches. One of our major goals is to present these trade-offs so that better implementations can be put into practice.

In this chapter, we discuss how to formulate the wireless networking problem as a resource-allocation optimization issue. Specifically, we study what the resources are, what the parameters are, what the practical constraints are, and what the optimized performances across the different layers are. In addition, we address how to perform resource allocation in multiuser scenarios. The trade-offs between the different optimization goals and different users' interests are also investigated. The goal is to provide readers with a new perspective from the optimization point of view for wireless networking and resource-allocation problems.

Introduction

The available wireless radio resources are very limited, while there are an increasing number of mobile users. It is necessary to share a communication channel or physical communication medium among multiple users. The multiple-access scheme is a general strategy to allocate the limited resources, such as bandwidth and time, to guarantee the basic QoS, improve the system performances, and reduce the cost for the network infrastructures. Whereas multiple access considers the problem of allocating limited radio resources to multiple users, spectrum access decides whether an individual user can access a certain spectrum.

The basic idea of the multiple-access scheme is to combine several signals for transmission on a certain shared medium (e.g., a wireless channel). The signals are combined at the transmitter by a multiplexor (a “mux”) and split up at the receiver by a de-multiplexor. Based on how to divide the limited radio resources to multiple users, the multiple-access schemes can be classified as time-division multiple access (TDMA), frequency-division multiple access (FDMA), code-division multiple access (CDMA), space-division multiple access (SDMA), and others.

The multiple-access schemes need to be dynamically coordinated for a number of reasons: The users' data flows might not have data to transmit, the channel conditions are different for different users, and the QoS such as the delay constraints are different for different types of payloads. Based on how to coordinate access for the radio resources, multiple-access schemes can be classified into two types: scheduling and random access. In scheduling, there is a centralized control, the base station, that controls which user can transmit by using specific resources such as the bandwidth at different times. In random access, there is no such centralized control.

Introduction

In recent years, wireless networks, especially ad hoc networks that consist of a collection of radio transceivers without requiring centralized administration or a prearranged fixed network infrastructure, have been studied intensively. Considering the application scenarios in which the users are “selfish” and act noncooperatively to maximize their own interests, the performances of such networks will deteriorate dramatically because of the inefficient competition for the wireless resources among selfish users. The greediness of selfish users and the distributed network structure challenge the feasibility of the conventional approaches and require novel techniques for distributed and efficient networking. Thus ensuring cooperation among selfish users becomes an important issue for designing wireless networks.

To ensure the cooperation and study the behaviors of selfish users, game theory is a successful economy tool, which studies the mathematical models of conflict and cooperation between intelligent and rational decision makers. In the literature, different types of game approaches have been introduced to several areas of wireless communications. One of the most important is the pricing anarchy, in which a price is taxed for the resource usage so that cooperative behaviors can be enforced. Noncooperation game theory was studied in [268] for power-control problems, in which the pricing technique was used to achieve Pareto optimality. In [369], resource allocation was studied for a forward link two-cell CDMA voice network with multiple service classes. Noncooperative game theory has also been studied for self-organizing mobile ad hoc wireless networks (MANET). In [38, 368], reputation-based game approaches were proposed to encourage packet forwarding among users.

Because of fading channels, user mobility, energy/power resources, and many other factors, cross-layer design and multiuser optimization are the keys to ensuring overall system performance of wireless networks. And resource allocation is one of the most important issues for implementing future wireless networks.

In the past decade, we have witnessed significant progress in the advance of resource allocation over wireless networks. It is not only an important research topic, but is also gradually becoming an integral teaching material for graduate-level networking courses.

Yet there are few books available to date that can serve such a purpose. Why? Because the field of resource allocation is such a versatile area that covers a broad range of issues, it is not easy to develop a comprehensive book to cover them all. For instance, resource allocation across various networking layers encounters different design constraints and parameters; different networking scenarios have different performance goals and service objectives; and different formulations of resource allocations need to employ different optimization tools.

To respond to the need of such a book for graduate students, researchers, and engineers, we try to tackle the difficulties by bringing together our research in resource allocation over the past decade and the basic material of resource allocation and optimization techniques to form the foundation of this book. Its intent is to serve either as a textbook for advanced graduate-level courses on networking or as a reference book for self-study by researchers and engineers.

This book covers three main parts. In Part I, the basic principles of resource allocation is discussed.

With the advancement of multimedia compression technology and wide deployment of wireless networks, there is an increasing demand especially for wireless multimedia communication services. The system design has many challenges, such as fading channels, limited radio resources of wireless networks, heterogeneity of multimedia content complexity, delay and decoding dependency constraints of multimedia, mixed-integer optimization, and trade-offs among multiuser service objectives. To overcome these challenges, dynamic resource allocation is a general strategy used to improve the overall system performance and ensure individual QoS. Specifically in this chapter, we consider two aspects of design issues: cross-layer optimization and multiuser diversity. We study how to optimally transmit multiuser multimedia streams, encoded by current and future multimedia codecs, over resource-limited wireless networks such as 3G cellular systems, WLANs, 4G cellular systems, and future WLAN/WMANs.

Introduction

Over the past few decades, wireless communications and networking have experienced an unprecedented growth. With the advancement in multimedia coding technologies, transmitting real-time encoded multimedia programs over wireless networks has become a promising service for such applications as video-on-demand and interactive video telephony. In most scenarios, multiple multimedia programs are transmitted to multiple users simultaneously by sharing resource-limited wireless networks.

The challenges for transmitting multiple compressed multimedia payloads (such as videos) over wireless networks in real time lie in several factors. First, wireless channels are impaired by detrimental effects such as fading and CCIs. Second, there are limited radio resources, such as bandwidth and power, in the wireless networks.