Among the several next-generation passive optical network (NG-PON) requirements are the provisioning of higher bandwidth per subscriber, an increased splitting ratio, and an extended maximum reach compared with current Ethernet PON (EPON) and Gigabit PON (GPON) architectures. NG-PONs may offer additional functionalities such as protection (to be discussed in detail in Chapter 15), support topologies other than conventional tree structures, and they enable the consolidation of access, backhaul, and metro network infrastructures (Lin [2008]). In addition, substantial research activity is currently focused on the convergence of optical and wireless access architectures into bimodal fiber-wireless (FiWi) access networks (Ghazisaidi and Maier [2011]), a key feature of NG-PONs.

An important goal of FiWi research is to combine the most promising technologies proposed for wireless and optical access. Network coding (NC) is an example of such technologies. Consisting of bit- or packet-level coding operations, NC has been shown to improve throughput, simplify routing, and provide robustness against transmission errors and failures in various packet networks (Ho and Lun [2008]). In a recent study, significant throughput gains were demonstrated experimentally in NC-enabled WiFi-based mesh networks (Katti et al. [2008]).

In this chapter, we study the integration of NC within NG-PONs. The aim is to illustrate the NG-PON architectures where NC yields potential performance gains. Our illustrations and simulations demonstrate significant potential performance improvements while clarifying some underlying topological constraints of NC in various NG-PON scenarios.

Recently, various fiber-wireless (FiWi) network architectures have been investigated by integrating different optical and wireless technologies. While introducing optical fiber at higher network layers, e.g., aggregation layer, helps alleviate emerging bandwidth bottlenecks, the last hop is expected to be wireless for ubiquity and convenience, e.g., low-cost wireless home area networks (HANs) (He et al. [2008]). Between these two FiWi network hierarchy levels lies the “sweet spot” where optical technologies interface with their wireless counterparts. Two important sweet-spot technologies that play a key role in emerging FiWi networks are Ethernet passive optical network (EPON) and WiMAX. Clearly, EPON and WiMAX networks may be cascaded, as proposed in (Shen et al. [2007]). However, given the similarities of EPON and WiMAX (e.g., point-to-multipoint topology with a central control station performing dynamic bandwidth allocation (DBA) by means of centralized polling and scheduling) we argue that the two technologies are more likely to target the same network segment rather than being cascaded to cover different network segments. In other words, we expect that network operators will make a choice between EPON and WiMAX depending on a number of factors, e.g., right-of-way, and elaborate on the techno-economic comparison of the two technologies.

For the comparison of wired and wireless network technologies various techno-economic evaluation techniques have been proposed, as we will see shortly. During the last decade, the techno-economic evaluation of various network technologies has been an active research area.

In addition to the moment generating function (MGF) and characteristic function (CF) methods discussed in the preceding chapter, there are two other related methods that are frequently used in the study of probability theory. They are the generating function and the Laplace transform (LT).

Discrete RVs often assume integers or integral multiples of some unit, as is the case in counting applications and discrete-time systems. Then, the generating function method will be found to be a convenient device in probability analysis. When a random variable is continuous but nonnegative (e.g., waiting time and service time in a queueing system), we can make use of the rich theory of LTs in the analysis.

Since the CF exists for all distribution functions, both discrete and continuous, why should we study all these other transform methods that seem redundant? Certainly the CF should suffice in most situations, but generating functions and LTs are preferred whenever they are applicable, partly because their notation is somewhat simpler than that of the CF, and partly because there is a rich theory behind the generating function and LT methods, both of which have been widely used as operational methods in system theory that involves differential and integral equations. Thus, it is important for us to be sufficiently familiar with these transform methods to study the literature on probability theory and its applications.

Generating function

The notion of generating function can be more general than the probability generating function (PGF) that we will primarily discuss in this section.

In this chapter, we review recent radio-over-fiber (RoF) and radio-and-fiber (R&F) based fiber-wireless (FiWi) network design proposals and discuss previously addressed challenges. Beside cell-based RoF networks, we briefly describe a number of FiWi network architectures, which can be classified based on their wireless access technologies: WiMAX orWiFi. Table 11.1 summarizes previously proposed WiMAX and WiFi based FiWi network architectures. While passive optical networks (PONs) can be widely found in FiWi networks, wireless mesh networks (WMNs) have been used rarely so far. As we will see shortly, different challenges have been addressed such as routing and wireless channel assignment, which can be performed completely either in the wireless domain by the base station (BS) or access point (AP), or by an optical network element, e.g., central office (CO) or optical line terminal (OLT). The level of provided quality-of-service (QoS) largely depends on the performance of the implemented routing and resource management algorithms, including bandwidth allocation and channel assignment algorithms with absolute or relative QoS assurances. Reconfiguration is another previously addressed challenging issue that involves resource management in the wireless and/or optical part. For instance, as explained in greater detail below, in the unidirectional ring/PON architecture of Table 11.1, highly loaded optical network unit-wireless gateways (ONU-WGs) may be assigned to a lightly loaded PON by tuning their optical transceivers to the wavelength assigned to the lightly loaded PON, resulting in a decrease of network congestion and packet latency.

Long term evolution (LTE) has been defined by the third generation partnership project (3GPP) as fourth-generation (4G) cellular network technology for high-speed wireless end-users. In this chapter, we provide an overview of the salient features and most important specifications of LTE and next-generation LTE-Advanced networks.

PHY layer

The first amendment of LTE (release 8) provides a transmission rate of 300 Mb/s and operates in both time division duplex (TDD) and frequency division duplex (FDD) modes. 4G LTE provides simplicity for both operators and end-users (Pospishny et al. [2010]). LTE operators are given the flexibility to define the size of bandwidth, ranging from below 5 MHz up to 20 MHz. Furthermore, various user-friendly features have been considered in 4G LTE networks, including plug-and-play and self-configuration.

LTE aims at providing a smooth evolution from earlier 3GPP and 3GPP2 cellular networks such as wide-band code division multiple access/high-speed packet access (WCDMA/HSPA) and code division multiple access (CDMA2000) (Astely et al. [2009]). Typically, orthogonal frequency division multiplexing (OFDM) is used in the downlink radio transmission of LTE networks. Using narrow-band subcarriers in combination with a cyclic prefix leads to a radio transmission that is robust against time dispersion. As a result, the cost and power consumption of mobile end-users decrease due to the simplified receiver baseband processing. Moreover, LTE supports advanced multi-antenna schemes such as single/multiple-user multiple input multiple output (MIMO) antennas, transmit diversity, spatial multiplexing, and beamforming.

Wireless mesh networks (WMNs) have been envisioned to enhance flexibility, increase reliability, and improve performance of wireless networks. Although WMNs are not widely considered in wireless metropolitan area network (WMAN) deployments, IEEE 802.11 wireless local area network (WLAN) is an interesting technology to realize low-cost WMNs. In this chapter, we provide an overview of the salient features and most important specifications of WiFi-based WMNs and describe the major challenging issues of routing and medium access control (MAC) protocols. Moreover, we briefly describe the optional mesh mode of initial standard IEEE 802.16d for fixed WiMAX, which has been removed from the IEEE standard 802.16e for mobile WiMAX.

Characteristics

Typically, there are two main approaches in the design of wireless networks (Schiller [2003]):

1. Infrastructure networks: Wireless mobile stations (STAs) rely on an underlying infrastructure for communication. They communicate with each other via a central control point, e.g., an access point (AP). WMANs, such as the global system for mobile communications (GSM) and universal mobile telecommunications system (UMTS), are typical examples for infrastructure wireless networks.

2. Infrastructure-less networks: STAs communicate directly with each other. In infrastructure-less wireless networks, also known as mobile ad-hoc networks (MANETs), STAs are able to act as routers. Emergency search-and-rescue operations, corporate meetings, and military communications in hostile terrains are example applications of MANETs.

In this chapter we discuss spectral representations and eigenvector-based time-series analysis. We begin our discussion with a review of the Fourier series and Fourier transform of nonrandom functions, followed by the Fourier analysis of periodic WSS processes. Then we introduce the power spectrums of non-periodic WSS random processes, the Wiener–Khinchin formula, and the peoriodogram analysis of timeseries data. The eigenvector-based orthogonal expansion of random vectors and its continuous-time analog, known as the Karhuenen–Loéve expansion, are discussed in detail. Principal component analysis (PCA) and singular-value decomposition (SVD) are two commonly used statistical techniques applicable to any data presentable in matrix form, where correlation exists across its rows and/or columns. We also briefly discuss algorithms being developed for Web information retrieval, and they can be viewed as instances of general spectral expansion, the common theme of the present chapter.

The chapter ends with discussion of an important class of time series known as autoregressive moving average (ARMA), which is widely used in statistics and econometrics. Its spectral representation and state space formulation are also discussed.

Spectral representation of random processes and time series

In this section we consider the problem of representing a random process in terms of a series or integral with respect to some system of deterministic functions, such that the coefficients in this expansion are uncorrelated RVs. Such a representation is referred to as spectral representation or spectral expansion. Before we pursue this subject, let us briefly review the Fourier series expansion.

Fiber-to-the-home (FTTH) or close to it (FTTx) networks are poised to become the next major success story for optical fiber communications. Future FTTx access networks unleash the economic potential and societal benefit by opening up the first/last mile bandwidth bottleneck between bandwidth-hungry end-users and high-speed backbone networks. Owing to their longevity, low attenuation, and huge bandwidth, passive optical networks (PONs) are widely deployed to realize cost-effective FTTx access networks. Fiber has been envisioned for delivering broadband services for over 30 years. However, many roadblocks related to component and installation costs have slowed down the progress toward FTTx since it was first proposed. Currently, FTTH is being installed in many countries, but it still represents only a fraction of all deployed broadband lines (Shumate [2008]). The two major state-of-the-art PON standards IEEE 802.3ah Ethernet PON (EPON) and ITU-T G.984 Gigabit PON (GPON) consist both of a single upstream wavelength channel and a separate single downstream wavelength channel, whereby both channels are operated using time division multiplexing (TDM). EPON and GPON are expected to coexist for the foreseeable future as they evolve into next-generation PONs (NG-PONs) (Effenberger et al. [2007], Kazovsky et al. [2007]).

NG-PONs can be categorized into high-speed TDM PON, wavelength division multiplexing (WDM) PON, and long-reach PON (LR-PON) (Lin [2008], Effenberger et al. [2009a]).

In this chapter we study two different procedures for the analysis of time-dependent signals, locally in both frequency and time. These methods preceded the general discrete wavelet method and we shall see how they led to discrete wavelets. The first procedure, the “windowed Fourier transform” is associated with classical Fourier analysis while the second, is associated with scaling concepts related to discrete wavelets. Both of these procedures yield information about a time signal f(t) that is overcomplete. To understand this it is useful to return to our basic paradigm y = Φx where x is a signal, Φ is a sample matrix and y is the sample vector. Our problem is to recover the signal x from the samples y. In this chapter x = f(t) and Φ is an integral operator. However, for the moment let us consider the finite-dimensional case where x is an n-tuple, Φis an m × n matrix and y is an m-tuple. If m = n and Φ is invertible then we can obtain a unique solution x = Φ-1y. In the case of compressive sampling, however, m < n and the problem is underdetermined. It is no longer possible to obtain x from y in general, without special assumptions on x and Φ. Now suppose m > n. The problem is now overdetermined. In this case one can always find m-tuples y for which there is no x such that y = Φx.

Consider a linear system y = Φx where Φ can be taken as an m × n matrix acting on Euclidean space or more generally, a linear operator on a Hilbert space. We call the vector x a signal or input, Φ the transform–sample matrix–filter and the vector y the sample or output. The problem is to reconstruct x from y, or more generally, to reconstruct an altered version of x from an altered y. For example, we might analyze the signal x in terms of frequency components and various combinations of time and frequency components y. Once we have analyzed the signal we may alter some of the component parts to eliminate undesirable features or to compress the signal for more efficient transmission and storage. Finally, we reconstitute the signal from its component parts.

The three typical steps in this process are:

• Analysis. Decompose the signal into basic components. This is called analysis. We will think of the signal space as a vector space and break it up into a sum of subspaces, each of which captures a special feature of a signal.

• Processing. Modify some of the basic components of the signal that were obtained through the analysis. This is called processing.

• Synthesis. Reconstitute the signal from its (altered) component parts. This is called synthesis. Sometimes, we will want perfect reconstruction. Sometimes only perfect reconstruction with high probability. If we don't alter the component parts, we usually want the synthesized signal to agree exactly with the original signal. […]

Randomness in the real world

Repeated experiments and statistical regularity

One way to approach the notion of probability is through the phenomenon of statistical regularity. There are many repeating situations in nature for which we can predict in advance, from previous experiences, roughly what will happen, but not exactly what will happen. We say in such cases that the occurrences are random. The reason that we cannot predict future events exactly may be that (i) we do not have enough data about the condition of the given problem, (ii) the laws governing a progression of events may be so complicated that we cannot undertake a detailed analysis, or possibly (iii) there is some basic indeterminacy in the physical world. Whatever the reason for the randomness, a definite average pattern of results may be observed in many situations leading to random occurrences when the situation is recreated a great number of times. For example, if a fair coin is flipped many times, it will turn up heads on about half of the flips.

Another example of randomness is the response time of a web (i.e.,WorldWideWeb or WWW) access request you may send over the Internet in order to retrieve some information from a certain website. The amount of time you have to wait until you receive a response will not be precisely predictable, because the total round trip time depends on a number of factors.

Access networks connect business and residential subscribers to the central offices of service providers, which in turn are connected to metropolitan area networks (MANs) or wide area networks (WANs). Access networks are commonly referred to as the last mile or the first mile, whereby the latter term emphasizes their importance to subscribers. Future first-mile solutions have to not only meet the cost sensitivity constraints of access networks arising from the small number of cost-sharing subscribers but also have to provide an ever increasing amount of capacity due to emerging bandwidth-hungry multimedia applications such as video on demand (VoD), high-definition television (HDTV), digital cinema, split-screen video, and 3D online games. These new services and applications are expected to require data rates of up to 100 Mb/s per home, which cannot be provided by traditional narrowband access solutions, e.g., dial-up connections. To meet the bandwidth requirements of emerging and future video-dominated services and applications, legacy access networks have been replaced with broadband access networks over the last few years.

Definition

The term broadband is commonly used to refer to high-speed Internet access with data rates exceeding those of traditional dial-up Internet connections, which typically offer data rates of only 64 kb/s or below. More specifically, the Federal Communications Commission (FCC) used to define broadband service as data transmission speeds exceeding 200 kb/s in at least one direction, i.e., downstream (from the Internet to the subscriber's computer) or upstream (from the user's computer to the Internet).