In Chapter 4, we showed that any ℒ2 function u(t) can be expanded in various orthogonal expansions, using such sets of orthogonal functions as the T-spaced truncated sinusoids or the sinc-weighted sinusoids. Thus u(t) may be specified (up to ℒ2-equivalence) by a countably infinite sequence such as {uk,m; −∞ < k, m < ∞} of coefficients in such an expansion.

In engineering, n-tuples of numbers are often referred to as vectors, and the use of vector notation is very helpful in manipulating these n-tuples. The collection of n-tuples of real numbers is called ℝn and that of complex numbers ℂn. It turns out that the most important properties of these n-tuples also apply to countably infinite sequences of real or complex numbers. It should not be surprising, after the results of the previous chapters, that these properties also apply to ℒ2 waveforms.

A vector space is essentially a collection of objects (such as the collection of real n-tuples) along with a set of rules for manipulating those objects. There is a set of axioms describing precisely how these objects and rules work. Any properties that follow from those axioms must then apply to any vector space, i.e. any set of objects satisfying those axioms. These axioms are satisfied by ℝn and ℂn, and we will soon see that they are also satisfied by the class of countable sequences and the class of ℒ2 waveforms.

Introduction

Digital modulation (or channel encoding) is the process of converting an input sequence of bits into a waveform suitable for transmission over a communication channel. Demodulation (channel decoding) is the corresponding process at the receiver of converting the received waveform into a (perhaps noisy) replica of the input bit sequence. Chapter 1 discussed the reasons for using a bit sequence as the interface between an arbitrary source and an arbitrary channel, and Chapters 2 and 3 discussed how to encode the source output into a bit sequence.

Chapters 4 and 5 developed the signal-space view of waveforms. As explained in those chapters, the source and channel waveforms of interest can be represented as real or complex ℒ2 vectors. Any such vector can be viewed as a conventional function of time, x(t). Given an orthonormal basis {ϕ1(t), ϕ2(t), …} of ℒ2, any such x(t) can be represented as

Each xj in (6.1) can be uniquely calculated from x(t), and the above series converges in ℒ2 to x(t). Moreover, starting from any sequence satisfying Σj|xj|2 < ∞, there is an ℒ2 function x(t) satisfying (6.1) with ℒ2-convergence. This provides a simple and generic way of going back and forth between functions of time and sequences of numbers.

Introduction

This chapter provides a brief treatment of wireless digital communication systems. More extensive treatments are found in many texts, particularly Tse and Viswanath (2005) and Goldsmith (2005). As the name suggests, wireless systems operate via transmission through space rather than through a wired connection. This has the advantage of allowing users to make and receive calls almost anywhere, including while in motion. Wireless communication is sometimes called mobile communication, since many of the new technical issues arise from motion of the transmitter or receiver.

There are two major new problems to be addressed in wireless that do not arise with wires. The first is that the communication channel often varies with time. The second is that there is often interference between multiple users. In previous chapters, modulation and coding techniques have been viewed as ways to combat the noise on communication channels. In wireless systems, these techniques must also combat time-variation and interference. This will cause major changes both in the modeling of the channel and the type of modulation and coding.

Wireless communication, despite the hype of the popular press, is a field that has been around for over 100 years, starting around 1897 with Marconi's successful demonstrations of wireless telegraphy. By 1901, radio reception across the Atlantic Ocean had been established, illustrating that rapid progress in technology has also been around for quite a while.

Digital communication is an enormous and rapidly growing industry, roughly comparable in size to the computer industry. The objective of this text is to study those aspects of digital communication systems that are unique. That is, rather than focusing on hardware and software for these systems (which is much like that in many other fields), we focus on the fundamental system aspects of modern digital communication.

Digital communication is a field in which theoretical ideas have had an unusually powerful impact on system design and practice. The basis of the theory was developed in 1948 by Claude Shannon, and is called information theory. For the first 25 years or so of its existence, information theory served as a rich source of academic research problems and as a tantalizing suggestion that communication systems could be made more efficient and more reliable by using these approaches. Other than small experiments and a few highly specialized military systems, the theory had little interaction with practice. By the mid 1970s, however, mainstream systems using information-theoretic ideas began to be widely implemented. The first reason for this was the increasing number of engineers who understood both information theory and communication system practice. The second reason was that the low cost and increasing processing power of digital hardware made it possible to implement the sophisticated algorithms suggested by information theory.

Introduction

This chapter has a dual objective. The first is to understand analog data compression, i.e. the compression of sources such as voice for which the output is an arbitrarily varying real- or complex-valued function of time; we denote such functions as waveforms. The second is to begin studying the waveforms that are typically transmitted at the input and received at the output of communication channels. The same set of mathematical tools is required for the understanding and representation of both source and channel waveforms; the development of these results is the central topic of this chapter.

These results about waveforms are standard topics in mathematical courses on analysis, real and complex variables, functional analysis, and linear algebra. They are stated here without the precision or generality of a good mathematics text, but with considerably more precision and interpretation than is found in most engineering texts.

Analog sources

The output of many analog sources (voice is the typical example) can be represented as a waveform, {u(t): ℝ → ℝ} or {u(t): ℝ → ℂ}. Often, as with voice, we are interested only in real waveforms, but the simple generalization to complex waveforms is essential for Fourier analysis and for baseband modeling of communication channels. Since a real-valued function can be viewed as a special case of a complex-valued function, the results for complex functions are also useful for real functions.

Introduction to quantization

Chapter 2 discussed coding and decoding for discrete sources. Discrete sources are a subject of interest in their own right (for text, computer files, etc.) and also serve as the inner layer for encoding analog source sequences and waveform sources (see Figure 3.1). This chapter treats coding and decoding for a sequence of analog values. Source coding for analog values is usually called quantization. Note that this is also the middle layer for waveform encoding/decoding.

The input to the quantizer will be modeled as a sequence U1, U2, …, of analog random variables (rvs). The motivation for this is much the same as that for modeling the input to a discrete source encoder as a sequence of random symbols. That is, the design of a quantizer should be responsive to the set of possible inputs rather than being designed for only a single sequence of numerical inputs. Also, it is desirable to treat very rare inputs differently from very common inputs, and a probability density is an ideal approach for this. Initially, U1, U2, … will be taken as independent identically distributed (iid) analog rvs with some given probability density function (pdf) fu(u).

A quantizer, by definition, maps the incoming sequence U1, U2, …, into a sequence of discrete rvs V1, V2, … where the objective is that Vm, for each m in the sequence, should represent Um with as little distortion as possible.

We have already seen that optical networks come in a large number of various flavors. Optical networks may have different topologies, may be transparent or opaque, and may deploy time, space, and/or wavelength division multiplexing (TDM, SDM, and/or WDM). They may comprise tunable devices, for example, tunable transmitters, tunable optical filters, and/or tunable wavelength converters (TWCs). Furthermore, to improve their flexibility optical networks may make use of reconfigurable optical add-drop multiplexers (ROADMs) and/or reconfigurable optical cross-connects. We will use the term optical switching networks to refer to all the various types of flexible and reconfigurable optical networks that use any of the aforementioned multiplexing, tuning, and switching techniques. Thus, optical switching networks are single-channel or multichannel (WDM) networks whose configuration can be changed dynamically in response to varying traffic loads and network failures by controlling the state of their tunable and/or reconfigurable network elements accordingly. Optical switching networks are widely deployed in today's wide, metropolitan, access, and local area networks and can be found at every level of the existing network infrastructure hierarchy.

End-to-end optical networks

Optical switching networks have been commonly used in backbone networks in order to cope with the ever-increasing amount of traffic originating from an increasing number of users and bandwidth-hungry applications. As shown in Fig. 2.1, optical switching networks can be found not only in wide area long-haul backbone networks but they also become increasingly the medium of choice in metro(politan), access, and local area networks (Berthelon et al., 2000). As a matter of fact, both telcos and cable providers are steadily moving the fiber-to-copper discontinuity point out toward the end users at the network periphery.

In this part, we discuss and describe in great detail various switching techniques for optical wide area networks (WANs). A number of different optical switching techniques have been proposed for backbone wavelength division multiplexing (WDM) networks over the last few years. Our overview will focus on the major optical switching techniques that can be found in today's operational long-haul WDM networks or are expected to be likely deployed in future optical WANs. In our overview we do not claim to provide a comprehensive description of all proposed switching techniques. Instead, we try to focus on the major optical switching techniques and describe their underlying principles and operation at length. We believe that our overview of carefully selected optical switching techniques fully covers the different types of switching techniques available for optical WANs and helps the reader gain sufficient knowledge to anticipate and understand any of the unmentioned optical switching techniques that in most cases might be viewed as extensions or hybrids of the optical switching techniques discussed. For instance, a so-called light-trail is a generalization of a conventional point-to-point lightpath in which data can be dropped and added at any node along the path, as opposed to a lightpath where data can be added only by the source and dropped only by the destination node, respectively (Gumaste and Zheng, 2005). Another good example is fractional lambda switching (FλS) (Baldi and Ofek, 2002). FλS uses the globally available coordinated universal time (UTC) as a common time reference to synchronize all optical switches throughout the FλS network.

Access networks connect business and residential subscribers to the central offices (COs) 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 first mile, where the latter term emphasizes their importance to subscribers. In today's access networks, telephone companies deploy digital subscriber line (xDSL) technologies and cable companies deploy cable modems. Typically, these access networks are hybrid fiber coax (HFC) systems with an optical fiber–based feeder network between CO and remote node and an electrical distribution network between remote node and subscribers. These access technologies are unable to provide enough bandwidth to current high-speed Gigabit Ethernet local area networks (LANs) and evolving services and applications (e.g., distributed gaming or video on demand). Future first-mile solutions not only have to provide more bandwidth but also have to meet the cost-sensitivity constraints of access networks arising from the small number of costsharing subscribers.

In so-called FTTX access networks the copper-based distribution part of access networks is replaced with optical fiber (e.g., fiber to the curb [FTTC] or fiber to the home [FTTH]). In doing so, the capacity of access networks is sufficiently increased to provide broadband services to subscribers. Due to the cost sensitivity of access networks, these all-optical FTTX systems are typically unpowered and consist of passive optical components (e.g., splitters and couplers). Accordingly, they are called passive optical networks (PONs). PONs had attracted a great deal of attention well before the Internet spurred bandwidth growth.

GMPLS

LION

The European IST project Layers Interworking in Optical Networks (LION) is a multilayer, multivendor, and multidomain managed IP/MPLS over automatic switched optical network (ASON) with a GMPLS-based control plane (Cavazzoni et al., 2003). The ASON framework facilitates the set-up, modification, reconfiguration, and release of both switched and soft-permanent optical connections (lightpaths). Switched connections are controlled by clients as opposed to soft-permanent connections whose set-up and teardown are initiated by the network management system (NMS). An ASON consists of one or more domains, each belonging to a different network operator, administrator, or vendor platform. The points of interaction between different domains are called reference points. Figure 5.1 depicts the ASON reference points between various optical networks and client networks which are connected via lightpaths. Specifically, the reference point between a client network and an administrative domain of an optical network is called user-network interface (UNI). The reference point between the administrative domains of two different optical networks is called external network-network interface (E-NNI). The reference point between two domains (e.g., routing areas) within the same administrative domain of an optical network is called internal network-network interface (I-NNI). The LION testbed comprises three domains consisting of optical adddrop multiplexers (OADMs) and optical cross-connects (OXCs) from different vendors. For video-over-IP (VoIP) and computer-aided design (CAD) applications, the set-up and tear-down of soft-permanent connections through different domains using GMPLS signaling and interworking NMSs was experimentally validated. Furthermore, multilayer resilience tests were successfully carried out demonstrating MPLS fast reroute combined with optical restoration using a holdoff timer at the IP/MPLS layer.

In our introductory discussion of all-optical networks (AONs) in Section 1.5.1 we have seen that the concept of lightpath plays a key role in wavelength-routing optical networks. A lightpath is an optical point-to-point path of light that interconnects a pair of source and destination nodes, where intermediate nodes along the lightpath route the signal all-optically without undergoing OEO conversion. As each lightpath requires one wavelength on every traversed link and the number of both wavelengths and links in AONs is limited for cost and efficiency reasons, it is impossible to interconnect every pair of nodes by a dedicated lightpath. Nodes that cannot be directly connected via a lightpath may use multiple different lightpaths to exchange data. In the resultant multihop optical network, each intermediate node terminating a lightpath performs OEO conversion. As a consequence, such opaque multihop optical networks are unable to provide transparency. Also, note that the transmission capacity between node pairs connected via a lightpath is equal to the bandwidth of an entire wavelength channel. This transmission capacity is dedicated and cannot be shared by other nodes, leading to wasted bandwidth under bursty nonregular traffic. To improve the bandwidth utilization of lightpaths, electronic traffic grooming becomes necessary at each source node.

To avoid the loss of transparency and the need for electronic traffic grooming of lightpath-based optical networks, a novel solution for the design of transparent mesh wavelength division multiplexing (WDM) wide area networks was proposed in Chlamtac et al. (1999b).

Ethernet networks have come a long way and are widely deployed nowadays. In fact, 95% of today's local area networks (LANs) use Ethernet. Ethernet's transmission rate was originally set at 10 megabits per second (10 Mbps) in 1980 and evolved to higher speed versions ever since. A 100-Mbps version, also known as Fast Ethernet, was approved as IEEE standard 802.3u in 1995. In order to save time and standards development resources, physical signaling methods previously developed and standardized for Fiber Distributed Data Interface (FDDI) networks were reused in the IEEE standard 802.3u (Thompson, 1997). Fast Ethernet was immediately accepted by customers and its success prompted the development of an Ethernet standard for operation at 1000 Mbps (1 Gbps), leading to Gigabit Ethernet (GbE). The standard for Gigabit Ethernet, IEEE standard 802.3z, was formally approved in 1998. At present, 10-Gigabit Ethernet (10GbE) is the fastest of the Ethernet standards. The standardization of 10GbE began in March of 1999 and led to the 10GbE standard IEEE 802.3ae, which was formally approved in 2002.

In this chapter, we highlight the salient features of both 1 and 10 Gbps Ethernet. While 10GbE is the fastest existing Ethernet standard at the time of writing, it is worthwhile to mention that 10GbE does not represent the end of the development of ever-increasing higher-speed Ethernet networks. The standardization of 100-Gigabit Ethernet (100GbE) is currently under development by the IEEE 802.3 Higher Speed Study Group (HSSG). The HSSG was formed in 2006 and aims at providing a standard for 100GbE by the end of 2009.

The aforementioned wavelength division multiplexing (WDM) ring networks appear to be natural candidates to extend existing optical single-channel ring networks (e.g., RPR) to multichannel systems by means of WDM. In WDM rings, optical single-channel rings are multichannel upgraded by exploiting the already existing fiber infrastructure without requiring any additional fiber links and modifications of the ring topology. Clearly, deploying WDM on the existing ring infrastructure saves on fiber requirements. At the downside, however, WDM rings require all ring nodes to be WDM upgraded at the same time (e.g., each ring node is equipped with a transceiver array or wavelength (de)multiplexer). Furthermore, WDM rings are able to survive only a single link or node failure due to their underlying ring topology, similar to their single-channel counterparts.

An alternative approach to multichannel upgrade optical single-channel rings relies on topological modifications of the basic ring architecture. Many ways exist to modify and enhance the topology of ring networks, resulting in so-called augmented rings (Aiello et al., 2001). In this chapter, we describe a novel multichannel upgrade of optical single-channel ring networks where the ring network is left untouched and only a subset of ring nodes needs to be WDM upgraded and interconnected by a single–hop star WDM subnetwork in a pay-as-you-grow fashion (Maier and Reisslein, 2006). The resultant hybrid ring-star network, called RINGOSTAR, requires additional fiber links to build the star subnetwork, as opposed to WDM rings. Unlike WDM rings, however, RINGOSTAR does not require all ring nodes to be WDM upgraded at the same time.

We have briefly introduced the automatic switched optical network (ASON) framework for the control plane of optical networks in Section 2.5. The ASON framework facilitates the set-up, modification, reconfiguration, and release of both switched and soft-permanent optical connections. Switched connections are controlled by clients as opposed to soft-permanent connections whose set-up and tear-down are initiated by the network management system. An ASON consists of one or more domains, where each domain may belong to a different network operator, administrator, or vendor platform. In the ASON framework, the points of interaction between different domains are called reference points. Figure 5.1 depicts the ASON reference points between various optical networks and client networks (e.g., IP, asynchronous transfer mode [ATM], or Synchronous Optical Network/synchronous digital hierarchy [SONET/SDH] networks), which are connected via lightpaths. Specifically, the reference point between a client network and an administrative domain of an optical network is called user–network interface (UNI). The reference point between the administrative domains of two different optical networks is called external network–network interface (E-NNI). The reference point between two domains (e.g., routing areas), within the same administrative domain of an optical network is called internal network–network interface (I-NNI).

Multiprotocol label switching

The ASON framework may be viewed as a reference architecture for the control plane of optical switching networks. It is important to note that the framework addresses the ASON requirements but does not specify any control plane protocol. In transparent optical networks, such as ASON, intermediate optical add-drop multiplexers (OADMs) and optical cross-connects (OXCs) may be optically bypassed and thereby prevented from accessing the corresponding wavelength channels.

Optical fiber provides huge amounts of bandwidth which can be tapped into by means of dense wavelength division multiplexing (DWDM), where each fiber may carry tens or even hundreds of wavelength channels, each operating at electronic peak rate (e.g., 40 Gb/s). Given this huge number of high-speedwavelength channels, one may think that network capacity will not be an issue in future optical networks and it seems reasonable to deploy dynamic optical circuit switching (OCS) to meet future service requirements in support of existing and emerging applications. Typically, these optical circuits may be lightpaths that are dynamically set up and torn down by using a generalized multiprotocol label switching (GMPLS) based control plane to realize reconfigurable optical transport networks, leading to multiprotocol lambda switching (MPλS), as discussed at length in Chapter 5. While OCS may be considered a viable solution that can be realized using mature optics and photonics technologies, economics will ultimately demand that network resources are used more efficiently by decreasing the switching granularity from optical wavelengths to optical packets, giving rise to optical packet switching (OPS) (O'Mahony et al., 2001). Especially given the fact that networks increasingly become IP data-centric, OPS naturally appears to be a promising candidate to support bursty data traffic more efficiently than OCS by capitalizing on the statistical multiplexing gain. Furthermore, the connectionless service offered by OPS helps reduce the network latency in that OPS avoids the two-way reservation overhead of OCS. Note that in Chapter 9 we have seen that the same holds for optical burst switching (OBS) as well.