2

THE PHYSICAL LAYER

In this chapter, we look at the lowest layer in our reference model, the physical layer. It defines the electrical, timing, and other interfaces by which bits are sent as signals over channels. The physical layer is the foundation on which the network is built. The properties of different kinds of physical channels determine the per formance (e.g., throughput, latency, and error rate) so it is a good place to start our journey into network-land.

We will begin by introducing three kinds of transmission media: guided or wired (e.g., copper, coaxial cable, fiber optics), wireless (terrestrial radio), and sat- ellite. Each of these technologies has different properties that affect the design and performance of the networks that use them. This material provides background information on the key transmission technologies used in modern networks.

We then cover a theoretical analysis of data transmission, only to discover that Mother (Parent?) Nature puts some limits on what can be sent over a communica tions channel (i.e., a physical transmission medium used to send bits). Next comes digital modulation, which is all about how analog signals are converted into digital bits and back. After that we will look at multiplexing schemes, exploring how multiple conversations can be put on the same transmission medium at the same time without interfering with one another.

Finally, we will look at three examples of communication systems used in practice for wide area computer networks: the (fixed) telephone system, the mobile phone system, and the cable television system. Each of these is important in prac tice, so we will devote a fair amount of space to each one.

89

90 THE PHYSICAL LAYER CHAP. 2 2.1 GUIDED TRANSMISSION MEDIA

The purpose of the physical layer is to transport bits from one machine to an- other. Various physical media can be used for the actual transmission. Transmis- sion media that rely on a physical cable or wire are often called guided transmis- sion media because the signal transmissions are guided along a path with a physi- cal cable or wire. The most common guided transmission media are copper cable

(in the form of coaxial cable or twisted pair) and fiber optics. Each type of guided transmission media has its own set of trade-offs in terms of frequency, bandwidth, delay, cost, and ease of installation and maintenance. Bandwidth is a measure of the carrying capacity of a medium. It is measured in Hz (or MHz or GHz). It is named in honor of the German physicist Heinrich Hertz. We will discuss this in detail later in this chapter.

2.1.1 Persistent Storage

One of the most common ways to transport data from one device to another is to write them onto persistent storage, such as magnetic or solid-state storage (e.g., recordable DVDs), physically transport the tape or disks to the destination ma- chine, and read them back in again. Although this method is not as sophisticated as using a geosynchronous communication satellite, it is often more cost effective, especially for applications where a high data rate or cost per bit transported is the key factor.

A simple calculation will make this point clear. An industry-standard Ultrium tape can hold 30 terabytes. A box 60 × 60 × 60 cm can hold about 1000 of these tapes, for a total capacity of 800 terabytes, or 6400 terabits (6.4 petabits). A box of tapes can be delivered anywhere in the United States in 24 hours by Federal Express and other companies. The effective bandwidth of this transmission is 6400 terabits/86,400 sec, or a bit over 70 Gbps. If the destination is only an hour away by road, the bandwidth is increased to over 1700 Gbps. No computer net- work can even approach this. Of course, networks are getting faster, but tape den- sities are increasing, too.

If we now look at cost, we get a similar picture. The cost of an Ultrium tape is around $40 when bought in bulk. A tape can be reused at least 10 times, so the tape cost is maybe $4000 per box per usage. Add to this another $1000 for ship- ping (probably much less), and we have a cost of roughly $5000 to ship 800 TB. This amounts to shipping a gigabyte for a little over half a cent. No network can beat that. The moral of the story is:

Never underestimate the bandwidth of a station wagon full of tapes hurtling down the highway.

For moving very large amounts of data, this is often the best solution. Amazon has what it calls the ‘‘Snowmobile,’’ which is a large truck filled with thousands of

SEC. 2.1 GUIDED TRANSMISSION MEDIA 91

hard disks, all connected to a high-speed network inside the truck. The total capac ity of the truck is 100 PB (100,000 TB or 100 million GB). When a company has a huge amount of data to move, it can have the truck come to its premises and plug into the company’s fiber-optic network, then suck out all the data into the truck. Once that it is done, the truck drives to another location and disgorges all the data. For example, a company wishing to replace its own massive datacenter with the Amazon cloud might be interested in this service. For very large volumes of data, no other method of data transport can even approach this.

2.1.2 Twisted Pairs

Although the bandwidth characteristics of persistent storage are excellent, the delay characteristics are poor: Transmission time is measured in hours or days, not milliseconds. Many applications, including the Web, video conferencing, and online gaming, rely on transmitting data with low delay. One of the oldest and still most common transmission media is twisted pair. A twisted pair consists of two insulated copper wires, typically about 1 mm thick. The wires are twisted together in a helical form, similar to a DNA molecule. Two parallel wires constitute a fine antenna; when the wires are twisted, the waves from different twists cancel out, so the wire radiates less effectively. A signal is usually carried as the difference in voltage between the two wires in the pair. Transmitting the signal as the difference between the two voltage levels, as opposed to an absolute voltage, provides better immunity to external noise because the noise tends to affect the voltage traveling through both wires in the same way, leaving the differential relatively unchanged.

The most common application of the twisted pair is the telephone system. Nearly all telephones are connected to the telephone company (telco) office by a twisted pair. Both telephone calls and ADSL Internet access run over these lines. Twisted pairs can run several kilometers without amplification, but for longer dis tances the signal becomes too attenuated and repeaters are needed. When many twisted pairs run in parallel for a substantial distance, such as all the wires coming from an apartment building to the telephone company office, they are bundled to- gether and encased in a protective sheath. The pairs in these bundles would inter fere with one another if it were not for the twisting. In parts of the world where telephone lines run on poles above ground, it is common to see bundles several centimeters in diameter.

Twisted pairs can be used for transmitting either analog or digital information. The bandwidth depends on the thickness of the wire and the distance traveled, but hundreds of megabits/sec can be achieved for a few kilometers, in many cases, and more when varioustricks are used. Due to their adequate performance, widespread availability, and low cost, twisted pairs are widely used and are likely to remain so for years to come.

Twisted-pair cabling comes in several varieties. One common variety of twist- ed-pair cables now deployed in many buildings is called Category 5e cabling, or

92 THE PHYSICAL LAYER CHAP. 2

‘‘Cat 5e.’’ A Category 5e twisted pair consists of two insulated wires gently twisted together. Four such pairs are typically grouped in a plastic sheath to protect the wires and keep them together. This arrangement is shown in Fig. 2-1.

Twisted pair

Figure 2-1. Category 5e UTP cable with four twisted pairs. These cables can be used for local area networks.

Different LAN standards may use the twisted pairs differently. For example, 100-Mbps Ethernet uses two (out of the four) pairs, one pair for each direction. To reach higher speeds, 1-Gbps Ethernet uses all four pairs in both directions simul taneously, which requires the receiver to factor out the signal that istransmitted.

Some general terminology is now in order. Links that can be used in both di rections at the same time, like a two-lane road, are called full-duplex links. In contrast, links that can be used in either direction, but only one way at a time, like a single-track railroad line, are called half-duplex links. A third category consists of links that allow traffic in only one direction, like a one-way street. They are call- ed simplex links.

Returning to twisted pair, Cat 5 replaced earlier Category 3 cables with a simi lar cable that uses the same connector, but has more twists per meter. More twists result in less crosstalk and a better-quality signal over longer distances, making the cables more suitable for high-speed computer communication, especially 100-Mbps and 1-Gbps Ethernet LANs.

New wiring is more likely to be Category 6 or even Category 7. These cate- gories have more stringent specifications to handle signals with greater band- widths. Some cables in Category 6 and above can support the 10-Gbps links that are now commonly deployed in many networks, such as in new office buildings. Category 8 wiring runs at higher speeds than the lower categories, but operates only at short distances of around 30 meters and is thus only suitable in data cen ters. The Category 8 standard has two options: Class I, which is compatible with Category 6A; and Class II, which is compatible with Category 7A.

Through Category 6, these wiring types are referred to as UTP (Unshielded Twisted Pair) as they consist simply of wires and insulators. In contrast to these, Category 7 cables have shielding on the individual twisted pairs, as well as around the entire cable (but inside the plastic protective sheath). Shielding reduces the susceptibility to external interference and crosstalk with other nearby cables to meet demanding performance specifications. The cables are reminiscent of the

SEC. 2.1 GUIDED TRANSMISSION MEDIA 93

high-quality, but bulky and expensive shielded twisted pair cables that IBM intro- duced in the early 1980s. However, these did not prove popular outside of IBM in- stallations. Evidently, it is time to try again.

2.1.3 Coaxial Cable

Another common transmission medium is the coaxial cable (known to its many friends as just ‘‘coax’’ and pronounced ‘‘co-ax’’). It has better shielding and greater bandwidth than unshielded twisted pairs, so it can span longer distances at higher speeds. Two kinds of coaxial cable are widely used. One kind, 50-ohm cable, is commonly used when it is intended for digital transmission from the start. The other kind, 75-ohm cable, is commonly used for analog transmission and cable television. This distinction is based on historical, rather than technical, factors (e.g., early dipole antennas had an impedance of 300 ohms, and it was easy to use existing 4:1 impedance-matching transformers). Starting in the mid-1990s, cable TV operators began to provide Internet access over cable, which has made 75-ohm cable more important for data communication.

A coaxial cable consists of a stiff copper wire as the core, surrounded by an insulating material. The insulator is encased by a cylindrical conductor, often as a closely woven braided mesh. The outer conductor is covered in a protective plastic sheath. A cutaway view of a coaxial cable is shown in Fig. 2-2.

Copper core

Insulating material

Braided outer

conductor

Protective plastic

covering

Figure 2-2. A coaxial cable.

The construction and shielding of the coaxial cable give it a good combination of high bandwidth and excellent noise immunity (e.g., from garage door openers, microwave ovens, and more). The bandwidth possible depends on the cable quali ty and length. Coaxial cable has extremely wide bandwidth; modern cables have a bandwidth of up to 6 GHz, thus allowing many conversations to be simultaneously transmitted over a single coaxial cable (a single television program might occupy approximately 3.5 MHz). Coaxial cables were once widely used within the tele- phone system for long-distance lines but have now largely been replaced by fiber optics on long-haul routes. Coax is still widely used for cable television and met ropolitan area networks and is also used for delivering high-speed Internet con- nectivity to homes in many parts of the world.

94 THE PHYSICAL LAYER CHAP. 2 2.1.4 Power Lines

The telephone and cable television networks are not the only sources of wiring that can be reused for data communication. There is a yet more common kind of wiring: electrical power lines. Power lines deliver electrical power to houses, and electrical wiring within houses distributesthe power to electrical outlets.

The use of power lines for data communication is an old idea. Power lines have been used by electricity companies for low-rate communication such as re- mote metering for many years, as well in the home to control devices (e.g., the X10 standard). In recent years there has been renewed interest in high-rate communica tion over these lines, both inside the home as a LAN and outside the home for broadband Internet access. We will concentrate on the most common scenario: using electrical wires inside the home.

The convenience of using power lines for networking should be clear. Simply plug a TV and a receiver into the wall, which you must do anyway because they need power, and they can send and receive movies over the electrical wiring. This configuration is shown in Fig. 2-3. There is no other plug or radio. The data signal is superimposed on the low-frequency power signal (on the active or ‘‘hot’’ wire) as both signals use the wiring at the same time.

Electric cable Data signal

Power signal

Figure 2-3. A network that uses household electrical wiring.

The difficulty with using household electrical wiring for a network is that it was designed to distribute power signals. This task is quite distinct from distribut ing data signals, at which household wiring does a horrible job. Electrical signals are sent at 50–60 Hz and the wiring attenuates the much higher frequency (MHz) signals needed for high-rate data communication. The electrical properties of the wiring vary from one house to the next and change as appliances are turned on and off, which causes data signals to bounce around the wiring. Transient currents when appliances switch on and off create electrical noise over a wide range of fre- quencies. And without the careful twisting of twisted pairs, electrical wiring acts as a fine antenna, picking up external signals and radiating signals of its own. This be- havior means that to meet regulatory requirements, the data signal must avoid licensed frequencies such as the amateur radio bands.

SEC. 2.1 GUIDED TRANSMISSION MEDIA 95

Despite these difficulties, it is practical to send at least 500 Mbps short dis tances over typical household electrical wiring by using communication schemes that resist impaired frequencies and bursts of errors. Many products use proprietary standards for power-line networking, but standards are being developed.

2.1.5 Fiber Optics

More than a few people in the computer industry take enormous pride in how fast computer technology is improving as it follows Moore’s law, which predicts a doubling of the number of transistors per chip roughly every 2 years (Kuszyk and Hammoudeh, 2018). The original (1981) IBM PC ran at a clock speed of 4.77 MHz. Forty years later, PCs could run a four-core CPU at 3 GHz. This increase is of a factor of around 2500. Impressive.

In the same period, wide area communication links went from 45 Mbps (a T3 line in the telephone system) to 100 Gbps (a modern long-distance line). This gain is similarly impressive, more than a factor of 2000, while at the same time the error ^<5 per bit to almost zero. In the past decade, single CPUs have

rate went from 10

approached physical limits, which is why the number of CPU cores per chip is being increased. In contrast, the achievable bandwidth with fiber technology is in excess of 50,000 Gbps (50 Tbps) and we are nowhere near reaching these limits. The current practical limit of around 100 Gbps is simply due to our inability to convert between electrical and optical signals any faster. To build higher-capacity links, many channels are simply carried in parallel over a single fiber.

In this section, we will study fiber optics to learn how that transmission tech- nology works. In the ongoing race between computing and communication, com- munication may yet win because of fiber-optic networks. The implication of this would be essentially infinite bandwidth and a new conventional wisdom that com- puters are hopelessly slow so that networks should try to avoid computation at all costs, no matter how much bandwidth that wastes. This change will take a while to sink in to a generation of computer scientists and engineers taught to think in terms of the low transmission limits imposed by copper wires.

Of course, this scenario does not tell the whole story because it does not in- clude cost. The cost to install fiber over the last mile to reach consumers and bypass the low bandwidth of wires and limited availability of spectrum is tremen- dous. It also costs more energy to move bits than to compute. We may always have islands of inequities where either computation or communication is essentially free. For example, at the edge of the Internet we apply computation and storage to the problem of compressing and caching content, all to make better use of Internet access links. Within the Internet, we may do the reverse, with companies such as Google moving huge amounts of data across the network to where it is cheaper to perform storage or computation.

Fiber optics are used for long-haul transmission in network backbones, high- speed LANs (although so far, copper has often managed to catch up eventually),

96 THE PHYSICAL LAYER CHAP. 2

and high-speed Internet access such as fiber to the home. An optical transmission system has three key components: the light source, the transmission medium, and the detector. Conventionally, a pulse of light indicates a 1 bit and the absence of light indicates a 0 bit. The transmission medium is an ultra-thin fiber of glass. The detector generates an electrical pulse when light falls on it. By attaching a light source to one end of an optical fiber and a detector to the other, we have a unidirec tional (i.e., simplex) data transmission system that accepts an electrical signal, con- verts and transmits it by light pulses, and then reconverts the output to an electrical signal at the receiving end.

This transmission system would leak light and be useless in practice were it not for an interesting principle of physics. When a light ray passes from one medium to another—for example, from fused silica (glass) to air—the ray is refracted (bent) at the silica/air boundary, as shown in Fig. 2-4(a). Here we see a light ray incident on the boundary at an angle _ ₁ emerging at an angle ` ₁. The amount of refraction depends on the properties of the two media (in particular, their indices of refraction). For angles of incidence above a certain critical value, the light is refracted back into the silica; none of it escapes into the air. Thus, a light ray incident at or above the critical angle is trapped inside the fiber, as shown in Fig. 2-4(b), and can propagate for many kilometers with virtually no loss.

Air

Air/silica

`<sub>1</sub> `₂ `₃

boundary

_₁ _₂ _₃

Silica Light source (a) (b)

Total internal reflection

Figure 2-4. (a) Three examples of a light ray from inside a silica fiber impinging on the air/silica boundary at different angles. (b) Light trapped by total internal reflection.

The sketch of Fig. 2-4(b) shows only one trapped ray, but since any light ray incident on the boundary above the critical angle will be reflected internally, many different rays will be bouncing around at different angles. Each ray is said to have a different mode, so a fiber having this property is called a multimode fiber. If the fiber’s diameter is reduced to a few wavelengths of light (less than 10 microns, as opposed to more than 50 microns for multimode fiber), the fiber acts like a waveguide and the light can propagate only in a straight line, without bouncing, yielding a single-mode fiber. Single-mode fibers are more expensive but are widely used for longer distances; they can transmit signals approximately 50 times

SEC. 2.1 GUIDED TRANSMISSION MEDIA 97

farther than multimode fibers. Currently available single-mode fibers can transmit data at 100 Gbps for 100 km without amplification. Even higher data rates have been achieved in the laboratory for shorter distances. The choice between sin- gle-mode or multimode fiber depends on the application. Multimode fiber can be used for transmissions of up to about 15 km and can allow the use of relatively less expensive fiber-optic equipment. On the other hand, the bandwidth of multimode fiber becomes more limited as distance increases.

Transmission of Light Through Fiber

Optical fibers are made of glass, which, in turn, is made from sand, an inex- pensive raw material available in unlimited amounts. Glassmaking was known to the ancient Egyptians, but their glass had to be no more than 1 mm thick or the light could not shine through. Glass transparent enough to be useful for windows was developed during the Renaissance. The glass used for modern optical fibers is so transparent that if the oceans were full of it instead of water, the seabed would be as visible from the surface as the ground is from an airplane on a clear day.

The attenuation of light through glass depends on the wavelength of the light (as well as on some of the physical properties of the glass). It is defined as the ratio of input to output signal power. For the kind of glass used in fibers, the atten- uation is shown in Fig. 2-5 in units of decibels (dB) per linear kilometer of fiber. As an example, a factor of two loss of signal power corresponds to an attenuation of 10 log₁₀ 2 = 3 dB. We will discuss decibels shortly. In brief, it is a logarithmic way to measure power ratios, with 3 dB meaning a factor of two power ratio. The figure shows the near-infrared part of the spectrum, which is what is used in prac tice. Visible light has slightly shorter wavelengths, from about 0.4 to 0.7 microns. (1 micron is 10^<6 meters.) The true metric purist would refer to these wavelengths as 400 nm to 700 nm, but we will stick with traditional usage.

Three wavelength bands are most commonly used at present for optical com- munication. They are centered at 0.85, 1.30, and 1.55 microns, respectively. All three bands are 25,000 to 30,000 GHz wide. The 0.85-micron band was used first. It has higher attenuation and so is used for shorter distances, but at that wavelength the lasers and electronics could be made from the same material (gallium arsen ide). The last two bands have good attenuation properties (less than 5% loss per kilometer). The 1.55-micron band is now widely used with erbium-doped ampli fiers that work directly in the optical domain.

Light pulses sent down a fiber spread out in length as they propagate. This spreading is called chromatic dispersion. The amount of it is wavelength depen- dent. One way to keep these spread-out pulses from overlapping is to increase the distance between them, but this can be done only by reducing the signaling rate. Fortunately, it has been discovered that making the pulses in a special shape related to the reciprocal of the hyperbolic cosine causes nearly all the dispersion effects to cancel out, so it is now possible to send pulses for thousands of kilometers without

98 THE PHYSICAL LAYER CHAP. 2

2.0

1.8

1.6

)

0.85µ Band

1.30µ Band

1.55µ Band

m

k/

B

d(

1.4 1.2

n

1.0

o

i

t

a

u

0.8

n

e

t

t

0.6

A

0.4

0.2

0 0.8 0.9

1.0 1.1 1.2 1.3

1.4 1.5 1.6 1.7 1.8

Wavelength (microns)

Figure 2-5. Attenuation of light through fiber in the infrared region.

appreciable shape distortion. These pulses are called solitons. They are starting to be widely used in practice.

Fiber Cables

Fiber-optic cables are similar to coax, except without the braid. Figure 2-6(a) shows a single fiber viewed from the side. At the center is the glass core through which the light propagates. In multimode fibers, the core is typically around 50 microns in diameter, about the thickness of a human hair. In single-mode fibers, the core is 8 to 10 microns.

^Sheath Jacket

Core

(glass)

Cladding (glass)

Jacket

(plastic) Core Cladding

(a) (b)

Figure 2-6. (a) Side view of a single fiber. (b) End view of a sheath with three fibers.

The core is surrounded by a glass cladding with a lower index of refraction than the core, to keep all the light in the core. Next comes a thin plastic jacket to

SEC. 2.1 GUIDED TRANSMISSION MEDIA 99

protect the cladding. Fibers are typically grouped in bundles, protected by an outer sheath. Figure 2-6(b) shows a sheath with three fibers.

Terrestrial fiber sheaths are normally laid in the ground within a meter of the surface, where they are occasionally subject to attacks by backhoes or gophers. Near the shore, transoceanic fiber sheaths are buried in trenches by a kind of sea- plow. In deep water, they just lie on the bottom, where they can be snagged by fishing trawlers or attacked by a giant squid.

Fibers can be connected in three different ways. First, they can terminate in connectors and be plugged into fiber sockets. Connectors lose about 10 to 20% of the light, but they make it easy to reconfigure systems. Second, they can be spliced mechanically. Mechanical splices just lay the two carefully cut ends next to each other in a special sleeve and clamp them in place. Alignment can be improved by passing light through the junction and then making small adjustments to maximize the signal. Mechanical splices take trained personnel about 5 minutes and result in a 10% light loss. Third, two pieces of fiber can be fused (melted) to form a solid connection. A fusion splice is almost as good as a single drawn fiber, but even here, a small amount of attenuation occurs. For all three kinds of splices, reflec tions can occur at the point of the splice and the reflected energy can interfere with the signal.

Two kinds of light sources are typically used to do the signaling: LEDs (Light Emitting Diodes) and semiconductor lasers. They have different properties, as shown in Fig. 2-7. They can be tuned in wavelength by inserting Fabry-Perot or Mach-Zehnder interferometers between the source and the fiber. Fabry-Perot inter ferometers are simple resonant cavities consisting of two parallel mirrors. The light is incident perpendicular to the mirrors. The length of the cavity selects out those wavelengths that fit inside an integral number of times. Mach-Zehnder inter ferometers separate the light into two beams. The two beams travel slightly dif ferent distances. They are recombined at the end and are in phase for only certain wavelengths.

Item LED Semiconductor laser

Data rate Low High

Fiber type Multi-mode Multi-mode or single-mode Distance Short Long

Lifetime Long life Short life

Temperature sensitivity Minor Substantial

Cost Low cost Expensive

Figure 2-7. A comparison of semiconductor diodes and LEDs as light sources.

The receiving end of an optical fiber consists of a photodiode, which gives off an electrical pulse when struck by light. The response time of photodiodes, which convert the signal from the optical to the electrical domain, limits data rates to

100 THE PHYSICAL LAYER CHAP. 2

about 100 Gbps. Thermal noise is also an issue, so a pulse of light must carry enough energy to be detected. By making the pulses powerful enough, the error rate can be made arbitrarily small.

Comparison of Fiber Optics and Copper Wire

It is instructive to compare fiber to copper. Fiber has many advantages. To start with, it can handle much higher bandwidths than copper. This alone would require its use in high-end networks. Due to the low attenuation, repeaters are needed only about every 50 km on long lines, versus about every 5 km for copper, resulting in a big cost saving. Fiber also has the advantage of not being affected by power surges, electromagnetic interference, or power failures. Nor is it affected by corrosive chemicals in the air, important for harsh factory environments.

Oddly enough, telephone companies like fiber for a completely different rea- son: it is thin and lightweight. Many existing cable ducts are completely full, so there is no room to add new capacity. Removing all the copper and replacing it with fiber empties the ducts, and the copper has excellent resale value to copper refiners who regard it as very high-grade ore. Also, fiber is much lighter than cop- per. One thousand twisted pairs 1 km long weigh 8000 kg. Two fibers have more capacity and weigh only 100 kg, which reduces the need for expensive mechanical support systems that must be maintained. For new routes, fiber wins hands down due to its much lower installation cost. Finally, fibers do not leak light and are dif ficult to tap. These properties give fiber good security against wiretappers.

On the downside, fiber is a less familiar technology requiring skills not all en- gineers have, and fibers can be damaged easily by being bent too much. Since op tical transmission is inherently unidirectional, two-way communication requires ei ther two fibers or two frequency bands on one fiber. Finally, fiber interfaces cost more than electrical interfaces. Nevertheless, the future of all fixed data communi- cation over more than short distances is clearly with fiber. For a discussion of many aspects of fiber optics and their networks, see Pearson (2015).

2.2 WIRELESS TRANSMISSION

Many people now have wireless connectivity to many devices, from laptops and smartphones, to smart watches and smart refrigerators. All of these devices rely on wireless communication to transmit information to other devices and end- points on the network.

In the following sections, we will look at wireless communication in general, which has many other important applications besides providing connectivity to users who want to surf the Web from the beach. Wireless has advantages for even fixed devices in some circumstances. For example, if running a fiber to a building is difficult due to the terrain (mountains, jungles, swamps, etc.), wireless may be

SEC. 2.2 WIRELESS TRANSMISSION 101

more appropriate. It is noteworthy that modern wireless digital communication began as a research project of Prof. Norman Abramson of the University of Hawaii in the 1970s where the Pacific Ocean separated the users from their computer cen ter, and the telephone system was inadequate. We will discuss this system, ALOHA, in Chap. 4.

2.2.1 The Electromagnetic Spectrum

When electrons move, they create electromagnetic waves that can propagate through space (even in a vacuum). These waves were predicted by the British physicist James Clerk Maxwell in 1865 and first observed by the German physicist Heinrich Hertz in 1887. The number of oscillations per second of a wave is called its frequency, f, and is measured in Hz. The distance between two consecutive maxima (or minima) is called the wavelength, which is universally designated by the Greek letter h (lambda).

When an antenna of the appropriate size is attached to an electrical circuit, the electromagnetic waves can be broadcast efficiently and received by a receiver some distance away. All wireless communication is based on this principle.

In a vacuum, all electromagnetic waves travel at the same speed, no matter what their frequency. This speed, usually called the speed of light, c, is approxi- mately 3 × 10⁸ m/sec, or about 1 foot (30 cm) per nanosecond. (A case could be made for redefining the foot as the distance light travels in a vacuum in 1 nsec rath- er than basing it on the shoe size of some long-dead king.) In copper or fiber, the speed slows to about 2/3 of this value and becomes slightly frequency dependent. The speed of light is the universe’s ultimate speed limit. No object or signal can ever move faster than it.

The fundamental relation between f , h, and c (in a vacuum) is

h f = c (2-1)

Since c is a constant, if we know f , we can find h, and vice versa. As a rule of thumb, when h is in meters and f is in MHz, h f 5 300. For example, 100-MHz waves are about 3 meters long, 1000-MHz waves are 0.3 meters long, and 0.1-meter waves have a frequency of 3000 MHz.

The electromagnetic spectrum is shown in Fig. 2-8. The radio, microwave, in frared, and visible light portions of the spectrum can all be used for transmitting information by modulating the amplitude, frequency, or phase of the waves. Ultra- violet light, X-rays, and gamma rays would be even better, due to their higher fre- quencies, but they are hard to produce and modulate, do not propagate well through buildings, and are dangerous to living things.

The bands listed at the bottom of Fig. 2-8 are the official ITU (International Telecommunication Union) names and are based on the wavelengths, so the LF band goes from 1 km to 10 km (approximately 30 kHz to 300 kHz). The terms LF,

102 THE PHYSICAL LAYER CHAP. 2

10⁰ 10² 10⁴ 10⁶ 10⁸ 10¹⁰ 10¹² 10¹⁴ 10¹⁶ 10¹⁸ 10²⁰ 10²² 10²⁴ f (Hz)

Radio Microwave Infrared UV X-ray Gamma ray

Visible

light

10⁴ 10⁵ 10⁶ 10⁷ 10⁸ 10⁹ 10¹⁰ 10¹¹ 10¹² 10¹³ 10¹⁴ 10¹⁵ 10¹⁶ f (Hz)

Twisted pair

Coax

AM

Satellite

Terrestrial

microwave

Fiber optics

Maritime

radio

FM radio

TV

Band LF MF HF VHF UHF SHF EHF THF

Figure 2-8. The electromagnetic spectrum and its uses for communication.

MF, and HF refer to Low, Medium, and High Frequency, respectively. Clearly, when the names were assigned nobody expected to go above 10 MHz, so the high- er bands were later named the Very, Ultra, Super, Extremely, and Tremendously High Frequency bands. Beyond that, there are no names, but Incredibly, Astonish ingly, and Prodigiously High Frequency (IHF, AHF, and PHF) would sound nice. ¹² Hz, we get into the infrared, where the comparison is typically to light,

Above 10

not radio.

The theoretical basis for communication, which we will discuss later in this chapter, tells us the amount of information that a signal such as an electromagnetic wave can carry depends on the received power and is proportional to its bandwidth. From Fig. 2-8, it should now be obvious why networking people like fiber optics so much. Many GHz of bandwidth are available to tap for data transmission in the microwave band, and even more bandwidth is available in fiber because it is further to the right in our logarithmic scale. As an example, consider the 1.30-micron band of Fig. 2-5, which has a width of 0.17 microns. If we use Eq. (2-1) to find the start and end frequencies from the start and end wavelengths, we find the frequen- cy range to be about 30,000 GHz. With a reasonable signal-to-noise ratio of 10 dB, this is 300 Tbps.

Most transmissions use a relatively narrow frequency band, in other words, 6 f /f << 1). They concentrate their signal power in this narrow band to use the spectrum efficiently and obtain reasonable data rates by transmitting with enough power. The rest of this section describes three different types of transmission that make use of wider frequency bands.

SEC. 2.2 WIRELESS TRANSMISSION 103 2.2.2 Frequency Hopping Spread Spectrum

In frequency hopping spread spectrum, a transmitter hops from frequency to frequency hundreds of times per second. It is popular for military communication because it makes transmissions hard to detect and next to impossible to jam. It also offers good resistance to fading due to signals taking different paths from source to destination and interfering after recombining. It also offers resistance to narrowband interference because the receiver will not be stuck on an impaired fre- quency for long enough to shut down communication. This robustness makes it useful for crowded parts of the spectrum, such as the ISM bands we will describe shortly. This technique is used commercially, for example, in Bluetooth and older versions of 802.11.

As a curious footnote, the technique was co-invented by the Austrian-born film star Hedy Lamarr, who was famous for acting in European films in the 1930s under her birth name of Hedwig (Hedy) Kiesler. Her first husband was a wealthy armaments manufacturer who told her how easy it was to block the radio signals then used to control torpedoes. When she discovered that he was selling weapons to Hitler, she was horrified, disguised herself as a maid to escape him, and fled to Hollywood to continue her career as a movie actress. In her spare time, she invent- ed frequency hopping to help the Allied war effort.

Her scheme used 88 frequencies, the number of keys (and frequencies) on the piano. For their invention, she and her friend, the musical composer George Antheil, received U.S. patent 2,292,387. However, they were unable to convince the U.S. Navy that their invention had any practical use and never received any

royalties. Only years after the patent expired was the technique rediscovered and used in mobile electronic devices rather than for blocking signals to torpedoes dur ing war time.

2.2.3 Direct Sequence Spread Spectrum

A second form of spread spectrum, direct sequence spread spectrum, uses a code sequence to spread the data signal over a wider frequency band. It is widely used commercially as a spectrally efficient way to let multiple signals share the same frequency band. These signals can be given different codes, a method called code division multiple access that we will return to later in this chapter. This meth- od is shown in contrast with frequency hopping in Fig. 2-9. It forms the basis of 3G mobile phone networks and is also used in GPS (Global Positioning System). Even without different codes, direct sequence spread spectrum, like frequency hop- ping spread spectrum, can tolerate interference and fading because only a fraction of the desired signal is lost. It is used in this role in older versions of the 802.11b wireless LANs protocol. For a fascinating and detailed history of spread spectrum communication, see Walters (2013).

104 THE PHYSICAL LAYER CHAP. 2

Direct

sequence

(CDMA user with

Frequency hopping spread

different code)

Ultrawideband

underlay

spread

spectrum

spectrum

(CDMA user with different code)

Frequency

Figure 2-9. Spread spectrum and ultra-wideband (UWB) communication.

2.2.4 Ultra-Wideband Communication

UWB (Ultra-WideBand) communication sends a series of low-energy rapid pulses, varying their carrier frequencies to communicate information. The rapid transitions lead to a signal that is spread thinly over a very wide frequency band. UWB is defined as signals that have a bandwidth of at least 500 MHz or at least 20% of the center frequency of their frequency band. UWB is also shown in Fig. 2-9. With this much bandwidth, UWB has the potential to communicate at several hundred megabits per second. Because it is spread across a wide band of frequencies, it can tolerate a substantial amount of relatively strong interference from other narrowband signals. Just as importantly, since UWB has very little en- ergy at any given frequency when used for short-range transmission, it does not cause harmful interference to those other narrowband radio signals. In contrast to spread spectrum transmission, UWB transmits in ways that do not interfere with the carrier signals in the same frequency band. It can also be used for imaging through solid objects (ground, walls, and bodies) or as part of precise location sys tems. The technology is popular for short-distance indoor applications, as well as precision radar imaging and location-tracking technologies.

2.3 USING THE SPECTRUM FOR TRANSMISSION

We will now discuss how the various parts of the electromagnetic spectrum of Fig. 2-8 are used, starting with radio. We will assume that all transmissions use a narrow frequency band unless otherwise stated.

2.3.1 Radio Transmission

Radio frequency (RF) waves are easy to generate, can travel long distances, and can penetrate buildings easily, so they are widely used for communication, both indoors and outdoors. Radio waves also are omnidirectional, meaning that

SEC. 2.3 USING THE SPECTRUM FOR TRANSMISSION 105

they travel in all directions from the source, so the transmitter and receiver do not have to be carefully aligned physically.

Sometimes omni-directional radio is good, but sometimes it is bad. In the 1970s, General Motors decided to equip all its new Cadillacs with computer-con trolled anti-lock brakes. When the driver stepped on the brake pedal, the computer pulsed the brakes on and off instead of locking them on hard. One fine day an Ohio Highway Patrolman began using his new mobile radio to call headquarters, and suddenly the Cadillac next to him began behaving like a bucking bronco. When the officer pulled the car over, the driver claimed that he had done nothing and that the car had gone crazy.

Eventually, a pattern began to emerge: Cadillacs would sometimes go berserk, but only on major highways in Ohio and then only when the Highway Patrol was there watching. For a long, long time General Motors could not understand why Cadillacs worked fine in all the other states and also on minor roads in Ohio. Only after much searching did they discover that the Cadillac’s wiring made a fine an tenna for the frequency used by the Ohio Highway Patrol’s new radio system.

The properties of radio waves are frequency dependent. At low frequencies, radio waves pass through obstacles well, but the power falls off sharply with dis tance from the source—at least as fast as 1/r²in air—as the signal energy is spread more thinly over a larger surface. This attenuation is called path loss. At high fre- quencies, radio waves tend to travel in straight lines and bounce off obstacles. Path loss still reduces power, though the received signal can depend strongly on reflec tions as well. High-frequency radio waves are also absorbed by rain and other obstacles to a larger extent than are low-frequency ones. At all frequencies, radio waves are subject to interference from motors and other electrical equipment.

It is interesting to compare the attenuation of radio waves to that of signals in guided media. With fiber, coax, and twisted pair, the signal drops by the same frac tion per unit distance, for example, 20 dB per 100 m for twisted pair. With radio, the signal drops by the same fraction as the distance doubles, for example 6 dB per doubling in free space. This behavior means that radio waves can travel long dis tances, and interference between users is a problem. For this reason, all govern- ments tightly regulate the use of radio transmitters, with few notable exceptions, which are discussed later in this chapter.

In the VLF, LF, and MF bands, radio waves follow the ground, as illustrated in Fig. 2-10(a). These waves can be detected for perhaps 1000 km at the lower fre- quencies, less at the higher ones. AM radio broadcasting uses the MF band, which is why the ground waves from Boston AM radio stations cannot be heard easily in New York. Radio waves in these bands pass through buildings easily, which is why radios work indoors. The main problem with using these bands for data com- munication is their low bandwidth.

In the HF and VHF bands, the ground waves tend to be absorbed by the earth. However, the waves that reach the ionosphere, a layer of charged particles circling the earth at a height of 100 to 500 km, are refracted by it and sent back to earth, as

106 THE PHYSICAL LAYER CHAP. 2

Ground

wave

p he r e

_o s _o n _I

Earth's surface Earth's surface

(a) (b)

Figure 2-10. (a) In the VLF, LF, and MF bands, radio waves follow the curvature of the earth. (b) In the HF band, they bounce off the ionosphere.

shown in Fig. 2-10(b). Under certain atmospheric conditions, the signals can bounce several times. Amateur radio operators (hams) use these bands to talk long distance. The military also uses the HF and VHF bands for communication.

2.3.2 Microwave Transmission

Above 100 MHz, the waves travel in nearly straight lines and can therefore be narrowly focused. Concentrating all the energy into a small beam by means of a parabolic antenna (like the familiar satellite TV dish) gives a much higher sig- nal-to-noise ratio, but the transmitting and receiving antennas must be accurately aligned with each other. In addition, this directionality allows multiple transmitters lined up in a row to communicate with multiple receivers in a row without inter ference, provided some minimum spacing rules are observed. Before fiber optics, for decades these microwaves formed the heart of the long-distance telephone transmission system. In fact, MCI, one of AT&T’s first competitors after it was deregulated, built its entire system with microwave communications passing be tween towers tens of kilometers apart. Even the company’s name reflected this (MCI stood for Microwave Communications, Inc.). MCI has since gone over to fiber and through a long series of corporate mergers and bankruptcies in the telecommunications shuffle has become part of Verizon.

Microwaves are directional: they travel in a straight line, so if the towers are too far apart, the earth will get in the way (think about a Seattle-to-Amsterdam link). Thus, repeaters are needed periodically. The higher the towers are, the far ther apart they can be. The distance between repeaters goes up roughly with the square root of the tower height. For 100-meter towers, repeaters can be 80 km apart.

Unlike radio waves at lower frequencies, microwaves do not pass through buildings well. In addition, even though the beam may be well focused at the transmitter, there is still some divergence in space. Some waves may be refracted off low-lying atmospheric layers and may take slightly longer to arrive than the

SEC. 2.3 USING THE SPECTRUM FOR TRANSMISSION 107

direct waves. The delayed waves may arrive out of phase with the direct wave and thus cancel the signal. This effect is called multipath fading and is often a serious problem. It is weather and frequency dependent. Some operators keep 10% of their channels idle as spares to switch on when multipath fading temporarily wipes out a particular frequency band.

The demand for higher data rates is driving wireless network operators to yet higher frequencies. Bands up to 10 GHz are now in routine use, but at around 4 GHz, a new problem sets in: absorption by water. These waves are only a few centimeters long and are absorbed by rain. This effect would be fine if one were planning to build a huge outdoor microwave oven for roasting passing birds, but for communication it is a severe problem. As with multipath fading, the only solu tion is to shut off links that are being rained on and route around them.

In summary, microwave communication is so widely used for long-distance telephone communication, mobile phones, television distribution, and other pur- poses that a severe shortage of spectrum has developed. It has several key advan tages over fiber. The main one is that no right of way is needed to lay down cables. By buying a small plot of ground every 50 km and putting a microwave tower on it, one can bypass the telephone system entirely. This is how MCI managed to get started as a new long-distance telephone company so quickly. (Sprint, another early competitor to the deregulated AT&T, went a completely different route: it was formed by the Southern Pacific Railroad, which already owned a large amount of right of way and just buried fiber next to the tracks.)

Microwave is also relatively inexpensive. Putting up two simple towers (which can be just big poles with four guy wires) and putting antennas on each one may be cheaper than burying 50 km of fiber through a congested urban area or up over a mountain, and it may also be cheaper than leasing the telephone company’s fiber, especially if the telephone company has not yet even fully paid for the copper it ripped out when it put in the fiber.

2.3.3 Infrared Transmission

Unguided infrared waves are widely used for short-range communication. The remote controls used for televisions, Blu-ray players, and stereos all use infrared communication. They are relatively directional, cheap, and easy to build but have a major drawback: they do not pass through solid objects. (Try standing between your remote control and your television and see if it still works.) In general, as we go from long-wave radio toward visible light, the waves behave more and more like light and less and less like radio.

On the other hand, the fact that infrared waves do not pass through solid walls well is also a plus. It means that an infrared system in one room of a building will not interfere with a similar system in adjacent rooms or buildings: you cannot con trol your neighbor’s television with your remote control. Furthermore, security of infrared systems against eavesdropping is better than that of radio systems on

108 THE PHYSICAL LAYER CHAP. 2

account of this reason. Therefore, no government license is needed to operate an infrared system, in contrast to radio systems, which must be licensed outside the ISM bands. Infrared communication has a limited use on the desktop, for example, to connect notebook computers and printers with the IrDA (Infrared Data Associ- ation) standard, but it is not a major player in the communication game.

2.3.4 Light Transmission

Unguided optical signaling or free-space optics has been in use for centuries. Paul Revere used binary optical signaling from the Old North Church just prior to his famous ride. A more modern application is to connect the LANs in two build ings via lasers mounted on their rooftops. Optical signaling using lasers is inher- ently unidirectional, so each end needs its own laser and its own photodetector. This scheme offers very high bandwidth at very low cost and is relatively secure because it is difficult to tap a narrow laser beam. It is also relatively easy to install and, unlike microwave transmission, does not require a license from the FCC (Federal Communications Commission) in the United States and analogous gov- ernment bodies in other countries.

The laser’s strength, a very narrow beam, is also its weakness here. Aiming a laser beam 1 mm wide at a target the size of a pin head 500 meters away requires the marksmanship of a latter-day Annie Oakley. Usually, lenses are put into the system to defocus the beam slightly. To add to the difficulty, wind and temperature changes can distort the beam and laser beams also cannot penetrate rain or thick fog, although they normally work well on sunny days. However, many of these factors are not an issue when the use is to connect two spacecraft.

One of the authors (AST) once attended a conference at a modern hotel in Europe in the 1990s at which the conference organizers thoughtfully provided a room full of terminals to allow the attendees to read their email during boring pres- entations. Since the local phone company was unwilling to install a large number of telephone lines for just 3 days, the organizers put a laser on the roof and aimed it at their university’s computer science building a few kilometers away. They tested it the night before the conference and it worked perfectly. At 9 A.M. the next day, which was bright and sunny, the link failed completely and stayed down all day. The pattern repeated itself the next 2 days. It was not until after the conference that the organizers discovered the problem: heat from the sun during the daytime caused convection currents to rise up from the roof of the building, as shown in Fig. 2-11. This turbulent air diverted the beam and made it dance around the detector, much like a shimmering road on a hot day. The lesson here is that to work well in difficult conditions as well as good conditions, unguided optical links need to be engineered with a sufficient margin of error.

Unguided optical communication may seem like an exotic networking technol- ogy today, but it might soon become much more prevalent. In many places, we are surrounded by cameras (that sense light) and displays (that emit light using LEDs

SEC. 2.3 USING THE SPECTRUM FOR TRANSMISSION 109

Laser beam

misses the detector

Photodetector Region of

turbulent seeing

Heat rising

off the building

Figure 2-11. Convection currents can interfere with laser communication sys tems. A bidirectional system with two lasers is pictured here.

Laser

and other technology). Data communication can be layered on top of these displays by encoding information in the pattern at which LEDs turn on and off that is below the threshold of human perception. Communicating with visible light in this way is inherently safe and creates a low-speed network in the immediate vicinity of the display. This could enable all sorts of fanciful ubiquitous computing scenarios. The flashing lights on emergency vehicles might alert nearby traffic lights and vehicles to help clear a path. Informational signs might broadcast maps. Even fes tive lights might broadcast songs that are synchronized with their display.

2.4 FROM WAVEFORMS TO BITS

In this section, we describe how signals are transmitted over the physical media we have discussed. We begin with a discussion of the theoretical basis for data communication, and follow with a discussion of modulation (the process of converting analog waveforms to bits) and multiplexing (which allows a single physical medium to carry multiple simultaneous transmissions).

110 THE PHYSICAL LAYER CHAP. 2 2.4.1 The Theoretical Basis for Data Communication

Information can be transmitted on wires by varying some physical property such as voltage or current. By representing the value of this voltage or current as a single-valued function of time, f(t), we can model the behavior of the signal and analyze it mathematically. This analysis is the subject of the following sections.

Fourier Analysis

In the early 19th century, the French mathematician Jean-Baptiste Fourier proved that any reasonably behaved periodic function, g(t) with period T, can be constructed as the sum of a (possibly infinite) number of sines and cosines:

_{g(t) =}¹₂c + ^'n=1

Y ^a_n sin(2/ nft) + ^'n=1

Y ^b_n cos(2/ nft) (2-2)

where f = 1/T is the fundamental frequency, a_n and b_n ^{are the sine and cosine am-} plitudes of the nth harmonics (terms), and c is a constant that determines the mean value of the function. Such a decomposition is called a Fourier series. From the Fourier series, the function can be reconstructed. That is, if the period, T, is known and the amplitudes are given, the original function of time can be found by per

forming the sums of Eq. (2-2).

A data signal that has a finite duration, which all of them do, can be handled by just imagining that it repeats the entire pattern over and over forever (i.e., the in terval from T to 2T is the same as from 0 to T, etc.).

The a_n amplitudes can be computed for any given g(t) by multiplying both sides of Eq. (2-2) by sin(2/ kft) and then integrating from 0 to T. Since

T

0^{sin(2/ kft) sin(2/ nft) dt =¨}©_ª^{0 for k & n} T/2 for k = n

0

only one term of the summation survives: a_n. The b_n ^{summation vanishes com-} pletely. Similarly, by multiplying Eq. (2-2) by cos(2/ kft) and integrating between 0 and T, we can derive b_n. By just integrating both sides of the equation as it stands, we can find c. The results of performing these operations are as follows:

a_{n =}²T^T₀0 ^{g(t)sin(2/ nft) dt b}_{n =}²T^T₀0 ^{g(t) cos(2/ nft) dt c =2}T^T₀0 ^{g(t) dt}

Bandwidth-Limited Signals

The relevance of all of this to data communication is that real channels affect different frequency signals differently. Let us consider a specific example: the transmission of the ASCII character ‘‘b’’ encoded in an 8-bit byte. The bit pattern

SEC. 2.4 FROM WAVEFORMS TO BITS 111

that is to be transmitted is 01100010. The left-hand part of Fig. 2-12(a) shows the voltage output by the transmitting computer. The Fourier analysis of this signal yields the coefficients:

a_{n =}1_{/ n}[cos(/ n/4) < cos(3/ n/4) + cos(6/ n/4) < cos(7/ n/4)]

b_{n =}1_{/ n}[sin(3/ n/4) < sin(/ n/4) + sin(7/ n/4) < sin(6/ n/4)]

c = 3/4.

^{The root-mean-square amplitudes,} 3}}^a}}}

²_n + b²_n, for the first few terms are shown on

the right-hand side of Fig. 2-12(a). These values are of interest because their squares are proportional to the energy transmitted at the corresponding frequency. No transmission facility can transmit signals without losing some power in the process. If all the Fourier components were equally diminished, the resulting sig- nal would be reduced in amplitude but not distorted [i.e., it would have the same nice squared-off shape as Fig. 2-12(a)]. Unfortunately, all transmission facilities diminish different Fourier components by different amounts, thus introducing dis tortion. Usually, for a wire, the amplitudes are transmitted mostly undiminished from 0 up to some frequency f _c (measured in Hz) with all frequencies above this cutoff frequency attenuated. The width of the frequency range transmitted without being strongly attenuated is called the bandwidth. In practice, the cutoff is not really sharp, so often the quoted bandwidth is from 0 to the frequency at which the received power has fallen by half.

The bandwidth is a physical property of the transmission medium that depends on, for example, the construction, thickness, length, and material of a wire or fiber. Filters are often used to further limit the bandwidth of a signal. 802.11 wireless channels generally use roughly 20 MHz, for example, so 802.11 radios filter the signal bandwidth to this size (although in some cases an 80-MHz band is used).

As another example, traditional (analog) television channels occupy 6 MHz each, on a wire or over the air. This filtering lets more signals share a given region of spectrum, which improves the overall efficiency of the system. It means that the frequency range for some signals will not start at zero, but at some higher number. However, this does not matter. The bandwidth is still the width of the band of fre- quencies that are passed, and the information that can be carried depends only on this width and not on the starting and ending frequencies. Signals that run from 0 up to a maximum frequency are called baseband signals. Signals that are shifted to occupy a higher range of frequencies, as is the case for all wireless transmissions, are called passband signals.

Now let us consider how the signal of Fig. 2-12(a) would look if the bandwidth were so low that only the lowest frequencies were transmitted [i.e., if the function were being approximated by the first few terms of Eq. (2-2)]. Figure 2-12(b) shows the signal that results from a channel that allows only the first harmonic (the

112 THE PHYSICAL LAYER CHAP. 2

0 1 1 0 0 0 1 0 1

e d

u

t

i

l

p

m

a

s

m

r

0.50 0.25

0 Time T (a)

1

0

(b)

1

0

(c)

1

0

(d)

1

0

Time

(e)

1 2 3 4 5 6 7 8 9 10111213 1415 Harmonic number

1 harmonic

1

2 harmonics

1 2

4 harmonics

1 2 3 4

8 harmonics

1 2 3 4 5 6 7 8

Harmonic number

Figure 2-12. (a) A binary signal and its root-mean-square Fourier amplitudes. (b)–(e) Successive approximations to the original signal.

SEC. 2.4 FROM WAVEFORMS TO BITS 113

fundamental, f) to pass through. Similarly, Fig. 2-12(c)–(e) show the spectra and reconstructed functions for higher-bandwidth channels. For digital transmission, the goal is to receive a signal with just enough fidelity to reconstruct the sequence of bits that was sent. We can already do this easily in Fig. 2-12(e), so it is wasteful to use more harmonics to receive a more accurate replica.

Given a bit rate of b bits/sec, the time required to send the 8 bits in our ex- ample 1 bit at a time is 8/b sec, so the frequency of the first harmonic of this signal is b/8 Hz. An ordinary telephone line, often called a voice-grade line, has an arti ficially introduced cutoff frequency just above 3000 Hz. The presence of this restriction means that the number of the highest harmonic passed through is rough ly 3000/(b/8), or 24, 000/b (the cutoff is not sharp).

For some data rates, the numbers work out as shown in Fig. 2-13. From these numbers, it is clear that trying to send at 9600 bps over a voice-grade telephone line will transform Fig. 2-12(a) into something looking like Fig. 2-12(c), making accurate reception of the original binary bit stream tricky. It should be obvious that at data rates much higher than 38.4 kbps, there is no hope at all for binary signals, even if the transmission facility is completely noiseless. In other words, limiting the bandwidth limits the data rate, even for perfect channels. However, coding schemes that make use of several voltage levels do exist and can achieve higher data rates. We will discuss these later in this chapter.

Bps T (msec) First harmonic (Hz) # Harmonics sent

300 26.67 37.5 80

600 13.33 75 40

1200 6.67 150 20

2400 3.33 300 10

4800 1.67 600 5

9600 0.83 1200 2

19200 0.42 2400 1

38400 0.21 4800 0

Figure 2-13. Relation between data rate and harmonics for our very simple ex- ample.

There is much confusion about bandwidth because it means different things to electrical engineers and to computer scientists. To electrical engineers, (analog) bandwidth is (as we have described above) a quantity measured in Hz. To com- puter scientists, (digital) bandwidth is the maximum data rate of a channel, a quan tity measured in bits/sec. That data rate is the end result of using the analog band- width of a physical channel for digital transmission, and the two are related, as we discuss next. In this book, it will be clear from the context whether we mean ana log bandwidth (Hz) or digital bandwidth (bits/sec).

114 THE PHYSICAL LAYER CHAP. 2 2.4.2 The Maximum Data Rate of a Channel

As early as 1924, an AT&T engineer, Harry Nyquist, realized that even a per fect channel has a finite transmission capacity. He derived an equation expressing the maximum data rate for a finite-bandwidth noiseless channel. In 1948, Claude Shannon carried Nyquist’s work further and extended it to the case of a channel subject to random (i.e., thermodynamic) noise (Shannon, 1948). This paper is the most important paper in all of information theory. We will just briefly summarize their now classical results here.

Nyquist proved that if an arbitrary signal has been run through a low-pass filter of bandwidth B, the filtered signal can be completely reconstructed by making only 2B (exact) samples per second. Sampling the line faster than 2B times per second is pointless because the higher-frequency components that such sampling could recover have already been filtered out. If the signal consists of V discrete levels, Nyquist’s theorem states:

Maximum data rate = 2B log₂ V bits/sec (2-3)

For example, a noiseless 3-kHz channel cannot transmit binary (i.e., two-level) sig- nals at a rate exceeding 6000 bps.

So far we have considered only noiseless channels. If random noise is present, the situation deteriorates rapidly. And there is always random (thermal) noise pres- ent due to the motion of the molecules in the system. The amount of thermal noise present is measured by the ratio of the signal power to the noise power, called the SNR (Signal-to-Noise Ratio). If we denote the signal power by S and the noise power by N, the signal-to-noise ratio is S/N. Usually, the ratio is expressed on a log scale as the quantity 10 log₁₀ ^{S/N because it can vary over a tremendous range.} The units of this log scale are called decibels (dB), with ‘‘deci’’ meaning 10 and ‘‘bel’’ chosen to honor Alexander Graham Bell, who first patented the telephone. An S/N ratio of 10 is 10 dB, a ratio of 100 is 20 dB, a ratio of 1000 is 30 dB, and so on. The manufacturers of stereo amplifiers often characterize the bandwidth (frequency range) over which their products are linear by giving the 3-dB frequen- cy on each end. These are the points at which the amplification factor has been approximately halved (because 10 log₁₀ ^{0. 5 5 < 3).} Shannon’s major result is that the maximum data rate or capacity of a noisy channel whose bandwidth is B Hz and whose signal-to-noise ratio is S/N, is given by:

Maximum data rate = B log₂(1 + S/N)bits/sec (2-4)

This equation tells us the best capacities that real channels can have. For example, ADSL (Asymmetric Digital Subscriber Line), which provides Internet access over normal telephone lines, uses a bandwidth of around 1 MHz. The SNR depends strongly on the distance of the home from the telephone exchange, and an SNR of around 40 dB for short lines of 1 to 2 km is very good. With these characteristics,

SEC. 2.4 FROM WAVEFORMS TO BITS 115

the channel can never transmit much more than 13 Mbps, no matter how many or how few signal levels are used and no matter how often or how infrequently sam- ples are taken. The original ADSL was specified up to 12 Mbps, though users

sometimes saw lower rates. This data rate was actually very good for its time, with over 60 years of communications techniques having greatly reduced the gap be tween the Shannon capacity and the capacity of real systems.

Shannon’s result was derived from information-theory arguments and applies to any channel subject to thermal noise. Counterexamples should be treated in the same category as perpetual motion machines. For ADSL to exceed 12 Mbps, it must either improve the SNR (for example by inserting digital repeaters in the lines closer to the customers) or use more bandwidth, as is done with the evolution to ASDL2+.

2.4.3 Digital Modulation

Now that we have studied the properties of wired and wireless channels, we turn our attention to the problem of sending digital information. Wires and wire less channels carry analog signals such as continuously varying voltage, light intensity, or sound intensity. To send digital information, we must devise analog signals to represent bits. The process of converting between bits and signals that represent them is called digital modulation.

We will start with schemes that directly convert bits into a signal. These schemes result in baseband transmission, in which the signal occupies frequen- cies from zero up to a maximum that depends on the signaling rate. It is common for wires. Then we will consider schemes that regulate the amplitude, phase, or frequency of a carrier signal to convey bits. These schemes result in passband transmission, in which the signal occupies a band of frequencies around the fre- quency of the carrier signal. It is common for wireless and optical channels for which the signals must reside in a given frequency band.

Channels are often shared by multiple signals. After all, it is much more con- venient to use a single wire to carry several signals than to install a wire for every signal. This kind of sharing is called multiplexing. It can be accomplished in sev- eral different ways. We will present methods for time, frequency, and code division multiplexing.

The modulation and multiplexing techniques we describe in this section are all widely used for wires, fiber, terrestrial wireless, and satellite channels.

Baseband Transmission

The most straightforward form of digital modulation is to use a positive volt- age to represent a 1 bit and a negative voltage to represent a 0 bit, as can be seen in

116 THE PHYSICAL LAYER CHAP. 2

Fig. 2-14(a). For an optical fiber, the presence of light might represent a 1 and the absence of light might represent a 0. This scheme is called NRZ (Non-Return-to- Zero). The odd name is for historical reasons, and simply means that the signal follows the data. An example is shown in Fig. 2-14(b).

(a) Bit stream

(b) Non-Return to Zero (NRZ) (c) NRZ Invert (NRZI)

(d) Manchester

1 0 0 0 0 1 0 1 1 1 1

(Clock that is XORed with bits)

(e) Bipolar encoding

(also Alternate Mark

Inversion, AMI)

Figure 2-14. Line codes: (a) Bits, (b) NRZ, (c) NRZI, (d) Manchester, (e) Bipo

lar or AMI.

Once sent, the NRZ signal propagates down the wire. At the other end, the re- ceiver converts it into bits by sampling the signal at regular intervals of time. This signal will not look exactly like the signal that was sent. It will be attenuated and distorted by the channel and noise at the receiver. To decode the bits, the receiver maps the signal samples to the closest symbols. For NRZ, a positive voltage will be taken to indicate that a 1 was sent and a negative voltage will be taken to indi- cate that a 0 was sent.

NRZ is a good starting point for our studies because it is simple, but it is sel- dom used by itself in practice. More complex schemes can convert bits to signals that better meet engineering considerations. These schemes are called line codes. Below, we describe line codes that help with bandwidth efficiency, clock recovery, and DC balance.

Bandwidth Efficiency

With NRZ, the signal may cycle between the positive and negative levels up to every 2 bits (in the case of alternating 1s and 0s). This means that we need a band- width of at least B/2 Hz when the bit rate is B bits/sec. This relation comes from the Nyquist rate [Eq. (2-3)]. It is a fundamental limit, so we cannot run NRZ faster without using additional bandwidth. Bandwidth is often a limited resource, even

SEC. 2.4 FROM WAVEFORMS TO BITS 117

for wired channels. Higher-frequency signals are increasingly attenuated, making them less useful, and higher-frequency signals also require faster electronics. One strategy for using limited bandwidth more efficiently is to use more than two signaling levels. By using four voltages, for instance, we can send 2 bits at once as a single symbol. This design will work as long as the signal at the receiver is sufficiently strong to distinguish the four levels. The rate at which the signal changes is then half the bit rate, so the needed bandwidth has been reduced. We call the rate at which the signal changes the symbol rate to distinguish it from the bit rate. The bit rate is the symbol rate multiplied by the number of bits per symbol. An older name for the symbol rate, particularly in the context of de- vices called telephone modems that convey digital data over telephone lines, is the baud rate. In the literature, the terms ‘‘bit rate’’ and ‘‘baud rate’’ are often used incorrectly.

Note that the number of signal levels does not need to be a power of two. Often it is not, with some of the levels used for protecting against errors and simplifying the design of the receiver.

Clock Recovery

For all schemes that encode bits into symbols, the receiver must know when one symbol ends and the next symbol begins to correctly decode the bits. With NRZ, in which the symbols are simply voltage levels, a long run of 0s or 1s leaves the signal unchanged. After a while, it is hard to tell the bits apart, as 15 zeros look much like 16 zeros unless you have a very accurate clock.

Accurate clocks would help with this problem, but they are an expensive solu tion for commodity equipment. Remember, we are timing bits on links that run at many megabits/sec, so the clock would have to drift less than a fraction of a microsecond over the longest permitted run. This might be reasonable for slow links or short messages, but it is not a general solution.

One strategy is to send a separate clock signal to the receiver. Another clock line is no big deal for computer buses or short cables in which there are many lines in parallel, but it is wasteful for most network links since if we had another line to send a signal we could use it to send data. A clever trick here is to mix the clock signal with the data signal by XORing them together so that no extra line is need- ed. The results are shown in Fig. 2-14(d). The clock makes a clock transition in every bit time, so it runs at twice the bit rate. When it is XORed with the 0 level, it makes a low-to-high transition that is simply the clock. This transition is a logical 0. When it is XORed with the 1 level it is inverted and makes a high-to-low tran- sition. This transition is a logical 1. This scheme is called Manchester encoding and was used for classic Ethernet.

The downside of Manchester encoding is that it requires twice as much band- width as NRZ due to the clock, and we have learned that bandwidth often matters. A different strategy is based on the idea that we should code the data to ensure that

118 THE PHYSICAL LAYER CHAP. 2

there are enough transitions in the signal. Consider that NRZ will have clock re- covery problems only for long runs of 0s and 1s. If there are frequent transitions, it will be easy for the receiver to stay synchronized with the incoming stream of symbols.

As a step in the right direction, we can simplify the situation by coding a 1 as a transition and a 0 as no transition, or vice versa. This coding is called NRZI (Non- Return-to-Zero Inverted), a twist on NRZ. An example is shown in Fig. 2-14(c). The popular USB (Universal Serial Bus) standard for connecting computer per ipherals uses NRZI. With it, long runs of 1s do not cause a problem.

Of course, long runs of 0s still cause a problem that we must fix. If we were the telephone company, we might simply require that the sender not transmit too many 0s. Older digital telephone lines in the United States, called T1 lines (dis- cussed later) did, in fact, require that no more than 15 consecutive 0s be sent for them to work correctly. To really fix the problem, we can break up runs of 0s by mapping small groups of bits to be transmitted so that groups with successive 0s are mapped to slightly longer patterns that do not have too many consecutive 0s.

A well-known code to do this is called 4B/5B. Every 4 bits is mapped into a 5-bit pattern with a fixed translation table. The five bit patterns are chosen so that there will never be a run of more than three consecutive 0s. The mapping is shown in Fig. 2-15. This scheme adds 25% overhead, which is better than the 100% over- head of Manchester encoding. Since there are 16 input combinations and 32 output combinations, some of the output combinations are not used. Putting aside the combinations with too many successive 0s, there are still some codes left. As a bonus, we can use these nondata codes to represent physical layer control signals. For example, in some uses, ‘‘11111’’ represents an idle line and ‘‘11000’’ repres- ents the start of a frame.

Data (4B) Codeword (5B) Data (4B) Codeword (5B)

0000 11110 1000 10010

0001 01001 1001 10011

0010 10100 1010 10110

0011 10101 1011 10111

0100 01010 1100 11010

0101 01011 1101 11011

0110 01110 1110 11100

0111 01111 1111 11101

Figure 2-15. 4B/5B mapping.

An alternative approach is to make the data look random, known as scram- bling. In this case, it is very likely that there will be frequent transitions. A scrambler works by XORing the data with a pseudorandom sequence before it is transmitted. This kind of mixing will make the data themselves as random as the

SEC. 2.4 FROM WAVEFORMS TO BITS 119

pseudorandom sequence (assuming it is independent of the pseudorandom sequence). The receiver then XORs the incoming bits with the same pseudoran- dom sequence to recover the real data. For this to be practical, the pseudorandom sequence must be easy to create. It is commonly given as the seed to a simple ran- dom number generator.

Scrambling is attractive because it adds no bandwidth or time overhead. In fact, it often helps to condition the signal so that it does not have its energy in dom inant frequency components (caused by repetitive data patterns) that might radiate electromagnetic interference. Scrambling helps because random signals tend to be ‘‘white,’’ or have energy spread acrossthe frequency components.

However, scrambling does not guarantee that there will be no long runs. It is possible to get unlucky occasionally. If the data are the same as the pseudorandom sequence, they will XOR to all 0s. This outcome does not generally occur with a long pseudorandom sequence that is difficult to predict. However, with a short or predictable sequence, it might be possible for malicious users to send bit patterns that cause long runs of 0s after scrambling and cause links to fail. Early versions of the standards for sending IP packets over SONET links in the telephone system had this defect (Malis and Simpson, 1999). It was possible for users to send cer tain ‘‘killer packets’’ that were guaranteed to cause problems.

Balanced Signals

Signals that have as much positive voltage as negative voltage even over short periods of time are called balanced signals. They average to zero, which means that they have no DC electrical component. The lack of a DC component is an ad- vantage because some channels, such as coaxial cable or lines with transformers, strongly attenuate a DC component due to their physical properties. Also, one method of connecting the receiver to the channel called capacitive coupling passes only the AC portion of a signal. In either case, if we send a signal whose average is not zero, we waste energy as the DC component will be filtered out.

Balancing helps to provide transitions for clock recovery since there is a mix of positive and negative voltages. It also provides a simple way to calibrate re- ceivers because the average of the signal can be measured and used as a decision threshold to decode symbols. With unbalanced signals, the average may drift away from the true decision level due to a density of 1s, for example, which would cause more symbols to be decoded with errors.

A straightforward way to construct a balanced code is to use two voltage levels to represent a logical 1 and a logical zero. For example, +1 V for a 1 bit and <1 V for a 0 bit. To send a 1, the transmitter alternates between the +1 V and <1 V lev- els so that they always average out. This scheme is called bipolar encoding. In telephone networks, it is called AMI (Alternate Mark Inversion), building on old terminology in which a 1 is called a ‘‘mark’’ and a 0 is called a ‘‘space.’’ An ex- ample is given in Fig. 2-14(e).

120 THE PHYSICAL LAYER CHAP. 2

Bipolar encoding adds a voltage level to achieve balance. Alternatively, we can use a mapping like 4B/5B to achieve balance (as well as transitions for clock recovery). An example of this kind of balanced code is the 8B/10B line code. It maps 8 bits of input to 10 bits of output, so it is 80% efficient, just like the 4B/5B line code. The 8 bits are split into a group of 5 bits, which is mapped to 6 bits, and a group of 3 bits, which is mapped to 4 bits. The 6-bit and 4-bit symbols are then concatenated. In each group, some input patterns can be mapped to balanced out- put patterns that have the same number of 0s and 1s. For example, ‘‘001’’ is map- ped to ‘‘1001,’’ which is balanced. But there are not enough combinations for all output patterns to be balanced. For these cases, each input pattern is mapped to two output patterns. One will have an extra 1 and the alternate will have an extra 0. For example, ‘‘000’’ is mapped to both ‘‘1011’’ and its complement ‘‘0100.’’ As input bits are mapped to output bits, the encoder remembers the disparity from the previous symbol. The disparity is the total number of 0s or 1s by which the signal is out of balance. The encoder then selects either an output pattern or its alternate to reduce the disparity. With 8B/10B, the disparity will be at most 2 bits. Thus, the signal will never be far from balanced. There will also never be more than five consecutive 1s or 0s, to help with clock recovery.

Passband Transmission

Communication over baseband frequencies is most appropriate for wired trans- missions, such as twisted pair, coax, or fiber. In other circumstances, particularly those involving wireless networks and radio transmissions, we need to use a range of frequencies that does not start at zero to send information across a channel. Specifically, for wireless channels, it is not practical to send very low frequency signals because the size of the antenna needs to be a fraction of the signal wavelength, which becomes large at high transmission frequencies. In any case, regulatory constraints and the need to avoid interference usually dictate the choice of frequencies. Even for wires, placing a signal in a given frequency band is useful to let different kinds of signals coexist on the channel. This kind of transmission is called passband transmission because an arbitrary band of frequencies is used to pass the signal.

Fortunately, our fundamental results from earlier in the chapter are all in terms of bandwidth, or the width of the frequency band. The absolute frequency values do not matter for capacity. This means that we can take a baseband signal that occupies 0 to B Hz and shift it up to occupy a passband of S to S + B Hz without changing the amount of information that it can carry, even though the signal will look different. To process a signal at the receiver, we can shift it back down to baseband, where it is more convenient to detect symbols.

Digital modulation is accomplished with passband transmission by modulating a carrier signal that sits in the passband. We can modulate the amplitude, frequen- cy, or phase of the carrier signal. Each of these methods has a corresponding name.

SEC. 2.4 FROM WAVEFORMS TO BITS 121

In ASK (Amplitude Shift Keying), two different amplitudes are used to represent 0 and 1. An example with a nonzero and a zero level is shown in Fig. 2-16(b). More than two levels can be used to encode multiple bits per symbol.

0

1 0 1 1 0 0 1 0 0 1 0 0

(a)

(b)

(c)

(d)

Phase changes

Figure 2-16. (a) A binary signal. (b) Amplitude shift keying. (c) Frequency shift keying. (d) Phase shift keying.

Similarly, with FSK (Frequency Shift Keying), two or more different tones are used. The example in Fig. 2-16(c) uses just two frequencies. In the simplest form of PSK (Phase Shift Keying), the carrier wave is systematically shifted 0 or 180 degrees at each symbol period. Because there are two phases, it is called BPSK (Binary Phase Shift Keying). ‘‘Binary’’ here refers to the two symbols, not that the symbols represent 2 bits. An example is shown in Fig. 2-16(d). A bet ter scheme that uses the channel bandwidth more efficiently is to use four shifts, e.g., 45, 135, 225, or 315 degrees, to transmit 2 bits of information per symbol. This version is called QPSK (Quadrature Phase Shift Keying).

We can combine these schemes and use more levels to transmit more bits per symbol. Only one of frequency and phase can be modulated at a time because they

122 THE PHYSICAL LAYER CHAP. 2

are related, with frequency being the rate of change of phase over time. Usually, amplitude and phase are modulated in combination. Three examples are shown in Fig. 2-17. In each example, the points give the legal amplitude and phase combi- nations of each symbol. In Fig. 2-17(a), we see equidistant dots at 45, 135, 225, and 315 degrees. The phase of a dot is indicated by the angle a line from it to the origin makes with the positive x-axis. The amplitude of a dot is the distance from the origin. This figure is a graphical representation of QPSK.

90

180 0

90

0

90

270 (a)

270 (b)

180 0

270

(c)

Figure 2-17. (a) QPSK. (b) QAM-16. (c) QAM-64.

This kind of diagram is called a constellation diagram. In Fig. 2-17(b) we see a modulation scheme with a denser constellation. Sixteen combinations of am- plitudes and phase are used here, so the modulation scheme can be used to transmit 4 bits per symbol. It is called QAM-16, where QAM stands for Quadrature Am plitude Modulation. Figure 2-17(c) is a still denser modulation scheme with 64 different combinations, so 6 bits can be transmitted per symbol. It is called QAM-64. Even higher-order QAMs are used too. As you might suspect from these constellations, it is easier to build electronics to produce symbols as a combi- nation of values on each axis than as a combination of amplitude and phase values. That is why the patterns look like squares rather than concentric circles.

The constellations we have seen so far do not show how bits are assigned to symbols. When making the assignment, an important consideration is that a small burst of noise at the receiver not lead to many bit errors. This might happen if we assigned consecutive bit values to adjacent symbols. With QAM-16, for example, if one symbol stood for 0111 and the neighboring symbol stood for 1000, if the re- ceiver mistakenly picks the adjacent symbol, it will cause all of the bits to be wrong. A better solution is to map bits to symbols so that adjacent symbols differ in only 1 bit position. This mapping is called a Gray code. Figure 2-18 shows a QAM-16 constellation that has been Gray coded. Now if the receiver decodes the symbol in error, it will make only a single bit error in the expected case that the decoded symbol is close to the transmitted symbol.

SEC. 2.4 FROM WAVEFORMS TO BITS 123

Q

0000 0100

1100 1000

B

0001 0101

When 1101 is sent:

1101 1001

Point Decodes as Bit errors

E

C

A 1101 0

A

I

B 1100 1

0011 0111

D

C 1001 1

1111 1011

0010 0110

1110 1010

D 1111 1 E 0101 1

Figure 2-18. Gray-coded QAM-16.

2.4.4 Multiplexing

The modulation schemes we have seen let us send one signal to convey bits along a wired or wireless link, but they only describe how to transmit one bitstream at a time. In practice, economies of scale play an important role in how we use networks: It costs essentially the same amount of money to install and maintain a high-bandwidth transmission line as a low-bandwidth line between two different offices (i.e., the costs come from having to dig the trench and not from what kind of cable or fiber goes into it). Consequently, multiplexing schemes have been de- veloped to share lines among many signals. The three main ways to multiplex a single physical line are time, frequency, and code; there is also a technique called wavelength division multiplexing, which is essentially an optical form of frequency division multiplexing. We discuss each of these techniques below.

Frequency Division Multiplexing

FDM (Frequency Division Multiplexing) takes advantage of passband trans- mission to share a channel. It divides the spectrum into frequency bands, with each user having exclusive possession of some band in which to send a signal. AMradio broadcasting illustrates FDM. The allocated spectrum is about 1 MHz, roughly 500 to 1500 kHz. Different frequencies are allocated to different logical channels (stations), each operating in a portion of the spectrum, with the interchan- nel separation great enough to prevent interference.

For a more detailed example, in Fig. 2-19 we see three voice-grade telephone channels multiplexed using FDM. Filters limit the usable bandwidth to roughly 3100 Hz per voice-grade channel. When many channels are multiplexed together, 4000 Hz is allocated per channel. The excess bandwidth is called a guard band.

124 THE PHYSICAL LAYER CHAP. 2

It keeps the channels well separated. First, the voice channels are raised in fre- quency, each by a different amount. Then they can be combined because no two channels now occupy the same portion of the spectrum. Notice that even though there are gaps between the channels thanks to the guard bands, there is some over lap between adjacent channels. The overlap is there because real filters do not have ideal sharp edges. This means that a strong spike at the edge of one channel will be felt in the adjacent one as nonthermal noise.

Channel 1

1

r

Channel 2

o

tc

a

f

n

o

it

a

u

n

e

Channel 2 1

Channel 1 Channel 3 68 72

tt

A

60

64

Channel 3 1

300 3100

60 64

68 72

Frequency (kHz) (c)

Frequency (Hz) (a)

Frequency (kHz) (b)

Figure 2-19. Frequency division multiplexing. (a) The original bandwidths. (b) The bandwidths raised in frequency. (c) The multiplexed channel.

This scheme has been used to multiplex calls in the telephone system for many years, but multiplexing in time is now preferred instead. However, FDM continues to be used in telephone networks, as well as cellular, terrestrial wireless, and satel lite networks at a higher level of granularity.

When sending digital data, it is possible to divide the spectrum efficiently without using guard bands. In OFDM (Orthogonal Frequency Division Multi- plexing), the channel bandwidth is divided into many subcarriers that indepen- dently send data (e.g., with QAM). The subcarriers are packed tightly together in the frequency domain. Thus, signals from each subcarrier extend into adjacent ones. However, as seen in Fig. 2-20, the frequency response of each subcarrier is designed so that it is zero at the center of the adjacent subcarriers. The subcarriers can therefore be sampled at their center frequencies without interference from their neighbors. To make this work, a guard time is needed to repeat a portion of the symbol signals in time so that they have the desired frequency response. However, this overhead is much less than is needed for many guard bands.

SEC. 2.4 FROM WAVEFORMS TO BITS 125

Power

Separation f

One OFDM subcarrier(shaded)

Frequency

f₁f₅

f₂

f₃ f₄

Figure 2-20. Orthogonal frequency division multiplexing (OFDM).

OFDM has been around for a long time, but it only began to be adopted in the early 2000s, following the realization that it is possible to implement OFDM ef ficiently in terms of a Fourier transform of digital data over all subcarriers (instead of separately modulating each subcarrier). OFDM is used in 802.11, cable net- works, power-line networking, and fourth-generation (4G) cellular systems. Most often, one high-rate stream of digital information is split into a number of low-rate streams that are transmitted on the subcarriers in parallel. This division is valuable because degradations of the channel are easier to cope with at the subcarrier level; some subcarriers may be very degraded and excluded in favor of subcarriers that are received well.

Time Division Multiplexing

An alternative to FDM is TDM (Time Division Multiplexing). Here, the users take turns (in a round-robin fashion), each one periodically getting the entire bandwidth for a certain time interval. An example of three streams being multi- plexed with TDM is shown in Fig. 2-21. Bits from each input stream are taken in a fixed time slot and output to the aggregate stream. This stream runs at the sum rate of the individual streams. For this to work, the streams must be synchronized in time. Small intervals of guard time (analogous to a frequency guard band) may be added to accommodate small timing variations.

TDM is used widely as key technique in the telephone and cellular networks. To avoid one point of confusion, let us be clear that it is quite different from the al ternative STDM (Statistical Time Division Multiplexing). The prefix ‘‘statisti- cal’’ is added to indicate that the individual streams contribute to the multiplexed stream not on a fixed schedule, but according to the statistics of their demand. STDM is fundamentally like packet switching under another name.

126 THE PHYSICAL LAYER CHAP. 2 1

2

Round-robin

2 1 3 2 1 3

3

TDM

multiplexer

2

Guard time

Figure 2-21. Time Division Multiplexing (TDM).

Code Division Multiplexing

There is a third kind of multiplexing that works in a completely different way than FDM and TDM. CDM (Code Division Multiplexing) is a form of spread spectrum communication in which a narrowband signal is spread out over a wider frequency band. This can make it more tolerant of interference, as well as allowing multiple signals from different users to share the same frequency band. Because code division multiplexing is mostly used for the latter purpose it is commonly called CDMA (Code Division Multiple Access).

CDMA allows each station to transmit over the entire frequency spectrum all the time. Multiple simultaneous transmissions are separated using coding theory. Before getting into the algorithm, let us consider an analogy: an airport lounge with many pairs of people conversing. TDM is comparable to pairs of people in the room taking turns speaking. FDM is comparable to the pairs of people speak ing at different pitches, some high-pitched and some low-pitched such that each pair can hold its own conversation at the same time as but independently of the oth- ers. CDMA is somewhat comparable to each pair of people talking at once, but in a different language. The French-speaking couple just hones in on the French, rejecting everything that is not French as noise. Thus, the key to CDMA is to be able to extract the desired signal while rejecting everything else as random noise. A somewhat simplified description of CDMA follows.

In CDMA, each bit time is subdivided into m short intervals called chips, which are multiplied against the original data sequence (the chips are a bit se- quence, but are called chips so that the are not confused with the bits of the actual message). Typically, there are 64 or 128 chips per bit, but in the example given here we will use 8 chips/bit for simplicity. Each station is assigned a unique m-bit code called a chip sequence. For pedagogical purposes, it is convenient to write these codes as sequences of <1 and +1. We will show chip sequences in par- entheses.

To transmit a 1 bit, a station sends its chip sequence. To transmit a 0 bit, it sends the negation of its chip sequence. No other patterns are permitted. Thus, for m = 8, if station A is assigned the chip sequence (<1 < 1 < 1 + 1 + 1 < 1 + 1 + 1), it can send a 1 bit by transmitting the chip sequence and a 0 by transmitting its com- plement: (+1 + 1 + 1 < 1 < 1 + 1 < 1 < 1). It is really voltage levels that are sent, but it is sufficient for us to think in terms of the sequences.

SEC. 2.4 FROM WAVEFORMS TO BITS 127

Increasing the amount of information to be sent from b bits/sec to mb chips/sec for each station means that the bandwidth needed for CDMA is greater by a factor of m than the bandwidth needed for a station not using CDMA (assum ing no changes in the modulation or encoding techniques). If we have a 1-MHz band available for 100 stations, with FDM each one would have 10 kHz and could send at 10 kbps (assuming 1 bit per Hz). With CDMA, each station uses the full 1 MHz, so the chip rate is 100 chips per bit to spread the station’s bit rate of 10 kbps across the channel.

In Fig. 2-22(a) and (b), we show the chip sequences assigned to four example stations and the signals that they represent. Each station has its own unique chip sequence. Let us use the symbol S to indicate the m-chip vector for station S, and S for its negation. All chip sequences are pairwise orthogonal, by which we mean that the normalized inner product of any two distinct chip sequences, S and T (written as S•T), is 0. It is known how to generate such orthogonal chip sequences using a method known as Walsh codes. In mathematical terms, orthogonality of the chip sequences can be expressed as follows:

_{S•T >}¹m^m

Y ^S_iT_i = 0 (2-5)

i=1

In plain English, as many pairs are the same as are different. This orthogonality property will prove crucial later. Note that if S•T = 0, then S•T is also 0. The nor- malized inner product of any chip sequence with itself is 1:

_{S•S =}¹m^mi=1

Y ^S_iS_{i =}¹m^m

Y ^S2_{i =}¹m^mi=1

i=1

Y^(±1)2 = 1

0.20v This follows because each of the m terms in the inner product is 1, so the sum is m. Also, note that S•S = < 1.

A = (–1 –1 –1 +1 +1 –1 +1 +1)

B = (–1 –1 +1 –1 +1 +1 +1 –1)

C = (–1 +1 –1 +1 +1 +1 –1 –1)

D = (–1 +1 –1 –1 –1 –1 +1 –1)

(a)

S₁ = C = (–1 +1 –1 +1 +1 +1 –1 –1) S₂ = B+C = (–2 0 0 0 +2 +2 0 –2) S₃ = A+B = ( 0 0 –2 +2 0 –2 0 +2) S₄ = A+B+C = (–1 +1 –3 +3 +1 –1 –1 +1) S₅ = A+B+C+D = (–4 0 –2 0 +2 0 +2 –2) S₆ = A+B+C+D = (–2 –2 0 –2 0 –2 +4 0)

(b)

S₁ C = [1+1+1+1+1+1+1+1]/8 = 1 S₂ C = [2+0+0+0+2+2+0+2]/8 = 1 S₃ C = [0+0+2+2+0–2+0–2]/8 = 0 S₄ C = [1+1+3+3+1–1+1–1]/8 = 1 S₅ C = [4+0+2+0+2+0–2+2]/8 = 1 S₆ C = [2–2+0–2+0–2–4+0]/8 = –1

(c) (d)

Figure 2-22. (a) Chip sequences for four stations. (b) Signals the sequences represent (c) Six examples of transmissions. (d) Recovery of station C’s signal.

128 THE PHYSICAL LAYER CHAP. 2

During each bit time, a station can transmit a 1 (by sending its chip sequence), it can transmit a 0 (by sending the negative of its chip sequence), or it can be silent and transmit nothing. We assume for now that all stations are synchronized in time, so all chip sequences begin at the same instant. When two or more stations trans-

mit simultaneously, their bipolar sequences add linearly. For example, if in one chip period three stations output +1 and one station outputs <1, +2 will be re- ceived. One can think of this as signals that add as voltages superimposed on the channel: three stations output +1 V and one station outputs <1 V, so that 2 V is re- ceived. For instance, in Fig. 2-22(c) we see six examples of one or more stations transmitting 1 bit at the same time. In the first example, C transmits a 1 bit, so we just get C’s chip sequence. In the second example, both B and C transmit 1 bits, so we get the sum of their bipolar chip sequences, namely:

(<1 < 1 + 1 < 1 + 1 + 1 + 1 < 1) + (<1 + 1 < 1 + 1 + 1 + 1 < 1 < 1) = (<2 0 0 0 + 2 + 2 0 < 2)

To recover the bit stream of an individual station, the receiver must know that station’s chip sequence in advance. It does the recovery by computing the nor- malized inner product of the received chip sequence and the chip sequence of the station whose bit stream it is trying to recover. If the received chip sequence is S and the receiver is trying to listen to a station whose chip sequence is C, it just computes the normalized inner product, S•C.

To see why this works, just imagine that two stations, A and C, both transmit a 1 bit at the same time that B transmits a 0 bit, as in the third example. The receiver sees the sum, S = A + B + C, and computes

S•C = (A + B + C)•C = A•C + B•C + C•C = 0 + 0 + 1 = 1

The first two terms vanish because all pairs of chip sequences have been carefully chosen to be orthogonal, as shown in Eq. (2-5). Now it should be clear why this property must be imposed on the chip sequences.

To make the decoding process more concrete, we show six examples in Fig. 2-22(d). Suppose that the receiver is interested in extracting the bit sent by station C from each of the six signals S₁through S₆^{. It calculates the bit by sum-} ming the pairwise products of the received S and the C vector of Fig. 2-22(a) and then taking 1/8 of the result (since m = 8 here). The examples include cases where

C is silent, sends a 1 bit, and sends a 0 bit, individually and in combination with other transmissions. As shown, the correct bit is decoded each time. It is just like speaking French.

In principle, given enough computing capacity, the receiver can listen to all the senders at once by running the decoding algorithm for each of them in parallel. In real life, suffice it to say that this is easier said than done, and it is useful to know which senders might be transmitting.

In the ideal, noiseless CDMA system we have studied here, the number of sta tions that send concurrently can be made arbitrarily large by using longer chip se- ⁿ stations, Walsh codes can provide 2

quences. For 2

ⁿ orthogonal chip sequences

SEC. 2.4 FROM WAVEFORMS TO BITS 129 ⁿ. However, one significant limitation is that we have assumed that all

of length 2

the chips are synchronized in time at the receiver. This synchronization is not even approximately true in some applications, such as cellular networks (in which CDMA has been widely deployed starting in the 1990s). It leads to different de- signs.

As well as cellular networks, CDMA is used by satellites and cable networks. We have glossed over many complicating factors in this brief introduction. Engin- eers who want to gain a deep understanding of CDMA should read Viterbi (1995) and Harte et al. (2012). These references require quite a bit of background in com- munication engineering, however.

Wavelength Division Multiplexing

WDM (Wavelength Division Multiplexing) is a form of frequency division multiplexing that multiplexes multiple signals onto an optical fiber using different wavelengths of light. In Fig. 2-23, four fibers come together at an optical com- biner, each with its energy present at a different wavelength. The four beams are combined onto a single shared fiber for transmission to a distant destination. At the far end, the beam is split up over as many fibers as there were on the input side. Each output fiber contains a short, specially constructed core that filters out all but one wavelength. The resulting signals can be routed to their destination or recom- bined in different ways for additional multiplexed transport.

Fiber 1

spectrum

Fiber 2

spectrum

Fiber 3

spectrum

Fiber 4

spectrum

Spectrum on the

shared fiber

r e

w

o

P

h

h₁

r e

w

o

P

h

r e

w

o

P

h

r e

w

o

P

h

r

e

w

o

P

Filter

h h₂

Fiber 1

h² Fiber 2

h₁+h₂+h₃+h₄

h₄

h³ _{Fiber 3}Combiner Splitter

h₁

h Long-haul shared fiber ₄

h F ₃ iber 4

Figure 2-23. Wavelength division multiplexing.

There is really nothing new here. This way of operating is just frequency di- vision multiplexing at very high frequencies, with the term WDM referring to the

130 THE PHYSICAL LAYER CHAP. 2

description of fiber optic channels by their wavelength or ‘‘color’’ rather than fre- quency. As long as each channel has its own dedicated frequency (that is, its own wavelength) range and all the ranges are disjoint, they can be multiplexed together on the long-haul fiber. The only difference with electrical FDM is that an optical system using a diffraction grating is completely passive and thus highly reliable.

The reason WDM is popular is that the energy on a single channel is typically only a few gigahertz wide because that is the current limit of how fast we can con- vert between electrical and optical signals. By running many channels in parallel on different wavelengths, the aggregate bandwidth is increased linearly with the number of channels. Since the bandwidth of a single fiber band is ca. 25,000 GHz (see Fig. 2-5), there is theoretically room for 2500 10-Gbps channels even at 1 bit/Hz (and higher rates are also possible).

WDM technology has been progressing at a rate that puts computer technology to shame. WDM was invented around 1990. The first commercially available sys tems had eight channels of 2.5 Gbps per channel; by 1998, systems with 40 chan- nels of 2.5 Gbps were on the market and rapidly being adopted; by 2006, there were products with 192 channels of 10 Gbps and 64 channels of 40 Gbps, capable of moving up to 2.56 Tbps; by 2019, there were systems that can handle up to 160 channels, supporting more than 16 Tbps over a single fiber pair. That is 800 times more capacity than the 1990 systems. The channels are also packed tightly on the fiber, with 200, 100, or as little as 50 GHz of separation.

Narrowing the spacing to 12.5 GHz makes it possible to support 320 channels on a single fiber, further increasing transmission capacity. Such systems with a large number of channels and little space between each channel are referred to as DWDM (Dense WDM). DWDM systems tend to be more expensive because they must maintain stable wavelengths and frequencies, due to the close spacing of each channel. As a result, these systems closely regulate their temperature to ensure that frequencies are accurate.

One of the drivers of WDM technology is the development of all-optical com- ponents. Previously, every 100 km it was necessary to split up all the channels and convert each one to an electrical signal for amplification separately before recon- verting them to optical signals and combining them. Nowadays, all-optical ampli fiers can regenerate the entire signal once every 1000 km without the need for mul tiple opto-electrical conversions.

In the example of Fig. 2-23, we have a fixed-wavelength system. Bits from input fiber 1 go to output fiber 3, bits from input fiber 2 go to output fiber 1, etc. However, it is also possible to build WDM systems that are switched in the optical domain. In such a device, the output filters are tunable using Fabry-Perot or Mach Zehnder interferometers. These devices allow the selected frequencies to be changed dynamically by a control computer. This ability provides a large amount of flexibility to provision many different wavelength paths through the telephone network from a fixed set of fibers. For more information about optical networks and WDM, see Grobe and Eiselt (2013).

SEC. 2.5 THE PUBLIC SWITCHED TELEPHONE NETWORK 131 2.5 THE PUBLIC SWITCHED TELEPHONE NETWORK

When two computers that are physically close to each other need to communi- cate, it is often easiest just to run a cable between them. Local Area Networks (LANs) work this way. However, when the distances are large or there are many computers or the cables have to pass through a public road or other public right of way, the costs of running private cables are usually prohibitive. Furthermore, in just about every country in the world, stringing private transmission lines across (or underneath) public property is illegal. Consequently, the network designers must rely on the existing telecommunication facilities, such as the telephone network, the cellular network, or the cable television network.

The limiting factor for data networking has long been the ‘‘last mile’’ over which customers connect, which might rely on any one of these physical technolo- gies, as opposed to the so-called ‘‘backbone’’ infrastructure for the rest of the ac- cess network. Over the past decade, this situation has changed dramatically, with

speeds of 1 Gbps to the home becoming increasingly commonplace. Although one contributor to faster last-mile speeds is the continued rollout of fiber at the edge of the network, perhaps an even more significant contributor in some countries is the sophisticated engineering of the existing telephone and cable networks to squeeze increasingly more bandwidth out of the existing infrastructure. It turns out that en- gineering the existing physical infrastructure to increase transmission speeds is a lot less expensive than putting new (fiber) cables in the ground to everyone’s homes. We now explore the architectures and characteristics of each of these phys ical communications infrastructures.

These existing facilities, especially the PSTN (Public Switched Telephone Network), were usually designed many years ago, with a completely different goal in mind: transmitting the human voice in a more-or-less recognizable form. A cable running between two computers can transfer data at 10 Gbps or more; the phone network thus has its work cut out for it in terms of transmitting bits at high rates. Early Digital Subscriber Line (DSL) technologies could only transmit data at rates of a few Mbps; now, more modern versions of DSL, can achieve rates ap- proaching 1 Gbps. In the following sections, we will describe the telephone sys tem and show how it works. For additional information about the innards of the telephone system, see Laino (2017).

2.5.1 Structure of the Telephone System

Soon after Alexander Graham Bell patented the telephone in 1876 (just a few hours ahead of his rival, Elisha Gray), there was an enormous demand for his new invention. The initial market was for the sale of telephones, which came in pairs. It was up to the customer to string a single wire between them. If a telephone owner wanted to talk to n other telephone owners, separate wires had to be strung to all n houses. Within a year, the cities were covered with wires passing over

132 THE PHYSICAL LAYER CHAP. 2

houses and trees in a wild jumble. It became immediately obvious that the model of connecting every telephone to every other telephone, as shown in Fig. 2-24(a), was not going to work.

(a) (b) (c)

Figure 2-24. (a) Fully interconnected network. (b) Centralized switch.

(c) Two-level hierarchy.

To his credit, Bell saw this problem early on and formed the Bell Telephone Company, which opened its first switching office (in New Haven, Connecticut) in 1878. The company ran a wire to each customer’s house or office. To make a call, the customer would crank the phone to make a ringing sound in the telephone com- pany office to attract the attention of an operator, who would then manually con- nect the caller to the callee by using a short jumper cable. The model of a single switching office is illustrated in Fig. 2-24(b).

Pretty soon, Bell System switching offices were springing up everywhere and people wanted to make long-distance calls between cities, so the Bell System began to connect the switching offices. The original problem soon returned: to connect every switching office to every other switching office by means of a wire between them quickly became unmanageable, so second-level switching offices were invented. After a while, multiple second-level offices were needed, as illus trated in Fig. 2-24(c). Eventually, the hierarchy grew to five levels.

By 1890, the three major parts of the telephone system were in place: the switching offices, the wires between the customers and the switching offices (by now balanced, insulated, twisted pairs instead of open wires with an earth return), and the long-distance connections between the switching offices. For a short tech- nical history of the telephone system, see Hawley (1991).

While there have been improvements in all three areas since then, the basic Bell System model has remained essentially intact for over 100 years. The follow ing description is highly simplified but gives the essential flavor nevertheless. Each telephone has two copper wires coming out of it that go directly to the tele- phone company’s nearest end office (also called a local central office). The dis tance is typically around 1 to 10 km, being shorter in cities than in rural areas. In

SEC. 2.5 THE PUBLIC SWITCHED TELEPHONE NETWORK 133

the United States alone there are about 22,000 end offices. The two-wire con- nections between each subscriber’s telephone and the end office are known in the trade as the local loop. If the world’s local loops were stretched out end to end, they would extend to the moon and back 1000 times.

At one time, 80% of AT&T’s capital value was the copper in the local loops. AT&T was then, in effect, the world’s largest copper mine. Fortunately, this fact was not well known in the investment community. Had it been known, some cor- porate raider might have bought AT&T, ended all telephone service in the United States, ripped out all the wire, and sold it to a copper refiner for a quick payback.

If a subscriber attached to a given end office calls another subscriber attached to the same end office, the switching mechanism within the office sets up a direct electrical connection between the two local loops. This connection remains intact for the duration of the call.

If the called telephone is attached to another end office, a different procedure has to be used. Each end office has a number of outgoing lines to one or more nearby switching centers, called toll offices (or, if they are within the same local area, tandem offices). These lines are called toll connecting trunks. The number of different kinds of switching centers and their topology varies from country to country depending on the country’s telephone density.

If both the caller’s and callee’s end offices happen to have a toll connecting trunk to the same toll office (a likely occurrence if they are relatively close by), the connection may be established within the toll office. A telephone network consist ing only of telephones (the small dots), end offices (the large dots), and toll offices (the squares) is shown in Fig. 2-24(c).

If the caller and callee do not have a toll office in common, a path will have to be established between two toll offices. The toll offices communicate with each other via high-bandwidth intertoll trunks (also called interoffice trunks). Prior to the 1984 breakup of AT&T, the U.S. telephone system used hierarchical routing to find a path, going to higher levels of the hierarchy until there was a switching office in common. This was then replaced with more flexible, non-hierarchical routing. Figure 2-25 shows how a long-distance connection might be routed.

Intermediate

Telephone End office

Toll

office

switching office(s)

Toll

office

End Telephone office

Local

Toll

Very high

Toll

Local

loop

connecting trunk

bandwidth intertoll

trunks

connecting

loop

trunk

Figure 2-25. A typical circuit route for a long-distance call.

134 THE PHYSICAL LAYER CHAP. 2

A variety of transmission media are used for telecommunication. Unlike mod- ern office buildings, where the wiring is commonly Category 5 or Category 6, local loops to homes mostly consist of Category 3 twisted pairs, although some local loops are now fiber, as well. Coaxial cables, microwaves, and especially fiber optics are widely used between switching offices.

In the past, transmission throughout the telephone system was analog, with the actual voice signal being transmitted as an electrical voltage from source to desti- nation. With the advent of fiber optics, digital electronics, and computers, all the trunks and switches are now digital, leaving the local loop as the last piece of ana log technology in the system. Digital transmission is preferred because it is not necessary to accurately reproduce an analog waveform after it has passed through many amplifiers on a long call. Being able to correctly distinguish a 0 from a 1 is enough. This property makes digital transmission more reliable than analog. It is also cheaper and easier to maintain.

In summary, the telephone system consists of three major components:

1. Local loops (analog twisted pairs between end offices and local houses and businesses).

2. Trunks (very high-bandwidth digital fiber-optic links connecting the switching offices).

3. Switching offices (where calls are moved from one trunk to another either electrically or optically).

The local loops provide everyone access to the whole system, so they are critical. Unfortunately, they are also the weakest link in the system. The main challenge for long-haul trunks involves collecting multiple calls and sending them out over the same fiber, which is done using wavelength division multiplexing (WDM). Finally, there are two fundamentally different ways of doing switching: circuit switching and packet switching. We will look at both.

2.5.2 The Local Loop: Telephone Modems, ADSL, and Fiber

In this section, we will study the local loop, both old and new. We will cover telephone modems, ADSL, and fiber to the home. In some places, the local loop has been modernized by installing optical fiber to (or at least very close to) the home. These installations support computer networks from the ground up, with the local loop having ample bandwidth for data services. Unfortunately, the cost of laying fiber to homes is substantial. Sometimes, it is done when local city streets are dug up for other purposes; some municipalities, especially in densely populated urban areas, have fiber local loops. By and large, however, fiber local loops are the exception, but they are clearly the future.

SEC. 2.5 THE PUBLIC SWITCHED TELEPHONE NETWORK 135 Telephone Modems

Most people are familiar with the two-wire local loop coming from a telephone company end office into houses. The local loop is also frequently referred to as the ‘‘last mile,’’ although the length can be up to several miles. Much effort has been devoted to squeezing data networking out of the copper local loops that are already deployed. Telephone modems send digital data between computers over the nar row channel the telephone network provides for a voice call. They were once widely used, but have been largely displaced by broadband technologies such as ADSL that reuse the local loop to send digital data from a customer to the end office, where they are siphoned off to the Internet. Both modems and ADSL must deal with the limitations of old local loops: relatively narrow bandwidth, attenua tion and distortion of signals, and susceptibility to electrical noise such as crosstalk.

To send bits over the local loop, or any other physical channel for that matter, they must be converted to analog signals that can be transmitted over the channel. This conversion is accomplished using the methods for digital modulation that we studied in the previous section. At the other end of the channel, the analog signal is converted back to bits.

A device that converts between a stream of digital bits and an analog signal that represents the bits is called a modem, which is short for ‘‘modulator demodu lator.’’ Modems come in many varieties, including telephone modems, DSL modems, cable modems, and wireless modems. In the case of a cable or DSL modem, the device is typically a separate piece of hardware that sits in between the physical line coming into the house and the rest of the network inside the home. Wireless devices typically have their own built-in modems. Logically, the modem is inserted between the (digital) computer and the (analog) telephone system, as seen in Fig. 2-26.

Computer

Local loop

(analog)

^{Trunk (digital, fiber)} Digital line

ISP 2

_Codec Modem End

Analog line

ISP 1

office

Codec Modem

Figure 2-26. The use of both analog and digital transmission for a com- puter-to-computer call. Conversion is done by the modems and codecs.

Telephone modems are used to send bits between two computers over a voice- grade telephone line, in place of the conversation that usually fills the line. The

136 THE PHYSICAL LAYER CHAP. 2

main difficulty in doing so is that a voice-grade telephone line is limited to only 3100 Hz, about what is sufficient to carry a conversation. This bandwidth is more than four orders of magnitude less than the bandwidth that is used for Ethernet or 802.11 (WiFi). Unsurprisingly, the data rates of telephone modems are also four orders of magnitude less than that of Ethernet and 802.11.

Let us run the numbers to see why this is the case. The Nyquist theorem tells us that even with a perfect 3000-Hz line (which a telephone line is decidedly not), there is no point in sending symbols at a rate faster than 6000 baud. Let us consid- er, for example, an older modem sending at a rate of 2400 symbols/sec, (2400 baud) and focus on getting multiple bits per symbol while allowing traffic in both directions at the same time (by using different frequencies for different directions).

The humble 2400-bps modem uses 0 volts for a logical 0 and 1 volt for a logi- cal 1, with 1 bit per symbol. One step up, it can use four different symbols, as in the four phases of QPSK, so with 2 bits/symbol it can get a data rate of 4800 bps.

A long progression of higher rates has been achieved as technology has im- proved. Higher rates require a larger set of symbols (see Fig. 2-17). With many symbols, even a small amount of noise in the detected amplitude or phase can re- sult in an error. To reduce the chance of errors, standards for the higher-speed modems use some of the symbols for error correction. The schemes are known as TCM (Trellis Coded Modulation). Some common modem standards are shown in Fig. 2-27.

Modem standard Baud Bits/symbol Bps

V.32 2400 4 9600

V.32 bis 2400 6 14,400

V.34 2400 12 28,800

V.34 bis 2400 14 33,600

Figure 2-27. Some modem standards and their bit rate.

Why does it stop at 33,600 bps? The reason is that the Shannon limit for the telephone system is about 35 kbps based on the average length and quality of local loops. Going faster than this would violate the laws of physics (department of thermodynamics) or require new local loops (which is gradually being done).

However, there is one way we can change the situation. At the telephone com- pany end office, the data are converted to digital form for transmission within the telephone network (the core of the telephone network converted from analog to digital long ago). The 35-kbps limit is for the situation in which there are two local loops, one at each end. Each of these adds noise to the signal. If we could get rid of one of these local loops, we would increase the SNR and the maximum rate would be doubled.

This approach is how 56-kbps modems are made to work. One end, typically an ISP (Internet Service Provider), gets a high-quality digital feed from the nearest

SEC. 2.5 THE PUBLIC SWITCHED TELEPHONE NETWORK 137

end office. Thus, when one end of the connection is a high-quality signal, as it is with most ISPs now, the maximum data rate can be as high as 70 kbps. Between two home users with modems and analog lines, the maximum is still 33.6 kbps.

The reason that 56-kbps modems (rather than 70-kbps modems) are in use has to do with the Nyquist theorem. A telephone channel is carried inside the tele- phone system as digital samples. Each telephone channel is 4000 Hz wide when the guard bands are included. The number of samples per second needed to recon- struct it is thus 8000. The number of bits per sample in North America is 8, of which one is used for control purposes, allowing 56,000 bits/sec of user data. In Europe, all 8 bits are available to users, so 64,000-bit/sec modems could have been used, but to get international agreement on a standard, 56,000 was chosen.

The end result is the V.90 and V.92 modem standards. They provide for a 56-kbps downstream channel (ISP to user) and a 33.6-kbps and 48-kbps upstream channel (user to ISP), respectively. The asymmetry is because there is usually more data transported from the ISP to the user than the other way. It also means that more of the limited bandwidth can be allocated to the downstream channel to increase the chances of it actually working at 56 kbps.

Digital Subscriber Lines (DSL)

When the telephone industry finally got to 56 kbps, it patted itself on the back for a job well done. Meanwhile, the cable TV industry was offering speeds up to 10 Mbps on shared cables. As Internet access became an increasingly important part of their business, the local telephone companies began to realize they needed a more competitive product. Their answer was to offer new digital services over the local loop.

Initially, there were many overlapping high-speed offerings, all under the gen- eral name of xDSL (Digital Subscriber Line), for various x. Services with more bandwidth than standard telephone service are sometimes referred to as broad- band, although the term really is more of a marketing concept than a specific tech- nical concept. Later, we will discuss what has become the most popular of these services, ADSL (Asymmetric DSL). We will also use the term DSL or xDSL as shorthand for all flavors.

The reason that modems are so slow is that telephones were invented for carry ing the human voice, and the entire system has been carefully optimized for this purpose. Data have always been stepchildren. At the point where each local loop terminates in the end office, the wire runs through a filter that attenuates all fre- quencies below 300 Hz and above 3400 Hz. The cutoff is not sharp—300 Hz and 3400 Hz are the 3-dB points—so the bandwidth is usually quoted as 4000 Hz even though the distance between the 3 dB points is 3100 Hz. Data on the wire are thus also restricted to this narrow band.

The trick that makes xDSL work is that when a customer subscribes to it, the incoming line is connected to a different kind of switch that does not have this

138 THE PHYSICAL LAYER CHAP. 2

filter, thus making the entire capacity of the local loop available. The limiting fac tor then becomes the physics of the local loop, which supports roughly 1 MHz, not the artificial 3100 Hz bandwidth created by the filter.

Unfortunately, the capacity of the local loop falls rather quickly with distance from the end office as the signal is increasingly degraded along the wire. It also depends on the thickness and general quality of the twisted pair. A plot of the po tential bandwidth as a function of distance is given in Fig. 2-28. This figure as- sumes that all the other factors are optimal (new wires, modest bundles, etc.).

50

40

30

s

p

b

M

20

10

⁰0 1000 2000 3000 4000 Meters

5000 6000

Figure 2-28. Bandwidth versus distance over Category 3 UTP for DSL.

The implication of this figure creates a problem for the telephone company. When it picks a speed to offer, it is simultaneously picking a radius from its end of fices beyond which the service cannot be offered. This means that when distant customers try to sign up for the service, they may be told ‘‘Thanks a lot for your

interest, but you live 100 meters too far from the nearest end office to get this ser- vice. Could you please move?’’ The lower the chosen speed is, the larger the ra- dius and the more customers are covered. But the lower the speed, the less attrac tive the service is and the fewer the people who will be willing to pay for it. This is where business meets technology.

The xDSL services have all been designed with certain goals in mind. First, the services must work over the existing Category 3 twisted-pair local loops. Sec- ond, they must not affect customers’ existing telephones and fax machines. Third, they must be much faster than 56 kbps. Fourth, they should be always on, with just a monthly charge and no per-minute charge.

To meet the technical goals, the available 1.1-MHz spectrum on the local loop is divided into 256 independent channels of 4312.5 Hz each. This arrangement is shown in Fig. 2-29. The OFDM scheme, which we saw in the previous section, is used to send data over these channels, though it is often called DMT (Discrete MultiTone) in the context of ADSL. Channel 0 is used for POTS (Plain Old

SEC. 2.5 THE PUBLIC SWITCHED TELEPHONE NETWORK 139

Telephone Service). Channels 1–5 are not used, to keep the voice and data signals from interfering with each other. Of the remaining 250 channels, one is used for upstream control and one is used for downstream control. The rest are available for user data.

256 4-kHz Channels

r

e

w

o

P

0 25 1100 kHz Voice Upstream Downstream

Figure 2-29. Operation of ADSL using discrete multitone modulation.

In principle, each of the remaining channels can be used for a full-duplex data stream, but harmonics, crosstalk, and other effects keep practical systems well below the theoretical limit. It is up to the provider to determine how many chan- nels are available for upstream and how many for downstream. A 50/50 mix of upstream and downstream is technically possible, but most providers allocate something like 80–90% of the bandwidth to the downstream channel since most users download more data than they upload. This choice gives rise to the ‘‘A’’ in ADSL. A common split is 32 channels for upstream and the rest downstream. It is also possible to have a few of the highest upstream channels be bidirectional for in- creased bandwidth, although making this optimization requires adding a special circuit to cancel echoes.

The international ADSL standard, known as G.dmt, was approved in 1999. It allows speeds of as much as 8 Mbps downstream and 1 Mbps upstream. It was superseded by a second generation in 2002, called ADSL2, with various im- provements to allow speeds of as much as 12 Mbps downstream and 1 Mbps upstream. ADSL2+ doubles the downstream throughput to 24 Mbps by doubling the bandwidth to use 2.2 MHz over the twisted pair.

The next improvement (in 2006) was VDSL, which pushed the data rate over the shorter local loops to 52 Mbps downstream and 3 Mbps upstream. Then, a series of new standards from 2007 to 2011, going under the name of VDSL2, on high-quality local loops managed to use 12-MHz bandwidth and achieve data rates of 200 Mbps downstream and 100 Mbps upstream. In 2015, Vplus was proposed for local loops shorter than 250 m. In principle, it can achieve 300 Mbps down- stream and 100 Mbps upstream, but making it work in practice is not easy. We may be near the end of the line here for existing Category 3 wiring, except maybe for even shorter distances.

Within each channel, QAM modulation is used at a rate of roughly 4000 symb- ols/sec. The line quality in each channel is constantly monitored and the data rate

140 THE PHYSICAL LAYER CHAP. 2

is adjusted by using a larger or smaller constellation, like those in Fig. 2-17. Dif ferent channels may have different data rates, with up to 15 bits per symbol sent on a channel with a high SNR, and down to 2, 1, or no bits per symbol sent on a chan- nel with a low SNR depending on the standard.

A typical ADSL arrangement is shown in Fig. 2-30. In this scheme, a tele- phone company technician must install a NID (Network Interface Device) on the customer’s premises. This small plastic box marks the end of the telephone com- pany’s property and the start of the customer’s property. Close to the NID (or sometimes combined with it) is a splitter, an analog filter that separates the 0–4000-Hz band used by POTS from the data. The POTS signal is routed to the existing telephone or fax machine. The data signal is routed to an ADSL modem, which uses digital signal processing to implement OFDM. Since most ADSL modems are external, the computer must be connected to them at high speed. Usually, this is done using Ethernet, a USB cable, or 802.11.

Voice

switch

Codec

Splitter

Telephone

line

NID

Telephone

Splitter

Computer

DSLAM

To ISP

ADSL

Ethernet

modem

Telephone company end office Customer premises Figure 2-30. A typical ADSL equipment configuration.

At the other end of the wire, on the end office side, a corresponding splitter is installed. Here, the voice portion of the signal is filtered out and sent to the normal voice switch. The signal above 26 kHz is routed to a new kind of device called a DSLAM (Digital Subscriber Line Access Multiplexer), which contains the same kind of digital signal processor as the ADSL modem. The DSLAM converts the signal to bits and sends packets to the Internet service provider’s data network.

This complete separation between the voice system and ADSL makes it rel- atively easy for a telephone company to deploy ADSL. All that is needed is buy ing a DSLAM and splitter and attaching the ADSL subscribers to the splitter.

SEC. 2.5 THE PUBLIC SWITCHED TELEPHONE NETWORK 141

Other high-bandwidth services delivered over the telephone network (e.g., ISDN) require the telephone company to make much greater changes to the existing switching equipment.

The next frontier for DSL deployments is to reach transmission speeds of 1 Gbps and higher. These efforts are focusing on a variety of complementary tech- niques, including a technique called bonding, which creates a single virtual DSL connection by combining two or more physical DSL connections. Obviously, if one combines two twisted pairs, one should be able to double the bandwidth. In some places, the telephone wires entering houses use a cable that in fact has two twisted pairs. The original idea was to allow two separate telephone lines and num- bers in the house, but by using pair bonding, a single higher-speed Internet con- nection can be achieved. Increasing numbers of ISPs in Europe, Australia, Cana- da, and the United States are already deploying a technology called G.fast that uses pair bonding. As with other forms of DSL, the performance of G.fast depends on the distance of the transmission; recent tests have seen symmetric speeds ap- proaching 1 Gbps at distances of 100 meters. When coupled with a fiber deploy- ment known as FTTdp (Fiber to the Distribution Point), which brings fiber to a distribution point of several hundred subscribers and uses copper to transmit data the rest of the way to the home (in VDSL2, this may be up to 1 kilometer, although at lower speeds). FTTdp is just one type of fiber deployment that takes fiber from the core of the network to some point close to the network edge. The next section describes various modes of fiber deployment.

Fiber To The X (FTTX)

The speed of last-mile networks is often constrained by the copper cables used in conventional telephone networks, which cannot transmit data at high rates over as long a distance as fiber. Thus, an ultimate goal, where it is cost effective, is to bring fiber all the way to a customer home, sometimes called FTTH (Fiber to the Home). Telephone companies continue to try to improve the performance of the local loop, often by deploying fiber as far as they can to the home. If not directly to the home itself, the company may provide FTTN (Fiber to the Node) (or neigh- borhood), whereby fiber is terminated in a cabinet on a street sometimes several miles from the customer home. Fiber to the Distribution Point (FTTdp), as men tioned above, moves fiber one step closer to the customer home, often bringing fiber to within a few meters of the customer premises. In between these options is FTTC (Fiber to the Curb). All of these FTTX (Fiber to the X) designs are sometimes also called ‘‘fiber in the loop’’ because some amount of fiber is used in the local loop.

Several variations of the form ‘‘FTTX’’ (where X stands for the basement, curb, or neighborhood) exist. They are used to note that the fiber deployment may reach close to the house. In this case, copper (twisted pair or coaxial cable) pro- vides fast enough speeds over the last short distance. The choice of how far to lay

142 THE PHYSICAL LAYER CHAP. 2

the fiber is an economic one, balancing cost with expected revenue. In any case, the point is that optical fiber has crossed the traditional barrier of the ‘‘last mile.’’ We will focus on FTTH in our discussion.

Like the copper wires before it, the fiber local loop is passive, which means no powered equipment is required to amplify or otherwise process signals. The fiber simply carries signals between the home and the end office. This, in turn, reduces cost and improves reliability. Usually, the fibers from the houses are joined toget- her so that only a single fiber reaches the end office per group of up to 100 houses. In the downstream direction, optical splitters divide the signal from the end office so that it reaches all the houses. Encryption is needed for security if only one house should be able to decode the signal. In the upstream direction, optical com- biners merge the signals from the houses into a single signal that is received at the end office.

This architecture is called a PON (Passive Optical Network), and it is shown in Fig. 2-31. It is common to use one wavelength shared between all the houses for downstream transmission, and another wavelength for upstream transmission.

Fiber

Rest of

network

^{Optical End office} splitter/combiner

Figure 2-31. Passive optical network for Fiber To The Home.

Even with the splitting, the tremendous bandwidth and low attenuation of fiber mean that PONs can provide high rates to users over distances of up to 20 km. The actual data rates and other details depend on the type of PON. Two kinds are com- mon. GPONs (Gigabit-capable PONs) come from the world of telecommunica tions, so they are defined by an ITU standard. EPONs (Ethernet PONs) are more in tune with the world of networking, so they are defined by an IEEE standard. Both run at around a gigabit and can carry traffic for different services, including Internet, video, and voice. For example, GPONs provide 2.4 Gbps downstream and 1.2 or 2.4 Gbps upstream.

Additional protocols are needed to share the capacity of the single fiber at the end office between the different houses. The downstream direction is quite easy. The end office can send messages to each different house in whatever order it likes. In the upstream direction, however, messages from different houses cannot be sent at the same time, or different signals would collide. The houses also cannot hear each other’s transmissions so they cannot listen before transmitting. The solution

SEC. 2.5 THE PUBLIC SWITCHED TELEPHONE NETWORK 143

is that equipment at the houses requests and is granted time slots to use by equip- ment in the end office. For this to work, there is a ranging process to adjust the transmission times from the houses so that all the signals received at the end office are synchronized. The design is similar to cable modems, which we cover later in this chapter. For more information on PONs, see Grobe and Elbers (2008) or Andrade et al. (2014).

2.5.3 Trunks and Multiplexing

Trunks in the telephone network are not only much faster than the local loops, they are different in two other respects. The core of the telephone network carries digital information, not analog information; that is, bits not voice. This necessi tates a conversion at the end office to digital form for transmission over the long- haul trunks. The trunks carry thousands, even millions, of calls simultaneously. This sharing is important for achieving economies of scale, since it costs essen tially the same amount of money to install and maintain a high-bandwidth trunk as a low-bandwidth trunk between two switching offices. It is accomplished with ver- sions of TDM and FDM.

Below, we will briefly examine how voice signals are digitized so that they can be transported by the telephone network. After that, we will see how TDM is used to carry bits on trunks, including the TDM system used for fiber optics (SONET). Then, we will turn to FDM as it is applied to fiber optics, which is called wavelength division multiplexing.

Digitizing Voice Signals

Early in the development of the telephone network, the core handled voice calls as analog information. FDM techniques were used for many years to multi- plex 4000-Hz voice channels (each comprising 3100 Hz plus guard bands) into larger and larger units. For example, 12 calls in the 60 kHz–to–108 kHz band are known as a group, five groups (a total of 60 calls) are known as a supergroup, and so on. These FDM methods are still used over some copper wires and microwave channels. However, FDM requires analog circuitry and is not amenable to being done by a computer. In contrast, TDM can be handled entirely by digital elec tronics, so it has become far more widespread in recent years. Since TDM can only be used for digital data and the local loops produce analog signals, a conver- sion is needed from analog to digital in the end office, where all the individual local loops come together to be combined onto outgoing trunks.

The analog signals are digitized in the end office by a device called a codec (short for ‘‘coder-decoder’’) using a technique is called PCM (Pulse Code Modu lation), which forms the heart of the modern telephone system. The codec makes 8000 samples per second (125 µsec/sample) because the Nyquist theorem says that this is sufficient to capture all the information from the 4-kHz telephone channel

144 THE PHYSICAL LAYER CHAP. 2

bandwidth. At a lower sampling rate, information would be lost; at a higher one, no extra information would be gained. Almost all time intervals within the tele- phone system are multiples of 125 µsec. The standard uncompressed data rate for a voice-grade telephone call is thus 8 bits every 125 µsec, or 64 kbps.

Each sample of the amplitude of the signal is quantized to an 8-bit number. To reduce the error due to quantization, the quantization levels are unevenly spaced. A logarithmic scale is used that gives relatively more bits to smaller signal ampli tudes and relatively fewer bits to large signal amplitudes. In this way, the error is proportional to the signal amplitude. Two versions of quantization are widely used: µ-law, used in North America and Japan, and A-law, used in Europe and the rest of the world. Both versions are specified in standard ITU G.711. An equiv- alent way to think about this process is to imagine that the dynamic range of the signal (or the ratio between the largest and smallest possible values) is compressed before it is (evenly) quantized, and then expanded when the analog signal is recreated. For this reason, it is called companding. It is also possible to compress the samples after they are digitized so that they require much less than 64 kbps. However, we will leave this topic for when we explore audio applications such as voice over IP.

At the other end of the call, an analog signal is recreated from the quantized samples by playing them out (and smoothing them) over time. It will not be exact ly the same as the original analog signal, even though we sampled at the Nyquist rate, because the samples were quantized.

T-Carrier: Multiplexing Digital Signals on the Phone Network

The T-Carrier is a specification for transmitting multiple TDM channels over a single circuit. TDM with PCM is used to carry multiple voice calls over trunks by sending a sample from each call every 125 µsec. When digital transmission began emerging as a feasible technology, ITU (then called CCITT) was unable to reach agreement on an international standard for PCM. Consequently, a variety of incompatible schemes are now in use in different countries around the world.

The method used in North America and Japan is the T1 carrier, depicted in Fig. 2-32. (Technically speaking, the format is called DS1 and the carrier is called T1, but following widespread industry tradition, we will not make that subtle dis tinction here.) The T1 carrier consists of 24 voice channels multiplexed together. Each of the 24 channels, in turn, gets to insert 8 bits into the output stream. The T1 carrier was introduced in 1962.

A frame consists of 24 × 8 = 192 bits plus one extra bit for control purposes, yielding 193 bits every 125 µsec. This gives a gross data rate of 1.544 Mbps, of which 8 kbps is for signaling. The 193rd bit is used for frame synchronization and signaling. In one variation, the 193rd bit is used across a group of 24 frames called an extended superframe. Six of the bits, in the 4th, 8th, 12th, 16th, 20th, and 24th positions, take on the alternating pattern 001011 . . . . Normally, the receiver

SEC. 2.5 THE PUBLIC SWITCHED TELEPHONE NETWORK 145 193-bit frame (125 µsec)

1 0

Channel 1

Channel 2

Channel 3

Channel 4

Channel 24

Bit 1 is a framing code

7 Data bits per

channel

per sample

Bit 8 is for signaling

Figure 2-32. The T1 carrier (1.544 Mbps).

keeps checking for this pattern to make sure that it has not lost synchronization. Six more bits are used to send an error check code to help the receiver confirm that it is synchronized. If it does get out of sync, the receiver can scan for the pattern and validate the error check code to get resynchronized. The remaining 12 bits are used for control information for operating and maintaining the network, such as performance reporting from the remote end.

The T1 format has several variations. The earlier versions sent signaling infor- mation in-band, meaning in the same channel as the data, by using some of the data bits. This design is one form of channel-associated signaling, because each channel has its own private signaling subchannel. In one arrangement, the least significant bit out of an 8-bit sample on each channel is used in every sixth frame. It has the colorful name of robbed-bit signaling. The idea is that a few stolen bits will not matter for voice calls. No one will hear the difference.

For data, however, it is another story. Delivering the wrong bits is unhelpful, to say the least. If older versions of T1 are used to carry data, only 7 of 8 bits, or 56 kbps, can be used in each of the 24 channels. Instead, newer versions of T1 provide clear channels in which all of the bits may be used to send data. Clear channels are what businesses who lease a T1 line want when they send data across the telephone network in place of voice samples. Signaling for any voice calls is then handled out-of-band, meaning in a separate channel from the data. Often, the signaling is done with common-channel signaling in which there is a shared sig- naling channel. One of the 24 channels may be used for this purpose.

Outside of North America and Japan, the 2.048-Mbps E1 carrier is used in- stead of T1. This carrier has 32 8-bit data samples packed into the basic 125-µsec frame. Thirty of the channels are used for information and up to two are used for signaling. Each group of four frames provides 64 signaling bits, half of which are

146 THE PHYSICAL LAYER CHAP. 2

used for signaling (whether channel-associated or common-channel) and half of which are used for frame synchronization or are reserved for each country to use as it wishes.

Time division multiplexing allows multiple T1 carriers to be multiplexed into higher-order carriers. Figure 2-33 shows how this can be done. At the left, we see four T1 channels being multiplexed into one T2 channel. The multiplexing at T2 and above is done bit for bit, rather than byte for byte with the 24 voice channels that make up a T1 frame. Four T1 streams at 1.544 Mbps really ought to generate 6.176 Mbps, but T2 is actually 6.312 Mbps. The extra bits are used for framing and recovery in case the carrier slips.

4 T1 streams in

7 T2 streams in 6 T3 streams in

4 0 5 1

1 T2 stream out

4:1 7:1 6:1

6 2

7 3

1.544 Mbps T1

6 5 4 3 2 1 0

6.312 Mbps T2

44.736 Mbps T3

274.176 Mbps T4

Figure 2-33. Multiplexing T1 streams into higher carriers.

At the next level, seven T2 streams are combined bitwise to form a T3 stream. Then, six T3 streams are joined to form a T4 stream. At each step, a small amount of overhead is added for framing and recovery in case the synchronization between sender and receiver is lost. T1 and T3 are widely used by customers, whereas T2 and T4 are only used within the telephone system itself, so they are not well- known.

Just as there is little agreement on the basic carrier between the United States and the rest of the world, there is equally little agreement on how it is to be multi- plexed into higher-bandwidth carriers. The U.S. scheme of stepping up by 4, 7, and 6 did not strike everyone else as the way to go, so the ITU standard calls for multiplexing four streams into one stream at each level. Also, the framing and re- covery data are different in the U.S. and ITU standards. The ITU hierarchy for 32, 128, 512, 2048, and 8192 channels runs at speeds of 2.048, 8.848, 34.304, 139.264, and 565.148 Mbps.

Multiplexing Optical Networks: SONET/SDH

In the early days of fiber optics, every telephone company had its own propri- etary optical TDM system. After the U.S. government broke up AT&T in 1984, local telephone companies had to connect to multiple long-distance carriers, all

SEC. 2.5 THE PUBLIC SWITCHED TELEPHONE NETWORK 147

with optical TDM systems from different vendors and suppliers, so the need for standardization became obvious. In 1985, Bellcore, the research arm of the Re- gional Bell Operating Companies (RBOCs), began working on a standard, called SONET (Synchronous Optical NETwork).

Later, ITU joined the effort, which resulted in a SONET standard and a set of parallel ITU recommendations (G.707, G.708, and G.709) in 1989. The ITU rec- ommendations are called SDH (Synchronous Digital Hierarchy) but differ from SONET only in minor ways. Virtually all of the long-distance telephone traffic in the United States, and much of it elsewhere, now uses trunks running SONET in the physical layer. For additional information about SONET, see Perros (2005). The SONET design had four major goals:

1. Carrier interoperability: SONET had to make it possible for different carriers to interoperate. Achieving this goal required defining a com- mon signaling standard with respect to wavelength, timing, framing structure, and other issues.

2. Unification across regions: some means was needed to unify the U.S., European, and Japanese digital systems, all of which were based on 64-kbps PCM channels but combined them in different (and incom- patible) ways.

3. Multiplexing digital channels: SONET had to provide a way to multi- plex multiple digital channels. At the time SONET was devised, the highest-speed digital carrier actually used widely in the United States was T3, at 44.736 Mbps. T4 was defined, but not used much, and nothing was even defined above T4 speed. Part of SONET’s mission was to continue the hierarchy to gigabits/sec and beyond. A standard way to multiplex slower channels into one SONET channel was also needed.

4. Management support: SONET had to provide support for operations, administration, and maintenance (OAM), which are needed to man- age the network. Previous systems did not do this very well.

An early decision was to make SONET a conventional TDM system, with the entire bandwidth of the fiber devoted to one channel containing time slots for the various subchannels. As such, SONET is a synchronous system. Each sender and receiver is tied to a common clock. The master clock that controls the system has ⁹. Bits on a SONET line are sent out at extremely

an accuracy of about 1 part in 10

precise intervals, controlled by the master clock.

The basic SONET frame is a block of 810 bytes put out every 125 µsec. Since SONET is synchronous, frames are emitted whether or not there are any useful data to send. Having 8000 frames/sec exactly matches the sampling rate of the PCM channels used in all digital telephony systems.

148 THE PHYSICAL LAYER CHAP. 2

The 810-byte SONET frames are best thought of as a rectangle of bytes, 90 columns wide by 9 rows high. Thus, 8 × 810 = 6480 bits are transmitted 8000 times per second, for a gross data rate of 51.84 Mbps. This layout is the basic SONET channel, called STS-1 (Synchronous Transport Signal-1). All SONET trunks are multiples of STS-1.

The first three columns of each frame are reserved for system management information, as illustrated in Fig. 2-34. In this block, the first three rows contain the section overhead; the next six contain the line overhead. The section overhead

is generated and checked at the start and end of each section, whereas the line over- head is generated and checked at the start and end of each line.

3 Columns

for overhead

87 Columns

9

_Rows. . . . . .

Sonet

frame (125 µsec)

Sonet

frame (125 µsec)

Section overhead

Line

overhead

Path

overhead

SPE

Figure 2-34. Two back-to-back SONET frames.

A SONET transmitter sends back-to-back 810-byte frames, without gaps be tween them, even when there are no data (in which case it sends dummy data). From the receiver’s point of view, all it sees is a continuous bit stream, so how does it know where each frame begins? The answer is that the first 2 bytes of each frame contain a fixed pattern that the receiver searches for. If it finds this pattern in the same place in a large number of consecutive frames, it assumes that it is in sync with the sender. In theory, a user could insert this pattern into the payload in a reg- ular way, but in practice, it cannot be done due to the multiplexing of multiple users into the same frame and other reasons.

The final 87 columns of each frame hold 87 × 9 × 8 × 8000 = 50. 112 Mbps of user data. This user data could be voice samples, T1 and other carriers, or packets. SONET is simply a container for transporting bits. The SPE (Synchronous Pay load Envelope), which carries the user data does not always begin in row 1, col- umn 4. The SPE can begin anywhere within the frame. A pointer to the first byte is contained in the first row of the line overhead. The first column of the SPE is the path overhead (i.e., the header for the end-to-end path sublayer protocol).

SEC. 2.5 THE PUBLIC SWITCHED TELEPHONE NETWORK 149

The ability to allow the SPE to begin anywhere within the SONET frame and even to span two frames, as shown in Fig. 2-34, gives added flexibility to the sys tem. For example, if a payload arrives at the source while a dummy SONET frame is being constructed, it can be inserted into the current frame instead of being held until the start of the next one.

The SONET/SDH multiplexing hierarchy is shown in Fig. 2-35. Rates from STS-1 to STS-768 have been defined, ranging from roughly a T3 line to 40 Gbps. Even higher rates will surely be defined over time, with OC-3072 at 160 Gbps being the next in line if and when it becomes technologically feasible. The optical carrier corresponding to STS-n is called OC-n but is bit for bit the same except for a certain bit reordering needed for synchronization. The SDH names are different, and they start at OC-3 because ITU-based systems do not have a rate near 51.84 Mbps. We have shown the common rates, which proceed from OC-3 in multiples of four. The gross data rate includes all the overhead. The SPE data rate excludes the line and section overhead. The user data rate excludes all three kinds of over- head and counts only the 86 payload columns.

SONET SDH Data rate (Mbps)

Electrical Optical Optical Gross SPE User

STS-1 OC-1 51.84 50.112 49.536 STS-3 OC-3 STM-1 155.52 150.336 148.608 STS-12 OC-12 STM-4 622.08 601.344 594.432 STS-48 OC-48 STM-16 2488.32 2405.376 2377.728 STS-192 OC-192 STM-64 9953.28 9621.504 9510.912 STS-768 OC-768 STM-256 39813.12 38486.016 38043.648

Figure 2-35. SONET and SDH multiplex rates.

As an aside, when a carrier, such as OC-3, is not multiplexed, but carries the data from only a single source, the letter c (for concatenated) is appended to the de- signation, so OC-3 indicates a 155.52-Mbps carrier consisting of three separate OC-1 carriers, but OC-3c indicates a data stream from a single source at 155.52 Mbps. The three OC-1 streams within an OC-3c stream are interleaved by col- umn—first column 1 from stream 1, then column 1 from stream 2, then column 1 from stream 3, followed by column 2 from stream 1, and so on—leading to a frame 270 columns wide and 9 rows deep.

2.5.4 Switching

From the point of view of the average telephone engineer, the phone system has two principal parts: outside plant (the local loops and trunks, since they are physically outside the switching offices) and inside plant (the switches, which are

150 THE PHYSICAL LAYER CHAP. 2

inside the switching offices). We have just looked at the outside plant. Now, it is time to examine the inside plant.

Two different switching techniques are used by the network nowadays: circuit switching and packet switching. The traditional telephone system is based on cir- cuit switching, although voice over IP technology relies on packet switching. We will go into circuit switching in some detail and contrast it with packet switching. Both kinds of switching are important enough that we will come back to them when we get to the network layer.

Circuit Switching

Traditionally, when you or your computer placed a telephone call, the switch ing equipment within the telephone system sought out a physical path all the way from your telephone to the receiver’s telephone and maintained it for the duration of the call. This technique is called circuit switching. It is shown schematically in Fig. 2-36(a). Each of the six rectangles represents a carrier switching office (end office, toll office, etc.). In this example, each office has three incoming lines and three outgoing lines. When a call passes through a switching office, a physical connection is established between the line on which the call came in and one of the output lines, as shown by the dotted lines.

In the early days of the telephone, the connection was made by the operator plugging a jumper cable into the input and output sockets. In fact, a surprising lit tle story is associated with the invention of automatic circuit-switching equipment. It was invented by a 19th-century Missouri undertaker named Almon B. Strowger. Shortly after the telephone was invented, when someone died, one of the survivors would call the town operator and say ‘‘Please connect me to an undertaker.’’ Unfor tunately for Mr. Strowger, there were two undertakers in his town, and the other one’s wife was the town telephone operator. He quickly saw that either he was going to have to invent automatic telephone switching equipment or he was going to go out of business. He chose the first option. For nearly 100 years, the cir- cuit-switching equipment used worldwide was known as Strowger gear. (History does not record whether the now-unemployed switchboard operator got a job as an information operator, answering questions such as ‘‘What is the phone number of an undertaker?’’)

The model shown in Fig. 2-36(a) is highly simplified, of course, because parts of the physical path between the two telephones may, in fact, be microwave or fiber links onto which thousands of calls are multiplexed. Nevertheless, the basic idea is valid: once a call has been set up, a dedicated path between both ends exists and will continue to exist until the call is finished.

An important property of circuit switching is the need to set up an end-to-end path before any data can be sent. The elapsed time between the end of dialing and the start of ringing can sometimes be 10 seconds, more on long-distance or interna tional calls. During this time interval, the telephone system is hunting for a path,

SEC. 2.5 THE PUBLIC SWITCHED TELEPHONE NETWORK 151

Physical (copper)

connection set up

when call is made

(a)

Switching office

Computer

(b)

Packets queued for subsequent transmission

Computer

Figure 2-36. (a) Circuit switching. (b) Packet switching.

as shown in Fig. 2-37(a). Note that before data transmission can even begin, the call request signal must propagate all the way to the destination and be acknow ledged. For many computer applications (e.g., point-of-sale credit verification), long setup times are undesirable.

As a consequence of the reserved path between the calling parties, once the setup has been completed, the only delay for data is the propagation time for the electromagnetic signal: about 5 milliseconds per 1000 km. Also, as a consequence of the established path, there is no danger of congestion—that is, once the call has

been put through, you never get busy signals. Of course, you might get one before the connection has been established due to lack of switching or trunk capacity.

Packet Switching

The alternative to circuit switching is packet switching, shown in Fig. 2-36(b) and described in Chap. 1. With this technology, packets are sent as soon as they are available. In contrast to circuit switching, there is no need to set up a dedicated path in advance. Packet switching is analogous to sending a series of letters using the postal system: each one travels independently of the others. It is up to routers

152 THE PHYSICAL LAYER CHAP. 2 Call request signal

Pkt 1

Propagation

Pkt 2

^delay Queueing

Pkt 1

Pkt 3

Pkt 2

delay

e

m

i

T

Time spent

hunting for an outgoing trunk

Data

Call

accept signal

Pkt 1

Pkt 3

Pkt 2

Pkt 3

AB

BC

CD

trunk

trunk

trunk

A B C

D A B C

D

(a)

(b)

Figure 2-37. Timing of events in (a) circuit switching, (b) packet switching.

to use store-and-forward transmission to send each packet on its way toward the destination on its own. This procedure is unlike circuit switching, where the result of the connection setup is the reservation of bandwidth all the way from the sender to the receiver and all data on the circuit follows this path. In circuit switching, having all the data follow the same path means that it cannot arrive out of order. With packet switching, there is no fixed path, so different packets can follow dif ferent paths, depending on network conditions at the time they are sent, and they may arrive out of order.

Packet-switching networks place a tight upper limit on the size of packets. This ensures that no user can monopolize any transmission line for very long (e.g., many milliseconds), so that packet-switched networks can handle interactive traf fic. It also reduces delay since the first packet of a long message can be forwarded before the second one has fully arrived. However, the store-and-forward delay of accumulating a packet in the router’s memory before it is sent on to the next router

SEC. 2.5 THE PUBLIC SWITCHED TELEPHONE NETWORK 153

exceeds that of circuit switching. With circuit switching, the bits just flow through the wire continuously. Nothing is ever stored and forwarded later. Packet and circuit switching also differ in other ways. Because no bandwidth is reserved with packet switching, packets may have to wait to be forwarded. This introduces queueing delay and congestion if many packets are sent at the same time. On the other hand, there is no danger of getting a busy signal and being unable to use the network. Thus, congestion occurs at different times with circuit switching (at setup time) and packet switching (when packets are sent). If a circuit has been reserved for a particular user and there is no traffic, its bandwidth is wasted. It cannot be used for other traffic. Packet switching does not waste bandwidth and thus is more efficient from a system perspective. Under- standing this trade-off is crucial for comprehending the difference between circuit switching and packet switching. The trade-off is between guaranteed service and wasting resources versus not guaranteeing service and not wasting resources. Packet switching is more fault tolerant than circuit switching. In fact, that is why it was invented. If a switch goes down, all of the circuits using it are termi- nated and no more traffic can be sent on any of them. With packet switching, packets can be routed around dead switches.

Another difference between circuit and packet switching is how traffic is billed. With circuit switching (i.e., for voice telephone calls over the PSTN), billing has historically been based on distance and time. For mobile voice, dis tance usually does not play a role, except for international calls, and time plays only a coarse role (e.g., a calling plan with 2000 free minutes costs more than one with 1000 free minutes and sometimes nights or weekends are cheap). With pack- et-switched networks, including both fixed-line and mobile networks, time con- nected is not an issue, but the volume of traffic is. For home users in the United States and Europe, ISPs usually charge a flat monthly rate because it is less work for them and their customers can understand this model. In some developing coun tries, billing is often still volume-based: users may purchase a ‘‘data bundle’’ of a certain size and use that data over the course of a billing cycle. Certain times of day, or even certain destinations, may be free of charge or not count against the data cap or quota; these services are sometimes called zero-rated services. Gener- ally, carrier Internet service providers in the Internet backbone charge based on traffic volumes. A typical billing model is based on the 95th percentile of five- minute samples: on a given link, an ISP will measure the volume of traffic that has passed over the link in the last five minutes. A 30-day billing cycle will have 8640 such five-minute intervals, and the ISP will bill based on the 95th percentile of these samples. This technique is often called 95th percentile billing.

The differences between circuit switching and packet switching are summa rized in Fig. 2-38. Traditionally, telephone networks have used circuit switching to provide high-quality telephone calls, and computer networks have used packet switching for simplicity and efficiency. However, there are notable exceptions. Some older computer networks have been circuit switched under the covers (e.g.,

154 THE PHYSICAL LAYER CHAP. 2

X.25) and some newer telephone networks use packet switching with voice over IP technology. This looks just like a standard telephone call on the outside to users, but inside the network packets of voice data are switched. This approach has let upstarts market cheap international calls via calling cards, though perhaps with lower call quality than the incumbents.

Item Circuit switched Packet switched

Call setup Required Not needed Dedicated physical path Yes No

Each packet follows the same route Yes No

Packets arrive in order Yes No

Is a switch crash fatal Yes No

Bandwidth available Fixed Dynamic Time of possible congestion At setup time On every packet Potentially wasted bandwidth Yes No

Store-and-forward transmission No Yes

Charging Per minute Per byte Figure 2-38. A comparison of circuit-switched and packet-switched networks.

2.6 CELLULAR NETWORKS

Even if the conventional telephone system someday gets multigigabit end-to- end fiber, people now expect to make phone calls and to use their phones to check email and surf the Web from airplanes, cars, swimming pools, and while jogging in the park. Consequently, there is a tremendous amount of interest (and investment) in wireless telephony.

The mobile phone system is used for wide area voice and data communication. Mobile phones (sometimes called cell phones) have gone through five distinct generations, widely called 1G, 2G, 3G, 4G, and 5G. The initial three generations provided analog voice, digital voice, and both digital voice and data (Internet, email, etc.), respectively. 4G technology adds additional capabilities, including ad- ditional physical layer transmission techniques (e.g., OFDM uplink transmissions), and IP-based femtocells (home cellular nodes that are connected to fixed-line Inter- net infrastructure). 4G does not support circuit-switched telephony, unlike its pre- decessors; it is based on packet switching only. 5G is being rolled out now, but it will take years before it completely replaces the earlier generations everywhere. 5G technology will support up to 20 Gbps transmissions, as well as denser deploy- ments. There is also some focus on reducing network latency to support a wider range of applications, for example, highly interactive gaming.

SEC. 2.6 CELLULAR NETWORKS 155 2.6.1 Common Concepts: Cells, Handoff, Paging

In all mobile phone systems, a geographic region is divided up into cells, which is why the handsets are sometimes called cell phones. Each cell uses some set of frequencies not used by any of its neighbors. The key idea that gives cellular systems far more capacity than previous systems is the use of relatively small cells and the reuse of transmission frequencies in nearby (but not adjacent) cells. The cellular design increases the system capacity as the cells get smaller. Furthermore, smaller cells mean that less power is needed, which leads to smaller and cheaper transmitters and handsets.

Cells allow for frequency reuse, which is illustrated in Fig. 2-39(a). The cells are normally roughly circular, but they are easier to model as hexagons. In Fig. 2-39(a), the cells are all the same size. They are grouped in units of seven cells. Each letter indicates a group of frequencies. Notice that for each frequency set, there is a buffer about two cells wide where that frequency is not reused, pro- viding for good separation and low interference.

B

B

G

C

G

C

A

A

F

D

F

D

E

E

B

G

C

A

F

D

E

(a) (b)

Figure 2-39. (a) Frequencies are not reused in adjacent cells. (b) To add more users, smaller cells can be used.

In an area where the number of users has grown to the point that the system is overloaded, the power can be reduced and the overloaded cells split into smaller microcells to permit more frequency reuse, as shown in Fig. 2-39(b). Telephone companies sometimes create temporary microcells, using portable towers with sat- ellite links at sporting events, rock concerts, and other places where large numbers of mobile users congregate for a few hours.

At the center of each cell is a base station to which all the telephones in the cell transmit. The base station consists of a computer and transmitter/receiver con- nected to an antenna. In a small system, all the base stations are connected to a

156 THE PHYSICAL LAYER CHAP. 2

single device called an MSC (Mobile Switching Center) or MTSO (Mobile Tele- phone Switching Office). In a larger one, several MSCs may be needed, all of which are connected to a second-level MSC, and so on. The MSCs are essentially end offices as in the telephone system, and are in fact connected to at least one telephone system end office. The MSCs communicate with the base stations, each other, and the PSTN using a packet-switching network.

At any instant, each mobile telephone is logically in one specific cell and under the control of that cell’s base station. When a mobile telephone physically leaves a cell, its base station notices the telephone’s signal fading away and then asks all the surrounding base stations how much power they are getting from it. When the answers come back, the base station then transfers ownership to the cell getting the strongest signal; under most conditions that is the cell where the telephone is now located. The telephone is then informed of its new boss, and if a call is in progress, it is asked to switch to a new channel (because the old one is not reused in any of the adjacent cells). This process, called handoff, takes about 300 milliseconds. Channel assignment is done by the MSC, the nerve center of the system. The base stations are really just dumb radio relays.

Finding locations high in the air to place base station antennas is a major issue. This problem has led some telecommunication carriers to forge alliances with the Roman Catholic Church, since the latter owns a substantial number of exalted po tential antenna sites worldwide, all conveniently under a single management.

Cellular networks typically have four types of channels. Control channels (base to mobile) are used to manage the system. Paging channels (base to mobile) alert mobile users to calls for them. Access channels (bidirectional) are used for call setup and channel assignment. Finally, data channels (bidirectional) carry voice, fax, or data.

2.6.2 First-Generation (1G) Technology: Analog Voice

Let us look at cellular network technology, starting with the earliest system. Mobile radiotelephones were used sporadically for maritime and military commu- nication during the early decades of the 20th century. In 1946, the first system for car-based telephones was set up in St. Louis. This system used a single large trans- mitter on top of a tall building and had a single channel, used for both sending and receiving. To talk, the user had to push a button that enabled the transmitter and disabled the receiver. Such systems, known as push-to-talk systems, were in- stalled beginning in the 1950s. Taxis and police cars often used this technology.

In the 1960s, IMTS (Improved Mobile Telephone System) was installed. It, too, used a high-powered (200-watt) transmitter on top of a hill but it had two fre- quencies, one for sending and one for receiving, so the push-to-talk button was no longer needed. Since all communication from the mobile telephones went inbound on a different channel than the outbound signals, the mobile users could not hear each other (unlike the push-to-talk system used in older taxis).

SEC. 2.6 CELLULAR NETWORKS 157

IMTS supported 23 channels spread out from 150 MHz to 450 MHz. Due to the small number of channels, users often had to wait a long time before getting a dial tone. Also, due to the large power of the hilltop transmitters, adjacent systems had to be several hundred kilometers apart to avoid interference. All in all, the limited capacity made the system impractical.

AMPS (Advanced Mobile Phone System), an analog mobile phone system invented by Bell Labs and first deployed in the United States in 1983, significantly increased the capacity of the cellular network. It was also used in England, where it was called TACS, and in Japan, where it was called MCS-L1. AMPS was for- mally retired in 2008, but we will look at it to understand the context for the 2G and 3G systems that improved on it. In AMPS, cells are typically 10 to 20 km across; in digital systems, the cells are smaller. Whereas an IMTS system 100 km across can have only one call on each frequency, an AMPS system might have 100 10-km cells in the same area and be able to have 10 to 15 calls on each frequency, in widely separated cells.

AMPS uses FDM to separate the channels. The system uses 832 full-duplex channels, each consisting of a pair of simplex channels. This arrangement is known as FDD (Frequency Division Duplex). The 832 simplex channels from 824 to 849 MHz are used for mobile to base station transmission, and 832 simplex channels from 869 to 894 MHz are used for base station to mobile transmission. Each of these simplex channels is 30 kHz wide.

The 832 channels in AMPS are divided into four categories. Since the same frequencies cannot be reused in nearby cells and 21 channels are reserved in each cell for control, the actual number of voice channels available per cell is much smaller than 832, typically about 45.

Call Management

Each mobile telephone in AMPS has a 32-bit serial number and a 10-digit tele- phone number in its programmable read-only memory. The telephone number in many countries is represented as a 3-digit area code in 10 bits and a 7-digit sub- scriber number in 24 bits. When a phone is switched on, it scans a preprogrammed list of 21 control channels to find the most powerful signal. The phone then broad- casts its 32-bit serial number and 34-bit telephone number. Like all the control information in AMPS, this packet is sent in digital form, multiple times, and with an error-correcting code, even though the voice channels themselves are analog.

When the base station hears the announcement, it tells the MSC, which records the existence of its new customer and also informs the customer’s home MSC of his current location. During normal operation, the mobile telephone reregisters about once every 15 minutes.

To make a call, a mobile user switches on the phone, (at least conceptually) enters the number to be called on the keypad, and hits the CALL button. The phone then transmits the number to be called and its own identity on the access

158 THE PHYSICAL LAYER CHAP. 2

channel. If a collision occurs there, it tries again later. When the base station gets the request, it informs the MSC. If the caller is a customer of the MSC’s company (or one of its partners), the MSC looks for an idle channel for the call. If one is found, the channel number is sent back on the control channel. The mobile phone then automatically switches to the selected voice channel and waits until the called party picks up the phone.

Incoming calls work differently. To start with, all idle phones continuously lis ten to the paging channel to detect messages directed at them. When a call is placed to a mobile phone (either from a fixed phone or another mobile phone), a packet is sent to the callee’s home MSC to find out where it is. A packet is then sent to the base station in its current cell, which sends a broadcast on the paging channel of the form ‘‘Unit 14, are you there?’’ The called phone responds with a ‘‘Yes’’ on the access channel. The base then says something like: ‘‘Unit 14, call for you on channel 3.’’ At this point, the called phone switches to channel 3 and starts making ringing sounds (or playing some melody the owner was given as a birthday present).

2.6.3 Second-Generation (2G) Technology: Digital Voice

The first generation of mobile phones was analog; the second generation is digital. Switching to digital has several advantages. It provides capacity gains by allowing voice signals to be digitized and compressed. It improves security by al lowing voice and control signals to be encrypted. This, in turn, deters fraud and eavesdropping, whether from intentional scanning or echoes of other calls due to RF propagation. Finally, it enables new services such as text messaging.

Just as there was no worldwide standardization during the first generation, there was also no worldwide standardization during the second, either. Several dif ferent systems were developed, and three have been widely deployed. D-AMPS (Digital Advanced Mobile Phone System) is a digital version of AMPS that coexists with AMPS and uses TDM to place multiple calls on the same frequency channel. It is described in International Standard IS-54 and its successor IS-136. GSM (Global System for Mobile communications) has emerged as the dominant system, and while it was slow to catch on in the United States it is now used virtu- ally everywhere in the world. Like D-AMPS, GSM is based on a mix of FDM and TDM. CDMA (Code Division Multiple Access), described in International Standard IS-95, is a completely different kind of system and is based on neither FDM nor TDM. While CDMA has not become the dominant 2G system, its tech- nology has become the basis for 3G systems.

Also, the name PCS (Personal Communications Services) is sometimes used in the marketing literature to indicate a second-generation (i.e., digital) system. Originally it meant a mobile phone using the 1900 MHz band, but that distinction is rarely made now. The dominant 2G system in most of the world is GSM which we now describe in detail.

SEC. 2.6 CELLULAR NETWORKS 159 2.6.4 GSM: The Global System for Mobile Communications

GSM started life in the 1980s as an effort to produce a single European 2G standard. The task was assigned to a telecommunications group called (in French) Groupe Speciale´ Mobile. The first GSM systems were deployed starting in 1991 and were a quick success. It soon became clear that GSM was going to be more than a European success, with the uptake stretching to countries as far away as Australia, so GSM was renamed to have a more worldwide appeal.

GSM and the other mobile phone systems we will study retain from 1G sys tems a design based on cells, frequency reuse across cells, and mobility with hand- offs as subscribers move. It is the details that differ. Here, we will briefly discuss some of the main properties of GSM. However, the printed GSM standard is over 5000 [sic] pages long. A large fraction of this material relates to engineering as- pects of the system, especially the design of receivers to handle multipath signal propagation, and synchronizing transmitters and receivers. None of this will be even mentioned here.

Fig. 2-40 shows that the GSM architecture is similar to the AMPS architecture, though the components have different names. The mobile itself is now divided into the handset and a removable chip with subscriber and account information

called a SIM card, short for Subscriber Identity Module. It is the SIM card that activates the handset and contains secrets that let the mobile and the network ident ify each other and encrypt conversations. A SIM card can be removed and plugged into a different handset to turn that handset into your mobile as far as the network is concerned.

Air

interface

^HLR BSC

^SIM PSTN

card

MSC

BSC

VLR

Handset

Cell tower and base station

Figure 2-40. GSM mobile network architecture.

The mobile talks to cell base stations over an air interface that we will de- scribe in a moment. The cell base stations are each connected to a BSC (Base Sta tion Controller) that controls the radio resources of cells and handles handoff. The BSC in turn is connected to an MSC (as in AMPS) that routes calls and con- nects to the PSTN (Public Switched Telephone Network).

To be able to route calls, the MSC needs to know where mobiles can currently be found. It maintains a database of nearby mobiles that are associated with the

160 THE PHYSICAL LAYER CHAP. 2

cells it manages. This database is called the VLR (Visitor Location Register). There is also a database in the mobile network that gives the last known location of each mobile. It is called the HLR (Home Location Register). This database is used to route incoming calls to the right locations. Both databases must be kept up to date as mobiles move from cell to cell.

We will now describe the air interface in some detail. GSM runs on a range of frequencies worldwide, including 900, 1800, and 1900 MHz. More spectrum is al located than for AMPS in order to support a much larger number of users. GSM is a frequency division duplex cellular system, like AMPS. That is, each mobile transmits on one frequency and receives on another, higher frequency (55 MHz higher for GSM versus 80 MHz higher for AMPS). However, unlike with AMPS, with GSM a single frequency pair is split by time division multiplexing into time slots. In this way, it is shared by multiple mobiles.

To handle multiple mobiles, GSM channels are much wider than the AMPS channels (200 kHz versus 30 kHz). One 200-kHz channel is shown in Fig. 2-41. A GSM system operating in the 900-MHz region has 124 pairs of simplex chan- nels. Each simplex channel is 200 kHz wide and supports eight separate con- nections on it, using time division multiplexing. Each currently active station is as- signed one time slot on one channel pair. Theoretically, 992 channels can be sup- ported in each cell, but many of them are not available, to avoid frequency conflicts with neighboring cells. In Fig. 2-41, the eight shaded time slots all belong to the same connection, four of them in each direction. Transmitting and receiving does not happen in the same time slot because the GSM radios cannot transmit and re- ceive at the same time and it takes time to switch from one to the other. If the mobile device assigned to 890.4/935.4 MHz and time slot 2 wanted to transmit to the base station, it would use the lower four shaded slots (and the ones following them in time), putting some data in each slot until all the data had been sent.

The TDM slots shown in Fig. 2-41 are part of a complex framing hierarchy. Each TDM slot has a specific structure, and groups of TDM slots form multi frames, also with a specific structure. A simplified version of this hierarchy is shown in Fig. 2-42. Here we can see that each TDM slot consists of a 148-bit data frame that occupies the channel for 577 µsec (including a 30-µsec guard time after each slot). Each data frame starts and ends with three 0 bits, for frame delineation purposes. It also contains two 57-bit Information fields, each one having a control bit that indicates whether the following Information field is for voice or data. Be tween the Information fields is a 26-bit Sync (training) field that is used by the re- ceiver to synchronize to the sender’s frame boundaries.

A data frame is transmitted in 547 µsec, but a transmitter is only allowed to send one data frame every 4.615 msec, since it is sharing the channel with seven other stations. The gross rate of each channel is 270,833 bps, divided among eight users. However, as with AMPS, the overhead eats up a large fraction of the band- width, ultimately leaving 24.7 kbps worth of payload per user before error cor rection is applied. After error correction, 13 kbps is left for speech. While this is

SEC. 2.6 CELLULAR NETWORKS 161 _Channel TDM frame

959.8 MHz

935.4 MHz 935.2 MHz

y

c

n

e

124

Base

to mobile

2

1

u

q

e

r

F

914.8 MHz

890.4 MHz 890.2 MHz

Time

124

Mobile

to base

2

1

Figure 2-41. GSM uses 124 frequency channels, each of which uses an eight

slot TDM system.

substantially less than 64 kbps PCM for uncompressed voice signals in the fixed telephone network, compression on the mobile device can reach these levels with little loss of quality.

32,500-Bit multiframe sent in 120 msec

C

0 1 2 3 4 5 6 7 8 9 10 11 13 14 15 16 17 18 19 20 21 22 23 24

T

L

Reserved

1250-Bit TDM frame sent in 4.615 msec

0 1 2 3 4 5 6 7

148-Bit data frame sent in 547 µsec

000 Information Sync Information 000

Bits 3 57 26 57 3 Voice/data bit

Figure 2-42. A portion of the GSM framing structure.

for future use

8.25–bit

(30 µsec) guard time

As can be seen from Fig. 2-42, eight data frames make up a TDM frame and 26 TDM frames make up a 120-msec multiframe. Of the 26 TDM frames in a

162 THE PHYSICAL LAYER CHAP. 2

multiframe, slot 12 is used for control and slot 25 is reserved for future use, so only 24 are available for user traffic.

However, in addition to the 26-slot multiframe shown in Fig. 2-42, a 51-slot multiframe (not shown) is also used. Some of these slots are used to hold several control channels used to manage the system. The broadcast control channel is a continuous stream of output from the base station containing the base station’s identity and the channel status. All mobile stations monitor their signal strength to see when they have moved into a new cell.

The dedicated control channel is used for location updating, registration, and call setup. In particular, each BSC maintains a database of mobile stations cur rently under its jurisdiction, the VLR. Information needed to maintain the VLR is sent on the dedicated control channel.

The system also has a common control channel, which is split up into three logical subchannels. The first of these subchannels is the paging channel, which the base station uses to announce incoming calls. Each mobile station monitors it continuously to watch for calls it should answer. The second is the random access channel, which allows users to request a slot on the dedicated control channel. If two requests collide, they are garbled and have to be retried later. Using the dedi- cated control channel slot, the station can set up a call. The assigned slot is announced on the third subchannel, the access grant channel.

Finally, GSM differs from AMPS in how handoff is handled. In AMPS, the MSC manages it completely without help from the mobile devices. With time slots in GSM, the mobile is neither sending nor receiving most of the time. The idle slots are an opportunity for the mobile to measure signal quality to other nearby base stations. It does so and sends this information to the BSC. The BSC can use it to determine when a mobile is leaving one cell and entering another so it can per form the handoff. This design is called MAHO (Mobile Assisted HandOff).

2.6.5 Third-Generation (3G) Technology: Digital Voice and Data

The first generation of mobile phones was analog voice, and the second gen- eration was digital voice. The third generation of mobile phones, or 3G as it is called, is all about digital voice and data. A number of factors drove the industry to 3G technology. First, around the time of 3G, data traffic began to exceed voice traffic on the fixed network; similar trends began to emerge for mobile devices. Second, phone, Internet, and video services began to converge. The rise of smart- phones, starting with Apple’s iPhone, which was first released in 2007, accelerated the shift to mobile data. Data volumes are rising steeply with the popularity of iPhones. When the iPhone was first released, it used a 2.5G network (essentially an enhanced 2G network) that did not have enough data capacity. Data-hungry iPhone users further drove the transition to 3G technologies, to support higher data transmission rates. A year later, in 2008, Apple released an updated version of its iPhone that could use the 3G data network.

SEC. 2.6 CELLULAR NETWORKS 163

Operators initially took small steps in the direction of 3G by going to what is sometimes called 2.5G. One such system is EDGE (Enhanced Data rates for GSM Evolution), which is essentially GSM with more bits per symbol. The trou- ble is, more bits per symbol also means more errors per symbol, so EDGE has nine different schemes for modulation and error correction, differing in terms of how much of the bandwidth is devoted to fixing the errors introduced by the higher speed. EDGE is one step along an evolutionary path that is defined from GSM to other 3G technologies that we discuss in this section.

ITU tried to get a bit more specific about the 3G vision starting back around 1992. It issued a blueprint for getting there called IMT-2000, where IMT stood for International Mobile Telecommunications. The basic services that the IMT-2000 network was supposed to provide to its users are:

1. High-quality voice transmission.

2. Messaging (replacing email, fax, SMS, chat, etc.).

3. Multimedia (playing music, viewing videos, films, television, etc.). 4. Internet access (Web surfing, including pages with audio and video).

Additional services might be video conferencing, telepresence, group game play ing, and m-commerce (waving your telephone at the cashier to pay in a store). Furthermore, all these services are supposed to be available worldwide (with auto- matic connection via a satellite when no terrestrial network can be located), in- stantly (always on), and with quality of service guarantees. In other words, pie in the sky.

ITU envisioned a single worldwide technology for IMT-2000, so manufact- urers could build a single device that could be sold and used anywhere in the world. Having a single technology would also make life much simpler for network operators and would encourage more people to use the services.

As it turned out, this was more than a bit optimistic. The number 2000 stood for three things: (1) the year it was supposed to go into service, (2) the frequency it was supposed to operate at (in MHz), and (3) the bandwidth the service should have (in kbps). It did not make it on any of the three counts. Nothing was imple- mented by 2000. ITU recommended that all governments reserve spectrum at 2 GHz so devices could roam seamlessly from country to country. China reserved the required bandwidth but nobody else did. Finally, it was recognized that 2 Mbps is not currently feasible for users who are too mobile (due to the difficulty of performing handoffs quickly enough). More realistic is 2 Mbps for stationary indoor users, 384 kbps for people walking, and 144 kbps for connections in cars.

Despite these initial setbacks, a great deal has been accomplished since then. Several IMT-2000 proposals were made and, after some winnowing, it came down to two primary ones: (1) WCDMA (Wideband CDMA), proposed by Ericsson

164 THE PHYSICAL LAYER CHAP. 2

and pushed by the European Union, which called it UMTS (Universal Mobile Telecommunications System) and (2) CDMA2000, proposed by Qualcomm in the United States

Both of these systems are more similar than different; both are based on broad- band CDMA. WCDMA uses 5-MHz channels and CDMA2000 uses 1.25-MHz channels. If the Ericsson and Qualcomm engineers were put in a room and told to come to a common design, they probably could find one in an hour. The trouble is that the real problem is not engineering, but politics (as usual). Europe wanted a system that interworked with GSM, whereas the United States wanted a system that was compatible with one already widely deployed in the United States (IS-95). Each side (naturally) also supported its local company (Ericsson is based in Swe- den; Qualcomm is in California). Finally, Ericsson and Qualcomm were involved in numerous lawsuits over their respective CDMA patents. To add to the confu- sion, UMTS became a single 3G standard with multiple incompatible options, in- cluding CDMA2000. This change was an effort to unify the various camps, but it just papers over the technical differences and obscures the focus of ongoing efforts. We will use UMTS to mean WCDMA, as distinct from CDMA2000.

Another improvement of WCDMA over the simplified CDMA scheme we de- scribed earlier is to allow different users to send data at different rates, independent of each other. This trick is accomplished naturally in CDMA by fixing the rate at which chips are transmitted and assigning different users chip sequences of dif ferent lengths. For example, in WCDMA, the chip rate is 3.84 Mchips/sec and the spreading codes vary from 4 to 256 chips. With a 256-chip code, around 12 kbps is left after error correction, and this capacity is sufficient for a voice call. With a 4-chip code, the user data rate is close to 1 Mbps. Intermediate-length codes give intermediate rates; in order to get to multiple Mbps, the mobile must use more than one 5-MHz channel at once.

We will focus our discussion on the use of CDMA in cellular networks, as it is the distinguishing feature of both systems. CDMA is neither FDM nor TDM but a kind of mix in which each user sends on the same frequency band at the same time. When it was first proposed for cellular systems, the industry gave it approximately the same reaction that Columbus first got from Queen Isabella when he proposed reaching India by sailing in the wrong direction. However, through the persistence of a single company, Qualcomm, CDMA succeeded as a 2G system (IS-95) and matured to the point that it became the technical basis for 3G.

To make CDMA work in the mobile phone setting requires more than the basic CDMA technique that we described in Sec. 2.4. Specifically, we described a sys tem called synchronous CDMA, in which the chip sequences are exactly orthogo- nal. This design works when all users are synchronized on the start time of their chip sequences, as in the case of the base station transmitting to mobiles. The base station can transmit the chip sequences starting at the same time so that the signals will be orthogonal and able to be separated. However, it is difficult to synchronize the transmissions of independent mobile phones. Without some special efforts,

SEC. 2.6 CELLULAR NETWORKS 165

their transmissions would arrive at the base station at different times, with no guar- antee of orthogonality. To let mobiles send to the base station without synchroni- zation, we want code sequences that are orthogonal to each other at all possible offsets, not simply when they are aligned at the start.

While it is not possible to find sequences that are exactly orthogonal for this general case, long pseudorandom sequences come close enough. They have the property that, with high probability, they have a low cross-correlation with each other at all offsets. This means that when one sequence is multiplied by another sequence and summed up to compute the inner product, the result will be small; it would be zero if they were orthogonal. (Intuitively, random sequences should al- ways look different from each other. Multiplying them together should then pro- duce a random signal, which will sum to a small result.) This lets a receiver filter unwanted transmissions out of the received signal. Also, the auto-correlation of pseudorandom sequences is also small, with high probability, except at a zero off- set. This means that when one sequence is multiplied by a delayed copy of itself and summed, the result will be small, except when the delay is zero. (Intuitively, a delayed random sequence looks like a different random sequence, and we are back to the cross-correlation case.) This lets a receiver lock onto the beginning of the wanted transmission in the received signal.

The use of pseudorandom sequences lets the base station receive CDMA mes- sages from unsynchronized mobiles. However, an implicit assumption in our dis- cussion of CDMA is that the power levels of all mobiles are the same at the re- ceiver. If they are not, a small cross-correlation with a powerful signal might over- whelm a large auto-correlation with a weak signal. Thus, the transmit power on

mobiles must be controlled to minimize interference between competing signals. It is this interference that limits the capacity of CDMA systems.

The power levels received at a base station depend on how far away the trans- mitters are as well as how much power they transmit. There may be many mobile stations at varying distances from the base station. A good heuristic to equalize the received power is for each mobile station to transmit to the base station at the inverse of the power level it receives from the base station. In other words, a mobile station receiving a weak signal from the base station will use more power than one getting a strong signal. For more accuracy, the base station also gives each mobile feedback to increase, decrease, or hold steady its transmit power. The feedback is frequent (1500 times per second) because good power control is impor tant to minimize interference.

Now let us describe the advantages of CDMA. First, CDMA can improve ca- pacity by taking advantage of small periods when some transmitters are silent. In polite voice calls, one party is silent while the other talks. On average, the line is busy only 40% of the time. However, the pauses may be small and are difficult to predict. With TDM or FDM systems, it is not possible to reassign time slots or fre- quency channels quickly enough to benefit from these small silences. However, in CDMA, by simply not transmitting one user lowers the interference for other users,

166 THE PHYSICAL LAYER CHAP. 2

and it is likely that some fraction of users will not be transmitting in a busy cell at any given time. Thus CDMA takes advantage of expected silences to allow a larger number of simultaneous calls.

Second, with CDMA each cell uses the same set of frequencies. Unlike GSMand AMPS, FDM is not needed to separate the transmissions of different users. This eliminates complicated frequency planning tasks and improves capacity. It

also makes it easy for a base station to use multiple directional antennas, or sec tored antennas, instead of an omnidirectional antenna. Directional antennas con- centrate a signal in the intended direction and reduce the signal (and interference) in other directions. This, in turn, increases capacity. Three-sector designs are com- mon. The base station must track the mobile as it moves from sector to sector. This tracking is easy with CDMA because all frequencies are used in all sectors.

Third, CDMA facilitates soft handoff, in which the mobile is acquired by the new base station before the previous one signs off. In this way, there is no loss of continuity. Soft handoff is shown in Fig. 2-43. It is easy with CDMA because all frequencies are used in each cell. The alternative is a hard handoff, in which the old base station drops the call before the new one acquires it. If the new one is unable to acquire it (e.g., because there is no available frequency), the call is disconnected abruptly. Users tend to notice this, but it is inevitable occasionally with the current design. Hard handoff is the norm with FDM designs to avoid the cost of having the mobile transmit or receive on two frequencies simultaneously.

(a) (b) (c)

Figure 2-43. Soft handoff (a) before, (b) during, and (c) after.

2.6.6 Fourth-Generation (4G) Technology: Packet Switching

In 2008, the ITU specified a set of standards for 4G systems. 4G, which is sometimes also called IMT Advanced is based completely on packet-switched network technology, including to its predecessors. Its immediate predecessor was a technology often referred to as LTE (Long Term Evolution). Another precursor and related technology to 4G was 3GPP LTE, sometimes called ‘‘4G LTE.’’ The terminology is a bit confusing, as ‘‘4G’’ effectively refers to a generation of mobile communications, where any generation may, in fact, have multiple standards. For example, ITU considers IMT Advanced as a 4G standard, although it also accepts LTE as a 4G standard. Other technologies such as the doomed WiMAX (IEEE

SEC. 2.6 CELLULAR NETWORKS 167

802.16) are also considered 4G technologies. Technically, LTE and ‘‘true’’ 4G are different releases of the 3GPP standard (releases 8 and 10, respectively). The main innovation of 4G over previous 3G systems is that 4G networks use packet switching, as opposed to circuit switching. The innovation that allows packet switching is called an EPC (Evolved Packet Core), which is essentially a simplified IP network that separates voice traffic from the data network. The EPC network carries both voice and data in IP packets. It is thus a (VoIP) Voice over IP network, with resources allocated using the statistical multiplexing approaches de- scribed earlier. As such, the EPC must manage resources in such a way that voice quality remains high in the face of network resources that are shared among many users. The performance requirements for LTE include, among other things, peak throughput of 100 Mbps upload and 50 Mbps download. To achieve these higher rates, 4G networks use a collection of additional frequencies, including 700 MHz, 850 MHz, 800 MHz, and others. Another aspect of the 4G standard is ‘‘spectral ef ficiency,’’ or how many bits can be transmitted per second for a given frequency; for 4G technologies, peak spectral efficiency should be 15 bps/Hz for a downlink and 6.75 bps/Ghz for uplink.

The LTE architecture includes the following elements as part of the Evolved Packet Core, as shown in Chap. 1 as Fig. 1-19.

1. Serving Gateway (S-GW). The SGW forwards data packets to ensure that packets continue to be forwarded to the user’s device when switching from one eNodeB to another.

2. MME (Mobility Management Entity). The MME tracks and pages the user device and chooses the SGW for a device when it first con- nects to the network, as well as during handoffs. It also authenticates the user’s device.

3. Packet Data Network Gateway (P-GW). The PDN GW interfaces between the user device and a packet data network (i.e., a pack- et-switched network), and can perform such functions such as address allocation for that network (e.g., via DHCP), rate limiting, filtering, deep packet inspection, and lawful interception of traffic. User de- vices establish connection-oriented service with the packet gateway using a so-called EPS bearer, which is established when the user de- vice attaches to the network.

4. HSS (Home Subscriber Server), The MME queries the HSS to de termine that the user device corresponds to a valid subscriber.

The 4G network also has an evolved Radio Access Network (RAN). The radio access network for LTE introduces an access node called an eNodeB, which performs operations at the physical layer (as we focus on in this chapter), as well as the MAC (Medium Access Control), RLC (Radio Link Control), and PDCP

168 THE PHYSICAL LAYER CHAP. 2

(Packet Data Control Protocol) layers, many of which are specific to the cellular network architecture. The eNodeB performs resource management, admission con trol, scheduling, and other control-plane functions.

On 4G networks, voice traffic can be carried over the EPC using a technology called VoLTE (Voice over LTE), making it possible for carriers to transmit voice traffic over the packet-switched network and removing any dependency on the legacy circuit-switched voice network.

2.6.7 Fifth-Generation (5G) Technology

Around 2014, the LTE system reached maturity, and people began to start thinking about what would come next. Obviously, after 4G comes 5G. The real question, of course, is ‘‘What Will 5G Be?’’ which Andrews et al. (2014) discuss at length. Years later, 5G came to mean many different things, depending on the

audience and who is using the term. Essentially, the next generation of mobile cel lular network technology boils down to two main factors: higher data rates and lower latency than 4G technologies. There are specific technologies that enable faster speed and lower latency, of course, which we discuss below.

Cellular network performance is often measured in terms of aggregate data rate or area capacity, which is the total amount of data that the network can serve in bits per unit area. One goal of 5G is to improve the area capacity of the network by three orders of magnitude (more than 1000 times that of 4G), using a combina tion of technologies:

1. Ultra-densification and offloading. One of the most straightforward ways to improve network capacity is by adding more cells per area. Whereas 1G cell sizes were on the order of hundreds of square kilo- meters, 5G aims for smaller cell sizes, including picocells (cells that are less than 100 meters in diameter) and even femtocells (cells that have WiFi-like range of tens of meters). One of the most important

benefits of the shrinking of the cell size is the ability to reuse spec trum in a given geographic area, thus reducing the number of users that are competing for resources at any given base station. Of course, shrinking the cell size comes with its own set of complications, in- cluding more complicated mobility management and handoff.

2. Increased bandwidth with millimeter waves. Most spectrum from pre- vious technologies has been in the range of several hundred MHz to a few GHz, corresponding to wavelengths that are in range of centime ters to about a meter. This spectrum has become increasingly crowded, especially in major markets during peak hours. There are considerable amounts of unused spectrum in the millimeter wave range of 20<300 GHz, with wavelengths of less than 10 millimeters. Until recently, this spectrum was not considered suitable for wireless