McGraw Hill CDMA Capacity and Quality Optimization Feb 2003 ISBN 0071399194 pdf

  Part

  1 Key Radio Concepts

  Part 1 of this text, “Key Radio Concepts,” is provided for readers who are not already familiar with the engineering principles of radio and how they apply to cellular systems. It also will benefit radio experts in two ways. First of all, it will help our readers explain these concepts to people in other fields and to businesspeople. Second, today’s code division multiple access (CDMA) wireless technology is built on a series of developments going back over 30 years. It is easy to be expert in a system and not to know where it came from or to have an in-depth knowledge of how it works. However, in understanding the history of our field and the challenges faced by our predecessors, we gain a deeper expertise, improving our ability to handle the problems we face today.

  Chapter 1, “Radio Engineering Concepts,” defines the fundamentals of radio, including frequency, amplitude and power, and modulation. It also includes explanations of multiple access and modulation, a description of how a radio signal is altered by an antenna and by the space between the transmitter and receiver, and how we calculate signal power through those changes.

  In Chapter 2, “Radio Signal Quality,” we discuss impairments to the radio signal, such as noise, interference, distortion, and multipath. Chapter 2 also covers the measurement of radio signals, errors in those measurements, and the measurement of both analog and digital radio signals.

  Chapters 3 and 4 describe the components at the two sides of the radio-air interface, the user terminal and the base station. Chapter 3,

  “The User Terminal,” describes the components of a user terminal,

  commonly known as a cell phone. Chapter 4, “The Base Station,” describes the cellular base station: the antennas that receive the signal through the tower and cable, the power amplifier, the receiver, the components that transmit cellular signals, those which send telephone calls through the link to the mobile switching center, and

2 Key Radio Concepts

  Chapter 5, “Basic Wireless Telephony,” provides a picture of how all the parts of a cellular network work together to create the wireless

signal path and how the whole cellular system is laid out, i.e., its

architecture.

  

In Chapters 6 and 7 we describe the early analog and digital

cellular radio technologies. In Chapter 6, “Analog Wireless

  Telephony (AMPS),” we describe the original Advanced Mobile Phone

  Service (AMPS) analog cellular technology that pioneered the

cellular architecture as the first radio system relying on managed

interference. In Chapter 7, “TDMA Wireless Telephony (GSM),” we introduce the world’s first and largest digital cellular system,

Europe’s Global System for Mobility (GSM) time division multiple

access (TDMA) technology, which is serving about 700 million users worldwide in 2002.

  Having built a solid background in the fundamentals of radio and the evolution of cellular telephony, we turn to code division multiple access (CDMA) in Chapter 8. In Chapter 8, “The CDMA Principle,” we discuss the underlying concept of CDMA, called spread spectrum, the mathematical derivation of the CDMA method of managed same- cell interference, and the principles of key CDMA components such as

the rake filter and power control. We also describe how CDMA

operates in both the forward and reverse directions and how it

performs handoffs as subscribers move from cell to cell.

  The CDMA cellular networks our readers support embody both concepts developed for the first analog cellular systems and also the latest digital chipsets and technologies. With the background provided in Part I, “Key Radio Concepts,” cellular engineers will be well prepared to understand the latest CDMA technology so that we can design and optimize today’s CDMA networks.

  Chapter

  1 Radio Engineering Concepts

  We all know what radio is, at least enough to get by. This chapter is for our readers who came to cellular from landline telephony or information technology and for those who want a refresher in the basics of radio engineering.

1.1 Radio

  Radio is electromagnetic radiation, a changing electric field accompanied by a similarly changing magnetic field that propagates at high speed, as illustrated in Fig. 1.1. A ra- dio wave is transmitted by creating an electrical voltage in a conducting antenna, by putting a metal object in the air and sending pulses of electricity that become radio waves. Similarly, a radio signal is received by measuring electrical voltage changes in an antenna, by putting another metal object in the air and detecting the very tiny pulses of electricity generated by the varying electrical field of the radio waves.

  The technology of radio transmission is developing the ability to transmit a radio signal containing some desired information and developing a receiver to pick up just that particular signal and to extract that desired information. One of the latest tech- nologies to do this is code division multiple access (CDMA), a long way from the dit-dah Morse code transmission of the earliest wireless equipment. Both Morse code and CDMA, however, are digital radio technologies.

  We use radio to get some kind of information, a signal, from one place to another us- ing a radio wave. We put that signal onto the radio medium, the carrier we call it, with some kind of scheme that we call modulation. The Morse code sender uses the simple modulation scheme of a short transmission burst as a dit and a longer transmission burst as a dah. The demodulation scheme does the reverse: The telegraph receiver makes audible noise during a radio burst, and the listener hears short and long bursts of noise as dits and dahs. Morse code is simple and elegant, and it used the technology of its day efficiently.

  All the components of the process of radio communications were already present in the telegraph. There is a meaningful message to be sent that was coded into a specific for- mat, the letters of the alphabet. The formatted message, the signal, is then modulated

4 Key Radio Concepts

  Electric Field

  Magnetic Field

  Wave Motion Figure 1.1 An electromagnetic radio wave. the letters to form words. In this case, the formatted message is a sequence of letters, a digital signal.

  The meaningful message in telephony is primarily spoken voice. The formatting stage is done with a microphone and amplifiers to form an electrical voltage over time that represents the speech, an analog signal in this case. If this signal is fed into an amplifier and a speaker, then we hear meaningful voice output.

1.2 Frequency

  In addition to their magnitude, analog signals such as audio, electricity, and radio also have the attribute of frequency. We all know frequency as the pitch of a sound or the station numbers on a car radio, but frequency is a deep, basic, fundamental, primal mathematical concept that deserves some attention.

  The simplest view of frequency is that it is the number of waves that pass a given point at a given time. In this simplified view, wavelength is in inverse ratio to fre- quency, with the speed of transmission as the constant.

  1 We measure frequency in cycles per second, or hertz (Hz). Frequencies we use in real

  life vary considerably. We have the very low 50 or 60 Hz of electrical power from the

  2

  wall outlet. Sound we hear is air pressure waves varying from 20 Hz to 20 kHz. Our AM radio stations operate from 500 kHz to 1.6 MHz, and FM and older broadcast ₁ More mathematical texts often measure frequencies in radians per second and usually use the Greek letter omega ␻ for radian frequency values, where ␻ ⫽ 2␲f. ₂ While almost everybody reading this knows that kHz stands for kilohertz, 1000 hertz, some of

  Radio Engineering Concepts

  5

  television stations are in the very high frequency (VHF) band around 100 MHz. Air- craft radios operate in the VHF band as well.

  10 Electromagnetic radiation propagates at the speed of light c, which is about 3 ⫻ 10 cm/s.

  Therefore, Advanced Mobile Phone Service (AMPS), the U.S. analog cellular system, at 900 MHz frequency, has a wavelength of about 33 cm, and the primary cdmaOne fre- quency, 1.9 GHz, has a wavelength of about 16 cm. Wavelength is a major element in determining the types of attentuation that we will need to manage. For example, in the upper microwave bands used for satellite transmission, wavelength is a fraction of a centimeter, and raindrops can cause attenuation. However, rain is not a problem for cellular systems. Attenuation tends to occur when the intervening objects are of a size

  3

  about equal to one-half the transmission wavelength. To put radio frequencies into perspective, the visible red laser light used in fiber optic cable is around 500 THz, 500,000,000,000,000 cycles per second, with a wavelength of about 0.00006 cm.

  In a sound wave, there is some atmospheric pressure at every instant of time, so we can say that the atmospheric pressure is a function of time, and we can describe that function as the time response of the sound wave. In our human experience, sound usu- ally comes in periodic waves, and the number of waves per unit time determines the pitch, the frequency of the sound. Normal sound is a mixture of many frequencies, and

  4 its frequency response is often more informative than its time response.

  A radio wave has a voltage at every instant of time, so its time response is voltage rather than air pressure. Radio also is usually transmitted in periodic waves with an associated frequency. As in the case of sound, radio waves usually contain many fre- quencies, and their frequency response is important.

  A function can be represented as f(x). In the case of electrical voltage over time, we can represent the voltage v at each time t as v(t). The mathematical concept of a func-

  tion tells us that there is one f(x) for each x or, in our electrical case, one specific volt- age v(t) for each time t.

  Fourier analysis tells us that we can think of the same v(t) in another form as V(s), where s is one particular frequency rather than an instant of time. The function V(s) is a little more complicated than v(t) because it contains not only the amplitude of fre- quency s but also its phase. The relationship between time response v(t) and frequency response V(s) is a pair of integrals from college calculus. _∞

  ist V(s) ⫽ v(t)e dt (1.1)

  

_∞

t⫽⫺∞

_⫺ its v(t) ⫽ V(s)e ds

  (1.2) ₃

s⫽⫺∞

  The coauthor who lives in Texas notes that this could mean that 3-in hail interferes in the CDMA band. Frankly, we’re a lot more concerned about equipment damage than about radio in- terference when the hail is the size of tennis balls. ₄ The audible difference between an oboe and a violin playing the same steady note B ♭ is in their response at higher frequencies. Those higher frequencies are called harmonics. The audible dif-

6 Key Radio Concepts

  While our time and frequency intervals in real life do not go from minus infinity (⫺∞) to plus infinity (⫹∞), an important message from these two integrals is that frequency response V(s) depends on the time response v(t) over an extended period of time and, conversely, that the time response v(t) is determined by knowing enough about the fre- quency response V(s). Equations (1.1) and (1.2) for time and frequency are nearly sym- metric, and they tell us that there is a duality in the time-frequency relationship. A sig- nal v(t) consisting of a single continuous unchanging wave v(t) ⫽ sin(2␲ft) has only one frequency f, as shown in Fig. 1.2.

  An important asymmetry in the time-frequency duality is the notion of phase shift. Consider the waveforms shown in Fig. 1.3. In each case we have two frequencies, one twice the other. However, the phase relationship between the two waves is different in the two cases, and their pictures are quite different.

  Frequency is often a more natural representation of our radio world than voltage amplitude. To put this another way, it is often easy and natural to work with frequency in radio system design. For example, we can build frequency filters that restrict a re- ceiver to a certain range of frequency so that the received signal is not affected by ac- tivity at other frequencies. This all seems very natural today, hardly worth going over, but the core technology CDMA, the subject of this book, pushes radio technology very hard and tests these basic ideas. Thus, understanding the fundamental concept of ra- dio frequency is a prerequisite to having a thorough understanding of CDMA.

  Technology has changed, and VHF has become an anachronistic acronym. The ultra- high frequency (UHF) band is the upper hundreds of megahertz, and it was allocated in the United States to television stations. As cable television has reduced the need for

  70 UHF TV stations, the UHF band has been reallocated to other services, including the first North American cellular telephone service.

  Since then, the competition for the UHF band has become severe, and wireless telephony has moved into the microwave band, above 1 GHz. It has been a constant v (t) = sin(2πft) t

  Radio Engineering Concepts

  7

  volts time volts time Figure 1.3 Phase relationships. challenge to design cost-effective radio transmitters and receivers in the microwave band, and it becomes more difficult as frequencies get higher.

1.3 Multiple Access

  In the very first days of radio, it sufficed to get a signal from here to there over the ra- dio airwaves. We can imagine the listeners’ excitement the first time they heard a live voice carried across the ocean on a radio wave and received for their ears. We also can imagine the desire to carry more than one radio signal. While radio link users can wait their turns in an ordered sequence, radio is only really useful when many users can use

8 Key Radio Concepts

  Radio has been used for both broadcast and two-way communication. In broadcast, a single signal is meant for a large community of receivers, whereas we typically picture two-way radio as having two individual stations communicating with each other.

  The usual picture of broadcast is a commercial radio station, but there are private broadcast channels of distribution. Pagers are a form of broadcast radio; a single source sends data over the airwaves for a large community of receivers.

  The two-way walkie-talkie has evolved into sophisticated communications systems used in aviation, trucking, railroads, police, and the wireless telephone systems of to- day. Some systems often have one broadcast direction, a dispatcher talking to all the taxicabs or an air traffic controller talking to all the airplanes, with individuals reply- ing on a common frequency with no privacy.

  Wireless telephone systems require another level of sophistication because they manage separate two-way communication links in the same system. Unlike airline pi- lots, wireless callers do not want to be bothered by other telephone conversations on the same system. Wireless telephone users take their privacy seriously, and maintain- ing separate and confidential calls is an important component of system design.

  In the earliest days of radio, we used frequency to discriminate among radio signals, and we called the system frequency division multiple access (FDMA). Each radio user gets a frequency range, although there may be other users on other frequencies. Com- mercial radio stations (both AM and FM) are assigned frequencies in their large geo- graphic areas, and our receiver sets easily discriminate among the stations and allow us to exclude all but the one to which we are listening. Like broadcast radio, the first mobile telephone systems and, later, the first cellular systems were FDMA-based.

  When the leap was made from analog to digital modulation described in Chap. 7, it was more efficient to use a larger frequency band and to divide it up among several sig- nals using time slots. The system is synchronized so that each receiver knows which transmitted time slots belong to that receiver’s signal. This time division multiple ac-

  cess (TDMA) is more complicated than FDMA, but it uses the radio frequency more ef-

  ficiently. The Global System for Mobility (GSM), which started in Europe and became a worldwide standard, is a TDMA system with eight time slots aggregated into a sin- gle larger frequency band.

  FDMA and TDMA have some kind of absolute protection from other broadcasts on the signal channels in the radio medium. A single frequency band or time slot gets minimal interference from other frequency bands or time slots because at the exact moment of re- ception, no other transmitter is broadcasting on the specified frequency. However, in the world of spread spectrum, a single stream of radio is shared simultaneously. Code divi- sion multiple access (CDMA), the subject of this book, is a spread-spectrum system that transmits many signals in the same radio band at the same time.

  Allow us to use our favorite analogy for explaining CDMA. Consider a few dozen peo- ple in a small room all talking in pairs. Each listener knows his or her speaker’s voice and can tune out the other voices that interfere with his or her own conversation. This tuning-out ability has limitations and the ability of these listeners to understand their speakers runs out if we have too many people talking at the same time. In CDMA, we assign each digital stream its own distinct voice in the form of a digital code, and all of these streams coexist on the same radio channel all at the same time.

  Spread spectrum came from military research where resistance to enemy jamming was the major design issue. There are several spread-spectrum technologies, and

  Radio Engineering Concepts

  9

  1.4 Bandwidth as Real Estate

  We define radio territory by land area and frequency range. A transmission license au- thorizes its owner to transmit only within a specified geographic region and between lower and upper frequency bounds set in the license. These licenses are regulated by governments in just about every country in the world today. Here in the United States, the Federal Communications Commission (FCC) gives out broadcast licenses based on the service being offered and the technology being used. In the United States, it would be fair to say that regulation of the radio spectrum is tighter and more restrictive than mineral rights but looser and freer than airspace, which is controlled minute by minute by the Federal Aviation Administration (FAA).

  The allocation of radio frequency carries with it the obligation not to transmit on any

  other frequency bands. More frequency bandwidth means more capacity, in the form

  of more channels for FDMA and TDMA systems and more bits when using CDMA technology.

  We refer to radio frequency ranges as bandwidth or spectrum. The usual discussion is about the frequency range, with the geographic coverage region assumed. There are hot debates over where one region ends and a neighboring region begins, but we will concentrate on the bandwidth issues in our CDMA discussions. Readers should keep in mind, however, that negotiating with geographic neighbors for compatible service is every bit as important as making sure radio transmission is contained within allocated spectrum. We will discuss the technical issue of calls being served by different wireless systems in Sec. 12.5.5.

  As in any other acquisition, some frequencies are more desirable than others. Just as the downtown real estate commands a premium in most big cities, so also, in radio, lower frequencies are less demanding to operate. Lower-frequency amplifiers and an- tennas are simpler, and radio coverage is broader at a given power level. The lower fre- quencies are already firmly claimed by radio and television stations, police communi- cations, and other long-established users.

  In the early days of cellular, we were lucky enough to get radio spectrum allocations in the 900-MHz band, the upper end of “the UHF wasteland.” We called it that because cable television was clearly alleviating the need for 70 UHF TV stations. Even before cable, most of us remember there being only a few U.S. TV stations numbered 14 through 83.

  More recently, wireless has been pushed up into the microwave band. Much of this push is a consequence of our own success. As the demand for wireless telephone service has increased, we have become hungry for more bandwidth to satisfy that demand, and that bandwidth is out there in the microwave band.

  1.5 Amplitude and Power

  The amplitude of a radio wave is the electromagnetic voltage level as it propagates through space. Similarly, the amplitude of a sound wave is the pressure variation as it propagates through the air or other medium. Alas, amplitude and power are different, and this creates more than a little confusion.

  The power of an electromagnetic (or audio) event is the energy per unit time. We are all familiar with power in units of watts or horsepower. In a car engine, for example, it

10 Key Radio Concepts

  or current. In an audio event, power is the air pressure multiplied by the air velocity. In both radio and sound, this means that the power level is proportional to the square of the amplitude.

  To expand this idea a little more fully: In an electromagnetic wave, the amplitude is the voltage, and the current is proportional to that voltage. Power is voltage times cur- rent, so the power is proportional to the square of amplitude. In an audio event, am- plitude affects both the air pressure and air velocity, so power is proportional to the square of amplitude there as well.

  Amplitude is measured in volts, which we almost never use in discussions of radio

  5 systems, and power is measured in watts, which we use constantly.

  A typical base-station radio transmitter in our mobile telephone world has about 100 W of effective radiated power (ERP). A typical broadcast radio or television (TV) sta- tion might have 1 million W ERP, so our mobile radio stations are in the lightweight division. The telephone itself is usually limited to 1 W, the bantamweight division. However, this comparatively puny signal reliably gets hundreds of millions of calls through every day.

  An effective medium for sending information, radio is not an efficient medium for sending energy. The mobile telephone signal transmitted at 1 W is typically 0.0000000000001 W, or 100 fW, at the base-station receiver. Losing 99.99999999999 percent of the energy sounds wasteful, but our receivers are able to demodulate this tiny signal to recreate the signal modulated at the transmitting end. We can demodu- late and understand such a weak signal by engineering our wireless systems so that the other signals competing with it are even weaker.

  The crucial issue in getting a signal through is not the amount of power; it is the ratio between the power of the signal and the power of the noise or interference, the

  signal-to-noise (S/N) ratio or the signal-to-interference (S/I) ratio. As long as this ratio is high enough at the receiver, the amount of power received is irrelevant.

  Since every electrical amplifier has its own noise, the receiver has some internal noise level, and we want our signal to be stronger than the noise. Maximizing the S/N ratio is the key to good radio design. Electrical engineers are designing superb low- noise receivers, and it is the job of the wireless telephone system planners to get as much signal and as little that is not our own signal to the receiver as possible.

1.6 Decibel Notation

  The power ratios in radio are often huge. We broadcast 100 W of power only to have

  13

  10 fW get into the receiver. Throwing numbers like 10,000,000,000,000, 10 , around gets tiresome and confusing. The Americans and British do not even agree on what to call such a large number; it is called 10 trillion in the United States, but it is called 10 billion in England.

  There is a more fundamental point, however. Ratios are often the essential matter, and we need some notation for describing ratios as ratios and articulating the differ- ences between ratios. Fortunately, the decibel scale does the job nicely.

  Named after Alexander Graham Bell, the bel is defined as a factor of 10, so 2 bels is a factor of 100 and 3 bels is a factor of 1000. As shown in Table 1.1, bels add where the

1.1 Decibel Conversion to Ratios

  1

  1

  0.6

  13 6 3.98107 298.11 1 0.60206 13 6.0206 4 6 dB 300.00

  1

  0.7

  13 7 5.01187 401.19 1 0.77815 13 7.7815 6 500.00

  1

  0.8

  13 8 6.30957 530.96

  1

  0.9

  13 9 7.94328 694.33

  1

  2

  0.5

  10 10 900.00

  1

  2

  2

20 100 9,900.00

  1

  3

  2 30 1,000

  1

  4

  2 40 10,000

  1

  5

  2 50 100,000 10 100 10,000,000,000 13 130 10,000,000,000,000

  13 5 3.16227 216.23

  factors multiply, so a 2-bel change followed by a 3-bel change is a 5-bel change because 1000 times 100 is 100,000. Negative bels are reduction factors, so ⫺1 bel is a factor of 0.1 and ⫺4 bels is a factor of 0.0001.

  Fractional bels require a little high-school mathematics. One-half of a bell would be the square root of 10, approximately 3.16228 on a calculator. Using a logarithm table or the

  13 0.1 1.02329

  LOG

  function on a calculator, we can see that a factor of 2 would be 0.30103 bel and a factor of 3 would be 0.47712 bel. Using the addition rule, we see that a factor of 6 is 0.30103 ⫹ 0.47712 ⫽ 0.77815 bel.

  The bel scale becomes more intuitive when we multiply the values by 10 and use decibels (dB) instead of bels. A factor of 10 is 10 dB, and a factor of 100,000 is 50 dB. And a path loss of 10,000,000,000,000 comes out as 130 dB.

  The fractions are easier to deal with in decibels, too. A factor of 2 is 3 dB. Sure, the

  exact value for a factor of 2 is 3.0103 dB and the exact value for 3 dB is 1.9952, but it

  is a very rare occasion where the 0.2 percent difference is going to be important enough to matter. After living in the engineering world for a few weeks, most of us use 3 dB for a factor of 2 and 6 dB for a factor of 4 as freely as 20 dB for a factor of 100. After 6 months, most of us do not even remember which of these is the approximation and which is the mathematically derived exact value.

  Using 5 dB instead of 4.77 dB for a factor of 3 is a little bit looser, but much of the time the difference between a factor of 3 and a factor of 3.16228 is not that important. We are not endorsing sloppy arithmetic, only using notation that articulates what needs to be communicated and is typical in the field of radio engineering.

Table 1.1 shows some decibel values converted to their ratios. After a while in radio,

  Radio Engineering Concepts

  11 TABLE

  Factor Typical Percentage Bels Decibels (exact ratio) rounding increase

  1

  0.01

  2.33

  13 4 2.51188 151.19 1 0.47712 13 4.7712 3 5 dB 200.00

  1

  0.1

  13 1 1.25892

  25.89

  1

  0.2

  13 2 1.58489

  58.49

  1

  0.3

  13 3 1.99526

  99.53 1 0.30103 13 3.0103 2 3 dB 100.00

  1

  0.4

  1

12 Key Radio Concepts

  So far we have a ratio scale of decibels, but we have no units. The most familiar ap- plication of decibels in everyday life (for most of us anyway) is sound pressure level (SPL). A committee decreed that a pressure wave of 0.0002 dynes per square centime- ter is the unit of sound pressure level, the 0-dB point. We denote this very quiet level as 0 dB SPL. A subway train that is 1,000,000,000 times louder, 90 dB louder, is there- fore 90 dB SPL. And if I buy a pair of earplugs that say “15 dB attenuation” right on the box, I can expect the resulting subway sound level in my ears to be 75 dB SPL, which is 90 dB SPL minus 15-dB earplug attenuation.

  In the radio world, our 0-dB point, 0 dBm, is 1 mW of ERP. A 1-W radio signal is 30 dBm, a 100-W radio signal is 50 dBm, and a received power level of 10 fW is ⫺110 dBm. Losing 99.99999999999 percent between the transmitter and the receiver is ex- pressed as 130 dB of path loss in our decibel notation.

  Most of the time in radio engineering we stay in the decibel-ratio world of units. The magnitude range is one reason, but there is an even more compelling reason to think in terms of decibels rather than absolute amounts. The performance of a radio link is almost always defined in terms of the S/N or S/I ratio.

  These concepts are important in any radio engineering, but CDMA makes it partic- ularly important because small changes in signal make comparable changes in capac- ity. The connection is often direct: A 0.5-dB change in signal quality is a 0.5-dB change in system capacity, which should be a 12 percent difference in revenue. (Before you scoff at 12 percent, ask yourself what a 12 percent change in your own salary is worth to you.)

  And there is a more subtle reason to think in terms of ratios. There is a statistical notion, the law of large numbers, that tells us when we add a large number of random variables the sum tends toward a particular statistical shape called a normal distribu-

  6 tion, the famous bell-shaped curve we read about.

  Another term for a normal distri- bution is a gaussian distribution, named after the mathematician Karl Friedrich Gauss (1777–1855). In a radio path, the random variables are path losses from line-of-sight distance, buildings, trees, hills, and even rainy weather, and these path losses multi- ply in absolute numbers and add in decibel-ratio units. If distance path loss averages 80 dB, for example, buildings add another 15 dB of path loss, trees add 10 dB, and hilly terrain another 25 dB, then the total path loss will average 130 dB with a normal, bell- shaped, statistical variation in the decibel scale. We call this a log-normal distribution because it is normal in the logarithmic decibel scale.

  Because of the fundamental difference between voltage and power, we have two equations for decibels that look different but are really telling us the same thing:

  w

  2 ᎏ ᎏ d ⫽ 10 log (1.3) w

  1 v

  2 ᎏ ᎏ d ⫽ 20 log (1.4) v

  1 Equation (1.3) tells us the decibel expression for the ratio of two power levels w

  1

  and w in watts, whereas Eq. (1.4) tells us the decibel expression for the ratio of two

  2

  Radio Engineering Concepts

  13 voltage levels v

  and v . The assumption being made in Eq. (1.4) is that the electri-

  1

  2

  cal load, which we call impedance, is not changing as the voltage changes from v

  1 to v .

2 In the world of radio, we sometimes do not care about an extra 30 dB. So long as S/N

  ratios or bit error rates are low enough, an extra factor of 1000 in a signal strength does not matter. Other times we are concerned about 0.1 dB because a 2 percent difference in a particular factor is crucial to system capacity.

1.7 The Radio Path

  Our physics textbooks make it clear that electromagnetic fields and electromagnetic ra- diation radiate through open space in a vacuum with the same energy in the same spherical angle. Since the surface area of a spherical angle increases as the square of the distance from the source at the center, this tells us that the intensity (power) p of a radio wave decreases as the square of the distance r:

  ␣ ᎏ

  p ⫽ ᎏ (1.5)

  2 r

  (The constant term ␣ takes into account all the factors besides distance.) When we all live in an unobstructed vacuum, we can start using this kind of propagation

  7 model.

  As usual, real life is far more complicated than Physics 101 would have us believe. Let us start with the two basic assumptions in Eq. (1.5): no air and no obstructions.

  At frequencies up through 1 GHz and distances up to 10 km, it is pretty safe to ig- nore air losses. As we move up in frequency, the absorption of air becomes more im- portant, but cellular systems are operating at short enough distances that we believe

  8 that it is a minor factor in these systems, even on rainy days.

  Terrain obstruction is more important to our wireless system design than air and weather. Our planet’s surface is curved and hilly and covered with varying kinds of plant life and buildings. When Bell Telephone Laboratories engineers made their mea- surements, they found that radio power came down far faster than Eq. (1.5) suggests. After making many measurements and doing the best statistical analysis they could, they got an exponent of 3.84, as shown in Eq. (1.6):

  ␣ ᎏ

  p ⫽ ᎏ (1.6) 3 .84 r

  In conversation, we refer to this relationship as “38.4 dB per decade,” a loss of 38.4 dB (a factor of 7000) for each factor of 10 in distance. Considering how variable different places are and how much other factors affect a radio signal path, we have no problem _{7 8} But how are we going to speak and hear our telephones in the vacuum of space? As we recall from conversations back in the early days of cellular vision, circa 1970, using 60

  GHz for cellular radio was talked about because 60 GHz was an absorption frequency for atmo- spheric oxygen and would provide excellent cell-to-cell isolation for that reason. Even Bell Tele- phone Laboratories did not have 60-GHz amplifiers that were powerful enough or cheap enough

14 Key Radio Concepts

  calling the typical terrain loss an inverse fourth power, 40 dB per decade, as shown in Eq. (1.7):

  ␣ ᎏ

  p ⫽ ᎏ (1.7)

  4 r

  The higher-than-free-space loss rate is a good thing for wireless capacity rather than a bad thing. Our interferers tend to be further from our receivers than our desired sig- nal transmitters, so a tendency of the signal to deteriorate quickly with distance helps us discriminate between desired and undesired radio waves.

  While most engineers think and speak about path loss, we find it easier to think of the radio path or even path gain with the understanding that the number is going to be far less than 1 (negative decibels). We will refer to a radio path gain of ⫺130 dB or a higher radio path gain of ⫺110 dB. In this way, we do not have to remember which number to subtract, a mistake far easier to make in a spreadsheet than on a piece of paper. The notion of path gain rather than path loss also avoids the constant hassle of remembering that greater path loss means less radio signal.

  Life gets more complicated, however. The 40 dB per decade is an average over vary- ing terrain and surface clutter. Rolling hills make the radio path gain higher on the side near the antenna and lower on the far side. Wooded areas have lower path gain than clear areas, and this difference is greater in the summer when the trees have leaves. Buildings not only reduce the path gain on average, but they also greatly in- crease the signal variability as one moves from one place to another nearby place. Sig-

  nal variability is the variation in received signal strength from a fixed transmitter as a mobile unit is moved around a relatively small area.

  While the earth’s surface is almost always curved, it is not necessarily curved the same way in all places. Los Angeles and Salt Lake City are two U.S. cities built in val- leys, so their ground curves up instead of down. This means that cellular interference in these cities, and others with similar topography, is going to be different and very likely more difficult to manage than elsewhere.

  Bodies of water also affect propagation. Radio waves that would be absorbed or dif- fused by shrubbery can bounce off a water surface. This can form local radio “hot spots” near lakes and rivers.

  Because of the multiplicative nature of path gain reductions from terrain, buildings, and shrubbery, the statistical effect is a log-normal signal distribution, as described in Sec. 1.6.

  9 Typical standard deviations are about 10 dB. Understanding radio propagation is essen- tial to CDMA capacity and quality planning. Chapter 47 goes into the subject in depth.

1.8 Antenna Gain

  We see the term antenna gain, and we have to wonder: How can an antenna have gain? How can a piece of metal with no external source of power make a radio signal stronger? Well, an antenna can concentrate the radio energy in a specific direction and make that direction more powerful than it would have been from omnidirectional radiation.

  Antenna gain makes radio stronger the same way a cone-shaped megaphone makes a speaker louder in an intended direction.

  Radio Engineering Concepts

  15

Figure 1.4 Antenna with no gain and with 10 dB of gain.

  Consider a perfectly omnidirectional radio transmitter. The surface area of a sphere

  2

  is 4␲r , so we sometimes call this spherical symmetry a 4␲ radiator. If we focus the en- ergy in a circular pattern out of the sides of the antenna system, then we have a hori- zontally omnidirectional transmitter with much less energy coming out its top and bot- tom. This is illustrated in Fig. 1.4. By squeezing nearly all the energy into one-tenth

• –30˚ 30˚

  Sector 120 ˚ Sector 60˚

• –60˚ 60˚
• –30˚
• –60˚ 60˚
• 10dB +20dB
• 20dB 0dB
• 10dB

16 Key Radio Concepts

  the surrounding spherical area, we can achieve a factor of 10 increase in ERP, a 10-dB antenna gain. This is shown in the figure.

  Narrowing the field of this 10-dB gain antenna to a 120-degree horizontal sector gives us another factor of 3, that is, 5 dB, for a total antenna gain of 15 dB. There are two rea- sons to use such an antenna. First is the radio gain issue: Higher-gain antennas mean that we can reach further (coverage) using lower-power amplifiers (efficiency). However, a second reason to use a narrower beam is that we can be selective in our coverage area. If we use a 120-degree sector with one antenna, then the area behind that antenna, which we call the backlobe, can be served by another antenna. We call these separate ser- vice areas sectors. The lower the cross-interference between the two antennas, the more subscribers we can serve with those antennas. Antennas have different radiation pat-

  

terns typically drawn on a circular scale in decibels, as shown in Fig. 1.5.

  More selective antennas are more expensive, naturally, and the backlobe attenuation of a sector antenna is typically 15 dB. This is a substantial reduction in radio level but hardly elimination of radio signal. Thus, while it is easy to draw three or six sectors in Fig. 1.6 and picture each being served independently by its own antenna, there is sub- stantial backlobe interference. And the sector boundary has significant cross-interference as well because antennas do not have perfect directional filtering, as shown in Fig. 1.7.

  Wireless Telephone

  Radio Engineering Concepts

  17

  Nearly Equal On Both

  Sectors Figure 1.7 The sector boundary.

1.9 The Link Budget

  We sometimes express the combination of path gains and losses in a link budget, as shown in Table 1.2. In this simple link budget, the power level at the receiver is ⫺79 dBm. The manufacturer’s specifications or actual measurements might tell us that the re- ceiver noise level is ⫺105 dBm. The resulting S/N ratio (26 dB) is obtained by sub- tracting the noise (⫺105 dBm) from the signal strength (⫺79 dBm). In this example, a required S/N ratio of 20 dB was used. Surplus S/N is the extra signal strength above the minimum requirement that the communications link has to spare.

  As the radio environment gets more complicated, we can add components to the link budget to reflect this. Of course, a link budget can be either an estimate of what we ex- pect or a display of actual, measured results. Sometimes the link-budget concept is an

18 Key Radio Concepts

  TABLE

1.2 A Link Budget

  _⫹ 10-W amplifier 40 dBm _⫹ Transmit antenna gain 10 dB m _⫺ Radio path 130 dB m _⫹ Receive antenna gain 1 dB m

  _________ _⫺ Signal level (total) 79 dBm _⫺ Receiver noise level 105 dBm _⫹ Signal-to-noise (S/N) ratio 26 dB m _⫹ Required S/N ratio 20 dB m _⫹ Surplus S/N 6 dB m

1.10 Modulation

  Analog and digital signals are added to radio transmissions through very different types of modulation. For analog radio, the electrical signal modifies the carrier wave. For digital transmission, encoded bits alter the carrier.

  The heart of a wireless telephone technology is its radio modulation scheme. We of- ten refer to the full specification of the wireless modulation scheme, complete with all the signaling rules, as the air interface.

  1.10.1 Analog modulation

  We can send analog electrical signals (audio or video) on a radio link in two basic ways, amplitude modulation (AM) or frequency modulation (FM). AM means that the electri- cal voltage is matched by the amplitude of the radio wave. The receiver simply converts varying radio levels back to voltage that goes into an audio amplifier, a television or videocassette recorder (VCR), or some other terminal equipment. As shown on the left side of Fig. 1.8, AM is a continuous sine wave with its amplitude varying as the input signal changes. Should some other, interfering radio wave come along with its fre- quency close to the AM radio wave we are currently receiving (and demodulating), that wave will have its content added as a noise component to our received signal.

  As its name suggests, FM means the electrical voltage is matched by the frequency of the radio wave, and the receiver converts varying frequency back to signal voltage. As shown on the right side of Fig. 1.8, FM is a continuous sine wave with its frequency varying as the input signal changes. An interfering radio wave is less likely to affect the frequency component at our receiver, so the FM receiver tends to produce a less noisy reproduction of its signal from a noisy radio environment. If we have two FM sig- nals modulated around the same frequency, then there is some ratio between them that ensures that the stronger signal is the one we hear. We call this the capture ratio of an FM receiver, and a typical capture ratio is 1.0 dB. That means if the desired signal is 60 percent of the power at the receiver and somebody else’s signal is 40 percent, then a typical FM receiver should produce the desired signal.

  1.10.2 Digital modulation

  Radio Engineering Concepts

  19

AM FM

  s (t) s (t) Signal Signal t t

  Modulation Modulation v (t) v (t) t t Figure 1.8 AM and FM modulation schemes. signal. The contrast, of course, is with digital modulation, where the signal is turned into a sequence of binary digits, bits, and those bits are transmitted by modulation of the radio wave. Since CDMA, the subject of this book, is digital modulation, let us con- centrate on digital modulation.

  In digital modulation, we are adding bits to the radio signal. A bit is the smallest unit of information, represented by one of two states at a particular location. In writing, we usually represent bits as having a value of 0 or 1. Actually, the meaning associated with a bit could be a number (built from 0s and 1s) or a choice such as true/false or a repre- sentation of anything, including the human voice, through some particular code.