Practical Digital Wireless Signals pdf

Term DefinitionFilter a signal processing operation where the domain of the input and output signals is unchangedTransform a signal processing operation where the domain of the input and

develop a useful expertise in digital modulation with this practical guide, based on theauthor’s experience of over 30 years in industrial design You will understand thephysical meaning behind the mathematics of wireless signals and learn the intricaciesand tradeoffs in signal selection and design.

Key features:

Six modulation families and 12 modulation types are covered in depth

A quantitative ranking of relative cost incurred to implement any of 12 differentmodulation types

Extensive discussions of the Shannon Limit, Nyquist filtering, efficiency measures andsignal-to-noise measures

Radio wave propagation and antennas, multiple access techniques, and signal codingprinciples are all covered

Spread spectrum and wireless system operation requirements are presented

Earl McCune is a practicing engineer and Silicon Valley entrepreneur A graduate of UCBerkeley, Stanford University, and UC Davis, he has over 30 years of post-graduateindustry experience in wireless communications circuits and systems Now semi-retired,

he has founded two successful start-up companies, each of them winning industrialawards for their technical innovation

Series Editor

Steve C Cripps, Visiting Professor, Cardiff University

Peter Aaen, Jaime Pla´ and John Wood, Modeling and Characterization of RF and Microwave Power FETs

Dominique Schreurs, Máirtín O’Droma, Anthony A Goacher and Michael Gadringer,

RF Amplifier Behavioral Modeling

Fan Yang and Yahya Rahmat-Samii, Electromagnetic Band Gap Structures in Antenna Engineering

Enrico Rubiola, Phase Noise and Frequency Stability in Oscillators

Forthcoming

Sorin Voinigescu, High-Frequency Integrated Circuits

J Stephenson Kenney and Armando Cova, RF Power Amplifier Design and Linearization Stepan Lucyszyn, Advanced RF MEMS

Patrick Roblin, Nonlinear FR Circuits and the Large-Signal Network Analyzer

Dominique Schreurs, Microwave Techniques for Microelectronics

John L B Walker, Handbook of RF and Microwave Solid-State Power Amplifiers

EARL MCCUNE

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fundamentals

Preface page xvii Digital wireless signals: physical intuition and practical

Bounded power-spectral-density (B-PSD) bandwidth 30

Fractional power-containment bandwidth 31

2.6.3 Information bit-energy-to-noise-density (IBEND) E b /N0 53

Output-power control 72

3.1 DWC channel capacity – the fundamental work of Claude Shannon 75

4.3 ASK signal demodulation principles 115

4.3.2 Demodulating logamp/received signal-strength indication (RSSI) 120

Important special case: minimum shift keying (MSK) 131

5.2.6 Direct digital (frequency) synthesis (DDS, or also DDFS) 151

Basic OFDM principles 208

Important special case: 3G long-term evolution (LTE) 223

8.4 Summary 249

10.4 Coding for spectrum control and

10.5.4 Convolutional coding 287

12.6 Existing systems and their modulation selections 340

Tutorial Appendices

Appendix D: Quadrature modulation and demodulation principles 365

Remote Control ZigBee, RKE, TPMS

Cordless Telephone CT-1, PHS, DECT

Cellular Analog (historical), NADC, PDC, GSM/GPRS,

EDGE, Wideband-CDMA, HSDPA, HSUPA, LTE,cdmaOne (IS-95), cdma2000 1xRTT, EV-DOPublic Service Analog (historical), APCO-25, TETRA

Wireless Data 802.11 (DS and FH), Wi-Fi 1 (802.11b), Wi-Fi 2

(802.11a/g), WiMAX (fixed), WiMAX (mobile)Personal Area Bluetooth 1.0, Bluetooth – EDR 2.0, Bluetooth –

EDR 2.1

Wireless communications is rapidly becoming one of the ubiquitous technologicalunderpinnings of modern society (such as electric power, fossil fuels, automobiles,etc.) Few people think about the technology within their mobile phones, remote controls,garage door openers, GPS navigation devices, and so on They are always at hand andreliably work for the user.

Yet even within the electrical engineering (EE) community, radio communicationtechniques have a reputation as a “Black Art” that can only be successfully practiced

by “RF people” This is changing, albeit slowly Any significant progress in successfullyopening this vital technology widely to more practitioners must remove this “Black Art”stigma In my opinion this is best achieved through outreach from existing successful

“RF people” This outreach must occur through many channels, such as this book andnew courses in both academic and industrial training

Today it takes many years to train communications engineers in the intricacies ofwireless signal modulation tradeoffs I am a product of this decades-long process Much

of this difficulty, for me anyway, is a consequence of the mathematical approach taken toall modulation training The objective of this book is to begin to add a comprehensive yetphysical approach alongside this traditional modulation training

The contents of this book are drawn from the nearly 40 years of experience I have withradio communication technology Being much more of a physics-based person instead of

a mathematician, to build my own understanding of this material over these decades Ihave put in a lot of effort to get through the mathematics and into also understanding theunderlying physical relationships Through these pages I can share my results with you.One major premise of this book comes from advice I received from my father as Ibegan learning electronics: “Don’t memorize equations to learn the material Instead,carefully learn the fundamental principles Then as you need an equation, if it is notmemorized it can be quickly derived on the spot” He lived by this rule, and it hasdefinitely served me very well over the years And now in the age where computers domuch of the math anyway, it is vital to be able to check any computer output forreasonableness A surprising output may be the result of a programming error whichcan be quickly fixed to avoid embarrassment Then again, it may be a clue to a significanttechnology contribution The difference can only be known if fundamental physicalprinciples are well understood

The presentation order within this book is carefully planned so that material needed tounderstand the topic at hand has been presented previously as much as possible Cross

references to important sections are included to facilitate connections to supportingmaterial.

In this approach, mathematics is a tool for later illustration instead of the primarywindow through which to view and learn the material Certainly, for those readers whowish to delve more deeply into the theory of any topic, a suggested list for further readinginto the excellent theoretic literature is provided at the end of each chapter

Unique contributions in this book include:

Detailed discussion on the consequences of the Shannon capacity, showing how thislimit impacts bandwidth efficiency, transmitter power, and signal design

Introduction of a channel utilization factor U in Shannon’s capacity equation, showinghow system performance is affected when operation at the theoretical capacity is notattempted

A completely non-mathematical presentation on principles of coding for improvedbandwidth efficiency (compression), for error control, and for spectral shaping andlink control This presentation includes examples of how the error correction processworks when decoding convolutional codes

Clarification of the difference between signal to noise ratio and IBEND (also called E b /N0)

Clarification of the difference between power efficiency and energy efficiency

Quantification of six different measures of energy efficiency

Details on the Generalized Nyquist Filter Construction (GNFC) technique, showingthat the widely used spectral raised-cosine filter can be greatly improved

Resolution of the perceived ambiguity between “diplexer” and “duplexer” – these arevery different

Introduction of a family of “maximally smooth” pulses/windows at their endpoints: theDerivative Zeroed pulses

Using the superposition lowpass filter (SLPF) to greatly reduce transmitter hardware

and also eliminate the x/sinx corrector for conventional Nyquist filtering.

Demodulation principles, listed separately for all modulation types

Complete description for FSK modulation index h for two normalizations: fixed

frequency spacing, and fixed total deviation

Modified Carson’s Rule for estimating the bandwidth of FSK signals “60 dB down”

The first physical explanation I have ever seen for the FM threshold effect

Clarification of the difference between pure PSK, a constant envelope signal, andconventional PSK which really is a special case of QAM

Clarification that CPM is really a FSK, and is not a PSK

Presentation of OFDM-signal principles without using the inverse Fourier Transform –why the Fourier transform technique works for OFDM is derived later

Explanation of why, physically, matched filters work so well

Introduction of the Keep-it-Simple (KIS) technique of signal modulation selection

Quantified comparison among 12 digital modulation types to illustrate their relativecosts of implementation

This book is aimed at practitioners in industry who may be new to digital tions via radio It assumes a basic familiarity with radio concepts, so it is not a tutorial in

communica-general radio technology This book can be used as a supplementary reference foruniversity and graduate study Any architect of communications features in productswill find this very useful – particularly if they are new to digital radio.

Basic familiarity with analog modulation for AM, FM, and PM is covered in tutorialAppendix C, to provide an internal reference to the important topics drawn from fordigital modulations

A completely non-mathematical discussion of signal and information coding is in

Chapter 10 This chapter was a challenge because while coding is widely used and ofvital importance to modern digital communications, its successful implementationrequires intensive mathematical understanding Yet to understand what coding is andwhy it works it is not necessary to use mathematics at all For those needing to get intoimplementation details of coding a bibliography is presented for further study at the end

of Chapter 10

Saving the best for last, I wish to particularly acknowledge the tremendous help of

Dr Dietmar Wenzel in editing this manuscript, and to Professors Khaled Abdel-Ghaffar andZhi Ding from the University of California Davis in helping work out the non-mathematicaltreatment of coding principles Dr Floyd M Gardner remains a long time inspiration and aparticular guide for the ideas of Section 3.1 on consequences from Shannon’s limit The help

of David Huynh, Dave Jackson, and Javier Castelblanco from Agilent Technologies inmaking the many measurements in Appendix G made that part possible

Special thanks go to series editor Steven Cripps, who made it very clear to me that thisbook should be written NOW

And the tolerance of my wife Barbara to the seemingly endless hours spent writing,drawing, rewriting and editing needed for the preparation of this book is beyond measure

My gratitude to you is boundless!

I fervently hope that all who read this book, and who may use it as an additionalreference will enjoy this approach as much as I have enjoyed writing it

Earl McCune

This book presents the principles of signals used in digital wireless communicationssystems Intended to be a side-by-side complement to any of the excellent theoreticaltexts in use, this book explains physical meanings behind the theoretical mathematics ofcommunications signals Whereas a theoretical text presents these topics through thewindow of mathematics, here we take the opposite approach.

Of course mathematics is a vital part of any engineering activity, and when the topiccalls for some mathematics to further illustrate a point I do not shy away from including

it This is especially true for places where my experience has shown that typical examplesand illustrations in the theoretical textbooks could use a slightly different approach tomake the concepts clearer This is primarily found in the sections on Nyquist filtering,Shannon’s capacity limit, and on the performance of QAM in the presence of additivenoise

Besides discussing each of the fundamental digital modulations ASK, FSK, andconventional PSK, additional signal types of pure PSK, QAM, OFDM and spreadspectrum are also presented Following chapters on radio wave propagation, multipleaccess techniques, and signal coding principles, Chapter 12 provides answers to thequestion of “What signal type should I select for this wireless application?” Cost rankingsare derived to support cost-benefit analyses for any wireless application

This book is intended to be a reference which complements any textbook used byadvanced undergraduates and graduate students as they first encounter signals used fordigital wireless communications It also is a general reference on this topic for practicingengineers Product managers and market planners with an electrical engineering back-ground can easily skip over the math and still understand the physical principles, to help

in optimizing decisions on product feature definitions And at the end is a detailedpictorial side-by-side comparison of 30 separate signals covering the entire complexityrange discussed in the text

Term Definition

Filter a signal processing operation where the domain of the input and

output signals is unchangedTransform a signal processing operation where the domain of the input and

output signals is changedSignal Circle the circle of unit radius in the I-Q plane, containing all possible

constellation points

ACPR adjacent-channel power ratio

ADC analog-to-digital converter

AltCP alternate channel power

ARQ automatic repeat request

BASK binary amplitude-shift keying

BFSK binary frequency-shift keying

BH3 blackman-harris 3-term pulse (window)

B-PSD bounded power spectral density

BPSK binary phase-shift keying

CCDF complementary cumulative density function

CDF cumulative distribution function

CDM code-division multiplexing

CDMA code-division multiple access

CMOS complementary metal-oxide-semiconductorCNR carrier-to-noise ratio

CORDIC coordinated-rotation digital computer (algorithm)

CSMA carrier-sense multiple access

DDFS direct digital frequency synthesis

DDS direct digital synthesizer

DSP digital signal processing

DSSS direct-sequence spread spectrum

DWC digital wireless communication

DZEn derivative-zeroed even pulse (window) of order nDZn derivative-zeroed pulse (window) of order n

EDGE enhanced data rates for GSM evolution

EIRP effective isotropic radiated power

ENSB equivalent noise signal bandwidth

FDM frequency division multiplexing

FDMA frequency division multiple access

FEC forward error correction

FET field effect transistor

FHSS frequency-hopping spread spectrum

FIBP fractional in-band power

FUR Fourier uncertainty relation

GFSK Gaussian-filtered frequency-shift keying

GHz gigahertz (billion cycles per second)

GMSK Gaussian-filtered minimum shift keying

GNFC generalized Nyquist filter construction

GPRS general packet radio service

GSM global system of mobile communication

I in-phase axis; in-phase signal component

IBEND Individual-Bit-Energy-to-Noise Density ratio

IEEE Institute of Electrical and Electronic Engineers ™

ISI inter-symbol interference

ISR interference-to-signal ratio

kHz kilohertz (thousand cycles per second)

LTE long-term evolution of the third generation cellular network

M signal order, number of available signal states

MAI multiple access interference

M-ASK M-ary amplitude-shift keying

M-FSK M-ary frequency-shift keying

MHz megahertz (million cycles per second)

MIMO multiple-input multiple-output

M-PSK M-ary phase-shift keying

NBFM narrowband frequency modulation

NBPM narrowband phase modulation

OFDM orthogonal frequency division multiplexing, or orthogonal frequency

division modulation (preferred)O-FDMA orthogonal frequency division multiple access

O-PSK offset phase-shift keying

PAPR peak-to-average power ratio

pdf probability density function

PDF envelope probability density function

PDMA polarization division multiple access

Q quadrature axis; quadrature signal component

QAM quadrature amplitude modulation

RLL run-length limited

RSC recursive systematic convolutional (encoder)

RSSI receive signal-strength indication

SC-FDMA single carrier frequency division multiple access

SLPF superposition lowpass filter

SNR signal-to-noise ratio

SRC spectral raised cosine

SRRC spectral square-root raised cosine

SSQAM step-square quadrature amplitude modulation

TDM time division multiplexing

TDMA time division multiple access

TETRA TErresTrial RAdio, a TDMA network designed for public service

applications

tQAM triangular arrangement of QAM constellation points

TSAD time-shift angle demodulator

UHF ultra high frequency (300–3000 MHz)

UMTS universal mobile telephone service

VCO voltage-controlled oscillator

VHF very high frequency (30–300 MHz)

WBFM wideband frequency modulation

W-CDMA wideband code division multiple access

WLAN wireless local area network

There are two conventions followed in the use of terminology within this book They are:

1 Terms and ratios in linear units are in lower case letters

2 Terms and ratios in logarithmic (dB) units are in UPPER CASE letters

One of the tendencies I have noted in the literature is that this separation is rarely applied.This forces a reader to infer what an author is trying to convey from either the widercontext of the writing, or from long contemplation after finishing reading in order todiscern the author’s intent Both of these are causes for ambiguity, and at a minimum areopportunities for misunderstanding In any work that is trying to teach principles andconcepts this is certainly bad

I have tried to contribute toward adding clarity by following these two conventions.This means that within each discussion if needed I have invented a lower case or uppercase term as appropriate While a reader who goes directly to a particular chapter in thisbook and does not read this page might think that the unconventional notation may be atypographical error, I can assure you that this is very deliberate on my part

I hope that these conventions actually do contribute to additional clarity in the standing of wireless communications signals

under-List of terms new in this book

BWFSK modified Carson’s Rule result for estimating FSK signal bandwidth, with

units of frequency (This does not follow the convention: capitalized BW isthe traditional acronym for bandwidth.)

cp cyclic prefix factor, value is between 0 and 1

cPSK conventional PSK, a QAM signal with envelope variations where the signal

constellation is restricted to points on the unit circle

edr envelope dynamic range, the ratio of peak signal amplitude over minimum

signal amplitude

EDR decibel conversion of edr

γ B/C, the inverse of channel capacity density

ibend individual bit energy to noise density ratio, a descriptive name for E b /N0

IBEND decibel conversion of ibend

papr peak to average power ratio

PAPR decibel conversion of papr

pPSK pure PSK, a constant envelope signal modulated solely in phase

snr direct ratio of signal power over noise power in a specified bandwidthSNR decibel conversion of snr

U channel capacity utilization factor, value is between 0 and 1

ψPE power efficiency, one property of a signal constellation

and distinct As far as the information is concerned, what the signal does in between these time instances is of no concern But – and this is an extremely important BUT – the

usefulness of the signal in actual transmission is extremely sensitive to the detail of the

signal behavior at all times, particularly the time intervals between the information

points Indeed, much of this book is concerned with the fine details of what the DWCsignal of choice is doing at all times

So let us begin by examining what makes us consider that these signals are digital Nomatter if signal phase, frequency, amplitude, or some combination is used for modula-

tion, all digital wireless communication signals are a sequence of states This simply

means that the information in the digital wireless communication signal can only berepresented by a (usually short) finite list of particular and very specific signal character-istics Outside of this very restricted set of signal characteristics, the information content

of the signal is undefined Also, these specific characteristics can only occur at particular

times, which are themselves also very restricted We define the signal state as any

particular member of this restricted set of signal characteristics and times

All wireless signals are transmitted using the electromagnetic spectrum (radio quencies, RF), which is a universally shared resource As such, the actual use of theelectromagnetic spectrum is subject to sharing rules, which are usually set by governmentregulatory agencies Because these government agencies are (supposedly) interestedsolely in the general public good, these sharing rules usually focus on having the digitalwireless communication signal use a minimum amount of the electromagnetic spectrum.This is to insure that a greater number of users may also be using digital wirelesscommunication signals at the same time – certainly a public good Furthermore, each

fre-of these signals must not harmfully interfere with another Since harmful interference canresult from signal power, signal frequency, and signal simultaneity, all of these char-acteristics are regulated in these sharing rules

The most obvious interest of spectrum sharing is occupied frequency, or more fically, occupied frequency range This is called bandwidth, and it is an extremelyprecious characteristic of the electromagnetic spectrum The most obvious way to

speci-facilitate this sharing is to ensure that the digital wireless communication signal uses aminimum amount of bandwidth But the many users of these digital wireless commu-nication signals usually want to maximize the information transferred by the digitalwireless communication, which tends to require a larger amount of bandwidth.Reconciling these conflicting desires is a major concern of all digital wireless commu-nication signal designers, and is the major part of this book Both the selection of thesignal state set and the specific behavior of the digital wireless communication signalbetween states and state times are critical to successful resolution of this inherent conflict.Signal operating times are also of critical importance One particular issue here iswhether the desired digital wireless communication is one-way (simplex), two-way(duplex), or multi-way (multiplex) A huge amount of effort, and product cost, depends

on the approach taken to this time aspect of digital wireless communication

Finally, following nearly a century of experience with digital wireless tions, a particular set of measures has evolved to both determine the quality of the digitalwireless communication signal itself as well as to provide assurance that the digitalwireless communication signal meets regulatory requirements While certainly notexhaustive, these measures are usually sufficient to ensure that the digital wirelesscommunication meets its overall objectives Further, while sufficient measures are almostalways specified for digital wireless communication signals, experience shows that thesemeasures are not uniformly enforced The digital wireless communication engineer must

communica-be aware of this enforcement, or partial lack thereof, to assure a successful productdesign

1.1 Radio communications: what really happens?

Radio communication is simply a transfer of energy, and along with it information, from

a transmitter to a receiver That being said, there are a large number of considerations thatany radio communication designer must be aware of in order to assure a high probability

of success

Radio communication is electromagnetic This means that all of the physics ofelectromagnetism, as described by Maxwell’s equations, directly applies Light is alsoelectromagnetic, so the physics that holds for light being visible at a distance also holdsfor radio being receivable at a distance Of course, the frequencies of visible light andradio are very different, so some differences are experienced But it is very important tounderstand that the underlying physical principles are exactly the same

Photons are the physical entities that transfer electromagnetic energy This is also truefor radio, but this is never discussed Why? Because they really don’t matter like they dofor visible light For a quick example, consider a one milliwatt transmitter operating at

2440 MHz Photon energy is directly related to frequency, so the energy of a 2440 MHzphoton is (6.63 × 10−34joule sec)(2.440 × 109sec−1) = 1.62 × 10−24joules per photon.For a transmitter generating one milliwatt, which is 0.001 joule per second, there must be6.2 × 1020photons generated every second to transfer this energy Another way to look atthis is to note that there are also (6.2 × 1020)/(2.440 × 109) = 2.5 × 1011photons per RF

cycle This is so many photons that it is impossible to detect them individually, so wemeasure instead the average power transferred as radiated energy.

The job of the transmitter is to generate the largest possible radiated field And the job

of the receiver is to collect as much of the radiated field as possible to recover thetransmitted signal The laws of physics tell us that both of these objectives are met whenthe antennas on each side are physically sized comparable to the signal wavelength, orlarger Visualize, for example, that the receiver is casting a net into the air to collect thetransmitter’s field as it goes by Clearly, a good net is a large net Unfortunately, almost allproduct marketing objectives desire antennas to be extremely small, or even invisible.This directly contradicts the physics necessary to be efficient, so antennas acceptable tonormal product marketing desires are inherently the opposite of what is necessary forhigh performance DWC

In essence, the transmitter is like an audio speaker, which must be physically large to

be heard at a long distance The receiving antenna is equivalent to your ear It is mucheasier to hear something far away if your ear is enhanced with a large cone (or somethingsimilar, which is much larger than your ear) Radio communication is no different!

1.2 Modulation states: “keyed”

All wireless communication, indeed all passband electronic communication, is based onmanipulations of the sinusoid waveform This is not arbitrary, because the solution toMaxwell’s equations for a propagating signal is a sinusoid Nearly always written usingthe cosine, the fundamental signal equation is

As this signal equation shows, there are three parameters available for modulation of the

wireless signal: amplitude A, frequency ω, and phase Units of the frequency and phaseparameters are radians-per-second and radians respectively

By definition, digital communication is the transfer of information that is alreadyavailable in discrete, or quantized, form Correspondingly, digital modulation is alsodefined in discrete values, called states, as discussed above The simplest states are ONand OFF These two states are used by the original digital communication, telegraphy usingMorse Code, sent by the operator’s hand using a tool called a key One example of atelegraph key used for Morse Code communication is shown in Figure 1.1 By historicaltradition the term “keying” remains with us to describe all digital modulations

States have two fundamental characteristics: a duration, and a value In nearly allDWC signals the state duration is the same among all states (It is actually a significantand costly complication if the state durations are not all exactly the same.) State valuesare drawn from a finite set of the available signal parameters of amplitude, frequency, andphase The digital communication signal is made up of a sequence of individual statevalues, each of them holding constant for the defined state duration, and having sometype of transition from one to the next as shown in Figure 1.2

A signal that uses states which only change the signal amplitude is called Shift Keying (ASK) Similarly, a signal that uses states which differ only in signalfrequency is called Frequency-Shift Keying (FSK) Keeping with this pattern, a signalthat uses states which differ only in signal phase is called Phase-Shift Keying (PSK).Compound modulations definitely exist and are widely used.

Amplitude-While this view of signal states is straightforward, it is not yet complete As mentionedearlier, in all practical systems the DWC signal is a continuous-time analog waveform.With a continuously varying waveform, how do we define and measure the state? This isclarified by considering the behavior of the signal within regions centered about eachpossible state value, shown in Figure 1.3 Each region is centered around a state value,and has a time duration equal to and aligned with the state duration After examining thesignal waveform within a state duration, the receiver makes a decision regarding theintended signal-state value This process is repeated for each state-duration interval.For successful communication these signal states must correspond to the incomingdigital information This is done by mapping each signal state to an input informationsymbol at the transmitter Naturally, the number of signal states available should equal

Time

State Duration

State Duration

State Duration

Signal State

Figure 1.2 Definition of a signal state, showing the pairing of state value and state duration

Figure 1.1 Example of a common telegraph key, the J38

the number of information symbols used This allows each symbol value to be uniquelymapped to a separate signal state With each possible symbol mapped to a different state,successful demodulation of the states results in the communication of any possiblemessage The receiver reverses this process, providing the information-symbol valuewhich corresponds to the signal-state decision made following each state-durationinterval.

State definitions are made in either one or two dimensions The simplest dimensional state set is the simple binary pair, either defined as {1, 0}, or sometimesmore conveniently by the balanced set {1, −1} States can also be constructed in larger one-dimensional sets, such as the four-element set {−3, −1, 1, 3} Commonly, states can also beconstructed as a set of two-dimensional elements, such as {(0, 0); (0, 1); (1, 1); (1, 0)}.Three-dimensional (or higher) state sets are physically possible, but are only used extre-mely rarely For all practical purposes, only the one- and two-dimensional sets are used Forthis reason only these will be considered in this book

one-While state values are well understood and unambiguously defined, the concept ofstate duration is often discussed in an ambiguous manner Much of the ambiguity comesfrom confusing states for symbols (or vice versa), bits for symbols, and general confusionabout the term “baud” To avoid these problems, experience has taught me that this set ofdefinitions is clear and unambiguous:

Symbol time (Ts): The time duration that an information symbol is mapped onto thesignal, which equals the time duration of a signal state: unit is seconds (usuallymicroseconds)

Bit time (Tb): The time duration of an input binary bit: unit is seconds (usuallynanoseconds)

State Duration: The time duration of a physical signal state, equal to the symbol time

Symbol rate (f s): The reciprocal of the symbol time, equal to the number of signal statestransmitted per second of time Unit is baud*

Time

State Duration

State Duration

State Duration

Signal State (Nominal Value)

Signal State (Region)

Figure 1.3 Recovering signal state information from a continuous analog waveform – decisions here

are based on the length of time spent within any signal state region

Bit rate (f b ): The number of binary bits transmitted per second: unit is bps (bits per

second) It is strongly recommended that Symbol rate be used in describing a DWCsignal

Baud rate: When commonly used the term “baud rate” is often mistakenly used to mean

“bit rate”, where it more correctly would mean “symbol rate” This ambiguity must beavoided! Baud is strictly a unit of measure for rate.*

Note: Bit time is only unambiguous if it refers to a single binary bit stream comprising the

input information This term should never be used when describing a DWC signal !

The universal term Symbol Time is correct

* The unit baud (Bd) is an official SI unit for symbol rate Baud is named in honor of

J M Emile Baudot (1845–1903) who established a five-bits-per-character code fortelegraph use which became an international standard (commonly called the Baudotcode)

Time (period) and Frequency are often used nearly interchangeably within the technicalliterature, with sometimes confusing results While this lax usage is unfortunatelytolerated in the literature, within this book the use of these terms shall be clear andunambiguous

1.3 DWC signal representations

1.3.1 “ Digital” modulations of an analog signal

All actual signals used for digital wireless communication are purely analog in theirnature Time is not quantized at all for propagating DWC signals The actual signaltherefore is one continuous-time electromagnetic wave Generalizing (1.1) to explicitlyshow the three possible modulations leads to the general signal equation

s tð Þ ¼ A tð Þ cos ω tð ð Þt þ  tð ÞÞ: (1:2)Individual manipulation of these three parameters directly corresponds to Amplitude

shift keying (A(t)), frequency shift keying (ω(t)), and phase shift keying ((t)) These

basic modulations are shown in Figure 1.4

1.3.2 Polar representation

From the signal equation (1.1), a polar representation of the modulation (magnitude andphase) would appear to be a very natural method to describe modulations This isequivalent to describing the signal modulation in polar coordinates, magnitude andphase This is presented in Figure 1.5

But there is a big problem: mathematically it is very difficult to handle the anglemodulations FSK and PSK The main cause of the mathematical difficulty comes fromthe fact that the phase and frequency terms are contained within the argument of thesinusoid This makes the mathematics for these modulations very nonlinear

One way that this is handled is by the concept of phasors A phasor is simply ashorthand method to describe the modulation in magnitude and phase – but not in

frequency – of a DWC signal The simplest form is A / Sometimes the exponentialform is used, which is Aej Please refer to Appendix A for more details about phasors,their derivation, and their use

The usual method used to mathematically handle nonlinear problems is to find a way touse known linear approximations for them DWC engineers have also followed this strategy,and have adopted the following way to “stay linear”: Quadrature Modulation (QM)

(a) Frequency Shift Keying (FSK)

A

P

φ

Zero-Phase Reference Axis

Figure 1.5 Polar coordinate signal representation of signal modulation P = A<

coordinates In signal processing, the use of Cartesian coordinates is called quadraturemodulation Developed in Appendix D, the quadrature signal equation is

s tð Þ ¼ I tð Þ cos ωð ctÞ þ Q tð Þ sin ωð ctÞ (1:3)

The modulation components I(t) and Q(t) are simply projections of the signal’s polar

coordinates on the in-phase and quadrature axes Using the same polar representationfrom Figure 1.5, the equivalent quadrature modulation components I and Q are shown inFigure 1.6

There unfortunately is significant confusion from multiple, yet equivalent, tions of the quadrature signal While the quadrature signal format is examined in greatdetail in Appendix D, some clarification of these multiple description styles is importanthere

descrip-Because of the quadrature nature of the two carriers used, it has proven extremelyconvenient during mathematical analysis of modulated signals to consider the modula-

tion components I(t) and Q(t) to be parts of a single complex number C(t) = I(t) + jQ(t).

While this has mathematically proven to be an extremely successful approach, it has led

to a major confusion because alternative names are sometimes used for I(t) and Q(t) In

keeping with the notation of complex numbers, these alternative names are “real part” for

I(t) and worse, “imaginary part” for Q(t) What is imaginary about Q(t)??

Of course, nothing is imaginary about either I(t) or Q(t) They are both very real

waveforms Yet I have forgotten how many times I have had to explain this to an engineernew to the wireless communication field upon their early encounters with the use of the

name “imaginary” to refer to the Q(t) component To be consistent, I also strongly object

to the use of “real” when referring to I(t) for this same reason It is much better, and very

consistent, to only use the names “in-phase” component and “quadrature” component

–1 –0.5 0 0.5 1

A P

In-Phase Axis

Quadrature Axis

I Q

Figure 1.6 Quadrature (I and Q) signal representations, showing equivalence to the polar representation.

when referring to I(t) and Q(t) respectively This ties the modulation component directly

to the carrier type it is applied to, which is perfectly descriptive of what DWC engineersactually do

There is another lax use of language which leads to confusion Here I refer to the term

“complex modulation” to refer to C(t) above What we really mean is that “complex

number notation is used in this modulation analysis”, and not “this modulation iscomplicated” It is far better to the training of new communications engineers to remainexplicit and unambiguous in our language We should stop using the term “complexmodulation” to both avoid confusion and to be very clear in what we mean

1.3.4 Transformations between signal representations

Any digital modulation state can be described in either polar or quadrature nates The relationship between them is the well known polar-rectangular transforma-tion pair:

These transformations are unique, which simply means that only one answer is provided

by either transformation For example, if the Cartesian coordinates I and Q are known then the polar coordinates A and are uniquely determined The reverse is also true.Clearly the translations (1.4) are nonlinear As a result, signal component bandwidth isnot conserved Indeed, when signal magnitude goes to zero the phase in the polardescription becomes undefined, and usually the derivative of the magnitude becomesnot-continuous Thus, the polar signal description under certain conditions has disconti-nuities that do not appear in the Quadrature description

Note particularly that the polar signal magnitude A(t) is always non-negative (positive

or zero) This leads us to a very important distinction we must make between the termsamplitude and magnitude

Amplitude: a signed parameter relating to scaling of a sinusoid signal

Magnitude: a non-negative (positive or zero) measure of the peak value of a sinusoidsignal

Whenever polar coordinates are discussed, only magnitude is defined However tude is appropriate for arbitrary scaling of a sinusoid How these are important andseparate concepts is presented in this example

ampli-One very simple example of these concepts is a bi-phase-shift keying (BPSK) signalgenerated with a quadrature modulator Consider a design where a sine wave is applied as

Q(t) while I(t) is held at zero The resulting signal is found using

I tð Þ ¼ 0

Q tð Þ ¼ sin ωð btÞ for s tð Þ ¼ 0  cos ωð ctÞ þ sin ωð btÞ sin ωð ctÞ:

Using the Quadrature to Polar transformation we get the following transform:

A tð Þ ¼ þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi0

ð Þ2þ sin ωð ð btÞÞ2q

2sgn Q tð ð ÞÞ Further, werecognize that the magnitude is the absolute value of the modulating waveform,

A tð Þ ¼ sin ωj ð btÞj ¼ Q tj ð Þj Note that the signal magnitude is zero at the times whenthe phase switches These waveforms are presented in Figure 1.7

0.2 0.4 0.6 0.8 1

Figure 1.7 Waveform correspondences for Q-component based BPSK: a) the input I(t) and Q(t) waveforms,

b) the resulting signal waveform c) magnitude of the signal waveform, and d) phase of the signalwaveform

1.4 Frequency-domain representations

The frequency domain is an essential tool in working with DWC signals This simplymeans that signal analysis is done using frequency as the independent variable, instead ofusing time The transformation between the time domain and the frequency domain is theFourier Transform, which is well explained in books listed at the end of this chapter.Using frequency domain analysis we have an extremely valuable tool to evaluate signalbandwidth and other related metrics

One aspect of the frequency domain to time domain transformation is that it issymmetrical This is a very useful property to keep in mind, since most communicationengineers tend to think of the time domain and the frequency domain in very differentterms The transform pairs within Figure 1.8 are an attempt to clarify this symmetry, andthrough that to unify some thinking about time and frequency relationships

To begin, the first example signal is a time impulse (more correctly, a Dirac impulse intime) The corresponding spectrum is equal valued at all frequencies This type ofspectrum is called “white” because white light contains all colors at once (though we

do not worry about the light colors having equal weight or not) We must be careful here –this is NOT “white noise”, it is rather simply a white spectrum Noise is a special case thathas much discussion in Chapter 2

One well known relationship from the Fourier Transform is “the transform of arectangle is the sinc”, where sinc(x) = sin(πx)/πx The symmetry of this relationship

is shown in Figure 1.8 between parts a and e, and parts b and d In Figure 1.8b, the “timerectangle” is a very short burst of an RF signal Transformed into the frequency domainthere is a peak at the frequency of the RF signal, with much energy spread both aboveand below the RF signal frequency There are many lobes to the spectrum on each side –theoretically there are an infinite number of them Even practically there are a hugenumber of them because as this figure shows, they do not reduce in magnitude very fastwith increasing difference frequency away from the RF signal In row four the reverse isshown Here the frequency spectrum is absolutely restricted between two frequencies.The time domain signal that corresponds to this has a sinc envelope and infiniteduration

This infinite duration time domain signal is a problem because any time domain signal

of infinite duration is not causal and therefore impossible to realize Which means,correspondingly, that absolute bandlimiting with this “brickwall” bandpass filter is also

impossible The best any engineer and designed product will ever be able to do is to

approximate this ideal, desired situation

Another rule to remember this is: “Absolute duration restrictions in one domain forceinfinite durations or extents in the other.”

Since infinite duration signals are impossible, we naturally think about compromises

on how to get signals that are “finite enough” in both the time domain and the frequencydomain One natural question is to ask is whether a signal shape exists that is identical inboth the time and frequency domains And the answer to this question is yes: the veryfamous Gaussian This is shown in Figure 1.8c

Figure 1.8e shows a special case that should be familiar to all electrical engineers This

is the Fourier Series case, where a constant magnitude sinusoid in the time domaintransforms to a single impulse in the frequency domain This is the symmetrical partner ofFigure 1.8a: an impulse in the time domain transforms to uniform energy density

Figure 1.8 Relating time waveforms and frequency domain characteristics: a) impulse in the time domain,

b) rectangle (modulated RF signal) in the time domain, c) Gaussian shaped pulse in both domains,d) rectangle (“brickwall” bandlimiting) in the frequency domain, and e) impulse in the frequencydomain