RF Technologies For Low Power Wireless Communications

Department of Electrical Engineering and Computer ScienceThe University of Michigan, Ann Arbor Larry Milstein Department of Electrical and Computer Engineering University of California—S

RF TECHNOLOGIES FOR LOW POWER

WIRELESS COMMUNICATIONS

Edited by Tatsuo Itoh, George Haddad, James Harvey Copyright # 2001 John Wiley & Sons, Inc ISBNs: 0-471-38267-1 (Hardback); 0-471-22164-3 (Electronic)

RF TECHNOLOGIES FOR LOW POWER WIRELESS COMMUNICATIONS

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Formerly of the field artillery

The caissons go rolling along

James Harvey

Peter M Asbeck, Department of Electrical and Computer Engineering, University

of California—San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0407Alexander Balandin, Department of Electrical Engineering, University ofCalifornia—Riverside, 3401 Watkins Drive, Riverside, CA 92521-0403Andrew R Brown, Department of Electrical Engineering and Computer Science,The University of Michigan, 2105 Lurie Engineering Center, 1221 Beal Avenue,Ann Arbor, MI 48109-2122

M Frank Chang, Device Research Laboratory, Department of ElectricalEngineering, University of California—Los Angeles, 405 Hilgard Avenue, LosAngeles, CA 90095-1594

William R Deal, Malibu Networks, Inc., 26637 Agoura Road, Calabasas, CA 91302Jack East, Department of Electrical Engineering and Computer Science, University

of Michigan, 2105 Lurie Engineering Center, 1221 Beal Avenue, Ann Arbor, MI48109-2122

George I Haddad, Department of Electrical Engineering and Computer Science,University of Michigan, 2105 Lurie Engineering Center, 1221 Beal Avenue,Ann Arbor, MI 48109-2122

James F Harvey, U.S Army Research Office, P.O Box 12211, Research TrianglePark, NC 27709-2211

Tatsuo Itoh, Device Research Laboratory, Department of Electrical Engineering,University of California—Los Angeles, 405 Hilgard Avenue, Los Angeles,

CA 90095-1594

vii

Linda P B Katehi, Department of Electrical Engineering and Computer Science,University of Michigan, 2105 Lurie Engineering Center, 1221 Beal Avenue, AnnArbor, MI 48109-2122

Larry Larson, Department of Electrical and Computer Engineering, University ofCalifornia—San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0407

Larry Milstein, Department of Electrical and Computer Engineering, University ofCalifornia—San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0407

Clark T.-C Nguyen, Center for Integrated Microsystems, Department of ElectricalEngineering and Computer Science, University of Michigan, Ann Arbor, MI48109-2122

Sergio P Pacheco, Radiation Laboratory, Department of Electrical Engineeringand Computer Science, University of Michigan, Ann Arbor, MI 48109-2122Dimitris Pavlidis, Department of Electrical Engineering and Computer Science,University of Michigan, 2105 Lurie Engineering Center, 1221 Beal Avenue, AnnArbor, MI 48109-2122

Zoya Popovic, Department of Electrical Engineering, University of Colorado,Campus Box 425, Boulder, CO 80309-0425

Yongxi Qian, Device Research Laboratory, Department of Electrical Engineering,University of California—Los Angeles, 405 Hilgard Avenue, Los Angeles, CA90095–1594

Vesna Radisic, HRL Laboratories, 3011 Malibu Canyon Road, Malibu, CA 4799

90265-Gabriel M Rebeiz, Department of Electrical Engineering and Computer Science,University of Michigan, 2105 Lurie Engineering Center, 1221 Beal Avenue, AnnArbor, MI 48109-2122

Donald Sawdai, Department of Electrical Engineering and Computer Science,University of Michigan, 2105 Lurie Engineering Center, 1221 Beal Avenue, AnnArbor, MI 48109-2122

Wayne Stark, Department of Electrical Engineering and Computer Science,University of Michigan, 2105 Lurie Engineering Center, 1221 Beal Avenue, AnnArbor, MI 48109-2122

Robert J Trew, U.S Department of Defense, 4015 Wilson, Suite 209, Arlington,

James F Harvey, Robert J Trew, and Dwight L Woolard

1 Wireless Communications System Architecture and Performance 9Wayne Stark and Larry Milstein

2 Advanced GaAs-Based HBT Designs for Wireless

M Frank Chang and Peter M Asbeck

Dimitris Pavlidis, Donald Sawdai, and George I Haddad

4 Si/ SiGe HBT Technology for Low-Power Mobile

Larry Larson and M Frank Chang

Kang L Wang and Alexander Balandin

6 Power Amplifier Approaches for High Efficiency and Linearity 189Peter M Asbeck, Zoya Popovic, Tatsuo Itoh, and Larry Larson

7 Characterization of Amplifier Nonlinearities and Their Effects

Jack East, Wayne Stark, and George I Haddad

ix

8 Planar-Oriented Passive Components 265Yongxi Qian and Tatsuo Itoh

William R Deal, Vesna Radisic, Yongxi Qian, and Tatsuo Itoh

Sergio P Pacheco and Linda P B Katehi

11 Micromachined K-Band High-Q Resonators, Filters, and Low

Andrew R Brown and Gabriel M Rebeiz

12 Transceiver Front-End Architectures Using Vibrating

Clark T.-C Nguyen

WIRELESS COMMUNICATIONS

U S Army Research Office, Research Triangle Park, NC

Robert J Trew

U S Department of Defense, Arlington, VA

The driving purpose of recent advances in communications technology has been tountether users, allowing them complete mobility and freedom of movement whilemaintaining their connection to electronic services The wireless revolution has led

to an expectation that voice, fax, and data services, and even internet access, can beavailable anywhere, without recourse to specific locations in a fixed infrastructureand even while moving or traveling The last requirement tying the user to a fixedinfrastructure is the requirement for power, either wall plug or battery recharging.For a commercial system, this requirement is manifested in the time between batteryrecharging, which is the only time the user is truly free of the fixed infrastructure.There have been very impressive advances in battery technology, resulting in longertimes between battery recharges However, battery technology is beginning toapproach practical limits, still short of the real physical limits dictated by physicalchemistry Many technologists doubt that further advances in storage batterytechnology will produce more than a factor of 2 improvement in battery lifetime.The other end of this issue is the electronics systems that consume the power Ifelectronics systems can be designed to consume less power to accomplish the samefunctionality, then batteries will last longer without recharge For military systemsthe situation is more complicated Military operators of most manpacked and manportable electronic systems are accustomed to the use of disposable batteries in order

to avoid the requirement for recharging during a combat operation However,

Edited by Tatsuo Itoh, George Haddad, James Harvey Copyright # 2001 John Wiley & Sons, Inc ISBNs: 0-471-38267-1 (Hardback); 0-471-22164-3 (Electronic)

1

transport of the batteries required for missions of more than a day become asignificant load on the soldier, particularly as new concepts such as the Land Warriorand future soldier systems add significant electronic functionality to the individualsoldier A major concern is the weight in both the electronic equipment and batteriesthat the soldier must carry in combat In addition, there are huge logistics require-ments generated throughout the supply chain by the need to supply batteries in largequantities to front line troops This issue is a major concern affecting plans forstrategic airlift, strategic mobility, and the ability to project military force throughoutthe world It affects transportation requirements, adds administrative effort just tokeep track of the batteries through the system, and is a large procurement expense.There are also battery issues for unpiloted aerial vehicles (UAVs) and loiteringmissiles with mission times exceeding a few minutes Battery requirements musttrade off against the aerial vehicle payload or against its range and maximum missiontime Even in helicopters, with a large capacity power source from the engines, thereare concerns The greater the power usage in the electronics equipment, the heavierthe equipment becomes Also the power conditioning equipment for the electronicssystems adds weight in proportion to the power required For helicopters, weighttrades off against lift, which can be critical in combat, or against the other payload.Several years ago, a program in low power electronics was initiated by the ArmyResearch Office This program was focused on addressing the issue of RF andmicrowave systems with a major concern for the prime power required for wirelesstransmitters At about the same time DARPA (Defense Advanced ResearchPrograms Agency) initiated a program to address the reduction of power in digitaland computing systems The DARPA program was directed toward techniques toreduce processing power in CMOS-based electronics One thrust was to reduce thebias voltage of CMOS transitors Adiabatic switching techniques were also explored.

As a complement to these programs, five years ago the Office of the Secretary ofDefense (OSD) initiated a multidisciplinary university research initiative (MURI)program to augment the Army program in RF and microwave systems This programran for five years and involved researchers in four universities: the University ofCalifornia Los Angeles (UCLA), the University of California San Diego (UCSD),the University of Michigan, and the University of Colorado at Boulder The office ofDeputy Undersecretary of Defense for Science and Technology provided the fundingand program oversight for the MURI, while the day-to-day technical managementwas exercised by the Army Research Laboratory’s Army Research Office (ARO).The principal investigators from that MURI are the authors of this book, whichpresents the results of the sponsored research The presentation is coherent, placingthe advances made during the program in perspective for a reader with a generalelectrical engineering background The material in the book is presented to thedesign community in order to take advantage of the research in reducing powerconsumption in RF systems The MURI effort focused primarily on communicationssystems However, most of the research concepts can be applied to other RF systems,such as radar or target seekers in missiles Currently most of the wireless market is inthe high megahertz to low gigahertz frequency range, although satellite, wirelesslocal area network (WLAN), and local multipoint distribution service (LMDS)

systems utilize higher frequencies, up to 60 GHz New concepts have been proposed,such as high altitude, long operation (HALO) platform communications in the

48 GHz range Hunger for bandwidth and spectrum availability will drive bothcommercial and military communications systems to higher wireless frequencies.For this reason the research was not limited to the traditional cell phone/PCSfrequencies It was not possible in this book to go into as much technical detail ineach topical area as is contained in the many technical publications resulting fromthe research The book attempts to present the concepts and conclusions in anunderstandable manner and to allow the reader to reference the detailed publicationsfor more in-depth information as required

The goal of this research program was to develop techniques to accomplish the

RF functions at the lowest expenditure of energy Certain RF functions require adisproportionate fraction of the system power One such example is the poweramplifier stage of a radio transmitter Here the focus of the research was directedtoward reduction of the power losses, rather than the power itself A primary goalwas determination of an optimal solution within system constraints However, theintent of the research was not to address circuit optimization in isolation, but toconsider an RF system as an interacting network of subsystems that could beoptimized both on the subsystem level and on a global basis The resultingcomprehensive approach requires a highly interdisciplinary effort involving deviceand semiconductor materials science, circuit engineering, electromagnetics, antennaengineering, and communications systems engineering As this introduction is beingwritten, even a good cell phone is limited by very low efficiency in transmit mode

We believe that the concepts described in this book can open the door to efficienciesapproaching 20% Although the power consumed by a cell phone peaks in thetransmit mode, the receive or standby mode is also very important because it istypically used for long periods of time, resulting in significant power drain Receivemode issues are also addressed in this book

Chapter 1 addresses low power RF issues from a system architecture point ofview It examines the power and energy usage implications of modulation (includingspread spectrum) and coding techniques, including such trade-offs as bandwidthversus efficiency and bandwidth versus energy It discusses frequency hopping,direct sequence, and multicarrier direct sequence spread spectrum techniques andexamines the effects of amplifier nonlinearities on the power requirements formulticarrier transmitters and on receiver architectures In order to achieve thelinearity needed for low error rate modulation and low noise receiver operation, it isnecessary to operate amplifiers with a narrower range of voltage or current swings.This results in lower efficiencies The trade-offs between efficiency, linearity, biterror rate, and the modulation and coding schemes are complex, and these issues areintroduced in this chapter

Chapters 2–5 focus on issues of device physics, materials science, fabricationprocesses, and circuit issues for the active device building blocks for RF com-ponents Although CMOS technology has made impressive advances in RFcapability, this area was not included in the MURI research program because therewas already significant effort being made in commercial industry These four

chapters deal with GaAs, InP, SiGe, and GaN technologies, respectively GaAsHBTs are currently in widespread use in commercial wireless systems because oftheir attractive performance, circuit integration, and fabrication characteristics.GaAs devices also represent a relatively mature technology Chapter 2 examines theissues of emitter design and collector design on GaAs HBT performance andreliability A unique on-ledge Schottky diode potentiometer is presented that iscapable of direct, quantitative, in-place monitoring of the emitter ledge passivation.

An analytic model is discussed to explain the physics of the potentiometer and torelate its measurements to the HBT performance The effect of the ledge passivation

on performance, noise characteristics, and failure mechanisms is explored Theeffect of collector design on performance and reliability is also examined inChapter 2 The DHBT (double heterojunction bipolar transistor) structure with aGaInP collector is shown to have significant potential advantages over singleheterojunction designs, including better breakdown voltages, lower offset voltages,and lower knee voltage Innovative designs are proposed to mitigate some of thedisadvantages of the DHBT design In Chapter 3, InP devices and circuits arediscussed InP devices will operate at higher frequencies than GaAs-based devices.HEMTs made in this technology generally have better noise performance, whileHBTs demonstrate higher gain and better scaling features due to lower surfacerecombination, better process control due to etching selectivity, and better heatdissipation for power devices due to higher thermal conductivity Moreover, theoffset voltage and lower contact and sheet resistances of the emitter cap andcollector layers of InP-based HBTs lead to smaller knee voltage The smaller kneeand turn-on voltages allow the use of low voltage batteries and increase the amplifierefficiency However, the InP technology is newer and the available substrates aresmaller (4 in vs 6 in.) and more expensive Most InP HBT research has focused onNPN devices, that is, device structures doped N-type in the emitter and collectorlayers and P-type in the base, because of their speed The MURI research focused ondeveloping a complementary PNP InP HBT technology, in order to facilitateefficient, linear Class B power amplifier or output buffer circuits To place thetechnology issues in perspective, the physics of NPN and PNP InP HBTs is alsodiscussed and comparisons are made to GaAs technology Finally, push–pulloperation of complementary NPN and PNP InP HBT circuits is demonstrated.Chapter 4 is a discussion of Si/SiGe HBT technology In general, SiGe technologyhas greater limitations in frequency range and breakdown voltage (restricting itspower applications) than GaAs or InP technology, but it is compatible with siliconplanar technology It has the desirable characteristics of providing greater frequencyand gain performance, and higher power efficiency than silicon BJT devices Si/SiGeHBTs perform quite well in the low gigahertz frequency region, which is the highmarket volume personal communications application region This technology offersthe potential for low cost systems integrating analog and digital functions on a singledie for lower frequency wireless applications The specific contribution of the MURIresearch is in analyzing the device physics and in formulating the design rules forpower amplifier circuits, although this chapter contains substantial additionalperspective of the SiGe technology Research into GaN devices has been conductedunder a number of governmental programs because they promise the generation of

significantly higher power levels at high microwave or millimeter wave frequenciesthan single GaAs or InP devices At higher frequencies, solid state sources ofmoderate power must use some kind of spatial or corporate combining structure,which inevitably introduces losses By reducing the degree of combining requiredfor a given power level, GaN RF power sources can be much more efficient thancomparable sources based on other semiconductor technologies One of the mainbarriers to the use of GaN in communications systems is its relative noisiness TheMURI research focused on this noise issue, and the results are reported in Chapter 5.Chapters 6 and 7 focus on the power amplifier stage, where signal power is raised

to a highest RF level in the transmitter The efficiency of this stage is the upper boundfor the efficiency of the overall system, and considerable attention has been paid toimproving efficiency in the power amplifier Amplifiers are generally much moreefficient when operated in their power saturation region This results in a trade-off ofefficiency and linearity, with the high linearity requirements of modern commu-nications systems pushing conventional amplifier circuits into an inefficient mode ofoperation Chapter 6 presents several unconventional approaches to efficient poweramplifier concepts The use of a dc–dc converter to provide a continuously optimizedsupply voltage is discussed The use of Class E and F switching amplifiers in micro-wave systems is presented, and the trade-off with linearity is examined Techniques

to preserve efficiency and linearity simultaneously, the LINC amplifier (linearamplification with nonlinear components) and Class S amplifiers, are also consi-dered And a novel approach to the self-consistent design of the amplifier and theantenna structure is applied to eliminate the conventional matching network, and itslosses, between these transmitter stages The possibility of using antennas forharmonic filters, in addition to radiation, is presented for increasing the amplifierefficiency Chapter 7 presents an analysis of the nonlinearities in a power amplifierand new analytical tools to quantitatively address the complex nonlinear effects onthe wide band of frequencies inherent in digital signals

Passive components can be major sources of loss and inefficiency in planar RFcircuits Particularly at higher frequencies, interconnects can be very lossy, withlosses to the substrate and to radiation, as well as ohmic losses in the metal Planarantennas can have major losses to substrate modes, which can also seriously degradethe antenna patterns of arrays, effectively further reducing the efficiency of theantenna as well as complicating interfering antenna problems by radiating inunwanted directions and reception through sidelobes The control of unwantedfrequencies and spectral regrowth presents a special problem for truly planarfabricated or wafer scale integrated circuits On-wafer approaches to the reduction ininterference and frequency problems result in more complicated circuitry, withassociated additional power consumption

Chapter 8 presents two concepts that have the potential for a significant effect onthese components The SIMPOL technique provides very low loss interconnects forthe integration of high performance microwave RF components with CMOS digitalcircuits This technique opens the door to system-on-a-chip concepts, which havemany system advantages in addition to reduced connection losses The secondconcept is based on the so-called photonic bandgap structures (or electromagneticbandgap structures) Periodic passive structures can provide planar approaches to

harmonic tuning of high efficiency microwave amplifiers, reduced transmission lineleakage, low loss slow wave structures, improved planar filters, the elimination ofantenna substrate modes, and a perfect magnetic impedance surface, which affordsflexibility in the design of high efficiency antennas.

Chapter 9 reviews planar antenna approaches, including some innovative cations of the older concept of the quasi-Yagi antenna, and discusses the design ofactive integrated antennas Active integrated antennas are active semiconductordevices or circuits integrated directly within the planar antenna structure This type

appli-of integrated antenna circuit presents the opportunity to reduce losses between thepower amplifier and the antenna due to impedance matching circuits It also enables thedesign of an antenna array consisting of essentially nonlinear, nonreciprocal antennaelements, for application, for example, in phase conjugating, retroreflective arrays.Micromachining fabrication methods harness the manufacturing processesresponsible for the VLSI planar IC industry for RF circuits and circuit components.These techniques can have orders-of-magnitude impact on the size, weight, and cost

of RF systems and can enable a corresponding significant reduction in power sipation Micromachining techniques form an overarching circuit integrationtechnology based on extremely low loss transmission lines and metallic componentstructures, an inexpensive self-packaging process that eliminates spurious electro-magnetic packaging effects, monolithically integrated high Q filters and resonators,the wafer-scale integration of circuits based on different substrate materials, and anatural three-dimensional layered integration capability These techniques canessentially eliminate radiation and substrate losses from transmission lines and otherpassive structures, reducing losses to solely ohmic losses Thus a planar circuitstructure can approach waveguide performance, although the planar structurescannot equal the waveguide performance because the waveguide structure has moremetal and therefore smaller ohmic losses Micromachining fabrication techniquesalso offer the opportunity for entirely new device structures, such as the combination

dis-of RF electrical and mechanical functions in a single device, the RF MEMS (microelectro mechanical systems) devices The micromachined and MEMS devices, such

as high Q filters and switches, can replace one-for-one components in existing radio

or radar architectures, resulting in simple, low loss, on-chip planar circuits Of moreinterest is the ability to engineer entirely new planar monolithic architectures withreduced power requirements These micromachining and MEMS techniques are anenabling technology for such architectures as fully duplex communications, radarsimultaneous transmit/receive, common aperture and common electronics, cognitiveradio, and reconfigurable aperture systems And planar high Q components can

be used to increase RF circuit selectivity, thereby reducing power consumption Thehigh Q components also reduce the specifications for dynamic range and phasenoise in the active circuit components, allowing lower-power-consuming designs ofthe active components The research under the MURI program focused on some ofthe critical issues of this new technology, and these results are discussed in Chapters

10, 11, and 12

Chapter 10 deals with MEMS switches for RF applications Mechanical andelectrical design considerations for fixed beam, compliant beam, and cantilever

beam switches are discussed and concepts for high isolation switching are duced RF MEMS switches have relatively low RF insertion loss (on the order of0.2 dB or less), virtually zero dc power consumption, small size, and are constructedusing a batch planar fabrication process MEMS devices have switched several watts

intro-of RF power in laboratory experiments, providing the hope that research into thebasic physical mechanical, thermal, and electrical mechanisms of operation will lead

to reliable switching of moderate power levels by single MEMS switches.Conventional RF MEMS switches require between 40 and 80 volts to activatereliably, which is useful for some applications Compliant switches can activate with

as little as 5 volts, but other performance features must be traded off to achieve theselow activation voltages These MEMS switches can be used in place of manysemiconductor switches in RF circuits that can tolerate the slower MEMS switchingtimes (on the order of milliseconds), for example, in phased array beam steering andreconfigurable antenna structures Chapter 11 describes innovative concepts inmicromachined circuits to integrate high Q filters directly with an active semicon-ductor device to produce a planar circuit low phase noise oscillator The MEMSdevices described in Chapter 10 are basically switches, while the micromachinedresonators and filters in Chapter 11 are nonmechanical filters based on purelyelectrical resonators In contrast, Chapter 12 describes RF MEMS devices based onvery high Q mechanical resonators, which couple to the electrical signal The result

is a very small (on the order of 100 microns in size), very high Q (greater than 10,000

in vacuum) MEMS filter These filters have been demonstrated at VHF and have thepotential for application at UHF The filters are ultra low loss and require ultra small

dc activation energies Because of their extremely small size, they provide thepotential for their massive use in entirely new RF architectures that utilize frequencyselectivity to achieve low power consumption On the other hand, the small size andthe inherently mechanical nature of operation place a significantly increasedemphasis on packaging issues

Individual research areas started under this MURI program continue undervarious other government programs The research on power amplifiers inspired aworkshop on this subject, which evolved into an annual IEEE Topical Workshop onPower Amplifiers for Wireless Communications These individual topical areas ofresearch continue to be of strong interest to the military and commercial RF sectors.However, the editors strongly feel that the success of many of these areas was due totheir being conducted and managed in a university environment with a strongmultidisciplinary and interdisciplinary structure

This book is written for graduate students and engineering professionals withgeneral background of electrical engineering Although it is assumed that they arefamiliar with the background subjects such as electromagnetic fields, antennas,microwave devices, and communications systems, no detailed knowledge is expec-ted Although the contents are coherently organized, individual chapters can also beread independently Although reasonably extensive reference lists are included ineach chapter, the wealth in information in related subjects is enormous Readers withinterest in specific subjects may refer to the latest publications such as IEEETransactions

Department of Electrical Engineering and Computer Science

The University of Michigan, Ann Arbor

Larry Milstein

Department of Electrical and Computer Engineering

University of California—San Diego

Low power consumption has recently become an important consideration in thedesign of commercial and military communications systems In a commercialcellular system, low power consumption means long talk time or standby time In amilitary communications system, low power is necessary to maximize a missiontime or equivalently reduce the weight due to batteries that a soldier must carry Thisbook focuses attention on critical devices and system design for low powercommunications systems Most of the remaining parts of this book considerparticular devices for achieving low power design of a wireless communicationssystem This includes mixers, oscillators, filters, and other circuitry In this chapter,however, we focus on some of the higher level system architecture issues for lowpower design of a wireless communications system To begin we discuss some of thegoals in a wireless communications system along with some of the challenges posed

by a wireless medium used for communications

Edited by Tatsuo Itoh, George Haddad, James Harvey Copyright # 2001 John Wiley & Sons, Inc ISBNs: 0-471-38267-1 (Hardback); 0-471-22164-3 (Electronic)

9

1.2 PERFORMANCE GOALS AND WIRELESS MEDIUM CHALLENGES

A system level (functional) block diagram of a wireless communications system isshown in Figure 1.1 In this figure the source of information could be a voice signal,

a video signal, situation awareness information (e.g., position information of asoldier), an image, a data file, or command and control data The source encoderprocesses the information and formats the information into a sequence ofinformation bits 2 f1g The goal of the source encoder is to remove theunstructured redundancy from the source so that the rate of information bits at theoutput of the source encoder is as small as possible within a constraint oncomplexity The channel encoder adds structured redundancy to the information bitsfor the purpose of protecting the data from distortion and noise in the channel Themodulator maps the sequence of coded bits into waveforms that are suitable fortransmission over the channel In some systems the modulated waveform is alsospread over a bandwidth much larger than the data rate These systems, calledspread-spectrum systems, achieve a certain robustness to fading and interference notpossible with narrowband systems The channel distorts the signal in several ways.First, the signal amplitude decreases due to the distance between the transmitter andreceiver This is generally referred to as propagation loss Second, due to obstaclesthe signal amplitude is attenuated This is called shadowing Finally, because ofmultiple propagation paths between the transmitter antenna and the receiverantenna, the signal waveform is distorted Multipath fading can be eitherconstructive, if the phases of different paths are the same, or destructive, if thephases of the different paths cause cancellation The destructive or constructivenature of the fading depends on the carrier frequency of the signal and is thus calledfrequency selective fading For a narrowband signal (signal bandwidth small relative

to the inverse delay spread of the channel), multipath fading acts like a randomattenuation of the signal When the fading is constructive the bit error probabilitycan be very small When the fading is destructive the bit error probability becomesquite large The average overall received amplitude value causes a significant loss inperformance (on the order of 30–40 dB loss) However, with proper error controlcoding or diversity this loss in performance can essentially be eliminated

leaver

Deinter-Channel Decoding

Source

Decoding

In addition to propagation effects, typically there is noise at the receiver that isuncorrelated with the transmitted signal Thermal (shot) noise due to motion of theelectrons in the receiver is one form of this noise Other users occupying the samefrequency band or in adjacent bands with interfering sidelobes is another source ofthis noise In commercial as well as military communications systems interferencefrom other users using the same frequency band (perhaps geographically separated)can be a dominant source of noise In a military communications system hostilejamming is also a possibility that must be considered Hostile jamming can easilythwart conventional communications system design and must be considered in amilitary communications scenario.

The receiver’s goal is to reproduce at the output of the source decoder theinformation-bearing signal, be it a voice signal or a data file, as accurately aspossible with minimal delay and minimal power consumed by the transmitter andreceiver The structure of the receiver is that of a demodulator, channel decoder,and source decoder The demodulator maps a received waveform into a sequence ofdecision variables for the coded data The channel decoder attempts to determine theinformation bits using the knowledge of the codebook (set of possible encodedsequences) of the encoder The source decoder then attempts to reproduce theinformation

In this chapter we limit discussion to an information source that is random datawith equal probability of being 0 or 1 with no memory; that is, the bit sequence is asequence of independent, identically distributed binary random variables For thissource there is no redundancy in the source, so no redundancy can be removed by asource encoder

There are important parameters when designing a communications system Theseinclude data rate Rb(bits/s, or bps), at the input to the channel encoder, the bandwidth

W (Hz), received signal power P (watts), noise power density N0=2 (W/Hz), and biterror rate Pe;b There are fundamental trade-offs between the amount of power orequivalently the signal-to-noise ratio used and the data rate possible for a given biterror probability, Pe;b For ideal additive white Gaussian noise channels with nomultipath fading and infinite delay and complexity, the relation between data rate,received power, noise power, and bandwidth for Pe;b approaching zero wasdetermined by Shannon as [1]

interpretation of this condition is that for lower spectral efficiency, lower signalenergy is required for reliable communications The trade-off between bandwidthefficiency and energy efficiency is illustrated in Figure 1.2 Besides the trade-off for

an optimal modulation scheme, the trade-off is also shown for three modulationtechniques: binary phase shift keying (BPSK), quaternary phase shift keying(QPSK), and 8-ary phase shift keying (8PSK)

In this figure the only channel impairment is additive white Gaussian noise Otherfactors in a realistic environment are multipath fading, interference from other users,and adjacent channel interference In addition, the energy is the received signalenergy and does not take into account the energy consumed by the processingcircuitry For example, power consumption of signal processing algorithms(demodulation, decoding) are not included Inefficiencies of power amplifiers andlow noise amplifiers are not included These will be discussed in subsequent sectionsand chapters These fundamental trade-offs between energy consumed fortransmission and data rate were discovered more than 50 years ago by Shannon(see Cover and Thomas) [1] It has been the goal of communications engineers tocome close to achieving the upper bound on data rate (called the channel capacity) orequivalently the lower bound on the signal-to-noise ratio

To come close to achieving the goals of minimum energy consumption, channelcoding and modulation techniques as well as demodulation and decoding techniquesmust be carefully designed These techniques are discussed in the next two sections

In this section we describe several different modulation schemes We begin withnarrowband techniques whereby the signal bandwidth and the data rate are roughly

Optimal Modulation

equal In wideband techniques, or spread-spectrum techniques, the signal bandwidth

is much larger than the data rate These techniques are able to exploit the selective fading of the channel For more details see Proakis [2]

frequency-1.3.1 Narrowband Techniques

A very simple narrowband modulation scheme is binary phase shift keying (BPSK).The transmitter and receiver for BPSK are shown in Figures 1.3 and 1.4,respectively A sequence of data bits bl2 1 is mapped into a data stream andfiltered The filtered data stream is modulated onto a carrier and is amplified beforebeing radiated by the antenna The purpose of the filter is to confine the spectrum ofthe signal to the bandwidth mask for the allocated frequency The signal is convertedfrom baseband by the mixer to the desired center or carrier frequency(upconversion) The signal is then amplified before transmission With ideal devices(mixers, filters, amplifiers) this is all that is needed for transmission However, the

mixers and amplifiers typically introduce some additional problems The amplifier,for example, may not be completely linear The nonlinearity can cause thebandwidth of the signal to increase (spectral regrowth), as will be discussed later.For now, assume that the filter, mixer, and amplifier are ideal devices In this casethe transmitted (radiated) signal can be written as

The simplest channel model is called the additive white Gaussian noise (AWGN)channel In this model the received signal is the transmitted signal (appropriatelyattenuated) plus additive white Gaussian noise:

The noise is assumed to be white with two-sided power spectral density N0=2 W/Hz.The receiver for BPSK is shown in Figure 1.4 The front end low noise amplifiersets the internal noise figure for the receiver The mixer converts the radio frequency(RF) signal to baseband The filter rejects out-of-band noise while passing thedesired signal The optimal filter in the presence of additive white Gaussian noisealone is the matched filter (a filter matched to the transmitter filter) This verysimplified diagram ignores many problems associated with nonideal devices For thecase of ideal amplifiers and a transmit filter and receiver filter satisfying the Nyquistcriteria for no intersymbol interference [2], the receiver filter output can beexpressed as

Xl¼ ffiffiffiffi

E

p

bl 1þ Zl;where E is the received energyðE ¼ a2PTÞ and Zlis a Gaussian distributed randomvariable with mean zero and variance N0=2 The decision rule is to decide

bl 1¼ þ1 if Xl> 0 and to decide bl 1¼ 1 otherwise For the simple case of anadditive white Gaussian noise channel, the error probability is

@

1A;

where QðxÞ ¼R1

ð1= ffiffiffiffiffiffi2ppÞexpð u2=2Þ du This is shown in Figure 1.5

From Figure 1.5 it can be seen that in order to provide error probabilities around

10 5 it is necessary for the received signal-to-noise ratio to E=N0¼ 9:6 dB Thecapacity curve for BPSK in Figure 1.2, however, indicates that if we are willing tolower the rate of transmission we can significantly save on energy For example, it ispossible to have a nearly 0 dB signal-to-noise ratio if we are willing to reduce therate of transmission by 50% Thus about 9.6 dB decrease in signal power is possiblewith a 50% reduction in transmission rate

The above analysis is for the case of additive white Gaussian noise channels.Unfortunately, wireless channels are not accurately modeled by just additive whiteGaussian noise A reasonable model for a wireless channel with relatively smallbandwidth is that of a flat Rayleigh fading channel While there are more complexmodels, the Rayleigh fading channel model is a model that provides the essentialeffect In the Rayleigh fading model the received signal is still given by Eq (1.3).However, a is a Rayleigh distributed random variable that is sometimes large(constructive addition of multiple propagation paths) and sometimes small(destructive addition of multiple propagation paths) However, the small values of

a cause the signal-to-noise ratio to drop and thus the error probability to increasesignificantly The large values of a corresponding to constructive addition of themultiple propagation paths result in the error probability being very small However,when the average error probability is determined there is significant loss inperformance The average error probability with Rayleigh fading and BPSK is

r

da¼1

2 12

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

E=N0

where f (r) is the Rayleigh density and E is the average received energy The averageerror probability as a function of the average received energy is shown in Figure 1.6.Included in this figure is the performance with just white Gaussian noise As can beseen from the figure, there is a significant loss in performance with Rayleigh fading.

At a bit error rate of 10 5the loss in performance is about 35 dB In early cations systems the transmitted power was boosted to compensate for fading.However, there are more energy efficient ways to compensate for fading

communi-For a Rayleigh fading channel the fundamental limits on performance are known

as well The equations determining the limits are significantly more complicated [3].Nevertheless, they can be evaluated and are shown in Figure 1.7 By examining thecurve for BPSK we can see that it is possible to reduce the loss in performance toabout 2 dB (rather than 35 dB) if proper signal (coding) design is used Thus byreducing the data rate by 50% with proper coding a 33 dB savings in energy ispossible One method of signaling that reduces this performance loss is by the use ofwideband signals, as discussed in the next section

1.3.2 Wideband Techniques

Wideband signals have the potential of overcoming the problem of fading [4] This isbecause the fading characteristics are frequency dependent Different frequenciesfade differently because the phase relationships of different paths change as thefrequency changes In addition, wideband techniques are able to handle interferencefrom jammers or from other users There are several techniques that are employedfor wideband communications systems Two popular techniques are direct-sequence

(DS) spread spectrum and frequency-hopped spread spectrum We first discussdirect-sequence spread spectrum.

1.3.2.1 DS Spread Spectrum Conceptually, a direct-sequence spread spectrumworks as shown in Figure 1.8 A data sequence is first encoded for error protection.The encoded waveform is then modulated using a standard narrowband modulationtechnique (e.g., BPSK) The narrowband waveform is then spread over a widerbandwidth with a spreading code as shown in the figure At the receiver the receivedsignal is despread by mixing with an identical spreading code followed by anarrowband demodulator The result is then used for decoding or error correction

If there are multiple users using the same bandwidth at the same time but with

Optimal modulation

Code

Narrowband Demodulation Decoder

different spreading codes then the received waveform consists of the sum of thesignals of the different users (as shown in the figure) However, after mixing with thespreading code of the desired user, only the signal of the desired user becomesnarrowband The other users’ signals, since they have a different spreading code thanthat used by the receiver, remain wideband signals The narrowband demodulatorthen removes much of the interference The amount by which the interferencesignals are reduced in power is roughly equal to the ratio of the bandwidth of thewideband signal to the narrowband signal This is often referred to as the processinggain of the system.

The situation for a jamming signal is similar Consider a jammer that transmitsenergy in a narrow bandwidth directly in the band of the desired user The receivedsignal will consist of a sum of the desired signal and the jamming signal, as shown inFigure 1.9 The receiver processes the signal by first mixing with a replica of theuser’s spreading code (assumed not available to the jammer) The desired signalgets despread while the jamming signal becomes spread After demodulation thejamming signal power gets reduced by a factor equal to the processing gain.The above are conceptual descriptions of the way in which a direct-sequencespread-spectrum system rejects interference In both cases the receiver depicted isnot the optimal receiver The receivers depicted are optimal only if the interference

is white Gaussian noise Better receivers exist for multiuser interference and forjamming interference In addition, for jamming signals, we have not considered theworst possible jamming signal of a given power Power consumption occurs mainly

in two places in this conceptual diagram The first is at the transmitter in amplifyingthe signal If the signal is not constant envelope, then nonlinearities of the amplifiercause distortion When the amplifier is operating in the linear region the powerefficiency of the amplifiers is small If the envelope is constant, then, while thenonlinearities do not affect the signal, the signal has higher sidelobes than anonconstant envelope signal Significant power is also needed for the despreadingoperation For example, if the despreading is done digitally then an analog-to-digitalconverter is needed with dynamic range equal to that of the jamming signal and

Data

Encoder NarrowbandModulation

Spreading Code

Demodulation

Spreading Code

bandwidth of the desired signal This combination of high dynamic range andbandwidth leads to high power consumption for the digital circuitry needed todespread Thus despreading a spread-spectrum signal and thereby rejectingunwanted interference requires circuitry with significant power consumption.Below we specify a simple direct-sequence spread-spectrum system We analyzethe performance in the presence of jamming, in a fading channel, and in multiple-access interference The transmitter for a direct-sequence system is shown inFigure 1.10 The data sequence b(t) consists of a sequence of data bits of duration T.The data sequence is multiplied with a binary spreading sequence a(t), which has Ncomponents called chips per data bit.

In Figure 1.10, b(t) represents the data and can be expressed as

bðtÞ ¼ X1 l¼ 1

blpTðt l TÞ; bl2 fþ1; 1g;

where pT(t) is a rectangular pulse of unit amplitude and duration T beginning at

t¼ 0 Similarly, the spreading code a(t) is written as

aðtÞ ¼ X1 l¼ 1

alpTcðt lTcÞ; al2 fþ1; 1g;

where alis a binary symbol2 1 and Tc¼ T=N In this case it is useful to model ai

as a sequence of independent, identically distributed binary random variablesequally likely to be 1 The number of chips per bit is often referred to as the

‘‘processing gain.’’ It is the factor by which the signal is spread The transmittedsignal is then

sðtÞ ¼ ffiffiffiffiffiffi

2P

paðtÞ bðtÞ cosð2p fctÞ:

The transmitted signal has power P In Figure 1.11 we show a data signal and theresult of multiplying by a spreading signal with 7 chips per bit

The receiver consists of a mixer followed by a filter matched to the spreadingcode of the transmitter as shown in Figure 1.12 A typical filter output is shown in

PA

s(t) b(t)

a(t) cos(2 πf c t )

Figure 1.13 In this figure the filter output is sampled every T seconds At these timesthe filter impulse response is completely correlated with the incoming desired signaland produces a large amplitude (positive or negative depending on the sign of thedata bit) signal The sample output corresponds to a data sequence consisting of twopositive polarity data bits followed by two negative polarity data bits followed by apositive polarity bit For the case of an additive channel (no fading) with interferenceand a lowpass filter matched to the transmitted pulse shape (rectangular assumedhere), the output of the filter at time i T can be expressed as

Zði TÞ ¼ ffiffiffiffi

E

p

bi 1þ I þ Zi;where I represents the contribution due to the interference and Zi is the output attime iT due to background noise (e.g., thermal noise)

The component of the output of the receiver due to interference will depend onthe nature of the interference (jamming, multiuser, etc.) as well as the spreadingcode a(t) used For simplicity in what follows we will assume that the spreading codeconsists of a sequence of independent and identically distributed random variableswith equal probability of being þ 1 and 1.

One simple measure of performance of a communications system is the noise ratio at the output of the receiver The signal-to-noise ratio (SNR) is defined as

jðtÞ ¼ ffiffiffiffiffiffi

2 J

pcosð2p fctÞ:

Then the signal-to-noise ratio at the output of the receiver is given by

J=N:From this we can see the effect of spreading is to reduce the effective jammingpower by a factor of N, the processing gain If the jamming signal has a random

phase offset from the desired signal then the SNR would be increased by a factor of

2 The error probability can be approximated from the SNR by assuming the output

of the receiver due to the interfering signal has a Gaussian density With thisassumption,

Pe;b Qð ffiffiffiffiffiffiffiffiffiffi

SNR

pÞ:

Now consider the case of multiuser interference Assume that there are K userswith unique spreading codes (modeled as a random sequence) In addition, assumethere are random delays and phases between the users With these assumptions thesignal-to-noise ratio for user 1 is given by

k¼2Ei=ð3NÞ þ N0=2;

where K is the number of users, Eiis the received energy per bit for user i, and N0=2

is the two-sided power spectral density of the background noise Again it is clearhow the spreading reduces the effect of the interference The factor of 3 arises due tothe random phase and delays between users

Finally, consider the case of multipath interference Because multipath is notadditive but rather multiplicative the model needs updating Consider a simplemodel whereby the received signal is a sum of delayed versions of the transmittedsignal plus additive white Gaussian noise That is,

rðtÞ ¼XL l¼1

alsðt tlÞ þ nðtÞ:

For simplicity, assume that the delays are separated by at least Tcseconds In thiscase the paths are said to be resolvable This implies that the output of the matchedfilter consists of peaks that are nonoverlapping and thus can be resolved Consider theideal case of a spread-spectrum signal with zero sidelobes In this case the output ofthe filter consists of a peak for each multipath present If we assume that the corre-lations are ideal (so that the output consists of just impulses) and that the amplitude

of each path is independent and Rayleigh distributed, then the performance improvesdramatically compared to a single-path system as shown in Figure 1.14

1.3.2.2 Frequency-Hopped Spread-Spectrum Frequency-hopped spread trum works by pseudorandomly changing the center frequency of the carrier over aset of frequencies The sequence of frequencies used is called the frequency-hoppingpattern In a jamming environment this can force the jammer to spread its powerover a very wide bandwidth in order to guarantee that the transmitted signal isdisrupted (to some extent) When the jammer spreads its signal over the wholebandwidth the amount of power in each frequency slot is a small fraction of the total

spec-power Thus the effectiveness of a wideband jammer is reduced in proportion to thebandwidth over which the signal is spread If the spreading is large enough thejammer is not effective at disrupting communications If the jammer only jams afraction of the band but with high power in certain slots then the performance can beseverely degraded (as opposed to a wideband jammer with the same total power).However, in this case a proper error control code and decoding algorithm thatcorrects errors in slots jammed can change the optimal jamming strategy fromnarrowband to broadband and thus regain the advantage of spreading the spectrum.For multiple access, different users have different frequency-hopping patternsand different users will collide occasionally These collisions can be handled withthe use of appropriate error control coding A code with a very low rate is needed for

a large number of interferers while for a small number of interferers a large rate codeshould be employed To maximize the information throughput per unit bandwidth anoptimal code rate and number of users can be found

For fading channels, provided the frequency separation between slots is largerthan the coherence bandwidth, different frequencies will fade independently If thebandwidth within a slot is small compared to the coherence bandwidth then thefading will be nonselective within a hop An error control code will be able to correcterrors from a badly faded hop It is interesting to note that the (uncoded)performance in a fading environment is actually worse than the performance in ajamming environment In both cases the performance degradation (without coding)

is on the order of 30–40 dB compared to additive white Gaussian noise This can

be reduced somewhat in the partial-band jamming case by spreading over a verylarge bandwidth However, with the proper combination of coding and spreading

3 5 10 20 AWGN

a jammer’s optimum strategy is to jam the whole bandwidth With this optimumjamming strategy the performance of a spread-spectrum system with worst-case jam-ming becomes the same as an additive noise channel with the same average power.

In this sense then, a jammer can be defeated with the right combination of spreadingand coding In fact, the required signal-to-noise ratio with proper spreading andcoding with a partial-band jammer is lower than the required signal-to-noise ratio for

an uncoded spread-spectrum system with just additive noise of the same averagepower

1.3.2.3 Multicarrier Techniques Multicarrier modulation techniques haverecently gained significant popularity in the United States and Europe In the UnitedStates multicarrier is used for digital subscriber loop (DSL) applications, while inEurope it is used in digital audio broadcasting (DAB) Multicarrier works byemploying more than one carrier simultaneously Consider an encoded data streamb(t) consisting of data bits with rate Rb¼ 1=Tbbits per second The data stream isconverted from a single stream into M separate streams via a serial-to-parallelconverter as shown in Figure 1.15 After the serial-to-parallel converter the datastreams are mixed onto M different carriers before being combined and amplified Atthe receiver the inverse process in used The received signal is mixed down tobaseband using M different carriers After mixing down to baseband the signal isfiltered before a decision is made regarding each bit

There are several motivations for considering multicarrier modulation techniquesand several disadvantages of multicarrier techniques For high data rate (relative tothe inverse delay spread of the channel) applications, single-carrier systems sufferfrom severe intersymbol interference This interference can be mitigated bysufficient equalization but requires significant complexity at the receiver to do this

Channel

Encoder

Serial to Parallel

PA cos(2 πfM − 2t )

cos(2 πf M t )

cos(2 πf c t ) cos(2 πf 1 t )

By using multiple carriers the data rate on each carrier is reduced by a factor M Thismeans that the intersymbol interference is reduced by a factor of M and the receivercomplexity is also reduced However, the peak-to-mean power ratio at the input tothe power amplifier now becomes large For amplifiers operating with high backoff(not near saturation) this is not a problem However, operating an amplifier with highbackoff is typically not very efficient If the amplifier is operating with low backoffthen the large envelope variations cause distortion because of intermodulationproducts that fall in band or in adjacent channels Another advantage of multicarriermodulation is that the frequency occupancy can be rather flexible That is, we canbuild a system that occupies noncontiguous frequency bands If we consider a linearamplifier and additive white Gaussian noise alone then the performance on multi-carrier modulation is identical to a single-carrier system Multicarrier techniques canalso be applied to direct-sequence spread-spectrum systems In such a system thedata stream on each carrier is spread with a spreading code This gives a multicarriersystem the advantage with respect to interference that a direct-sequence system has.Later we will show the performance of multicarrier direct-sequence systems withnonideal amplifier characteristics.

Coding techniques are crucial to reducing the power consumption of digitalcommunications systems The basic idea of coding is to add redundancy to thetransmitted data For example, for every four information bits we might want totransmit four information bits and three parity bits or redundant bits In this way thefour information bits are encoded into seven coded bits If we representthe information bits by b0; b1; b2; b3; which are 0 or 1, then the coded bitsare determined by p4¼ b0þ b1þ b2; p5¼ b0þ b1þ b3; and p6 ¼ b1þ b2þ b3,where the equations are interpreted to mean mod 2 addition The transmittedcodeword is ðb0; b1; b2; b3; p4; p5; p6Þ and is said to have block length 7 At thereceiver the information bits can be determined even if a bit is received in error byrecomputing the parity equations For example, if the third bit (b2) is received inerror then the first and last parity equations are not satisfied Because b2 is the onlybit that participates in only those two parity equations, it is found to be the bit in errorand the decoder can correct the error The code described above is called theHamming code and can correct any pattern of a single error If the energy used totransmit a single bit of information is denoted by Eband the energy used to transmit

an encoded bit is E, then for this example 4Eb¼ 7E or E ¼ 4Eb=7 So each codedbit actually has less energy than what is allocated for an information bit Because ofthis, the signal-to-noise ratio for each coded bit is reduced by a factor of 4/7 fromwhat could be used in an uncoded system In spite of this, the error correctioncapability of the code makes up for this loss when the signal-to-noise ratio isreasonably large

In practice, convolutional codes are used in many communications systemsbecause of their excellent performance In Figure 1.16 we show the bit error

probability for a typical convolutional code compared to an uncoded system In thisexample the modulation is BPSK and the channel has just additive white Gaussiannoise This code has rate 1/2 meaning that for each information bit two coded bits aretransmitted From this figure we can see a 5 dB power performance improvementcompared to an uncoded system The disadvantage is that the bandwidth efficiencyhas been reduced by a factor of 2.

In Figure 1.17 the performance in Rayleigh fading (a more realistic environment)

is shown In this case the improvement is about 37 dB compared to an uncodedsystem This illustrates the benefits in energy efficiency of coding relative to anuncoded system The penalty paid for this improved energy efficiency is a decrease

in bandwidth efficiency plus additional complexity at the receiver Recently, anothercoding technique called turbo codes was invented These codes achieve even betterperformance provided their block length is sufficiently long

DIRECT-SEQUENCE MULTICARRIER WAVEFORMS

1.5.1 Introduction

Multicarrier (MC) direct-sequence (DS) signaling, as described in Section 1.3, hascertain desirable properties relative to single-carrier DS, such as flexibility indeploying the waveform over a noncontiguous bandwidth That is, if certainsegments of a given frequency band are occupied with narrowband signals, the

Figure 1.16 Error probability of BPSK with convolutional coding in additive white Gaussiannoise

subcarriers that constitute the MC waveform can be interspersed between thenarrowband signals so as not to cause any interference However, MC signaling isnot without its drawbacks, and arguably first among them is the fact that thecomposite envelope is not constant Indeed, one can have a very high ratio of peak-to-average power and thus be susceptible to degradation due to nonlinearamplification.

In this section, we attempt to quantify the extent of this degradation; we alsopresent a technique that can regain some of the lost performance by suppressing, atthe receiver, some of the intermodulation products that were generated at thetransmitter In particular, we consider a binary communications system operatingover a frequency-selective Rayleigh fading channel The communications systememploys convolutional coding with soft decision decoding

1.5.2 System and Channel Description

A block diagram of the transmitter is shown in Figure 1.18 (see also Xu and Milstein[5]); it consists of a rate-1/M convolutional encoder, followed by an interleaver, aserial-to-parallel converter, an MC modulator, and a power amplifier The input–output characteristic for the power amplifier when the input is a single sine wave isshown in Figure 1.19 Note that this particular amplifier is assumed to exhibit onlyAM/AM conversion (i.e., it has no AM/PM conversion); this type of characteristic istypical of a solid state amplifier, as opposed to a traveling-wave tube

The receiver is shown in Figure 1.20; the incoming waveform is demodulated,deinterleaved, and finally decoded

Impulse modulator H (f)

Power Amplifier

Zonal Filter

Σ

Impulse modulator H (f)

ck ,1(n)

dk ,1d

PA model: Bessel function expansion

Figure 1.19 Power amplifier transfer function for single carrier

r (t ) Bank of M

Despreadors

P/S (M ) Deinterleaver

Soft Decision Viterbi Decoder

ˆbk

Figure 1.20 Receiver block diagram for user k

As indicated above, an enhanced receiver will also be considered, whereby theenhancement will come from appropriate signal processing at the receiver so that theintermodulation distortion caused by the nonlinear amplifier at the transmitter isreduced A block diagram of this enhanced receiver is shown in Figure 1.21, and it isseen that the only change from the original receiver is the insertion, after each of the

M despreaders, of an interference suppression filter designed via a minimum squared error criterion

mean-Finally, the channel introduces additive white Gaussian noise (AWGN), as well asflat Rayleigh fading on each subcarrier The fading is assumed to be sufficiently slow

so that it remains essentially constant over several symbols

1.5.3 Performance Results

In the results that follow, the number of subcarriers, denoted by M, is taken to be 4.Figure 1.22 shows the levels of both third order and fifth order intermodulation (IM)products as a function of the drive level into the amplifier Also shown is the desiredsignal response at each input level It is seen that when the amplifier is driven heavilyinto saturation, the output levels of both third and fifth order intermodulationproducts can approach the level of the desired output

When the above amplifier output is transmitted across the channel, and thereceiver of Figure 1.20 is used, the resulting average probability of error is shown inFigure 1.23 It is seen that as the level of the signal into the amplifier is continuallyincreased, a point is reached whereby the performance experiences rapid

Bank of M MMSE Reciver

Bank of M

MMSE

training Rate 1/M Convolutional Encoder and Interleaver

Soft Decision Viterbi Decoder

degradation In order to reduce that degradation, the receiver of Figure 1.21 can beused, and its performance is also shown in Figure 1.23 Note that when the initialdegradation is small, the enhanced receiver provides no noticeable benefit However,when the initial degradation is large, the enhanced receiver reduces the averageprobability of error by about an order of magnitude.

As another illustration of the effect of the nonlinear amplifier, consider the use ofthe MC DS waveform in a code division multiple access (CDMA) environment.Assume that each user in the system transmits asynchronously using identical poweramplifiers The signal at any receiver then is the sum of all the intermodulationproducts coming out of each of the transmitters In Figure 1.24, average probability

of error curves are shown plotted against the number of simultaneously active users

in the system There are curves corresponding to two distinct drive levels (persubcarrier) into the amplifier: 0.5 and 0.6 Also, the performances for the tworeceivers of Figures 1.20 and 1.21 are shown System performance corresponding to

a perfectly linear amplifier is also presented

It can be seen that, as the number of users in the system increases, the curvescorresponding to the presence of intermodulation distortion diverge from the linearamplifier curves To see what is happening, it is necessary to understand theoperation of the suppression filters Each filter is implemented as a tapped delay line,whereby the number of taps has been set equal to the processing gain per subcarrier;

in this particular example, the processing gain is 32 When the total number ofinterfering waveforms is less than the number of taps, the suppression filter has asufficient number of degrees of freedom to provide some measure of attenuation to

Input amplitude to PA (per subcarrier) (M =4)

PA model: Bessel function expansion

Desired signal output 2A −B IMD A+B −C IMD 3A −2B IMD 2A+B −2C IMD 3A −B−C IMD 2A+B −C−D or A+B+C−2D IMD

Figure 1.22 Desired signal and IM term amplitudes for multiple carriers (M¼ 4)

MC RAKE with IM,input amplitude=0.6 (per carrier)

MC MMSE with IM,input amplitude=0.6 (per carrier)

MC RAKE with IM,input amplitude=0.5 (per carrier)

MC MMSE with IM,input amplitude=0.5 (per carrier)