DiplomarbeitDesign and Real-Time Measurements ofEqualization S hemes for HSDPAAusgeführt zum Zwe ke der Erlangung des akademis hen Grades einesDiplom-Ingenieurs unter Leitung vonUniv.-Prof. Dipl.-Ing. Dr. te hn. Markus RuppDipl.-Ing. Christian MehlführerE389Institut für Na hri htente hnik und Ho hfrequenzte hnikeingerei ht an der Te hnis hen Universität WienFakultät für Elektrote hnik und Informationste hnikvonStefan GeirhoferMatrikelnummer: 9925111Adresse: 1020 Wien, Ausstellungsstraÿe 63/21Wien im Januar 2005

Abstra tThe development of third generation wireless networks like UMTS has signi�- antly extended the mobile equipment's apabilities and allows for a plethoraof new servi es, whi h in their majority are based on the Internet Proto ol(IP). While UMTS annot handle the resulting asymmetri load su� ientlywell, `beyond 3G' s hemes like the High Speed Downlink Pa ket A ess (HS-DPA) are tailored to the requirements of pa ket tra� and further in reasethe data rate up to 14.4Mbit/s.HSDPA requires a su� iently high hannel quality for indeed attaining su hdata rates. As a matter of fa t, this renders the usage of the onventionalRAKE re eiver impossible and ne essitates that the interferen e reatedthrough multiple a ess be mitigated. This thesis onsiders equalization asan attra tive method to a hieve this goal.In ontrast to other ontributions this thesis uses real-time measurementsover a physi al hannel at 2.45GHz to evaluate the suitability of di�erentequalization s hemes. This not only leads to a really representative ompari-son but also helps to illuminate implementation hallenges just as they wouldo ur in the industrial development of a devi e. The measurement part ofthis work is fa ilitated by using the MIMO testbed developed at the Insti-tute of Communi ations and RF-Engineering, whi h allows for an e� ientinterfa e between Matlab and the radio-frequen y equipment.The omparison between di�erent equalizers is based both on performan eand omplexity as it would be essential in a pra ti al implementation. Inparti ular it is shown that adaptive solutions require only little omputa-tional omplexity while almost living up to the performan e of the moresophisti ated s hemes, involving the inversion of large matri es.

i

ZusammenfassungDie Entwi klung von Mobilfunknetzen der dritten Generation, wie beispiels-weise UMTS, hat zu einer Fülle von neuen Diensten geführt die überwiegendauf dem Internet Protokoll basieren. Die daraus resultierende asymetris heDatenrate wird von UMTS aber nur unzurei hend unterstützt, was zu derEntwi klung von `beyond 3G' S hemata geführt hat. HSDPA ist ein sol hesÜbertragungsverfahren, das Datenraten bis zu 14.4Mbit/s erlaubt.Um diese Datenrate au h wirkli h zu errei hen ist eine hinrei hend gute Ka-nalqualität unerläÿli h. In der Praxis führt dies dazu, dass der konventoniel-le RAKE-Empfänger unbrau hbar wird, da er der entstehenden Interferenzni ht Re hnung trägt. Diese Arbeit widmet si h deshalb Entzerrerstruktu-ren, die die entstandene Interferenz unterdrü ken, und damit die Leistungdes Systems stark verbessern.Im Gegensatz zu anderen Arbeiten zu diesem Thema basiert der Verglei hzwis hen vers hiedenen Entzerrungsstrukturen auf Messungen über physika-lis he Kanäle bei 2.45GHz. Damit ergibt si h ni ht nur ein wirkli h repräsen-tativer Verglei h zwis hen den vers hiedenen S hemata, sondern es könnenau h parasitäte E�ekte untersu ht werden, beispielsweise der Ein�uss unge-nauer Syn hronisierung oder fehlerbehafteter Kanals hätzung.Der Verglei h zwis hen den unters hiedli hen Entzerrerstrukturen basiert so-wohl auf deren Leistungsvermögen als au h auf deren Komplexität. Im Be-sonderen werden niedrigkomplexe adaptive Te hniken untersu ht und es wirdgezeigt, dass diese tatsä hli h eine mit komplexeren Methoden verglei hbareLeistung zeigen.

ii

A knowledgmentsI would like to thank my advisors, Univ.-Prof. Dr. Markus Rupp andDipl.-Ing. Christian Mehlführer for their guidan e and support throughoutworking on this diploma thesis. I am also indebted to Dr. Christoph Me k-lenbräuker of the Tele ommuni ations Resear h Center Vienna (ftw.) forsupporting this work and for many fruitful dis ussions. I owe my gratitudeto Univ.-Prof. Dr. Arpad L. S holtz, Dr. Werner Keim, Dipl.-Ing. RobertLangwieser, and Lukas Mayer for supporting the measurement pro ess andfor many insightful omments. Stefan GeirhoferStatement of OriginalityI hereby ertify that the work presented in this diploma thesis is my own andthat other authors' ontributions are appropriately ited. Stefan GeirhoferVienna, January 27, 2005

iii

Contents1 Introdu tion 11.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 S ope of Work . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 Measurement Con�guration 42.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Signal Generation . . . . . . . . . . . . . . . . . . . . . . . . . 62.2.1 User Channels . . . . . . . . . . . . . . . . . . . . . . . 62.2.2 Pilot Channel . . . . . . . . . . . . . . . . . . . . . . . 72.2.3 Syn hronization Channel . . . . . . . . . . . . . . . . . 72.2.4 RRC-Filtering . . . . . . . . . . . . . . . . . . . . . . . 82.3 Physi al Channel . . . . . . . . . . . . . . . . . . . . . . . . . 92.3.1 Testbed Interfa ing . . . . . . . . . . . . . . . . . . . . 92.3.2 Analog Up- and Down onversion . . . . . . . . . . . . 92.3.3 Channel Emulation . . . . . . . . . . . . . . . . . . . . 102.3.4 Noise Generation . . . . . . . . . . . . . . . . . . . . . 102.4 Re eive Pro essing . . . . . . . . . . . . . . . . . . . . . . . . 112.4.1 Testbed Interfa e . . . . . . . . . . . . . . . . . . . . . 112.4.2 Syn hronization Pro edure . . . . . . . . . . . . . . . . 122.4.3 Channel Estimation . . . . . . . . . . . . . . . . . . . . 132.4.4 Re eiver Implementation . . . . . . . . . . . . . . . . . 142.5 Mathemati al Signal Model . . . . . . . . . . . . . . . . . . . 152.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

iv

CONTENTS v3 Equalizer Analysis 173.1 RAKE Re eiver . . . . . . . . . . . . . . . . . . . . . . . . . . 173.2 Chip-Rate MMSE Equalizer . . . . . . . . . . . . . . . . . . . 193.3 Fra tionally Chip-Spa ed MMSE Equalizer . . . . . . . . . . . 203.4 Symbol-Rate MMSE Equalizer . . . . . . . . . . . . . . . . . . 223.5 Adaptive Equalization . . . . . . . . . . . . . . . . . . . . . . 243.5.1 Symbol-Rate Adaptive Equalizer . . . . . . . . . . . . 243.5.2 Chip-Rate Adaptive Equalizer . . . . . . . . . . . . . . 253.5.3 Constant Modulus Algorithm . . . . . . . . . . . . . . 263.6 Modi�ed RAKE Stru tures . . . . . . . . . . . . . . . . . . . . 273.6.1 MMSE-RAKE Re eiver . . . . . . . . . . . . . . . . . 283.6.2 Adaptive RAKE Re eiver . . . . . . . . . . . . . . . . 283.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294 Measurement Results 314.1 Measurement Veri� ation . . . . . . . . . . . . . . . . . . . . . 314.1.1 Pulse Shape . . . . . . . . . . . . . . . . . . . . . . . . 314.1.2 Power Levels in the Transmission Chain . . . . . . . . 324.1.3 BER for Idealized Channels . . . . . . . . . . . . . . . 334.2 Measurement Results . . . . . . . . . . . . . . . . . . . . . . . 364.2.1 MMSE Equalizer vs. RAKE Re eiver . . . . . . . . . . 374.2.2 Equalizer Length Analysis . . . . . . . . . . . . . . . . 414.2.3 Fra tionally Chip-Spa ed Equalization . . . . . . . . . 424.2.4 Adaptive Equalizer Performan e . . . . . . . . . . . . . 424.2.5 Tra king of Time-Variant Channels . . . . . . . . . . . 474.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 475 Con lusions 52A Detailed Measurement Con�guration 54List of Abbreviations 58

Chapter 1Introdu tionOver the last years, ommuni ation networks have seen a tremendous in reasein tra� , espe ially aused by appli ations that rely on the Internet Proto ol(IP). In �xed networks, IP-tra� even outweighs the onventional ir uit-swit hed tra� and the same trend is about to happen in ellular networks.Based on this predi tion, the International Tele ommuni ations Union(ITU) has established goals for the third and fourth generation wireless net-works. Spe i� ally, there is a need for high data rate and IP-oriented proto- ols that an rea h data rates in the 10-100Mbit/s range.HSDPA is one of these �beyond 3G� s hemes and o�ers data rates upto 14.4Mbit/s. In order to a hieve this, it makes important hanges to the onventional UMTS framework as to provide for a fast and reliable trans-mission while paying attention to the spe i� needs of di�erent appli ations,i.e. spee h, data or streaming tra� . It is beyond the s ope of this work togive a thorough overview of all the design revisions. Instead, the fo us lieson those hanges relevant to the physi al layer of the system.Adaptive Modulation and Coding First and foremost, this is the intro-du tion of Adaptive Modulation and Coding (AMC) instead of fastpower ontrol. The idea behind this s heme is not to ontrol the powerof a spe i� user su h that a desired quality of servi e is met, but toprovide the user with the data rate he an urrently handle. Conse-quently, this means that if a user is urrently experien ing a very poor hannel quality, he will only be allo ated a low bit rate, simply be ausethe hannel does not allow for faster transmission. However, if a user ismomentarily experien ing a very good hannel, then a higher bit rateis assigned. 1

CHAPTER 1. INTRODUCTION 2Hybrid Automati Repeat Request Another very important hange isthe introdu tion of the Hybrid Automati Repeat Request (HARQ),whi h represents a fast and e�e tive retransmission strategy. The in-trodu tion of this method is very important for HSDPA be ause other-wise high laten ies for the retransmission would result in forbiddinglyhigh amounts of temporary bu�ers.1.1 MotivationAs outlined above, HSDPA enhan es UMTS with several new on epts thattailor it to the spe i� requirements of transmitting pa ket data. Spe i� ally,AMC sele ts a bit rate that orresponds to the hannel quality experien edby the user.Ultimately, the term hannel quality is slightly misleading in the way thatit is not only in�uen ed by the hannel itself, but also by the re eiver beingused. In fa t, it is possible to in rease the overall bit rate�and thus thesystem performan e�by employing re eiver stru tures that are apt to opewith the hannel indu ed impairments in a better way.However, employing more sophisti ated re eiver stru tures is at the ostof making the re eiver and thus the mobile devi e more expensive. Thisadditional omplexity has to be arefully analyzed and ompared to the per-forman e gain. In this evaluation we have to take into a ount that employingmore sophisti ated re eiving s hemes remedies other performan e limitations,for instan e the average number of retransmissions.The system performan e in UMTS is limited by the loss of orthogonalityof the spreading odes introdu ed by the multi-tap hara teristi s of the hannel. As a onsequen e, it is no longer possible to perfe tly separate theuser hannels; this leads to additional interferen e, alled Multiple A essInterferen e (MAI).Whereas the onventionally employed RAKE re eiver annot ope withthis situation at all, it is possible for an equalizer to ompensate for the distor-tion brought about by the hannel and to restore orthogonality. In this waythe multiple a ess interferen e is greatly redu ed�ideally it is ompletelysuppressed�and thus the bit error rate is signi� antly ameliorated.1.2 S ope of WorkThe goal of this thesis is to design and ompare known equalization te h-niques (MMSE, sele ted adaptive te hniques) as well as new proposals

CHAPTER 1. INTRODUCTION 3(MMSE-RAKE, adaptive RAKE). Other than related publi ations, this workfounds the performan e omparison on measurements over a physi al han-nel at radio-frequen y. Thus, the results are truly representative for a realHSDPA implementation and allow for exploring pra ti al problems like thee�e ts of non-perfe t syn hronization or impairments of the RF-equipment.The measurements were performed with a MIMO testbed developed at theInstitute of Communi ations and Radio-Frequen y Engineering.Another emphasis lies in omparing the di�erent s hemes in terms ofperforman e and omplexity. In parti ular, the omputational ost of the se-le ted algorithms is pointed out and ways to in rease e� ien y are dis ussed.

Chapter 2Measurement Con�gurationThis thesis ompares equalization s hemes that are suited for a real-timeimplementation in an HSDPA system. Known stru tures as well as newproposals are examined and ompared by measurements over a real hannelat 2.45GHz. The performan e omparison is thus truly representative for anHSDPA implementation.The measurement part of this work has been ondu ted using the MIMOtestbed developed at the Institute of Communi ations and Radio-Frequen yEngineering in SISO operation [1, 2, 3, 4℄. A great advantage of using thisequipment is that it allows for a great amount of �exibility and fa ilitatesdrawing a omparison between di�erent s hemes.2.1 OverviewThis se tion brie�y des ribes the used hardware and its setup. The ne essaryaspe ts of the HSDPA standard are presented and details on the hardware's on�guration are given. A blo k diagram of the hardware on�guration isshown in Fig. 2.1. The setup an be split into three parts, namely the signalgeneration (Matlab prepro essing), the physi al hannel (testbed on�gu-ration), and the re eive pro essing (again performed in Matlab).Signal Generation and Prepro essing In the �rst part of the setup thesignals are generated a ording to the HSDPA standard [5, 6, 7℄. Be-sides the user hannels this in orporates the pilot and the syn hroniza-tion hannel. The �rst is (mainly) used for hannel estimation whereasthe latter is needed to obtain syn hronization at the re eiver. Upongeneration of the hip-spa ed signals, upsampling and �ltering with a4

CHAPTER 2. MEASUREMENT CONFIGURATION 5Signal

GenerationRRCFilter

Inte

rfac

e

LA

N

Mat

lab

Transmit PC

Up-converter

ChannelEmulator

Down-converter

NoiseGenerator

ReceivePC

Inte

rfac

e

ReceiverRRCFilter

Synch-ronization

ChannelEstimation

Signal Generation

RF: 2.45GHzIF: 70MHz IF: 70MHz

Physical Channel

Receive Processing

LA

N

Mat

lab

Spirent TAS4500-FLEX

Noise/Com UFX EbNo

Figure 2.1: Blo k diagram of the measurement on�gurationroot raised osine (RRC) �lter are ne essary in order to bandlimit thesignal to approximately 5MHz.Physi al Channel and Testbed Interfa e In the next step, the transmitsignal is passed on to the transmit PC of the MIMO testbed, whi hin turn generates a physi al signal at an intermediate frequen y of70MHz. This signal is then up onverted to the desired radio-frequen yof 2.45GHz and traverses the Spirent TAS4500-FLEX hannel emula-tor, whi h an be on�gured to emulate various hannel models. Sub-sequently, the signal is down onverted to 70MHz and white Gaussiannoise is physi ally added with a noise generator (Noise/Com UFX-EbNo IF1). Finally the signals are dete ted by the re eive PC of theMIMO testbed and returned to the measurement PC for further pro- essing.Re eive Pro essing Lastly, the fra tionally hip-spa ed samples dete tedby the re eive PC are again pro essed in Matlab. Spe i� ally, it is

CHAPTER 2. MEASUREMENT CONFIGURATION 6�rst ne essary to obtain syn hronization and then to downsample tothe hip-rate. Sin e the hannel is truly unknown due to its physi alnature, it is ne essary to perform hannel estimation for those s hemesthat require this information. At last, the re eiver analysis is performedand parameters su h as the BER are measured. The postpro essing is omputationally expensive and has been performed in luster opera-tion.In the next se tions these parts will be des ribed in detail.2.2 Signal GenerationIn Fig. 2.2 the blo k diagram of the signal generation is shown. HSDPA em-ploys W-CDMA for multiuser ommuni ation and thus in orporates spread-spe trum te hniques into the standard. In fa t, there are three di�erent kindsof signals; besides the user hannels there is a pilot, whi h is used for hannelestimation, and a syn hronization hannel.QPSK Spread

16QAM

16QAM

Spread

Spread

Synch.

Pilot

User data

User data

scc

Figure 2.2: Blo k diagram of the signal generation. The hannels are mod-ulated with either QPSK or 16QAM, spread with Walsh-Hadamard odesand �nally multiplied with the ell's primary s rambling ode. At last, thesyn hronization hannel is added.2.2.1 User ChannelsIn the s ope of this thesis we shall onsider the user hannels to arry randombit streams with a uniform distribution of 0's and 1's. In parti ular, thespe i� s of higher layers need not be taken into a ount, be ause we are only

CHAPTER 2. MEASUREMENT CONFIGURATION 7interested in getting a representative pi ture for the un oded bit error rate ofthe system. In the following the term �number of odes� refers to the numberof a tive user odes on urrently used. This is not ne essarily equal to thenumber of users be ause a single user an be allo ated multiple hannels(spreading odes) in HSDPA.After the generation of the random bit streams, the user hannels aremodulated using the 16QAM onstellation depi ted in Fig. 2.3(b). In thes ope of this thesis it is assumed that all user hannels are modulated with16QAM although in a real HSDPA system this onstellation will only besele ted if the hannel quality is su� iently high. In fa t there is a dire tmapping between the Channel Quality Indi ator (CQI) and the modulationformat and ode-rate to use [5℄. The limitation to 16QAM is justi�ablebe ause we are on erned with devising equalization for high data rate ap-pli ations.Subsequently, the modulated signal is spread with a �xed spreading fa torof 16, i.e. its Fourier bandwidth is in reased by this value. The spreadingoperation is performed with Walsh-Hadamard sequen es being orthogonal toea h other. The zeroth ode (all-one) is used for the pilot hannel.Finally, the user hannels as well as the pilot are added up and s rambledwith the primary s rambling ode of the ell in order to uniquely identify thebase station in use.2.2.2 Pilot ChannelThe pilot hannel is generated similarly to the user hannels and is primarilyused for hannel estimation. In the SISO ase onsidered in this thesis, thepilot is the onstant all-one sequen e mapped with the QPSK onstellationshown in Fig. 2.3(a). Consequently, the onstellation point �−1−j � is alwaystransmitted. The pilot hannel is spread with the zeroth spreading ode (all-one), added to, and s rambled together with the user hannels.2.2.3 Syn hronization ChannelIn ontrast to the other hannels being orthogonal to ea h other, the syn- hronization hannel is neither spread nor s rambled and thus generates in-terferen e [6℄. The transmission of this hannel is ne essary though, as to omplete the ell sear h pro edure, i.e. as to syn hronize the user equipmentto the base station in the �rst pla e.The syn hronization splits up into the primary and the se ondary syn- hronization hannel. The �rst is a deterministi Golay sequen e that is sent

CHAPTER 2. MEASUREMENT CONFIGURATION 810 00

0111

Im{u[k]}

1

1

Re{u[k]}

(a) QPSK onstellation1000

1100 0100

0000

1001

1101

0001

0101

1010

1110

0010

0110

1011

1111

0011

0111

a/3

a/3

a

a

Re{u[k]}

Im{u[k]}

]}

a=1.3416, a/3=0.4472(b) 16QAM onstellationFigure 2.3: Modulation s hemes used for HSDPA. QPSK: bit energy Eb = 2;16QAM: average bit energy E {Eb} = 2.during the �rst 256 hips of ea h slot [6, p.23℄ . Using a orrelation te hniquethe user equipment an thus a hieve slot-syn hronization. The latter is sentto obtain frame syn hronization and to uniquely determine the ode groupof the primary s rambling ode [7, p.60℄. In the s ope of this thesis it is onlyne essary to a hieve slot syn hronization and therefore the se ondary syn- hronization ode is only transmitted for modeling the interferen e it wouldoriginate in a real system.2.2.4 RRC-FilteringSo far the generation of the signals at the hip-rate has been des ribed.However, in order to be able to transmit these signals physi ally, we need toupsample and �lter them with a root raised osine �lter (as spe i�ed in thestandard [8℄). In this way, the signals be ome bandlimited. Sin e the RRC�ltering is performed both at the transmitter and the re eiver, we overall geta raised osine pulse, obeying the Nyquist riterion. The rollo� fa tor for theRRC �lter is hosen as 0.22 a ording to the spe i� ation. Details on theRRC pulse shape an, for instan e, be found in [9℄.

CHAPTER 2. MEASUREMENT CONFIGURATION 92.3 Physi al ChannelIn the next step, the transmit signal thus onstru ted is passed on to thetransmit PC of the MIMO testbed. The testbed has been developed atthe Institute of Communi ations and Radio-Frequen y Engineering and isdes ribed in detail in [1℄. Seen from the measurement PC, the operation ofthe testbed is transparent in that omplex baseband samples are passed onto and returned from the testbed.2.3.1 Testbed Interfa ingThe on�guration of the testbed interfa e on the transmitter side is depi tedin Fig. 2.4. First, it again shows the root raised osine �lter that is needed toappropriately bandlimit the signal. The DAC of the testbed is operating at200MSa/s and thus an overall interpolation fa tor of approximately 48 mustbe hosen (resulting in an input sampling rate of 4.167M /s). The overallinterpolation fa tor was then divided into an RRC interpolation of six and ahardware interpolation of eight within the transmit PC.6 RRC

Pulse shaping

8 DACLAN

Transmit PC

200MSa/s

4.16

7Mcp

s

25M

Sa/

s

physical signal70MHz

Figure 2.4: Transmitter-testbed interfa e.The input hip-rate results to 4.167M /s, sin e the DAC's sampling rateis �xed. Admittedly, this does not orrespond to the UMTS hip-rate of3.84M /s but this in�uen e was deemed negligible throughout this thesis.Resampling with the fra tion 12/13 would orre t for this abberation, but atthe ost of in reased omputation time.2.3.2 Analog Up- and Down onversionThe frequen y onversions (from 70MHz to 2.45GHz and vi e versa) areperformed with up- and down onversion modules, respe tively. These devi eshave been developed and built by R. Langwieser in the s ope of a separatediploma thesis [10℄. The spe i� ations of the up- and down onverters, the�lters, as well as the lo al os illator an be found in his work.

CHAPTER 2. MEASUREMENT CONFIGURATION 102.3.3 Channel EmulationThe measurement on�guration used in this thesis is highly �exible and anbe easily modi�ed to examine di�erent propagation hara teristi s. In thiswork we shall only onsider hannel emulation, but the setup an be easilyextended to allow for measurements over the air interfa e with real antennas.In order to a hieve repeatable measurement results, a Spirent TAS4500FLEX hannel emulator is used and on�gured to emulate the Pedestrian B hannel [11℄, a frequen y sele tive Rayleigh fading hannel model standard-ized by ITU (the spe i� ation for this tapped delay line model is shown inTab. 2.1). Note that the taps of this hannel model do not oin ide withthe sampling instants. As to investigate on this e�e t, a slightly modi�ed hannel was onsidered too, where the taps have been moved su h that they oin ide with the losest hip instant (also shown in Tab. 2.1).An important hallenge when using the hannel emulator are the large�u tuations in amplitude pertaining to the signal. In radio-frequen y engi-neering this is quantitatively analyzed by the so- alled Crest fa tor, whi h isde�ned for the signal x as CF = 20 logx

xrms , (2.1)i.e. as the logarithmi ratio of the signal's peak amplitude to its rms-value1.The Crest fa tor in an HSDPA system is signi� antly elevated sin e thetransmit signal is onstru ted as the summation of independent user han-nels. A ordingly, the Crest fa tor of the transmit signal depends on thenumber of CDMA- odes being simultaneously a tive and ranges from 7dB(one a tive CDMA- ode) to 12 dB (eight a tive CDMA- odes). This leads toproblems in the RF-setup sin e the peaks of the physi al signal must not bedistorted on the one hand, while additionally meeting the hannel emulator'sspe i� ations for the mean power levels (−30 to +5dBm) on the other side.2.3.4 Noise GenerationIn the next step additive white Gaussian noise is added with the Noise/ComUFX-EbNo IF1 noise generator. This is a tually a two-step pro ess sin e thedesired Eb/N0 on the hannel has to be on�gured in the �rst pla e, beforesending the data to be analyzed. This is solved by transmitting only thedesired user signal at �rst and then alibrating the devi e to this power level.Neither syn hronization nor re eive pro essing is ne essary in the �rst step,1rms stands for root-mean-squared

CHAPTER 2. MEASUREMENT CONFIGURATION 11Table 2.1: De�nition of the Pedestrian B hannel model. The relative delayin hips is al ulated for a hip rate of 4.167M /s as used throughout thisthesis. The modi�ed Pedestrian B model is devised su h that the delays areshifted to the adja ent hip instant.Model tap 1 tap 2 tap 3 tap 4 tap 5 tap 6Ped. B Rel. delay/ns 0 200 800 1200 2300 3700Rel. delay/ hips 0 0.83 3.33 5 9.58 15.42mod. Rel. delay/ns 0 240 720 1200 2400 3600Ped. B Rel. delay/ hips 0 1 3 5 10 15Rel. power/dB 0 -0.9 -4.9 -8.0 -7.8 -23.9sin e the noise generator simply alibrates itself to the total input power ofthis referen e measurement. In the next step, all hannels are transmittedand the orre t amount of noise is added to the system.Additionally, using this devi e is only possible if a bandpass �lter with abandwidth of about 20-30MHz is used before interfa ing the re eive PC. Thisis ne essary be ause the noise sour e of the devi e has a �xed bandwidth ofabout 65MHz. Without the bandpass �lter, the noise would lead to aliasingat the re eiver and the Eb/N0 ould no longer be adjusted.2.4 Re eive Pro essingThe re eiving part of the setup is the omputationally most involved one,sin e it has to perform syn hronization and hannel estimation besides pro- essing the data with the sele ted re eiver types.At �rst, the samples are fet hed from the re eive PC in form of Matlabvariables. Then, pre ise syn hronization is a hieved using a orrelation te h-nique, and downsampling to the hip-rate is performed. Additionally, thetruly unknown hannel is estimated sin e this information is required by thenon-adaptive s hemes, namely the RAKE re eiver and the di�erent MMSEre eivers. Finally, the re eiver s hemes are pro essed and the performan e isanalyzed.2.4.1 Testbed Interfa eThe on�guration on the re eive side of the testbed is depi ted in Fig. 2.5. It�rst shows the sampling of the physi al signal at 100MSa/s and a downsam-

CHAPTER 2. MEASUREMENT CONFIGURATION 12pling by a fa tor of 16 impli itly performed by the re eive PC. The resultingsignal at a rate of 6.25MSa/s is transferred over the LAN and upsampled to25MSa/s at the measurement PC. It is then hip-mat hed �ltered with thesame RRC �lter as at the transmitter (thereby reating a raised osine shapein total).16ADC

Receive PC

100MSa/s

LAN 4 RRC 6

Corr.synch. code 6

ph

ysi

cal

sig

nal

70M

Hz

6.25

MS

a/s

25M

Sa/

s

4.16

7Mcp

s

Figure 2.5: Re eiver-testbed interfa e.2.4.2 Syn hronization Pro edureAfter the hip-mat hed �ltering, it is ne essary to obtain a urate syn hro-nization. This is done by orrelating the signal with the known primarysyn hronization ode. Sin e this ode is not orthogonal to the other han-nels, it is (in most ases) only transmitted as a preamble for the testbedto get syn hronized (there is no ontribution to the power allo ation in this ase). The orrelation is performed at a rate of 25MSa/s, i.e. at P = 6 timesthe hip-rate. There is still a random error asso iated with this pro edure,namely the time o�set ǫ takes on values within− Tc

2 · P ≤ ǫ ≤ Tc

2 · P . (2.2)If this pre ision does not su� e, additional upsampling of the signals at25MSa/s by an arbitrary fa tor an be performed. Correspondingly, thebounds on ǫ be ome tighter and the a ura y of the syn hronization in reasesbut at the ost of additional omplexity. A suitable tradeo� has to be foundin this respe t.It should be noted that due to the spreading of the signals, the in�u-en e of non-perfe t syn hronization is less pronoun ed than in systems thatdo not employ spread-spe trum te hniques. Still, a areful onsiderationis indispensable, espe ially for te hniques that use fra tionally hip-spa edsignals.

CHAPTER 2. MEASUREMENT CONFIGURATION 132.4.3 Channel EstimationAfter syn hronization is obtained, the sele ted re eive stru tures an be pro- essed as if we were dealing with a simulation and not a measurement. Spe if-i ally, the setup of the testbed allows for implementing the stru tures inMatlab, speeding up the development time. However, other than in a sim-ulation, the hannel is truly unknown be ause it orresponds to the jointrealization of the hannel emulator together with the radio-frontend. There-fore, we require hannel estimation for those s hemes that do not a omplishthis impli itly, namely the MMSE equalizer and its di�erent modi� ations.As to estimate the hannel we exploit the ontinuously transmitted pilot.Spe i� ally, the stru ture depi ted in Fig. 2.6 was used for this purpose. At�rst, the re eived signal (at the hip-rate) is delayed with a tapped-delay line.Then, the orresponding signals for ea h tap are des rambled and despreadwith the pilot's spreading ode. We thus arrive at an estimate for the pilotsymbol, whi h an in turn be orrelated with its true value (the pilot hannelis perfe tly known). However, this orrelation will be noisy be ause there stillremains some interferen e from other user hannels. Nevertheless, sin e thisinterferen e is zero-mean it an be redu ed by �ltering, e.g. by omputinga moving-average. This results in estimates hi for the hannel's oe� ienthi. A brief mathemati al analysis will be presented in Se . 2.5 following theintrodu tion of the mathemati al signal model.

Tc

*scc

r[i]

Tc

Tc

*scc

*scc

)(0

spc

)(0

spc

)(0

spc

0u

Mov. Average

Mov. Average

Mov. Average

0h

2Lh

1Lh

0u

0u

Figure 2.6: Channel estimation

CHAPTER 2. MEASUREMENT CONFIGURATION 142.4.4 Re eiver ImplementationUpon estimating the hannel, the sele ted re eiver s hemes are pro essed.The implementation of the di�erent methods is mostly based on Matlabm-�les as to redu e the development time. The performan e of the Matlab ode is su� iently fast if loop stru tures an be omitted.The implementation of some adaptive equalizers turns out to be more hallenging, sin e we annot avoid loop stru tures due to the ne essity of ontinuously updating the �lter oe� ients. Thus, C implementations havebeen performed as to shorten the run-time whenever ne essary (a speed-up of 20-30 has been a hieved). Additionally, using the Mex-fun tionalityof Matlab allows for a tight integration with the remaining parts of thesystem.Although a satisfa tory performan e for all re eiving s hemes has beenrea hed, the amount of data asso iated with ea h individual measurement isstill hallenging due to several reasons:Time-Variant Channels When analyzing time-variant hannels, we needto get a representative pi ture of the hannel's statisti . Sin e we aredealing with a physi al hannel this requires us to measure over su�- iently long periods of time and naturally, this results in large amountsof data to be pro essed. For example, an a urate measurement ofa �at Rayleigh fading hannel ne essitates the transmission of about16,350 frames in total. This amounts to about 10GBytes of raw data.BER Quantization When analyzing re eiver stru tures at high values ofEb/N0, we are onfronted with very small bit error rates. Consequently,this requires to analyze large amounts of data as to obtain a represen-tative number of bit errors (and not only one or two within one blo k).Therefore, it is important to in rease the number of transmit blo ksespe ially at high values of Eb/N0.Random Abberations Sin e this thesis deals with measurements of aphysi al hannel, random in�uen es of the RF-equipment lead to �u -tuations in the results. By in reasing the amount of transmitted datawe an average out some of these parasiti e�e ts. For instan e, thenoise generator shows positive as well as negative abberations. By re- on�guring the devi e multiple times during a measurement this e�e tis redu ed.All of the above reasons require to analyze large amounts of data as toget a urate results. This goal an only be a hieved within a reasonable

CHAPTER 2. MEASUREMENT CONFIGURATION 15amount of time if we employ luster pro essing te hniques. Thus, a typi almeasurement involves two steps, namely1. A quisition of the measurement data and storage on a server omputer.A typi al measurement onsists of several GBytes of data. It shouldbe noted that only the syn hronized re eive samples are stored, i.e.syn hronization is only performed on e at the time of the measurement.2. In the next step a luster of omputers onne ts to the data and pro- esses it individually. Hen e the omputation time is redu ed drasti- ally. Additionally, a set of desired re eiver s hemes an be sele ted andpro essed at the same time su h that ommon parts, like the hannelestimation, are only performed on e, again saving omputation time.2.5 Mathemati al Signal ModelIn the above se tion the measurement setup is dis ussed in detail. Thisse tion introdu es the mathemati al notation needed in the following hapterand ombines the parts dis ussed above in a single diagram.The mathemati al signal model is depi ted in Fig. 2.7. In parti ular theuser bit streams are denoted by b1, . . . , bN−1 and b0 is the onstant pilotsequen e. All user hannels are mapped with 16QAM, only the pilot is mod-ulated with QPSK. The signals are spread with Walsh-Hadamard sequen esc(j)sp of length N = 16, only the pilot is spread with a ode length of N0 = 256.S rambling is performed with cs [i]. Then, the signals pass the hannel h[i]( omposed of the radio frontend and the hannel emulator). Additive whiteGaussian noise v[i] is then added, leading to the re eive signal r[i]. Theequalized re eive signal shall be denoted as y[i]; this signal is des rambled,despread and de oded to get estimates for the transmitted bits. In the fol-lowing, the length of the hannel in hips will be denoted as Lh; Lf standsfor the length of the equalizer in taps.Due to the spreading operation it is important to di�erentiate between sig-nals at the symbol-rate and at hip-rate. Spe i� ally, the signal u[i] ontainssymbols and is thus indexed at the symbol-rate. With the Walsh-Hadamardspreading odes c

(j)sp for the j-th user we thus �nd the hip-sampled signals[i] = cs [i] J−1∑

j=0

c(j)sp [i]uj

[⌊iN

⌋], (2.3)where ⌊·⌋ denotes the `�oor' operation and c

(j)sp [i] = c(j)sp [i mod N ]. Thesyn hronization ode has been ex luded from onsideration.

CHAPTER 2. MEASUREMENT CONFIGURATION 16h[i]

v[i]

s[i]

r[i]y[i]

QPSKu0[i]

u1[i]

uJ-1[i]

][0 ib

16QAM

16QAM

Synch.

f H[i]

QPSKû0[i]

û1[i]

ûJ-1[i]

16QAM

16QAM

scc

scc

][1 ib

][ibJ 1

)1(spc

)0(spc

)( 1Jspc

)0(spc

)1(spc

][ˆ0 ib

][ˆ1 ib

][ˆ ibJ 1

)( 1JspcFigure 2.7: Blo k diagram of the signal generation.A ording to Fig. 2.7 we immediately �nd that the re eived signal obeysthe relation

r[i] =

Lh−1∑

l=0

h[l]s[i − l] + v[i] =

Lh−1∑

l=0

h[l]J−1∑

j=0

cs [i − l]c(j)sp [i − l]uj

[⌊i−lN

⌋]+ v[i](2.4)The above signal an be used for estimating the hannel by des rambling,despreading with the pilot's Walsh-Hadamard ode, and orrelating with the(known) pilot symbol, namely

h[l] =1

|u0[i]|2u∗

0[i]N−1∑

k=0

c(0)sp [k]c∗s [iN+k+l]r[iN+k+l], i = 0, 1, 2, . . . . (2.5)2.6 SummaryIn this se tion the measurement setup has been des ribed in detail. Spe i�- ally, the setup is broken up into su in t parts, namely the signal generation,the physi al hannel, and the re eive pro essing. The importan e of on�g-uration parameters is dis ussed and implementation aspe ts are onsidered.Finally, a mathemati al signal model is presented preparing for the analyti alanalysis of the next hapter.

Chapter 3Equalizer AnalysisIn this se tion a mathemati al analysis of the re eiver stru tures under on-sideration is given. At �rst, the onventional RAKE re eiver is addressed andits limitations are shown. Then, the hip-spa ed MMSE equalizer is intro-du ed and some modi� ations are dis ussed (fra tionally hip-spa ed opera-tion, symbol-rate MMSE equalizer). Subsequently, adaptive te hniques arepresented, and their design parameters are analyzed. Finally, modi� ationsof the RAKE re eiver (both adaptive and non-adaptive) are presented and ompared to the other s hemes.3.1 RAKE Re eiverThe onventional RAKE re eiver employs a tapped delay line stru ture toapproximate a mat hed �lter re eiver for the hannel. In Fig. 3.1 this on eptis illustrated. At �rst, the input signal r[i] is delayed by multiples of the hip duration Tc, i.e. by a tapped delay line. However, note the di�eren eto the tapped delay line model of the hannel, where the delays were not onstrained to multiples of the hip-duration. Thus, the mat hed �lter ofthe RAKE re eiver is only approximate even if we assume perfe t hannelestimation.In the next step, the delayed signals are des rambled with c∗s and despreadwith the user's spreading ode1 (c(j)sp )∗ = c

(j)sp resulting in symbol estimates.Finally, these estimates are ombined with oe� ients al that are onstru tedfrom the hannel estimation to form a maximum ratio ombining (MRC)s heme.1The spreading ode is a real-valued sequen e. Therefore the onjugation an be omitted.17

CHAPTER 3. EQUALIZER ANALYSIS 18Tc

a0*scc

r[i]

Tc

Tc

aLa-2*scc

aLa-1*scc

Chan. Est.

)( jspc

)( jspc

)( jspc

ûj[i]

Figure 3.1: Blo k diagram of the onventional RAKE re eiver.Mathemati ally, we express this for the j-th user ode asuj[i] =

La−1∑

k=0

ak(c(j)sp )T (c∗s [iN ] ⊙ riN−τk

) , (3.1)where ⊙ denotes element-wise multipli ation,riN =

[r[iN ], r[iN − 1], . . . , r[iN − N + 1]

]T (3.2)is a ve tor of the last N re eived samples, andc∗s [iN ] =

[[c∗s [iN ], c∗s [iN − 1], . . . , c∗s [iN − N + 1]

]T (3.3) ontains the orresponding elements of the s rambling ode. The term τkdenotes the �nger pla ement, i.e. the k-th �nger orresponds to a delay ofτk hips. We an rewrite (3.1) to

uj[i] =La−1∑

k=0

ak(c(j)iN)H

riN−τk(3.4)by introdu ing

c(j)iN = c

(j)sp ⊙ cs [iN ] , (3.5)

CHAPTER 3. EQUALIZER ANALYSIS 19a time-variant ode ve tor that ombines the des rambling and despreadingoperation.Ea h of the paths in Fig. 3.1 is alled a �nger of the RAKE re eiver. Thetotal number of �ngers La allo ated to this re eiver is an important designparameter. Ultimately, it must be hosen large enough to apture most ofthe hannel's power, but small enough as not to pi k up too mu h additionalnoise.3.2 Chip-Rate MMSE EqualizerThe MMSE equalizer uses the estimated hannel impulse response h[i] to ompute the equalizer oe� ients f su h that the mean square error of theequalized re eive signal y[i] is minimum, i.e.J1(f) = E{∣

∣fHri − si−τ

∣∣2} (3.6)with

ri =[r[i], r[i − 1], . . . , r[i − Lf + 1]

]T (3.7)Note that the above equation takes a delayed version of the transmitted hip sequen e si−τ as the referen e (see Fig. 2.7). Emphati ally, not theuser symbols uj[i] are used be ause this would lead to a s rambling odedependent ost-fun tion (as to be dis ussed in Se . 3.4).Following the analysis of [12℄ the above equation an be reformulated toJ1(f) = E{(

fHri − si−τ

) (r

Hi f − s∗i−τ

)}. (3.8)The re eived signal r[i] is related to the transmitted hip stream s[i] and thenoise v[i] as follows

ri =

h0 · · · hLh−1 0. . . . . . . . .0 h0 · · · hLh−1

si + vi = Hsi + vi , (3.9)where si, vi have been de�ned analogously to ri.Substituting (3.9) into (3.8) yields

J1(f) = fHHE{

sisHi

}H

Hf + f

HE{viv

Hi

}f

− fHHE{

sis∗

i−τ

}− E{

si−τsHi

}H

Hf + E{

|si−τ |2}

= fH

(σ2

sHHH + σ2

vI)f − σ2

s fHHeτ − σ2

seTτ H

Hf + σ2

s ,

CHAPTER 3. EQUALIZER ANALYSIS 20where eτ denotes a unit ve tor with a one at the τ -th position. In the abovedevelopment we assume that s[i] is independent and identi ally distributedand that v[i] is white Gaussian noise, whi h is ne essary for the followingassumptions to hold true E{sis

Hi

}= σ2

sI (3.10)E{viv

Hi

}= σ2

vI (3.11)E{sis

∗

i−τ

}= σ2

seτ (3.12)E {si} = 0 (3.13)E {vi} = 0 . (3.14)Taking the gradient with respe t to f of the above expression gives∇J1(f) =

∂J1

∂f∗=

(σ2

sHHH + σ2

vI)f − σ2

sHeτ . (3.15)Setting (3.15) equal to zero and solving for f �nally yieldsf = σ2

s

(σ2

sHHH + σ2

vI)−1

Heτ . (3.16)In order to apply the above s heme, it is not only ne essary to estimatethe hannel, but also to invert a matrix of size Lf ×Lf , whi h is an expensiveoperation requiring (Lf )3 operations in a dire t implementation.There are numerous ways to redu e the omplexity of an a tual imple-mentation [13℄. First, we an exploit the Toeplitz stru ture of the matrix H,whi h enables us to perform the matrix inversion with quadrati (instead of ubi ) omplexity. It should be noted that H is only Toeplitz in the hip-spa ed ase; in the fra tionally hip-spa ed ase to be onsidered in the nextse tion H will be shown to have only blo k Toeplitz stru ture. However, evenin this ase the omplexity an be redu ed in a similar way.Besides exploiting the Toeplitz stru ture, it is also possible to apply otherte hniques to redu e the omputational omplexity. These in lude the usageof polyphase �lters and the introdu tion of Gauss-Seidel iterations, respe -tively [13℄.3.3 Fra tionally Chip-Spa ed MMSE EqualizerThe equalizer presented in the above se tion runs at the hip-rate. Runningthe equalizer at a higher rate, for instan e with a sampling rate of Tc/2 or

Tc/3 may improve the results.

CHAPTER 3. EQUALIZER ANALYSIS 21It is possible to devise the equalizer very similar to the last se tion. How-ever, we have to modify the relation between the re eived signal r[i] and thetransmitted signal s[i] sin e we are now dealing with an M times oversampledsystem. We still haveri = Hsi + vi , (3.17)but H is now de�ned di�erently [12℄, namely

H =

h0 · · · hLh−1 0. . . . . . . . .0 h0 · · · hLh−1

, (3.18)where

hi = [hiM , hiM+1, . . . , hiM+M−1]T . (3.19)This rede�nition is ne essary be ause we an essentially treat the M timesoversampled re eive signal as a ombination of M individual hannels [14℄.To illustrate this, let's fully write the matrix H for M = 2

H =

h0 h2 h4 h6 . . . hLh−1 0h1 h3 h5 h7 . . . hLh−2 0. . . . . . . . . . . . . . . . . .0 h0 h2 h4 h6 . . . hLh−1

0 h1 h3 h5 h7 . . . hLh−2

. (3.20)Additionally, the assumption made in (3.11) does not hold true any more.Spe i� ally, the noise v[i] is not un orrelated at the re eiver be ause the pulseshape as de�ned by the RRC �lters is Nyquist only at the hip-rate andtherefore the orrelation is zero only for hip-spa ed samples. Introdu ingthe signal w[i] as the �ltered noise, we an writew[i] = (hRRC ∗ v)[i] ⇒ wi = HRRCvi , (3.21)where w and v are ve tors of appropriate length and HRRC is a matrixdenoting the onvolution with the impulse response of the RRC �lter (de�nedsimilar to (3.18)). We thus arrive at,E{

wiwHi

}= HRRCE{

vivHi

}H

HRRC = σ2vHRRCHHRRC = σ2

vRRRC . (3.22)The other assumptions (3.10),(3.12) do not have to be modi�ed for the fra -tionally hip-spa ed equalizer. We an thus �nally writef = σ2

s

(σ2

sHHH + σ2

vRRRC)−1

Heτ . (3.23)

CHAPTER 3. EQUALIZER ANALYSIS 223.4 Symbol-Rate MMSE EqualizerWhereas the ost fun tion employed in the last se tions aims at restoringthe hip-spa ed signal s[i] at best, this is not the only possible meaningful riterion. In fa t, we an also demand that the symbol streams mat h asgood as possible, i.e.J2(f) = E{

|u0[i] − u0[i]|2}

. (3.24)The estimate u0[i] for the pilot symbol evaluates tou0[i] = c

HiN

fH

0

fH . . .

0 fH

︸ ︷︷ ︸

Lf×N+Lf−1

riN (3.25)with

riN =[r[iN ], r[iN − 1], . . . , r[iN − N − Lf + 2]

]. (3.26)For fa ilitating the analysis we rewrite this to

u0[i] = fH

cHiN 0

cHiN . . .

0 cHiN

︸ ︷︷ ︸

CiN

riN = fHCiNriN . (3.27)

The true pilot symbol is related to the hip-spa ed signal as followsu0[i] = c

HiN siN , (3.28)where

siN =[s[iN ], s[iN − 1], . . . , s[iN − N + 1]

]T. (3.29)The relation between the transmitted and the re eived signal is again de-s ribed by (3.9)

riN =

h0 · · · hLh−1 0. . . . . . . . .0 h0 · · · hLh−1

siN + viN = HsiN + viN ,

CHAPTER 3. EQUALIZER ANALYSIS 23note however that siN has a di�erent length than si for all matrix produ tsto be omputable.Using the above expressions yieldsE{(

cHiN siN − f

HCiN(HsiN + viN)

) (

sHiN ciN − (HsiN + viN)H

CHiN f

)}

.(3.30)and an be reformulated by using similar assumptions as in Se . 3.2J2(f) = f

HCiNE{

(HsiN + viN)(HsiN + viN)H}

CHiN f (3.31)

− fHCiNE{

(HsiN + viN )sHiN

}ciN (3.32)

− cHiNE{

siN(HsiN + viN)H}C

HiN f (3.33)

+ |u0[i]|2 . (3.34)Evaluating the expe tation operator yieldsJ2(f) = f

HCiN(σ2

sHHH + σ2

vI)CHiN f (3.35)

− fHCiNHRsciN (3.36)

− cHiNR

Hs H

HC

HiN f (3.37)

+ |u0[i]|2 , (3.38)whereRs = E{

siN sHiN

}. (3.39)Taking the gradient with respe t to f for the above expression gives

∇J2(f) = CiN(σ2sHH

H + σ2vI)C

HiN f − CiNHRsciN = 0 . (3.40)Solving the above equation �nally yields

f =(

CiN(σ2sHH

H + σ2vI)C

HiN

)−1

CiNHRsciN . (3.41)The above equation is a lot more ompli ated than the solution for the hip-spa ed MMSE equalizer (3.16) and depends on the time-variant odeve tor ciN (due to the s rambling ode being in orporated into the ost-fun tion). Consequently, an implementation of the above equation is notvery attra tive.However, this does not mean that the ost-fun tion (3.24) is useless. Onthe ontrary, the next se tion will show that this riterion an be easilyimplemented in an adaptive fashion. Sin e no matrix inverses have to be omputed in this ase, the dependen e on the ode ve tor is less signi� ant.

CHAPTER 3. EQUALIZER ANALYSIS 243.5 Adaptive EqualizationAdaptive equalizers are attra tive te hniques be ause they require very little omputational ost. Spe i� ally, they do not rely on ostly matrix inversionsthat are prone to hinder real-time implementations. Additionally, adaptivete hniques are able to tra k time-variant hannels, again an implementationadvantage. The main drawba k of adaptive solutions is that they optimizethe ost-fun tion only iteratively, making the onvergen e speed a very im-portant design parameter.In the following, sele ted adaptive te hniques are presented that use dif-ferent riteria of optimality. In parti ular, we onsider pilot-assisted s hemes,whi h use the ontinuously transmitted pilot hannel for updating the oef-� ients as well as a blind s heme deploying a onstant modulus argument.3.5.1 Symbol-Rate Adaptive EqualizerThe symbol-rate adaptive equalizer uses the ontinuously transmitted pilot- hannel to update the equalizer oe� ients. Spe i� ally, it des rambles anddespreads the equalized re eive signal and ompares it to the (known) pilotsymbol. Mathemati ally, this is formulated by the ost fun tionJ2(f) = E{

|u0[i] − u0[i]|2}

,whi h is identi al to (3.24) already used in Se . 3.4. However, sin e opti-mization is performed adaptively, the ost fun tion's dependen e on the timevarying ode ve tor is not signi� ant.f H[i]

][icsc

–

][iu0

)0(spc

r[i]

despreadother codesFigure 3.2: Blo k diagram of the symbol-rate pilot-assisted adaptive equal-izer.In order to minimize the ost-fun tion we employ a steepest-de ent te h-nique (e.g. [15℄)

f(i+1) = f

(i) − µ∇J2(f(i)) . (3.42)

CHAPTER 3. EQUALIZER ANALYSIS 25Substituting the estimated pilot symbol u0[i] (3.27) and evaluating thegradient in (3.42) with respe t to f yields∇J2(f) ,

∂J2

∂f∗= −E{

(u0[i] − u0[i])∗CiNriN

}

. (3.43)The expe tation operator in (3.42) and (3.43) stems from the analyti al anal-ysis. The implementation of this algorithm approximates the expe tation bythe instantaneous value. The step-size µ in the above formulas is hosensu h that the resulting bit error rate is smallest. Naturally, a small step sizeleads to an in reased onvergen e time, an in�uen e that will arefully be onsidered in Ch. 4.It has to be pointed out that in ontrast to the hip-spa ed MMSE equal-izer, this method performs the equalizer's update at the symbol rate, whi his N0 = 256 times slower for the pilot hannel. Naturally, this may degradethe performan e, espe ially for fast varying hannels.A possible approa h to mitigate this problem is to despread the pilot- hannel with a fa tor N = 16 instead of N0 = 256. This is indeed possiblebe ause the pilot hannel is spread with the zeroth ode orresponding tothe all-one sequen e. It is thus possible to use a shorter spreading ode oflength 16 (also all-one), while retaining orthogonality to the user spreading odes.3.5.2 Chip-Rate Adaptive EqualizerThe pilot-assisted adaptive equalizer des ribed in Se . 3.5.1 updates its o-e� ients at the symbol-rate, i.e. only every N = 16 or N0 = 256 hips. Forthis reason [12℄ proposes that the despreading operation be repla ed witha low-pass �lter. Indeed, this is possible be ause the pilot sequen e (andthus its symbol stream) is onstant and the interferen e is zero-mean. The ost-fun tion an be formulated asJ3 = E{

|z[i] − γ|2}

, (3.44)where z[i] is de�ned as shown in Fig. 3.3. The hoi e for the low-pass�lter A(z) is a deli ate question, be ause it represents an important design onsideration. Ultimately, there is a fundamental tradeo� between residualMAI after the �lter and the algorithm's ability to tra k time-variant hannels.An adequate tradeo� between these two extremes has to be found in orderto get a good performan e. In the s ope of this thesis we shall assume the�rst order low-pass �lterA(z) =

1 − ρ

1 − ρz−1(3.45)

CHAPTER 3. EQUALIZER ANALYSIS 26f H[i] A(z)

][icsc

–r[i] ][iz

despreadother codesFigure 3.3: Blo k diagram of the hip-rate adaptive equalizer.with the design parameter ρ. If ρ is hosen lose to unity then the �lter'se�e t is large, the opposite is true if ρ is hosen lose to zero. The resultingupdate equations presented in [12℄ are shown for the sake of ompleteness,

ai = (1 − ρ)ric∗s [i − τ ] + ρai−1 (3.46)

e[i] = (1 − ρ)(fHric

∗s [i − τ ] − γ) + ρe[i − 1] (3.47)f(i+1) = f

(i) − µaie∗[i] . (3.48)3.5.3 Constant Modulus AlgorithmThe adaptive equalization s hemes presented above use the ontinuouslytransmitted pilot hannel with known pilot symbols to update the equalizer oe� ients. In ontrast, the onstant modulus algorithm is a blind te hniqueexploiting the fa t that modulation s hemes su h as QPSK have a onstantmodulus. This an be used for implementing the following ost-fun tion,where γ =

√2 is the onstant modulus (see Fig. 2.3(a))

J4(f) = E{(|u0[i]|2 − γ2

)2} (3.49)This means that the pilot symbols, whi h are mapped with a QPSK onstel-lation, are for ed to lie on the unit ir le. The ost-fun tion an be minimizedadaptively by again using steepest-des ent, i.e.

f(i+1) = f

(i) − µ∇J4(f(i)) (3.50)

CHAPTER 3. EQUALIZER ANALYSIS 27The estimate for the pilot symbol is again equal to (3.27). We thus �nd thegradient in (3.50) to be∇J4(f) = 2E{

(|u0[i]|2 − γ2)∂

∂f∗u0[i]u

∗

0[i]

}

=

= 2E{

(|u0[i]|2 − γ2)∂

∂f∗f

HCiNriNr

HiNC

HiN f

}

=

= 2E{

(|u0[i]|2 − γ2)CiNriNrHiNC

HiN f

}

=

= 2E{

(|u0[i]|2 − γ2)u∗

0[i]CiNriN

}

.When in orporating CMA into the HSDPA standard, it is only possible touse the pilot hannel for updating the equalizer oe� ients as indi ated in theabove formulas. This restri tion stems from the fa t that the user hannelsare modulated with 16QAM, a onstellation that does not have a onstantmodulus. Therefore the s heme applied in this thesis annot be ompareddire tly to multiuser CMA as for instan e outlined in [16℄.Further, it should be noted that due to the stru ture of the ost-fun tion(3.49) there is no unique solution for the equalizer oe� ients [16℄. Spe if-i ally, the resulting signal onstellation still appears tilted, whi h an beadjusted by estimating this angle of rotation and orre ting for it by using ablo k of equalized data. The error in urred by this last adjustment is negli-gible if the blo k length is hosen su� iently long (one frame in the s ope ofthis thesis).3.6 Modi�ed RAKE Stru turesThe onventional RAKE re eiver as presented at the beginning of this thesisis tailored to ompensate for the e�e ts of multi-path hannels. In fa t, itis optimal if W-CDMA is not employed and the hannel estimation is per-fe t, be ause then the RAKE re eiver is indeed the mat hed �lter. However,this s enario does not apply to HSDPA. Instead, the multi-tap hara teris-ti s inevitably lead to interferen e generated from other (or even one's own) hannel, and sin e this interferen e is not taken into a ount the performan eof the onventional RAKE is severely limited. In the following, two methodsare presented, whi h modify the RAKE re eiver su h that the ombining isperformed with respe t to a more e�e tive riterion.

CHAPTER 3. EQUALIZER ANALYSIS 283.6.1 MMSE-RAKE Re eiverA �rst approa h is to impose a ost-fun tion on the RAKE re eiver that issimilar to the MMSE equalizer. We an demandJ5(a) = E

∣∣∣∣∣si −

La−1∑

k=0

akri−τk

∣∣∣∣∣

2

= E{∣

∣aHri − si

∣∣2}

, (3.51)where aH denotes the ombining oe� ients (see Fig. 3.1) and ri is the ve torof re eived samples that re�e ts the orresponding �nger pla ement. Nat-urally, we are interested in hoosing the number of �ngers La as small aspossible. The solution to the above ost-fun tion an be found very similarto the MMSE derivation.Spe i� ally, we arrive at

a = σ2s

(σ2

sHHH + σ2

vI)−1

Heτ (3.52)whi h has the same notation as (3.16). However, the matrix H must now berede�ned a ording to the �nger pla ement. We getH =

h0 · · · hLh0 0

0 0 h0 · · · hLh... ... ... ... ...0 h0 · · · hLh

0

, (3.53)if the �nger pla ement is hosenτ0 = 0, τ1 = 2, . . . , τLa−1 = 1 . (3.54)Obviously, this means that the Toeplitz stru ture is lost even if the �ngerpla ement is of in reasing order. While this ompli ates the use of the e�- ient stru tures outlined in Se . 3.2, it redu es the size of the matrix to beinverted to La × La instead of Lf × Lf . This is a signi� ant improvement if

La is indeed hosen small ompared to Lf .3.6.2 Adaptive RAKE Re eiverA symbol-rate adaptive modi� ation of the onventional RAKE re eiver isshown in Fig. 3.4. The ombining oe� ients al are now hosen su h thatthe ost-fun tionJ6(al) = E

∣∣∣∣∣u0 −

La−1∑

k=0

akcHiNriN−τk

∣∣∣∣∣

2

(3.55)

CHAPTER 3. EQUALIZER ANALYSIS 29Tc

a0*scc

r[i]

Tc

Tc

aLa-2*scc

aLa-1*scc

û0[i]

u0

–

)(0spc

)(0spc

)(0spc

Figure 3.4: Blo k diagram of the adaptive RAKE re eiver.is minimized. The adaptation is again performed with respe t to steepest-des ent, i.e.a

(i+1)l = a

(i)l − µ

∂J(i)6

∂al

. (3.56)The derivative in the above equation evaluates to∂J6

∂al

= E{(

u0 −La−1∑

k=0

akcHiNriN−τk

)∗

∂

∂al

(

u0 −La−1∑

k=0

akcHiNriN−τk

)}

=

= E{(

u0 −La−1∑

k=0

akcHiNriN−τk

)∗

cHiNriN−τl

}

. (3.57)3.7 SummaryAs to wrap up the mathemati al analysis presented so far, the equalizations hemes are ategorized in Fig. 3.5 a ording to both their rate (symbol-or hip-rate) and their way of minimizing the ost-fun tion (adaptive or bymatrix-inversion). The lassi� ation in Fig. 3.5 underlines that non-adaptives hemes are predestined for hip-rate implementation, sin e the ost-fun tionis thus not depending on either the spreading or the s rambling ode. Onthe other hand, a non-adaptive, symbol-rate implementation depends on thes rambling ode and is therefore less pra ti able.

CHAPTER 3. EQUALIZER ANALYSIS 30On the other hand, adaptive s hemes are typi ally well-suited for asymbol-rate implementation. The reason for this lies in the need for a signalwith only little MAI orruption for updating the equalizer oe� ients. At the hip-rate su h a signal an only be attained by implementing a low-pass �lteras explained in Se . 3.5.2. On the ontrary, at the symbol-level su h signalsare readily available be ause the despreading operation partially suppressesMAI (although not perfe tly).

—RAKE receiver—MMSE equalizer—(chip-rate)—Fractionally chip— spaced MMSE—MMSE-RAKE

Chip-rate Symbol-rate Chip-rate Symbol-rate

Non-adaptive Adaptive

Equalizer

—MMSE equalizer—(symbol rate)—CMA equalizer

—Adaptive—symbol-rate eq.—Adaptive CMA —equalizer—Adaptive RAKE

—Adaptive —chip-rate eq.

Figure 3.5: Categorization of the presented s hemes. The non-adaptive CMAequalizer as well as the symbol-rate MMSE equalizer have not been imple-mented but are shown for ompleteness.

Chapter 4Measurement ResultsThis hapter presents the measurement results obtained in the s ope of thisthesis. Before using the setup, its orre t operation is veri�ed extensively.These tests shall be explained in the �rst part of this hapter. Subsequently,the performan e of the equalization s hemes under onsideration is omparedand the in�uen e of ertain design parameters is explained.4.1 Measurement Veri� ationThe measurement veri� ation pro ess is separated into several distin tivesteps. At �rst, the spe i� ations for the transmit signal are examined, with-out using the re eiving part of the system. This analysis is mainly based onthe frequen y hara teristi s of the signal. Se ondly, the power levels at in-termediate steps in the transmission hain are measured and ompared to thespe i� ation of the RF devi es. Spe i� ally, we have to take are that higher-order intermodulation produ ts stay negligible and that the spe i� ations ofall devi es are met. Finally, the omplete measurement setup is tested bymeasuring the BER of idealized hannels, namely an AWGN hannel and a�at (1-tap) Rayleigh fading hannel, respe tively.4.1.1 Pulse ShapeAt �rst, the pulse shape of the physi al hannel at 2.45GHz is measuredright after the hannel emulator using a spe trum analyzer. The pulse shapeat this point in the transmission hain is root raised osine, sin e the signalhas yet been �ltered at the transmitter only (after the re eive �lter the pulseshape is raised osine). The results of this measurement are shown in Fig. 4.1as a s reen shot of the spe trum analyzer. The bandwidth of the signal is31

CHAPTER 4. MEASUREMENT RESULTS 32indeed 4.167M /s · 1.22 = 5.084MHz (the fa tor 1.22 a ounts for the rollo�fa tor). In Fig. 4.1 the spe trum has been averaged as to obtain a smootherpi ture and is ompared to the analyti al pulse shape. Indeed, there is a verygood �t that veri�es the orre t fun tionality of the transmitter with respe tto the frequen y hara teristi s of the signal.

2.445 2.45 2.455−90

−80

−70

−60

−50

−40

−30 RBW = 100kHz VBW = 1kHz SweepTime = 0.2s

f/GHz

P/

dB

m

Figure 4.1: Measurement of the pulse shape after the hannel emulator. Thebandwidth equals 4.167M /s·1.22 = 5.084MHz.The `bumps' in Fig. 4.1 lose to 2.45GHz orrespond to the syn hroniza-tion hannel (transmitted with 10% of the total power), whi h has a smallerbandwidth sin e it is not spread.4.1.2 Power Levels in the Transmission ChainSe ondly, it is ne essary to arefully observe the power levels at intermediatesteps in the transmission hain. We have to take are that signi� ant inter-modulation is ir umvented and that all spe i� ations for the RF-equipmentare met. This implies that the optimal setup depends on some design param-eters su h as the number of a tive odes and the hannel's hara teristi s.

CHAPTER 4. MEASUREMENT RESULTS 33In this se tion the design onsiderations shall be explained, detailed blo kdiagrams of the setup are shown in Appendix A.Number of Codes The number of odes in�uen es the optimal on�gura-tion insofar as the Crest fa tor (see Se . 2.3.3) of the transmitted signal hanges. As for all CDMA systems, in reasing the number of a tive odes leads to a higher Crest fa tor. This not only brings about di� ul-ties in the design of the RF-equipment but also ne essitates a arefulsetup: the hannel emulators, for instan e, must be on�gured su hthat peaks of the signal are not distorted while keeping the averagesignal power within the spe i� ation.Channel Chara teristi s In the s ope of this thesis stati as well as fading hannels are onsidered. Due to the fading the power level after the hannel varies a ording to the hannel's statisti , in our ase a ordingto a Rayleigh distribution. The resulting �u tuations of the signal arein the order of +10/�30 dB. Thus the setup has to be on�gured su hthat the spe i� ations are met for all power levels within this range.Additionally, in the ourse of measuring the BER for a �at Rayleighfading hannel (see next se tion) the statisti of the hannel emulator is an-alyzed. This is a omplished by saving the hannel estimates and generatinga histogram. This graph is shown in Fig. 4.2 together with the shape of aRayleigh distribution �tted to the measurement data.4.1.3 BER for Idealized ChannelsFinally, the measurement setup has been tested by on�guring the hannelemulator to idealized hannels, namely an AWGN hannel and �at (1-tap)Rayleigh fading hannel, respe tively.In the �rst ase we an dire tly ompare the measured urve for the biterror rate with its analyti al ounterpart. The nearest neighbor approxima-tion to the bit error rate of a 16QAM onstellation, transmitted through anAWGN hannel is easy to �nd (see e.g. [9℄)Pe,AWGN = P(E|16QAM) ≈ 3

4Q

(√SNR5

)

=3

4Q

(√

4Eb

5N0

)

, (4.1)where SNR = Es/N0 denotes the signal to noise ratio with respe t to thesymbol energy.

CHAPTER 4. MEASUREMENT RESULTS 34

0 1 2 3 4 5 6

x 107

0

20

40

60

80

100

120

140

160

180

200

|h0|

his

tog

ram

Figure 4.2: Histogram of the hannel oe� ient for a �at Rayleigh fading hannels. A total number of 7,000 estimates were utilized.Obtaining an analyti al result in the ase of a �at Rayleigh fading hannelrequires more e�ort. Following the analysis presented in [9℄, we �rst de�ne avariable signal to noise ratio after the hannel,SNR =a2Es

N0

, (4.2)where a is a Rayleigh distributed random variable. With this de�nition, we an immediately write down the bit error rate onditioned on a and thenremove the onditioning by integrating over the probability density fun tionof a, namelyPe,Rayl =

∫∞

0

P(E|a = α)f(α)dα ≈∫

∞

0

3

4Q

(√

4α2Eb

5N0

)

α

σ2e−α2/2σ2

dα .(4.3)Solving this integral similar to [9℄ yieldsPe,Rayl ≈ 3

8

(

1 −√

2Eb/N0

5 + 2Eb/N0

)

. (4.4)

CHAPTER 4. MEASUREMENT RESULTS 35The analyti al results gained above are ompared to the measurementresults in Fig. 4.3 and Tab. 4.1. Indeed, there is a very good mat h be-tween theory and measurement. The largest abberation of interest o urs atEb/N0 = 13dB and amounts to 0.15 dB. At very small values of Eb/N0 theerror is larger than this value, but this is partly due to the analyti al resultsbeing ina urate sin e the nearest neighbor approximation is not justi�ed forsmall Eb/N0. Moreover, this region is not of pra ti al interest anyway.It is also interesting to note that the equalizer shows a slightly betterperforman e than the RAKE re eiver at high Eb/N0. Theoreti ally, bothre eivers should exhibit the same performan e, be ause the orthogonality ofthe odes is not destroyed and hen e no MAI is brought about. However,sin e the results are based on measurements (and we an thus assume thatthere remains some distortion) the equalizer seems to partly orre t for theseparasiti e�e ts.

−2 0 2 4 6 8 10 12 1410

−6

10−5

10−4

10−3

10−2

10−1

100

Eb/N0 [dB]

BE

R

Static, RAKEStatic, MMSE Eq.Static, Analytical resultFlat Fading, RAKEFlat Fading, MMSE eq.Flat Fading, Analytical result

Figure 4.3: Measured BER for an AWGN and a �at Rayleigh fading hannel.The results are ompared to the analyti al formulas (4.1) and (4.4). Thelargest aberration of interest o urs at Eb/N0 = 13 dB.

CHAPTER 4. MEASUREMENT RESULTS 36Table 4.1: Quantitative omparison of Fig. 4.3. BER at given Eb/N0.Eb/N0/dB -3 0 3 6 9 12Stati 1-tap hannelAnalyti al 0.197 0.139 0.077 0.027 4.4·10

−3 1.4·10−4RAKE 0.212 0.145 0.080 0.029 0.004 1.4·10−4MMSE Eq. 0.212 0.144 0.081 0.029 0.005 1.4·10−4Flat Rayleigh fading hannelAnalyti al 0.222 0.175 0.125 0.081 0.048 0.026RAKE 0.241 0.185 0.141 0.087 0.051 0.030MMSE Eq. 0.236 0.182 0.140 0.085 0.050 0.030Table 4.2: Quantitative omparison of Fig. 4.3. Loss/dB in Eb/N0 at aspe i� BER; the analyti al results (4.1) and (4.4) are taken as referen e.Stati 1-tap hannelBER 0.1 0.01 5·10

−3 1·10−3 5·10

−4RAKE 0.14 0.07 0.02 0.04 0.16MMSE Eq. 0.15 0.06 -0.01 -0.03 0.07Flat Rayleigh fading hannelBER 0.2 0.1 0.05 0.03 0.02RAKE 0.51 0.46 0.20 0.56 0.62MMSE Eq. 0.45 0.37 0.14 0.48 0.504.2 Measurement ResultsThe last se tion illustrated that with the measurement setup at hand we anindeed a hieve very a urate results for idealized hannels. In this se tion wedeal with multi-tap hannels that bring about additional interferen e (MAI).In this ase the onventional RAKE re eiver is not optimal any more and thuswe an expe t a signi� ant performan e gain asso iated with implementingan equalizer.This performan e gain is quantitatively analyzed in the following. Ad-ditionally, we also present how to hoose various design parameters su hthat a good tradeo� between performan e and omplexity is stri ken. Subse-quently, sele ted adaptive te hniques requiring little omplexity are presentedand ompared to the MMSE equalizer. Finally, the tra king behavior of the

CHAPTER 4. MEASUREMENT RESULTS 37adaptive algorithms is ompared for time-variant hannels. A summary un-derlines the results of this hapter.4.2.1 MMSE Equalizer vs. RAKE Re eiverAt �rst, the MMSE equalizer is ompared to the onventional RAKE re eiverin order to examine how mu h performan e gain an be expe ted. The omparison is drawn for a stati Pedestrian B hannel �rst; then the analysisis extended to a model with ontinuous fading.Another important design parameter is how to hoose the power allo a-tion. In the following, if not denoted otherwise, 80% of the power will beallo ated to all a tive user hannels and 20% to the pilot hannel. The syn- hronization hannel is not transmitted together with the HSDPA hannels,in fa t only a preamble is added at the beginning of ea h transmitted blo k,syn hronization is performed, and �nally this preamble is dis arded again.The reason for not in luding the syn hronization hannel into the analysisis its non-orthogonality to the other hannels. In parti ular, it reates sig-ni� ant interferen e that overshadows the phenomena of primary interest inthis thesis.This leaving out of the syn hronization hannel does however not a�e tthe appli ability of our measurement results to a pra ti al HSDPA setup.Sin e both the primary and the se ondary syn hronization sequen e areperfe tly known, their interferen e an be an eled. Various ontributions[17, 18℄ show that this is indeed possible in the s ope of a real-time imple-mentation.Stati Pedestrian B ChannelLet's �rst onsider a stati Pedestrian B hannel (see Tab. 2.1). The resultsfor this setting are shown in Fig. 4.4 and illustrate that the MMSE equal-izer indeed shows a performan e gain of almost two de ades in BER. Theperforman e omparison is drawn with respe t to the number of odes thatare a tive on the hannel. Indeed, this parameter drasti ally in�uen es theperforman e of both s hemes. This is due to the fa t that the power allo- ation keeps the power of all hannels onstant, and thus the power of ea hindividual hannel de reases as we in rease the total number of a tive odes.The smaller amount of power per hannel in turn results in the interferen ehaving a greater impa t on the single hannel we hoose to de ode. As al-ready mentioned before, in reasing the number of a tive hannels also makesit harder to measure a urately, sin e we are dealing with smaller amountsof power per individual hannel.

CHAPTER 4. MEASUREMENT RESULTS 38

−2 0 2 4 6 8 10 12 1410

−4

10−3

10−2

10−1

100

Eb/N0 [dB]

BE

R

1 code: RAKE1 code: MMSE eq.4 codes: RAKE4 codes: MMSE eq.8 codes: RAKE8 codes: MMSE eq.(a) Pedestrian B

−2 0 2 4 6 8 10 12 1410

−4

10−3

10−2

10−1

100

Eb/N0 [dB]

BE

R

1 code: RAKE receiver1 code: MMSE equalizer4 codes: RAKE receiver4 codes: MMSE equalizer8 codes: RAKE receiver8 codes: MMSE equalizer(b) modi�ed Pedestrian BFigure 4.4: Chip-spa ed MMSE equalizer ompared to the onventionalRAKE re eiver for a di�erent number of a tive user hannels. The modi-�ed Pedestrian B model is a modi� ation of the original model with the tapsmoved to the adja ent hip instant (see Tab. 2.1).

CHAPTER 4. MEASUREMENT RESULTS 39E�e t of the Syn hronization ChannelIn this se tion the results of the non-orthogonal syn hronization sequen e areanalyzed for the AWGN and the Pedestrian B hannel model, respe tively.The power allo ation is hosen su h that in all ases the user hannels a - rue 80% of the total power. This means that either 10%/10% or 15%/5%are devoted to the pilot/syn hronization hannel. Sin e the syn hronizationsequen e is not orthogonal to the other hannels by de�nition, (this is nota result of the multi-tap hannel) it reates interferen e. This interferen ebe omes dominant above Eb/N0 ≈ 6 dB.In Fig. 4.5(a) the e�e ts of the syn hronization hannel are shown for astati AWGN hannel. Sin e there is no MAI in this ase, the RAKE re eiverand the MMSE equalizer show the same performan e. However, the BER forboth re eivers does not live up to the analyti al BER for a stati hannel,be ause due to the syn hronization hannel the system is interferen e limited.In Fig. 4.5(b) the same situation is depi ted for a stati Pedestrian B hannel. In addition to the interferen e due to the syn hronization hannel,MAI is brought about by the hannel and thus the equalizer shows a per-forman e gain ompared to the RAKE re eiver. Naturally, the interferen estemming from the syn hronization sequen e is not a ounted for.Pedestrian B Channel with FadingIn Fig. 4.6 the results for the Pedestrian B hannel with independent fadingof all taps are shown. The Doppler velo ity is hosen to be v = 3km/h ina ordan e with the 3GPP standard.The results are naturally worse ompared to the stati hannel. Measur-ing the above on�guration is more di� ult ompared to a stati hannel,sin e the syn hronization is not guaranteed to lo k on to the �rst tap. Inparti ular, the se ond tap and the third tap arry only slightly less powerthan the �rst one, having a loss of 0.9 dB and 4.9 dB, respe tively. For thisreason it is likely that we will sometimes syn hronize on either of these taps.In this work, this problem is ir umvented by in luding a `pre ursor' tothe hannel estimation. In this way we an make sure that all of the hannel'senergy is aptured, regardless on whi h tap we a tually syn hronize.Another problem results from the fa t that we are now dealing with atime-variant hannel. Sin e the orrelative hannel estimation assumes a onstant hannel, we have to redu e the blo k size su h that this approxima-tion is justi�ed. Sin e the hannel's Doppler velo ity is v = 3km/h, we wind

CHAPTER 4. MEASUREMENT RESULTS 40

−2 0 2 4 6 8 10 12 1410

-4

10-3

10-2

10-1

Eb/N0 [dB]

BE

R

RAKE, 5% synch.MMSE eq., 5% synch.RAKE, 10% synch.MMSE eq., 10% synch.Analytical BER(a) AWGN hannel

−2 0 2 4 6 8 10 12 1410

-2

10-1

Eb/N0 [dB]

BE

R

RAKE, 5% synch.MMSE Eq., 5% synch.RAKE, 10% synch.MMSE Eq., 10% synch.(b) Pedestrian B hannelFigure 4.5: In�uen e of the syn hronization hannel for a stati and a Pedes-trian B hannel, respe tively (1 user ode).

CHAPTER 4. MEASUREMENT RESULTS 41up with a Doppler frequen y offd =

vfc

c= 88.2Hz ⇒ td = 1/fd = 11.3ms . (4.5)For the hannel estimation, a period of three slots (one subframe) is hosen,whi h orresponds to a time of 2ms. This is already fairly large ompared to

td, but further de reasing the blo k size below these three slots de reases theperforman e of the hannel estimation sin e there is additional ontributionfrom interferen e. The adaptive te hniques are superior in this respe t, sin ethey iteratively minimize the ost-fun tion and hen e do not require separate hannel estimation.

−2 0 2 4 6 8 10 12 1410

-3

10-2

10-1

Eb/N0 [dB]

BE

R

1 code: RAKE1 code: MMSE eq.4 codes: RAKE4 codes: MMSE eq.8 codes: RAKE8 codes: MMSE eq.

Figure 4.6: Measurement for the Pedestrian B hannel with fading.4.2.2 Equalizer Length AnalysisA very important design hallenge when it omes to an a tual implementationis hoosing the length of the equalizer Lf appropriately. Ultimately, we fa e atradeo� between performan e and omplexity when determining this value,be ause we want to obtain good performan e (making Lf large) with low omputational ost (re all that we have to invert a matrix sized Lf × Lf ).This tradeo� is examined for the MMSE equalizer for the Pedestrian Band the modi�ed Pedestrian B hannel model. In Fig. 4.7 the results are

CHAPTER 4. MEASUREMENT RESULTS 42shown. The maximum delay of this hannel is 16 hips. If we start by hoos-ing Lf = 3Lh = 48 taps ( hip-spa ed) we obtain a good result, whi h doesnot improve any more by further in reasing Lf .When de reasing Lf the performan e �rst stays approximately the sameuntil Lf ≈ 32. De reasing Lf even further below this value leads to a signi�- ant degradation up to one de ade in BER at Lf ≈ 12. From the implemen-tation viewpoint it would thus be attra tive to hoose 25 < Lf < 32 be ausewe save omputational ost (a 32 × 32 instead of a 48 × 48 matrix inverse)while retaining almost the same performan e.4.2.3 Fra tionally Chip-Spa ed EqualizationIf the re eived signal r[i] is sampled at a multiple of the hip-rate (for instan eat twi e the hip-rate), we speak of a fra tionally hip-spa ed equalizer. InSe . 3.3 it has already been shown how to �nd the equalizer oe� ients (3.23)for this ase. In this se tion the measurement results for this s heme will bepresented.It has to be stressed that a fra tionally hip-spa ed solution has onsid-erably in reased omplexity ompared to the hip-spa ed te hnique. This isbe ause we now need more taps to span the ne essary time period that isdetermined by the hannel. Naturally, this leads to a larger matrix inverse,i.e. MLf × MLf instead of Lf × Lf , where M is the oversampling fa tor.Of ourse, if we invest more omplexity we would assume that the perfor-man e in reases. Unfortunately, our analysis shows that this is not the ase.We almost rea h the performan e of the hip-spa ed MMSE equalizer for lowEb/N0, but at higher values we fa e a slight but noti eable performan e lossasso iated with the fra tionally hip-spa ed method. This partly stems fromimperfe t hannel estimation sin e estimating a larger number of taps makesthe estimation less a urate.4.2.4 Adaptive Equalizer Performan eThe omparison between RAKE re eiver and MMSE equalizer was partlydrawn as to get a representative pi ture on what an possibly be a hievedby introdu ing an equalizer. This se tion will now deal with the sele tedadaptive te hniques and ompare their performan e to the MMSE equalizer.The great advantage of adaptive solutions is their omputational simpli -ity. Spe i� ally, they do not require a matrix inversion and are thereforewell suited for an implementation. A main drawba k on the other hand isthat due to the iterative solution of the ost-fun tion, onvergen e is only

CHAPTER 4. MEASUREMENT RESULTS 43

10 15 20 25 30 35 40 45 5010

-4

10-3

10-2

Lf in taps

BE

REb/N0=13dB

Eb/N0=14dB

Eb/N0=15dB

(a) Pedestrian B

10 15 20 25 30 35 40 45 5010

-4

10-3

10-2

Lf in taps

BE

R

Eb/N0=13dB

Eb/N0=14dB

Eb/N0=15dB

(b) modi�ed Pedestrian BFigure 4.7: Analysis of the equalizer lengthrea hed after a ertain amount of time. This has to be arefully analyzedand onsidered when it omes to omparing di�erent s hemes.Another important property of adaptive s hemes is their tra king behav-ior. Sin e the equalizer oe� ients are ontinuously updated, hannel vari-ations an be tra ked automati ally, whi h is an implementation advantage.In ontrast, the oe� ients of the non-adaptive s hemes have to be re om-

CHAPTER 4. MEASUREMENT RESULTS 44

−2 0 2 4 6 8 10 12 1410

-4

10-3

10-2

10-1

100

Eb/N0 [dB]

BE

R 1 code: RAKE1 code: MMSE eq.1 code: FS-MMSE eq.4 codes: RAKE4 codes: MMSE eq.4 codes: FS-MMSE eq.8 codes: RAKE8 codes: MMSE eq.8 codes: FS-MMSE eq.Figure 4.8: Measurement results for the fra tionally hip-spa ed MMSEequalizer ompared to the hip-spa ed MMSE ase and the onventionalRAKE re eiver.puted su� iently frequent, every time the hannel undergoes a signi� ant hange.Stati Pedestrian B ChannelThe performan e of the adaptive s hemes has been measured for a stati Pedestrian B hannel and is ompared to the MMSE solution in Fig. 4.10through Fig. 4.12 for a di�erent number of a tive odes. It is importantto note that the BER is measured after full onvergen e has been a hieved.Consequently, a variable blo k at the beginning of ea h measurement pro esshas to be ex luded from the analysis. Generally, all adaptive equalizations hemes (ex ept the RAKE stru tures) almost live up to the performan e ofthe MMSE equalizer or even show slightly better results.There are various approa hes to ompare the onvergen e speed. Themost intuitive is to analyze the so- alled learning- urve of the adaptive te h-niques [15℄. Sin e the sele ted adaptive te hniques perform the updates in theLMS-fashion, the learning urve show a monotonous de ay until onvergen eis rea hed and a onstant residual error remains. Two important parame-ters an be extra ted from these urves. First and foremost the onvergen e

CHAPTER 4. MEASUREMENT RESULTS 45time is important be ause it determines when onvergen e is rea hed. In thisthesis this is determined as the time instant when the mean squared error(MSE) has been improved by 90% and 99% respe tively, i.e.∣∣e[i onv]∣∣2 = α

∣∣e[0]

∣∣2 − (1 − α)

∣∣e[∞]

∣∣2 ≈ α

∣∣e[0]

∣∣2, (4.6)with

α = 0.1 or α = 0.01 . (4.7)The learning urve for the hip-spa ed adaptive equalizer is based on e[i] =|u0[i]−u0[i]| as for the other s hemes. This ensures a fair omparison althoughthe equalizer performs its updates with respe t to a di�erent ost-fun tion.Another parameter for analyzing the learning urve is the improvementin MSE that o urs in the s ope of the onvergen e pro ess. We shall de�nethis parameter as |e[0]|2/|e[∞]|2.

0 1 2 3 4 510

-4

10-3

10-2

10-1

100

101

time in frames

|e[i]

|2

Symbol-rate adaptive eq.Chip-rate adaptive eq.CMA adaptive eq.

Figure 4.9: Learning urves for the symbol-rate, the hip-rate and the CMAadaptive equalizer (see Tab. 4.3 and Tab. 4.4 for a quantitative omparison).The learning urves represent an ensemble average over three di�erent real-izations and a time average over 100 symbols.In the following the adaptive s hemes are ompared to the MMSE equal-izer and the onventional RAKE re eiver for one a tive user ode. The resultsfor four and eight a tive odes are similar and an be extra ted from Fig. 4.11and Fig. 4.12.

CHAPTER 4. MEASUREMENT RESULTS 46Table 4.3: Quantitative omparison of the learning urves shown in Fig. 4.9Method onvergen e/slots MSE improvement/dB|e[i]|2 ≈ 0.1 |e[i]|2 ≈ 0.01Symbol-rate eq. 1.66 4.63 35.2Chip-rate eq. 0.58 2.4 25.2CMA 2.8 12.2 31.0Table 4.4: Curve �t for the learning urves shown in Fig. 4.9 assuming themodel a · eb. Method a bSymbol-rate 8.26 -1.58/slotChip-rate 84.95 -4.70/slotCMA eq. 0.63 -0.47/slotSymbol-rate adaptive equalizer The symbol-rate adaptive equalizershows a good tradeo� between performan e and onvergen e speed.The largest abberation from the MMSE equalizer o urs at Eb/N0 =14dB and amounts to 0.5 dB. Convergen e is rea hed after approxi-mately two slots, the MSE improvement is approximately 35dB.Chip-rate adaptive equalizer The performan e of the hip-rate adaptiveequalizer is almost the same ompared to the MMSE equalizer up toEb/N0 = 10dB. Beyond this value the performan e saturates, a fa tthat stems from the low-pass �lter. In fa t, this �lter suppresses MAIonly partly, but at low Eb/N0 this residual interferen e is on ealed bythe white noise. At high Eb/N0 this is no longer the ase and thus theperforman e saturates.Convergen e is rea hed very fast, namely after less than one slot. TheMSE improvement amounts to 25 dB. It should be noted that thesevalues an be adjusted by the parameter ρ, in�uen ing the `quality' ofthe low-pass �lter (in the above analysis ρ = 0.95 was hosen).CMA-equalizer The CMA equalizer shows a very poor performan e forEb/N0 < 10dB. However for Eb/N0 > 10dB this hanges onsiderablyand at Eb/N0 = 15dB CMA omes losest to the MMSE solution,slightly outperforming the other te hniques.MMSE-RAKE The MMSE-RAKE re eiver outperforms the onventionalRAKE re eiver by approximately 2�3 dB at 12 dB < Eb/N0 < 15 dBfor a total number of La = 10 �ngers. The performan e an further be

CHAPTER 4. MEASUREMENT RESULTS 47in reased by making La larger, but at the ost of a larger matrix-inverse.On the ontrary, making La < 10 leads to performan e degradationand this s heme �nally performs poorer than the onventional RAKEre eiver.Adaptive RAKE re eiver The adaptive RAKE re eiver shows a perfor-man e only slightly (≈ 0.5 dB) better then the onventional RAKEre eiver. The onvergen e rate depends on the number of �ngers Laand is faster than the other adaptive s hemes. The urve in Fig. 4.10 orresponds to La = 16.4.2.5 Tra king of Time-Variant ChannelsIn addition to the above analysis the tra king behavior of the adaptives hemes has been measured for a �at (1-tap) Rayleigh fading hannel. TheDoppler velo ity has been set to v = 30km/h, orresponding to the speedstandardized for the ITU Vehi ular A model (this is also a standardizedmodel for HSDPA). A �at Rayleigh fading hannel (instead of a multi-tap hannel) is hosen, su h that no MAI is reated. This is important as toallow for a dire t omparison with the ideal situation gained from hannelestimation.The results for the di�erent adaptive s hemes are depi ted in Fig. 4.13 fora time period of �ve onse utive HSDPA frames. Indeed, all of the adaptives hemes are able to tra k the hannel with approximately the same a ura y.The �deep fades� of the hannel (they orrespond to peaks when plotting the`ideal' equalizer oe� ient) are not a urately tra ked, however this is ofminor importan e assuming that no reliable transmission an be a hievedduring su h fades anyway.4.3 SummaryThis hapter presents the results for the equalizer stru tures analyzed math-emati ally in Ch. 3 by using the on�guration outlined in Ch. 2. At �rst, the orre t operability of the setup is veri�ed and its a ura y is determined byperforming measurements of idealized hannel on�gurations for whi h ana-lyti al results an be obtained. It is proven that the measurement pro ess isindeed pre ise, the largest abberation turned out to be 0.15 dB.In the next step, a omparison of the equalization methods is drawn withrespe t to di�erent implementation aspe ts. First, the onventional RAKE

CHAPTER 4. MEASUREMENT RESULTS 48

−2 0 2 4 6 8 10 12 1410

−4

10−3

10−2

10−1

100

Eb/N0 [dB]

BE

R

RAKE receiverMMSE equalizerSymbol-rate adaptive eq.Chip-rate adaptive eq.CMA adaptive eq.MMSE-RAKEAdaptive RAKE(a) Pedestrian B

−2 0 2 4 6 8 10 12 1410

-4

10-3

10-2

10-1

100

Eb/N0 [dB]

BE

R

RAKE receiverMMSE equalizerSymbol-rate adaptive eq.Chip-rate adaptive eq.CMA adaptive eq.MMSE-RAKEAdaptive RAKE(b) modi�ed Pedestrian BFigure 4.10: Performan e of the adaptive s hemes for one a tive ode.

CHAPTER 4. MEASUREMENT RESULTS 49

−2 0 2 4 6 8 10 12 1410

-4

10-3

10-2

10-1

100

Eb/N0 [dB]

BE

R

RAKE receiverMMSE equalizerSymbol-rate adaptive eq.Chip-rate adaptive eq.CMA adaptive eq.MMSE-RAKEAdaptive RAKE(a) Pedestrian B

−2 0 2 4 6 8 10 12 1410

-4

10-3

10-2

10-1

100

Eb/N0 [dB]

BE

R

RAKE receiverMMSE equalizerSymbol-rate adaptive eq.Chip-rate adaptive eq.CMA adaptive eq.MMSE-RAKEAdaptive RAKE(b) modi�ed Pedestrian BFigure 4.11: Performan e of the adaptive s hemes for four a tive odes.

CHAPTER 4. MEASUREMENT RESULTS 50

−2 0 2 4 6 8 10 12 1410

-4

10-3

10-2

10-1

100

Eb/N0 [dB]

BE

R

RAKE receiverMMSE equalizerSymbol-rate adaptive eq.Chip-rate adaptive eq.CMA adaptive eq.MMSE-RAKEAdaptive RAKE(a) Pedestrian B

−2 0 2 4 6 8 10 12 1410

-4

10-3

10-2

10-1

100

Eb/N0 [dB]

BE

R

RAKE receiverMMSE equalizerSymbol-rate adaptive eq.Chip-rate adaptive eq.CMA adaptive eq.MMSE-RAKEAdaptive RAKE(b) modi�ed Pedestrian BFigure 4.12: Performan e of the adaptive s hemes for eight a tive odes.

CHAPTER 4. MEASUREMENT RESULTS 51

0 1 2 3 4 50

1

2

3

4

5

time in frames

Eq

. co

effi

cien

t (m

agn

itu

de)

Ideal (using channel est.)Symbol−rate adaptive eq.Chip−rate adaptive eq.CMA equalizer

Figure 4.13: Tra king behavior for a �at Rayleigh fading hannel with aDoppler velo ity of v = 30 km/h.re eiver is ompared to the MMSE equalizer, as to get an impression on what an possibly be a hieved. Subsequently, the impa t of the equalizer length Lfon the performan e is analyzed and we illustrate how this important designparameter an be hosen as to strike a balan e between performan e and omplexity.Finally, a thorough analysis of the sele ted adaptive te hniques is per-formed and a omparison to the MMSE equalizer is drawn. It is proven thatby employing adaptive methods we an indeed a hieve almost the same per-forman e, but at redu ed implementation ost. The onvergen e behavioris arefully analyzed and taken into a ount when omparing the di�erents hemes. A omparison of the tra king behavior on luded this hapter.

Chapter 5Con lusionsIn the �rst hapter a brief overview of the High Speed Downlink Pa ketA ess is given and the di�eren es to the onventional UMTS spe i� ationare pointed out. In parti ular, the on ept of adaptive modulation and odingis explained, sin e it makes equalization attra tive to in rease the hannelquality and thereby enhan e the overall performan e of the system.In ontrast to related publi ations this work founds its on lusions onmeasurements over a physi al hannel at a radio-frequen y of 2.45GHz. Thisnot only allows for truly representative results but also enables us to inves-tigate the in�uen es of di�erent re eiver designs. In parti ular, it is possibleto measure the e�e ts of ina urate syn hronization or impre ise hannelestimation on the other parts of the re eiver [19℄.The measurement part of this work has been performed with the MIMOtestbed developed at the Institute of Communi ations and Radio-Frequen yEngineering. The operational details of this devi e are given in Ch. 2 and theinterfa ing of the physi al hannel is explained thoroughly. Clearly, it hasto be emphasized that due to the spe i� setup of the testbed, it is possibleto dire tly interfa e the testbed from within Matlab su h that the re eivers hemes an be dire tly implemented with m- ode, thus greatly a eleratingthe implementation time. For the hip-rate adaptive equalizer the run-timeturned out not to be satisfa tory and thus an e� ient C implementation hasbeen performed using the Mex fun tionality of Matlab.Although all implementations have been made su� iently fast, the pro- essing time on a single omputer is forbiddingly high. The large omputationtime results from the fa t that large amounts of data have to be analyzed asto average over the hannel's statisti and other parasiti in�uen es. As aresult luster pro essing te hniques have been implemented su h that a mea-surement ampaign an be evaluated within a reasonable amount of time.52

CHAPTER 5. CONCLUSIONS 53The measurement results show that equalization indeed ameliorates thebit error rate by more than one de ade under representative onditions. Thein�uen e of the non-orthogonal syn hronization hannel is illustrated and itis shown how to hoose design parameters like the equalizer length Lf .Additionally, a main fo us of this work is to ompare the equalizations hemes both in terms of performan e and omplexity. Besides dis ussinge� ient implementations of the non-adaptive s hemes, this in ludes the de-sign of adaptive equalizers both at the symbol- and the hip-rate. Indeed,it is proven by measurement that the adaptive equalizers almost rea h theperforman e of the omplex MMSE re eiver or even outperform this s hemeunder some ir umstan es. Considering the fa t that adaptive s hemes areespe ially well-suited for tra king time-variant hannels, they are indeed avery good hoi e for a pra ti al implementation.

Appendix ADetailed MeasurementCon�gurationThe detailed measurement on�guration and devi e settings are shown inthis se tion. We have to di�erentiate between the setup for a stati hannel(Fig. A.1) and a fading hannel (Fig. A.2) respe tively.For the stati hannel on�guration the power levels at intermediate steps(indi ated in the diagram) are shown in the table below. Note the dependen yon the number of a tive user odes, aused by the varying Crest fa tor.# of odes pos. 1/dBm pos. 2/dBm pos. 3/dBm pos. 4/dBm1 -15.7 -22 -51 -114 -18.7 -25 -54 -158 -20.3 -26 -55 -16Settings for the Spirent TAS4500-FLEX Channel EmulatorCarrier Frequen y: 2.45GHz LO-Frequen y: 2.38GHzInput Referen e Level: -8.5 dBm Output Attenuator: 0 dBmModulation: Rayleigh Velo ity: 3 km/hSettings for the Noise/Com UFX-EbNo Noise GeneratorMode: Carrier/Noise Carrier Power: -20 dBm / -23 dBmSignal Bandwidth: 4.1MHz54

APPENDIXA.DETAILEDMEASUREMENTCONFIGURATION55

Up-converter

Transmitter

Host PCReceiver

Host PC

Measurement PC

ChannelEmulator

LO

Down-converter

LO

-6dB

LANLAN

GPIB

-5dBm

2.38GHz

-10dB

+13dBm2.31GHz

-10dB+30dB

AnzacAM110

-15.7

dB

m

-22d

Bm

-51.1

dB

m

n

Noise/ComUFX EbNo-IF1Pout=-20dBm

-13dB

-2.5

dB

m

1 2 3 4

Figure A.1: Detailed measurement on�guration for the stati ase.

APPENDIXA.DETAILEDMEASUREMENTCONFIGURATION56

Up-converter

Transmitter

Host PCReceiver

Host PC

Measurement PC

ChannelEmulator

LO

Down-converter

LO

-6dB

LANLAN

GPIB

-5dBm

2.38GHz

-10dB

+13dBm2.31GHz

+30dB

AnzacAM110

n

Noise/ComUFX EbNo-IF1Pout=-23dBm

-13dB

Figure A.2: Detailed measurement on�guration for the fading ase.

AbbreviationsADC Analog to Digital ConverterAMC Adaptive Modulation and CodingBER Bit Error RateCMA Constant Modulus AlgorithmCQI Channel Quality Indi atorDAC Digital to Analog ConverterHARQ Hybrid Automati Repeat RequestHSDPA High Speed Downlink Pa ket A essIP Internet Proto olITU International Tele ommuni ations UnionLAN Lo al Area NetworkLMS Least Mean SquareMAI Multiple A ess Interferen eMEX Matlab Exe utableMIMO Multiple Input Multiple OutputMMSE Minimum Mean Squared ErrorMSE Mean Squared ErrorQAM Quadrature Amplitude ModulationQPSK Quaternary Phase Shift Keying57

APPENDIX A. DETAILED MEASUREMENT CONFIGURATION 58RBW Resolution BandwidthRF Radio Frequen yRRC Root Raised CosineSISO Single Input Single OutputSNR Signal to Noise RatioUMTS Universal Mobile Tele ommuni ation SystemVBW Video BandwidthW-CDMA Wideband Code Division Multiple A ess

Bibliography[1℄ S. Caban, �Development and Setting-Up of a 4 × 4 Real-Time MIMOTestbed,� Diploma Thesis, Vienna University of Te hnology, 2004.[2℄ S. Caban, C. Mehlführer, R. Langwieser, A. L. S holtz, and M. Rupp,�Real-Time Matlab Extension for MIMO-Testbeds,� submitted toEURASIP JASP spe ial issue on MIMO testbeds, 2005.[3℄ C. Mehlführer, S. Geirhofer, S. Caban, and M. Rupp, �A Flexible MIMOTestbed with Remote A ess,� submitted to EUSIPCO, 2005.[4℄ E. As hba her, S. Caban, C. Mehlführer, G. Maier, and M. Rupp, �De-sign of a �exible and s alable 4x4 MIMO testbed,� 11th DSP Workshop,pp. 178�181, Aug. 2004.[5℄ 3GPP, �Multiplexing and hannel oding (FDD),� TS 25.212 V6.2.0,June 2004.[6℄ ��, �Spreading and modulation (FDD),� TS 25.213 V6.0.0, De . 2003.[7℄ ��, �Physi al layer pro edures (FDD),� TS 25.214 V5.9.0, June 2004.[8℄ ��, �UTRA (BS) FDD; radio transmission and re eption,� TS 25.104V6.6.0, June 2004.[9℄ J. G. Proakis and M. Salehi, Communi ation Systems Engineering,2nd ed. Prenti e Hall, 2002.[10℄ R. Langwieser, �Entwi klung von HF Baugrauppen für ein E htzeit-MIMO-Übertragungssystem,� Diploma Thesis, Vienna University ofTe hnology, 2004.[11℄ 3GPP, �User equipment (UE) radio transmission and re eption (FDD),�TS 25.101 V6.4.0, Mar. 2004. 59

BIBLIOGRAPHY 60[12℄ P. S hniter and A. R. Margetts, �Adaptive Chip-Rate Equalization ofDownlink Multirate Wideband CDMA,� Pro . 36th Asilomar Conf. onSignals, Systems and Computers, vol. 2, pp. 1228�1232, Nov. 2002.[13℄ L. Mailaender, �Low- omplexity implementation of CDMA downlinkequalization,� Se ond International Conf. on 3G Mobile Communi a-tion Te hnologies, no. 477, pp. 396�400, Mar. 2001.[14℄ C. R. Johnson, Jr., P. S hniter, T. J. Endres, J. D. Behm, D. R. Brown,and R. Casas, �Blind Equalization Using the Constant Modulus Algo-rithm: A Review,� Pro eedings of the IEEE, vol. 86, pp. 1927�1950, O t.1998.[15℄ S. Haykin, Adaptive Filter Theory. Prenti e Hall, 1992.[16℄ S. Weiss, M. Hadef, and M. Rupp, �Blind hip-rate equalisation for DS-CDMA downlink re eiver,� 37th Asilomar Conf. on Signals, Systems,and Computers, vol. 2, pp. 1283�1287, Nov. 2003.[17℄ M. Hartene k, M. Boloorian, S. Georgoulis, and R. Tanner, �Pra ti alaspe ts of an HSDPA 14 Mbps terminal,� Pro . 38th Asilomar Conf. onSignals, Systems and Computers, Nov. 2004.[18℄ K. Freudenthaler, F. Kaltenberger, S. Paul, C. Me klenbräuker, M. Hue-mer, and A. Springer, �Can ellation of interferen e from syn hronizationand pilot hannels on high speed downlink shared hannel in UMTS,�submitted to EW.2005, 2005.[19℄ S. Geirhofer, C. Mehlführer, and M. Rupp, �Design and Real-Time Mea-surement of HSDPA Equalizers,� submitted to SPAWC, 2005.