Turbo Equalization for HSPA

Institutionen för systemteknikDepartment of Electrical Engineering

Examensarbete

Turbo Equalization for HSPA

Examensarbete utfört i Kommunikationssystemvid Tekniska högskolan i Linköping

av

Cagatay Konuskan

LiTH-ISY-EX–10/4301–SE

Linköping 2010

Department of Electrical Engineering Linköpings tekniska högskolaLinköpings universitet Linköpings universitetSE-581 83 Linköping, Sweden 581 83 Linköping

Turbo Equalization for HSPA

Examensarbete utfört i Kommunikationssystemvid Tekniska högskolan i Linköping

av

Cagatay Konuskan

LiTH-ISY-EX–10/4301–SE

Handledare: Ning HeRadio Access Technologies, Ericsson AB

Niklas JohanssonRadio Access Technologies, Ericsson AB

Mikael Olofssonisy, Linköpings universitet

Examinator: Mikael Olofssonisy, Linköpings universitet

Linköping, 26 March, 2010

Avdelning, InstitutionDivision, Department

Division of Communication SystemsDepartment of Electrical EngineeringLinköpings universitetSE-581 83 Linköping, Sweden

DatumDate

2010-03-26

SpråkLanguage

� Svenska/Swedish� Engelska/English

�

�

RapporttypReport category

� Licentiatavhandling� Examensarbete� C-uppsats� D-uppsats� Övrig rapport�

�

URL för elektronisk versionhttp://www.commsys.isy.liu.se/en

http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-54640

ISBN—

ISRNLiTH-ISY-EX–10/4301–SE

Serietitel och serienummerTitle of series, numbering

ISSN—

TitelTitle

Turboutjämning för HSPATurbo Equalization for HSPA

FörfattareAuthor

Cagatay Konuskan

SammanfattningAbstract

New high quality mobile telecommunication services are offered everyday andthe demand for higher data rates is continuously increasing. To maximize theuplink throughput in HSPA when transmission is propagated through a dispersivechannel causing self-interference, equalizers are used. One interesting solution,where the equalizer and decoder exchange information in an iterative way, forimproving the equalizer performance is Turbo equalization.

In this thesis a literature survey has been performed on Turbo equalizationmethods and a chosen method has been implemented for the uplink HSPAstandard to evaluate the performance in heavily dispersive channels. Theselected algorithm has been adapted for multiple receiving antennas, oversampledprocessing and HARQ retransmissions. The results derived from the computerbased link simulations show that the implemented algorithm provide a gain ofapproximately 0.5 dB when performing up to 7 Turbo equalization iterations.Gains up to 1 dB have been obtained by disabling power control, not usingretransmission combining and utilizing a single receiver antenna. The algorithmhas also been evaluated considering alternative dispersive channels, Log-MAPdecoding, different code rates, number of Turbo equalization iterations andnumber of Turbo decoding iterations.

The simulation results do not motivate a real implementation of the chosenalgorithm considering the increased computational complexity and small gainachieved in a full featured receiver system. Further studies are needed beforeconcluding the HSPA uplink Turbo equalization approach.

NyckelordKeywords Turbo equalization, MMSE, HSPA, ISI, decoding, equalization, low complexity,

HARQ

http://www.commsys.isy.liu.se/en

http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-54640

AbstractNew high quality mobile telecommunication services are offered everyday and thedemand for higher data rates is continuously increasing. To maximize the uplinkthroughput in HSPA when transmission is propagated through a dispersive chan-nel causing self-interference, equalizers are used. One interesting solution, wherethe equalizer and decoder exchange information in an iterative way, for improvingthe equalizer performance is Turbo equalization.

In this thesis a literature survey has been performed on Turbo equalizationmethods and a chosen method has been implemented for the uplink HSPA stan-dard to evaluate the performance in heavily dispersive channels. The selectedalgorithm has been adapted for multiple receiving antennas, oversampled process-ing and HARQ retransmissions. The results derived from the computer based linksimulations show that the implemented algorithm provide a gain of approximately0.5 dB when performing up to 7 Turbo equalization iterations. Gains up to 1 dBhave been obtained by disabling power control, not using retransmission combiningand utilizing a single receiver antenna. The algorithm has also been evaluated con-sidering alternative dispersive channels, Log-MAP decoding, different code rates,number of Turbo equalization iterations and number of Turbo decoding iterations.

The simulation results do not motivate a real implementation of the chosenalgorithm considering the increased computational complexity and small gainachieved in a full featured receiver system. Further studies are needed beforeconcluding the HSPA uplink Turbo equalization approach.

i

ii

Acknowledgments

First of all I would like to thank Ning He and Niklas Johansson, my supervisorsat Ericsson Radio Access Technologies, for their valuable help and support duringmy work. This thesis would not have been possible without you. I am also grate-ful to Göran Klang, Yngve Selén, Sorour Falahati and all other members in thedepartment for their encouragement and advices.

I would also like to show my gratitude to Mikael Olofsson, examiner and super-visor at Linköping University, for his help during the thesis work and even moreimportant his great teachings in the telecommunication related courses.

Last but not least, special thanks to my family, friends and girlfriend for theirpatience and support during the hard time of my thesis work.

iii

iv

Notations

a the scalar aa the vector aA the matrix AA−1 inverse of the matrix Adiag(a) a matrix containing zeros except its diagonal

which is set to the values in vector a0 vector or matrix with all zeros∀ for all(·)∗ the elementwise complex conjugate(·)T the transpose(·)H the Hermitian or conjugate transpose|·| the absolute valueδ(t) the Dirac delta function(f ? g) the convolution of f with g

v

vi

Acronyms

3G 3rd Generation

3GPP 3rd Generation Partnership Project

ACK Acknowledgement

BER Bit Error Rate

BLER Block Error Rate

BPSK Binary Phase-Shift Keying

BS Base Station

CC Chase Combining

CDMA Code Division Multiple Access

CRC Cyclic Redundancy Check

DFE Decision Feedback Equalization

DPCCH Dedicated Physical Control Channel

DS-CDMA Direct Sequence Code Division Multiple Access

E-DCH Enhanced Dedicated Channel

E-DPCCH E-DCH Dedicated Physical Control Channel

E-DPDCH E-DCH Dedicated Physical Data Channel

E-TFC Enhanced Transport Format Combination

EUL Enhanced Uplink

EXIT Extrinsic Information Transfer

FIR Finite Impulse Response

GF Galois Field

GI Guard Interval

vii

GSM Global System for Mobile communications

HARQ Hybrid Automatic Repeat Request

HSDPA High Speed Downlink Packet Access

HSPA High Speed Packet Access

HSUPA High Speed Uplink Packet Access

I In-phase

IBI Inter Block Interference

ICI Inter Chip Interference

IR Incremental Redundancy

ISI Inter-Symbol Interference

ITU International Telecommunication Union

LE Linear Equalization

LLR Log-Likelihood Ratio

LMMSE Linear Minimum Mean Square Error

LMMSE-CE Linear Minimum Mean Square Error Chip Equalization

MAI Multiple Access Interference

MAP Maximum A Posteriori

MIMO Multiple Input Multiple Output

ML Maximum Likelihood

MMSE Minimum Mean Square Error

MRC Maximum-Ratio Combining

MSE Mean Square Error

MUD Multi-User Detection

NACK Negative Acknowledgement

OVSF Orthogonal Variable Spreading Factor

PAM Pulse Amplitude Modulation

PCCC Parallel Concatenated Convolutional Code

PDF Probability Density Function

viii

Q Quadrature

QAM Quadrature Amplitude Modulation

QPSK Quadrature Phase-Shift Keying

RC Raised Cosine

RRC Root Raised Cosine

RS Reed-Solomon

RSC Recursive Systematic Convolutional

SCCC Serial Concatenated Convolutional Code

SF Spreading Factor

SINR Signal-to-Interference-plus-Noise Ratio

SISO Soft-In Soft-Out

SOVA Soft-Output Viterbi Algorithm

TPC Transmit Power Control

TTI Transmission Time Interval

UE User Equipment

VA Viterbi Algorithm

WCDMA Wideband Code Division Multiple Access

ZF Zero Forcing

ix

x

List of Figures

Figure 2.1 Structure of rate 1/3 Turbo coder (dotted lines apply fortrellis termination only) . Figure source: [6]. . . . . . . . . . . . . . 7

Figure 2.2 4-PAM constellation. . . . . . . . . . . . . . . . . . . . . . . 8Figure 2.3 Spreading and despreading of Binary Phase-Shift Keying

(BPSK) symbols. Figure source: [52]. . . . . . . . . . . . . . . . . 9Figure 2.4 E-DPDCH frame structure. Figure source: [1]. . . . . . . . 10Figure 2.5 Spreading for E-DPDCH/E-DPCCH. Figure source: [7]. . . 11Figure 2.6 Linear equalizer implemented as a discrete FIR-filter. Figure

source: [21]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Figure 2.7 An example overview of the High Speed Packet Access (HSPA)

uplink transmission and reception process when two coding blocksand four physical data channels are used. . . . . . . . . . . . . . . 16

Figure 3.1 Original concatenated coding system. . . . . . . . . . . . . 18Figure 3.2 Concatenated encoder and decoder. . . . . . . . . . . . . . 18Figure 3.3 Serial concatenated convolutional encoder and decoder. . . 19Figure 3.4 Structure of original Turbo equalizer introduced by Douillard

et al. Figure source: [23]. . . . . . . . . . . . . . . . . . . . . . . . 20

Figure 4.1 Simplified overview of chosen Turbo equalization algorithm.See detailed signal flow in Figure 4.2. . . . . . . . . . . . . . . . . . 26

Figure 4.2 An example overview of a HSPA uplink reception schemeutilizing Turbo equalization. . . . . . . . . . . . . . . . . . . . . . . 27

Figure 4.3 SISO LMMSE Equalizer with two receiver antennas. . . . . 29Figure 4.4 SISO Max-Log-MAP Turbo decoder. . . . . . . . . . . . . . 36Figure 4.5 A simplified overview of Hybrid Automatic Repeat Request

(HARQ) transmission combining when two Turbo decoders andthree HARQ transmissions are used. . . . . . . . . . . . . . . . . . 39

Figure 5.1 Original tap placement of channels used in simulations. Forexact values used in simulations see Appendix B. . . . . . . . . . . 43

Figure 5.2 Turbo equalization iterative gain when simulation setup BPSK6is used in Pedestrian A channel. . . . . . . . . . . . . . . . . . . . . 44

Figure 5.3 Turbo equalization iterative gain when simulation setup PAM22is used in Pedestrian A channel. . . . . . . . . . . . . . . . . . . . . 45

xi

xii LIST OF FIGURES

Figure 5.4 Turbo equalization iterative gain when simulation setup PAM22is used in Pedestrian B channel. . . . . . . . . . . . . . . . . . . . . 47

Figure 5.5 Turbo equalization iterative gain when simulation setup PAM12is used in Pedestrian B channel. . . . . . . . . . . . . . . . . . . . . 48

Figure 5.6 Turbo equalization iterative gain when simulation setup BPSK6is used in Pedestrian B channel. . . . . . . . . . . . . . . . . . . . . 49

Figure 5.7 Turbo equalization iterative gain when simulation setup PAM22is used in TU channel. Except a transport block size of 20000 bitshas been used instead of a transport block size of 22000 bits, forachieving a code rate of 0.87. . . . . . . . . . . . . . . . . . . . . . 50

Figure 5.8 Compare Log-MAP andMax-Log-MAP Turbo decoders whenusing Turbo equalization with Pedestrian B channel and simulationsetup S-BPSK6. Except a transport block size of 10000 bits hasbeen used instead of a transport block size of 12000 bits, for achiev-ing a code rate of 0.87. . . . . . . . . . . . . . . . . . . . . . . . . . 51

Figure 5.9 Different combinations of internal Turbo decoder iterationsand Turbo equalization iterations. A different setup with 1 re-ceiver antenna, 4PAM modulation, ETFCS=20000, no retransmis-sions and no TPC has been used in Pedestrian B channel. . . . . . 52

Figure 5.10 Turbo equalization iterative gain when simulation setup S-BPSK6 used in Pedestrian B(3 kmph) channel. . . . . . . . . . . . 54

Figure 5.11 Turbo equalization iterative gain when simulation setup S-BPSK6 is used in Pedestrian B(30 kmph) channel. . . . . . . . . . 55

Figure C.1 Extrinsic Log-Likelihood Ratio (LLR) distribution after codeblock concatenation and rate matching. . . . . . . . . . . . . . . . 66

List of Tables

Table 4.1 Symbol alphabet BPSK . . . . . . . . . . . . . . . . . . 37Table 4.2 Symbol alphabet 4-PAM . . . . . . . . . . . . . . . . . 37Table 4.3 Conversion from L(bk,n,q) to

xk,n , E {xk,n} and vk,n , Cov {xk,n, xk,n} . . . . . . . . . . . . 37

Table 5.1 Simulation parameters . . . . . . . . . . . . . . . . . . 42

Table B.1 Propagation Conditions for Multi-Path FadingEnvironments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

xiii

xiv

Contents

Chapter 1: Introduction 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Chapter 2: HSPA Uplink 52.1 Channel Coding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.2 Interleaving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62.3 Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.4 Spreading and Scrambling . . . . . . . . . . . . . . . . . . . . . . . 82.5 Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.6 Retransmission Handling . . . . . . . . . . . . . . . . . . . . . . . . 132.7 Detailed Transmission and Reception . . . . . . . . . . . . . . . . . 14

Chapter 3: Turbo Equalization 173.1 The Turbo Principle Development . . . . . . . . . . . . . . . . . . 173.2 An Overview of Turbo Equalizers . . . . . . . . . . . . . . . . . . . 21

Chapter 4: Algorithm Description 254.1 Some Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

4.1.1 Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.1.2 LLR Values . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.1.3 Probabilistic Definitions . . . . . . . . . . . . . . . . . . . . 26

4.2 Chip Level SISO LMMSE Equalizer . . . . . . . . . . . . . . . . . 284.3 Descrambling & Despreading . . . . . . . . . . . . . . . . . . . . . 344.4 Soft Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.5 Deinterleaver, HARQ Combining & Rate Dematching . . . . . . . 354.6 SISO Turbo Decoder . . . . . . . . . . . . . . . . . . . . . . . . . . 354.7 Interleaver, HARQ & Rate Matching . . . . . . . . . . . . . . . . . 364.8 Soft Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.9 Spreading & Scrambling, Chip Mean & Covariance Calculation . . 384.10 Retransmission Handling . . . . . . . . . . . . . . . . . . . . . . . . 38

Chapter 5: Algorithm Evaluation 415.1 Simulation Environment . . . . . . . . . . . . . . . . . . . . . . . . 415.2 Simulation Setup and Parameters . . . . . . . . . . . . . . . . . . . 41

xv

xvi CONTENTS

5.3 Simulation Results and Analysis . . . . . . . . . . . . . . . . . . . 445.3.1 Performance in Lightly Dispersive Channels . . . . . . . . . 445.3.2 Performance in Heavily Dispersive Channels . . . . . . . . . 465.3.3 Decoding Algorithm . . . . . . . . . . . . . . . . . . . . . . 465.3.4 Code Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.3.5 Turbo Equalization and Turbo Decoding Iterations . . . . . 535.3.6 UE Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . 535.3.7 Other Discussions . . . . . . . . . . . . . . . . . . . . . . . 54

Chapter 6: Conclusions and Remarks 576.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 576.2 Further Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

Appendix A: Noise Correlation Matrix 61

Appendix B: Used Propagation Channels 63

Appendix C: LLR Distribution Between Iterations 65

Bibliography 67

Chapter 1

Introduction

1.1 BackgroundIn the last two decades the cellular networks providing wireless communicationshave been growing rapidly. The breakthrough came with the second generationsystems like Global System for Mobile communications (GSM). These systemswere designed considering speech and they have limited data handling capabilities.As the demand for other services than speech increased the 3rd Generation (3G)systems were introduced. Wideband Code Division Multiple Access (WCDMA)is one of the the main 3G air interfaces in the world and it provides higher bitrates than earlier systems, which allow high quality multimedia services. The firstWCDMA release, release 99, is based on dedicated resource allocation per user andis not optimally suited for data traffic, which often utilize the bandwidth resourcesin a non-continuous asymmetric way. Therefore WCDMA release 5, referred toas High Speed Downlink Packet Access (HSDPA), and release 6, referred to asEnhanced Uplink (EUL) or High Speed Uplink Packet Access (HSUPA), were in-troduced. The specifications for current and previous releases can be found onthe official 3rd Generation Partnership Project (3GPP) website [11]. HSDPA andEUL are together referred to as HSPA and considerably improve the data ratecompared to previous releases of the WCDMA specifications.

When the first 3G cellular networks were deployed the data rates did not ex-ceed 384 Kbps (kilobit per second). Today there are HSPA networks utilizing 2x2Multiple Input Multiple Output (MIMO) with data rates up to 28 Mbps (megabitper second) downlink and 11.5 Mbps uplink. By combining 2x2 MIMO antennatechniques with 64-Quadrature Amplitude Modulation (QAM), networks with upto 42 Mbps downlink could be ready for deployment in 2010 [10].

Everyday the number of users of mobile telecommunication systems is increas-ing and new high quality services are offered. Today there are over 500 millionWCDMA users and more than 200 million of them are utilizing HSPA [26]. Tomeet the continuously increasing demand for higher data rates and better coverage

1

2 Introduction

in mobile telecommunication systems several complex data transmission problemsneed to be solved. Since spectral bandwidth is an expensive and finite resource itis necessary to optimize the spectral efficiency of existing frequency bands, bothdownlink and uplink. One of the biggest problems to efficiently utilize availablebandwidth is Inter-Symbol Interference (ISI) caused by transmission in dispersivepropagation channels. As a consequence successful reception of the signal can of-ten be a difficult task.

One receiver technique widely researched the last decade is Turbo equalization[23, 48, 49, 50], which is the subject of this thesis work. Turbo equalization is aniterative equalization and decoding method for optimizing the reception of signalswhich suffer from ISI and require equalization. The system is based on the Turboprinciple which is used in Turbo codes.

1.2 PurposeThe purpose of this thesis is to understand the potential of Turbo equalizationapplied to the existing HSPA standard for improving uplink throughput in heavilydispersive propagation channels. The work is divided into three parts:

• Literature survey. Perform a literature survey on Turbo equalization forevaluation of Turbo equalization studies in terms of functionality, perfor-mance and complexity.

• Implementation. Select a suitable algorithm for implementation in a sim-ulator and include different HSPA uplink receiver features as oversampling,multiple antenna equalization, Transmit Power Control (TPC) and HybridAutomatic Repeat Request (HARQ) retransmission handling into the algo-rithm to create a realistic simulation environment.

• Evaluation. Evaluate the performance of the implemented receiver algo-rithm by simulations under lightly dispersive and heavily dispersive propa-gation channels. Finally analyze the simulation results and compare themwith results from previous studies on Turbo equalizers.

1.3 OutlineChapter 2 gives a brief overview of the HSPA physical layer and details on partscritical for Turbo equalization. In Chapter 3 the Turbo principle is explained,an overview of the research performed on Turbo equalization is presented andcomplexity and performance are discussed. Chapter 4 describes the implementedalgorithm. The simulation environment is described and results are evaluated inChapter 5. In Chapter 6 the conclusions from the simulation results are sum-marized and suggestions are given for future research. In Appendix A the noisecorrelation matrix used in the algorithm is explained and in Appendix B the exact

1.3 Outline 3

channel taps of channels used in the simulations are stated. Appendix C demon-strates how Turbo equalization iteratively improves the processed data.

4 Introduction

Chapter 2

HSPA Uplink

In this chapter a brief overview of HSPA uplink is given. For more detailed infor-mation the reader is referred to [21] or 3GPP specifications [1, 2, 3, 4, 5, 6, 7, 8, 9].

In HSPA uplink a new transport channel named Enhanced Dedicated Channel(E-DCH) is introduced for handling higher data rates through new features asfast scheduling, HARQ retransmissions and lower spreading factors. HSPA up-link is highly exposed to interference since all active User Equipments (UEs),devices as phones and computers communicating with the mobile network, si-multaneously transmit asynchronously over the same frequency band. There areactually two types of interference, Inter-Symbol Interference (ISI) and MultipleAccess Interference (MAI). The interference occurring when multiple UEs non-orthogonal signals add up at despreading is called MAI. If all UEs are transmittingwith the same power level, the signal from UEs most far away from the receivingBase Station (BS) would be affected by severe MAI or possibly not even detected.The problem is called the Near-Far Effect and is handled by so called TransmitPower Control (TPC) in WCDMA. TPC can shortly be described as the BS iscontrolling the transmission power of all UEs and trying to make the signal qualityof the UEs as equal as possible at reception in the BS. MAI is still present afterTPC but it is possible to reduce it and increase the network capacity by using socalled Multi-User Detection (MUD). Implementation examples on MUD are givenin [56] and [19].

For low data rates, noise and MAI are the dominating sources of interference.For high data rates of HSPA uplink usually self-interference becomes a more im-portant issue, even if this kind of interference also can be found at low data rates.Self interference arise in the presence of a dispersive multipath channel. In a dis-persive channel the transmitted signal from a single UE is received in the BS viamultiple different propagation paths due to reflection or refraction in the surround-ings. When these paths have different propagation delays a transmitted symbol isreceived in the BS at different time instances. This effect makes the symbols re-ceived in the BS interfere with each other when a stream of symbols is transmitted.

5

6 HSPA Uplink

This kind of self-interference is often called ISI or Inter Chip Interference (ICI).To combat the errors introduced by ISI different equalization techniques are used.

In this thesis single user uplink is evaluated and thereby MAI is not treated.Only noise and ISI are considered as interference sources and Turbo equalization isincorporated into the HSPA uplink receiver for mitigating the interference. Herefollows a description of the basic building modules of the transmit and receivechain in HSPA uplink.

2.1 Channel CodingChannel coding facilitates more reliable transmission of a modulated signal througha propagation channel. Bit errors caused by interference and noise can be detectedand/or corrected by a decoder in the receiver. In HSPA uplink a so called rate1/3 Parallel Concatenated Convolutional Code (PCCC) Turbo encoder is used.It consists of two 8-state constituent Recursive Systematic Convolutional (RSC)encoders and one Turbo code internal interleaver. The code rate can be increasedusing puncturing for reaching higher data rates, but this is done in expense ofdecreased error correction capability and higher transmission power. The internalTurbo code interleaver takes the input bits and outputs them in a totally differ-ent order so that the output bitstream has almost no correlation with the inputbitstream. The structure of the used encoder can be seen in Figure 2.1. xk in thefigure represents input bits while zk and z′k represents coded bit streams. Here zkand z′k are assumed to be independent due to the interleaver. Readers interestedin further details on the encoder used in HSPA uplink are referred to the 3GPPspecification [6].

The corresponding decoder in the receiver is fed with soft bit values represent-ing the probabilities of the received bits. The decoder then utilizes the knowninternal structure of the encoder for error correction and error detection. Turbodecoding will briefly be described in Chapter 3 but the interested reader can readmore about Turbo decoders in [43] and [51].

2.2 InterleavingIn the HSPA uplink standard an interleaver, called channel interleaver, is appliedafter the encoder at transmission. Then a deinterleaver, called channel deinter-leaver, is needed before the decoder in the receiver. The purpose of the interleaving,which usually is used in combination with error correcting codes, is to decorrelatepossible error bursts in a given time frame caused by ISI or imperfect channelequalization.

The Turbo encoder used in HSPA is based in conventional convolutional codes.Theoretically convolutional codes have infinite duration impulse responses but usu-

2.3 Modulation 7

Figure 2.1: Structure of rate 1/3 Turbo coder (dotted lines apply for trellistermination only) . Figure source: [6].

ally stronger dependency can be found within five times the code constraint length[32]. The channel interleaver distributes these stronger dependent bits within thewhole transmitted block which gives the strong error correcting capability for lo-cal error bursts at reception. The channel interleaver also plays a central role inTurbo equalization which will be explained in later chapters.

2.3 ModulationIn HSPA uplink two different real-valued modulation schemes for data transmissionare used, BPSK and 4-Pulse Amplitude Modulation (PAM). Simple BPSK mapseach bit bi to a symbol ai according to [7]

ai ={

+1, bi = 0−1, bi = 1,

(2.1)

while 4-PAMmaps two bits bi,1 and bi,2 using gray coding to a symbol ai accordingto [7]

ai =

+1.3416, bi,1 = 0, bi,2 = 1+0.4472, bi,1 = 0, bi,2 = 0−0.4472, bi,1 = 1, bi,2 = 0−1.3416, bi,1 = 1, bi,2 = 1

(2.2)

8 HSPA Uplink

or as illustrated in Figure 2.2.

Real-valued modulation is applied on each E-DCH Dedicated Physical DataChannel (E-DPDCH), described in Section 2.4, and they are later pair-wise addedin the form of the orthogonal In-phase (I) and Quadrature (Q) branches, represent-ing real and imaginary parts. This gives the resulting constellation QuadraturePhase-Shift Keying (QPSK) if a pair of BPSK modulated physical data channelsare added and 16-QAM if a pair of 4-PAM modulated physical data channels areadded. The constellation points in 4-PAM are closer to each other compared toBPSK. The benefit with 4-PAM is that each symbol represents two bits while aBPSK symbol correspond to one bit. 4-PAM results in higher throughput if thechannel and noise conditions, often measured in a Signal-to-Interference-plus-NoiseRatio (SINR) value, are allowing it. The downside is that 4-PAM has a higherSINR requirement while BPSK modulated data still may pass through withouterrors below this requirement. Given a transport format combination, so calledEnhanced Transport Format Combination (E-TFC) in HSPA uplink, there is afixed mapping to a modulation scheme and other parameters. A proper transportformat is selected for a given UE and BS to ensure that the Bit Error Rate (BER)is kept under an acceptable value allowing reliable transmission between them.

Figure 2.2: 4-PAM constellation.

2.4 Spreading and ScramblingWCDMA is based on the Direct Sequence Code Division Multiple Access (DS-CDMA) scheme. All active users in a WCDMA system share the same widefrequency band of 5 MHz simultaneously. Users are separated from each otherwith user specific codes consisting of a bipolar bit stream. The elements of a bitstream are called chips in a spreading system. A bit stream is thereby called a chipstream. The chip rate used in WCDMA is 3.84 Mcps (Mega chips per second) [2].Each information symbol which is about to be transmitted is multiplied with achip stream called spreading code, resulting in a new chip stream. At the receiverthe same spreading code is used on the transmitted chip stream to recover thesymbols. See Figure 2.3 where a BPSK modulated signal is spread and despread.The ratio between the resulting chip rate and the baseband information symbolrate is called spreading factor.

2.4 Spreading and Scrambling 9

Figure 2.3: Spreading and despreading of BPSK symbols. Figure source: [52].

Each so called Transmission Time Interval (TTI) is the time interval whendata is processed for transmission in the physical layer. In earlier releases of theWCDMA standard it is set to a minimum of 10 ms for uplink but the TTI has beenreduced to 2 ms to allow faster retransmissions in HSPA uplink. The E-DPDCHsare the HSPA uplink physical channels for data transmission. The transmissionradio frame structure for an E-DPDCH can be seen in Figure 2.4. Each radioframe of 10 ms is as seen divided into 15 parts called slots. A chip rate of 3.84Mcps will thus result in 2560 chips/slot [2]. The 2 ms TTI in HSPA uplink consistsof 3 slots which together are defined as a subframe. A subframe is the smallestdecodable part of the transmitted signal when a 2 ms TTI is used.

Figure 2.5 illustrates how data is multiplexed to E-DPDCHs using spreading.The information is spread in two steps. First a channelization spreading codeis applied separately on each physical data channel and secondly a scramblingcode is applied on all of them. The channelization codes used in E-DPDCHs areOrthogonal Variable Spreading Factor (OVSF) codes with Spreading Factors (SFs)down to 2. A property of the OVSF codes is that they in ideal conditions, syn-chronous transmission and reception in non-dispersive channels, preserve orthogo-nality between each other. Multiple physical data channels can be dedicated for auser in HSPA uplink and the same set of channelization codes are used by all usersfor separating their own physical data channels. In Figure 2.5 ced,k denotes theapplied real-valued channelization codes on modulated symbols in each channelnumber k. The symbols in each physical data channel k is later weighted by thegain factor βed,k shown in Figure 2.5 and mapped to the I and Q branches by using

10 HSPA Uplink

3GPP TR 25.808 V6.0.0 (2005-03)10Release 6T

7.3 Operation in SHO

8 Physical Channel Structure

8.1 Physical Channel Structure for Data Transmission

8.1.1 E-DPDCH The E-DPDCH is a new physical channel on which the CCTrCh of E-DCH type shall be mapped. The E-DPDCH definition and attributes are the same as the DPDCH except where noted.

Figure 8.1.1 shows the E-DPDCH frame structure. The E-DPDCH radio frame is divided in 5 subframes, each of length 2 ms; the first subframe starts at the start of each E-DPDCH radio frame and the 5th subframe ends at the end of each E-DPDCH radio frame.

Data

Slot #0 Slot #1 Slot #i Slot #14

1 radio frame = 10 ms

E-DPDCH

Slot #2

1 subframe = 2 ms

2560 chips

Figure 8.1.1: E-DPDCH frame structure

E-DPDCH slot formats, corresponding rates and number of bits are specified in table 8.1.1.

Table 8.1.1: E-DPDCH fields

Slot Format #I Channel Bit Rate (kbps)

SF Bits/ Frame

Bits/ Subframe

Bits/Slot Ndata

0 60 64 600 120 40 1 120 32 1200 240 80 2 240 16 2400 480 160 3 480 8 4800 960 320 4 960 4 9600 1920 640 5 1920 2 19200 3840 1280

8.1.2 Timing The radio frames of all the E-DPDCHs transmitted by a UE shall be time aligned with the UE's UL DPCCH radio frames.

3GPP

Figure 2.4: E-DPDCH frame structure. Figure source: [1].

the qed,k coefficient also shown in the same figure. Here q = 1 for the real-valuedI branch, and q = j for the imaginary-valued Q branch. The E-DCH DedicatedPhysical Control Channel (E-DPCCH) seen in the bottom of Figure 2.5 carriescontrol information. E-DPCCH is spread with SF 256 using code cec, weighted bythe gain factor βec and mapped using the qec coefficient. Another control channelwhich always is present in an active communication is the Dedicated Physical Con-trol Channel (DPCCH). It is not shown in the figure but information in DPCCH isalso multiplied with a gain factor βc and it is mapped to the Q branch. Finally allchip-streams from the physical channels are summed up to get a complex-valuedstream of chips. The complex valued scrambling codes applied to the summedup chip-stream can either be long Gold sequences of length 2 41 , correspondingto a 10 ms radio frame, or short primitive GF(2) polynomials of length 256. Inthe uplink the scrambling codes are used to separate users from each other. Thefact that they are not perfectly orthogonal makes the overall interference increasewith increased number of active users in the same frequency band. Short scram-bling codes can be used to ease the implementation of effective multiuser receivertechniques. Details on spreading code generation and spreading procedure donein HSPA uplink can be found in 3GPP specification [7].

2.5 EqualizationThe purpose of performing equalization in the receiver is to reduce ISI and restorethe transmitted signal back to its original shape. Equalizers can be divided intotwo groups, namely trellis based equalizers and linear filtering based equalizers.Maximum A Posteriori (MAP) symbol detection and Maximum Likelihood (ML)sequence detection are the commonly used trellis based equalizers. For complexityreasons linear filtering based equalizers, e.g. Linear Equalization (LE) and DecisionFeedback Equalization (DFE) are more commonly used instead of ML/MAP equal-izers. DFE also incorporate previously equalized symbols for ISI cancellation. The

2.5 Equalization 11

Figure 2.5: Spreading for E-DPDCH/E-DPCCH. Figure source: [7].

12 HSPA Uplink

parameters for filtering are selected by a cost criterion like Zero Forcing (ZF) orMinimum Mean Square Error (MMSE). The different equalizers are described in[51] and [40]. Due to the linearity of the spreading operation in WCDMA systemslinear receivers can be applied either at chip- or symbol-level. The equalizationwill then be performed either before or after despreading and the performancemight be different depending on chosen method. This is further explained in [24].

A simple receiver can be realized by a time-discrete Finite Impulse Response(FIR) filter w[n] with L filter taps applied to the received signal, as illustrated inFigure 2.6. In the figure, nn represents additive gaussian noise, h[n] representsthe discrete channel impulse response and rn represents the received signal inthe receiver. If the FIR filter w[n] is selected as the complex conjugate of thetime-reversed channel impulse response

wMRC [n] = h∗[−n] (2.3)

it becomes a so called Maximum-Ratio Combining (MRC) filter. The well knownRake receiver is a MRC filter applied on symbol level. MRC filtering cannot ac-tually do any equalization of dispersive channels causing ISI, it only maximizesthe filter output signal-to-noise ratio. MRC filtering is an appropriate receiverfor channels mainly disturbed by noise. It provides good performance for highspreading factors and BPSK modulation.

Equalization is needed when transmitting through a dispersive channel. If thefilter is selected according to

wZF [n] ? h[n] = 1, (2.4)

where ? denotes linear convolution, it is called Zero Forcing (ZF) equalization. ZFequalization gives full compensation for ISI but it also may increase the noise levelafter filtering. The noise enhancement can be very severe in the case of highlydispersive channels.

A more realistic solution is to use a filter that provides a trade-off betweennoise enhancement and ISI suppression. One commonly used method is the LinearMinimum Mean Square Error (LMMSE) equalization which minimizes the mean-square error

ε = E{|sn − sn|2} (2.5)between the equalized output sn and the transmitted signal sn. For a LMMSEtime-discrete filter, the filter weights can be found by solving the Wiener-Hopfequation [33]

RwMMSE = p⇐⇒ wMMSE = R−1p. (2.6)In this expression, R is the channel-output auto-correlation matrix of size L × L,which depends on the channel impulse response and noise level, and p is thechannel-output/channel-input cross-correlation vector of size L × 1 which dependson the channel impulse response. For channels with long time dispersion, requir-ing a large L in the FIR filter, the equalizer highly increases in complexity. The

2.6 Retransmission Handling 13

complexity increase due to the filtering itself and the inversion of matrix R.

Figure 2.6: Linear equalizer implemented as a discrete FIR-filter. Figure source:[21].

2.6 Retransmission HandlingWhen a packet, defined as the smallest decodable part of the transmitted signal, isreceived and fully decoded in the receiver an Acknowledgement (ACK) or NegativeAcknowledgement (NACK) is signaled for telling whether the packet was correctlyor incorrectly received respectively. Hybrid Automatic Repeat Request (HARQ) isan error-control method for data transmission which use retransmissions to achievereliable data transmission over an unreliable channel. If a NACK is signaled thesoft bits from the received demodulated symbols are stored in a soft bit buffer anda retransmission of the same information is scheduled. When the transmissionarrives the new received soft bits are combined with the one stored in the softbit buffer for increasing the probability of correct decoding. This continues untilthe receiver signals an ACK or a predefined number of allowed transmissions isexceeded.

There are two commonly used retransmission schemes in HSPA uplink systems:Chase Combining (CC) and Incremental Redundancy (IR). In CC the retrans-mitted packet contains exactly the same information as the previously receivederroneously packet. The packets can be combined coherently before decoding andtime diversity gain is then achieved. When IR is used the rate matching unit usesa different pattern at retransmission resulting in transmission of different encodedbits in case of puncturing is used. This method provides coding gain since eachretransmission can decrease the coding rate as additional parity bits from the re-

14 HSPA Uplink

transmissions are combined with bits of the previous transmissions. There is afixed number of simultaneous HARQ processes. When 2 ms TTI is applied 8 pro-cesses are used, the corresponding number of processes for 10 ms TTI is 4. Theprocesses are activated synchronously and thereby retransmissions of incorrectlyreceived packets are scheduled 8 or 4 packets later. If the decoding still results ina NACK signal after the maximum number of allowed transmissions is reached fora process, the soft bit buffer for that process is reset and the data is rescheduledin higher layers.

2.7 Detailed Transmission and ReceptionAn example of the HSPA uplink transmission and reception chain for a singleuser is given in Figure 2.7. The figure gives an overview of all components theinformation goes through. Source coded data, usually meaning some sort of datacompression, is input to the transmitter in the form of a HSPA uplink transportblock and hopefully restored at the end of the receiver. In the first step of thetransmitter a 24 bit Cyclic Redundancy Check (CRC) code is added. The purposeof the CRC code is error detection at the receiving end. After CRC code is added,the data block is fed into a code block segmentation unit whose purpose is to splitthe data into several parts since the Turbo encoder used in HSPA uplink handlesa maximum of 5114 bits [6]. The data is segmented into 2 Turbo encoders in theexample shown in the Figure 2.7. No segmentation is needed if the number ofbits are less than 5114 and only a single encoder is used. The encoded blocks areconcatenated and sent into the rate matching unit after channel coding. The ratematching unit performs puncturing or repetition for adjusting the amount of dataso it is suitable for the current transmission data-rate in the E-DCH DedicatedPhysical Data Channels (E-DPDCHs). The settings for rate matching are con-trolled by the transport format E-TFC signaled by the BS.

In Figure 2.7 4 physical data channels are used, which is the maximum numberof available physical data channels. They are separately interleaved and later mod-ulation is applied on each channel for mapping bits to symbols. BPSK or 4-PAM isused depending on current transport format. After modulation each physical datachannel is spread using a real-valued OVSF channelization spreading code. Twocodes with SF 2 and two codes with SF 4 are used in HSPA uplink for reaching themaximum transmission bitrate. There are also other channels present not shownin the figure, E-DCH Dedicated Physical Control Channel (E-DPCCH) and Ded-icated Physical Control Channel (DPCCH), carrying control information. Bothcontrol channels use a SF of 256. Each physical channel is also weighted by again factor and mapped to I and Q branches as described in Section 2.4. As seenin the overview figure, the resulting chip-streams are summed up to give a singlecomplex-valued stream of chips before scrambling is applied. After the scramblingprocess power control is applied to the chip-stream. Finally pulse shaping is doneusing a Root Raised Cosine (RRC) filter with a roll-off factor of 0.22 before thesignal is bandpass modulated and sent through the channel.

2.7 Detailed Transmission and Reception 15

The transmitted signal passes through a channel and arrives at the receiverwhere it is transferred back to baseband. More than one antenna can be used atthe receiver, as shown in Figure 2.7, to get diversity gain. Equalization is doneafter the received signal is filtered with the receiver RRC pulse shaping filter.Usually estimated channel coefficients, extracted from pilot symbols transmittedin the Dedicated Physical Control Channel (DPCCH), is used by the equalizer forestimating filter weights. The despreading, descrambling and I/Q demapping sep-arates the equalized signal back to real-valued chip-streams, each associated to aphysical channel. In the soft demodulator symbols are mapped to bit-probabilities,or so called Log-Likelihood Ratios (LLRs), required for optimal decoding. The bit-probabilities are separately deinterleaved and later concatenated to a single stream.The single stream of bit-probabilities is zero-padded or punctured according to therate-matching in the transmitter. If the block of data is a retransmission and IRis used, the bit-probabilities are also combined with previous transmissions. Re-sulting bit-probabilities are segmented to several code blocks if the HSPA uplinktransport block in the transmission process was encoded with multiple encoders.Decoding is done and the decoded bits from all decoders are concatenated if mul-tiple decoders are used. The resulting stream of decoded bits is CRC checked fordetecting errors possibly not corrected in the decoding. If an error is detected, thebit probabilities achieved before decoding are stored and a NACK signal is sentto the transmitter. If the maximum number of retransmissions is not reached forthe actual data packet, a retransmission is performed 8 subframes later, if 2 msTTI is used.

16 HSPA Uplink

Despreading & Descrambling

ScramblingChannel

estimator

Equalizer

Channel

Channel estimator

Power Adjustment

HARQ & Rate Matching Rate Dematching & HARQ Combining

Physical Channel ConcatenationPhysical Channel Segmentation

Code Block Concatenation


Code Block Segmentation


TurboEncoder

TurboEncoder

CRC CheckCRC Attachment

Spread-ing

Spread-ing

Modu -lation

Inter-leaver

Inter-leaver

Modu -lation

Modu -lation Soft

Demod -ulation

SoftDemod -ulation

Modu -lation Soft

Demod -ulation

SoftDemod -ulation

TurboDecoder

TurboDecoder

Deinter -leaver

Deinter -leaver

Deinter -leaver

Deinter -leaver

Spread-ing

Spread-ing

Inter-leaver

Inter-leaver

Square rootSquare root

Square root

Figure 2.7: An example overview of the HSPA uplink transmission and receptionprocess when two coding blocks and four physical data channels are used.

Chapter 3

Turbo Equalization

A receiver trying to find the most probable transmitted bits by taking all availableknowledge between transmission and observation into account would be optimalin terms of BER. Considering the complex statistical relationship occurring whenchannel coding, interleaving, modulation, channel knowledge and other factors areinvolved makes an optimal receiver implementation practically impossible. Mostreceiver designs are therefore similar to the HSPA reception described in the pre-vious chapter, where the observed signal is processed in multiple steps. One sub-optimal solution is a receiver based on iterative processing of information betweenthe equalization and decoding steps to improve BER in each iteration. The meth-ods based on this iterative processing are usually referred as Turbo equalizers, andthey are based on the Turbo principle [18], [29]. This chapter begins with a quickreview of the Turbo principle development and its basics since it is a vital partof the theory behind Turbo equalizers. Later in this chapter Turbo equalizationstudies performed until today are summarized and evaluated.

3.1 The Turbo Principle DevelopmentThe Turbo principle was in the beginning introduced for achieving efficient channelcoding, so called Turbo coding. This section will briefly present the developmentuntil today, where the Turbo principle is utilized in Turbo equalization.

The first concepts of concatenated coding schemes came early as in the 60’s.Forney et al. showed that high error-correction capacity which would require longcodes could be reached using a setup with two much shorter codes as seen in Fig-ure 3.1 [34]. In their proposal the inner encoder is a short block code and the outerencoder is an algebraic Reed-Solomon (RS) code [51]. The encoded signal passesthrough a channel which disturbs it. The received signal is then processed by theinner decoder and the binary output is passed to the outer decoder for correctingerrors which at the inner decoding stage could not be corrected.

17

18 Turbo Equalization

Figure 3.1: Original concatenated coding system.

The performance in this setup is not optimal due to two reasons. The first prob-lem is the communication between the decoders which is hard-bit based, meaningthat the outputs of the component decoders are binary decisions instead of proba-bilities of the received bits. The second issue is that the strong dependence betweenthe encoders is only used one-way, from inner to outer decoder, and not the otherway around.

Figure 3.2: Concatenated encoder and decoder.

In the 70’s NASA started to use concatenated codes for space applications[25]. The NASA system had two significant improvements compared to the earlierconcatenated codes. NASA started using a convolutional code as an inner code,decoded by the optimal Viterbi Algorithm (VA). Secondly NASA incorporated aninterleaver between the coding blocks as can be seen in Figure 3.2. The main pur-pose of the interleaver/deinterleaver between the encoders/decoders is to scatterpossible error bursts that can, due to the channel or structure of inner decoder,still slip through the inner decoder. This way the outer decoder can work moreeffectively.

In the late 80’s Battail [15] and Hagenauer et al. [30] introduced a so called Soft-Output Viterbi Algorithm (SOVA) as a solution to the above mentioned "hard-bit"

3.1 The Turbo Principle Development 19

problem. SOVA is a modified VA which can input soft channel measurements andoutput soft-bits, probabilities of received bits, from the inner decoder to furtherincrease the effectiveness of the outer decoder.

Figure 3.3: Serial concatenated convolutional encoder and decoder.

The next big progress in the evolution of concatenated codes came when Berrouet al. in the article "Near Shannon limit error-correcting coding and decoding:Turbo codes" [18] proposed a solution to the previous mentioned second problem.Feedback was introduced between decoding modules so that iterative decodingcan be done, as shown in Figure 3.3. It is this concept which today is known asTurbo coding. A Turbo code based transmitter has two or more error-correctingcode modules pairwise separated with an interleaver and the received signal islater decoded iteratively with the same number of decoding modules. The de-coder modules are so called Soft-In Soft-Out (SISO) modules for best exploitingthe information exchange between each other. The Soft-In Soft-Out (SISO) mod-ules that result in very high decoding performance in [18] are based on the MAPalgorithm.

The MAP algorithm is too complex for Turbo decoding implementation in re-ality. Turbo codes were therefore not used until it was discovered that it is possibleto reduce the decoding complexity almost without affecting the performance. Thedevelopment begun with the suggestions from Koch et al. [35] who proposed theMax-Log-MAP algorithm. The MAP algorithm is simplified by doing the calcula-tions in the logarithmic domain and by introducing approximations in some steps.While the complexity is massively cut down the approximations reduce the perfor-mance. The solution to the performance reductions came when Robertson et al.[42] proposed the Log-MAP algorithm which introduced a correction term to theapproximations used in the Max-Log-MAP algorithm. The Log-MAP algorithmshow performance close to the MAP algorithm even though its complexity in com-


parison is much lower. Today usually the Log-MAP or Max-Log-MAP algorithmis used in applications relying on Turbo decoding due to their good complexityversus performance properties.

The original Turbo codes introduced by Berrou et al. are Parallel ConcatenatedConvolutional Codes (PCCCs). The coding scheme used in WCDMA is based ona PCCC. Knowledge of the PCCC internal structure details is not necessary forthis thesis and will therefore not be discussed. The interested reader is referredto the brief article by B. Sklar [43] for details on PCCCs and [6] for the specificPCCC used in WCDMA.

Figure 3.4: Structure of original Turbo equalizer introduced by Douillard et al.Figure source: [23].

In 1996 Benedetto et al. proposed an alternative iterative coding scheme, SerialConcatenated Convolutional Codes (SCCCs) [17]. Figure 3.3 shows a simplifiedillustration over SCCC encoding and decoding. Turbo equalization is based onthe SCCC structure. Here the inner encoder in Figure 3.3 is replaced by a time-discrete multipath channel and the inner decoder with an equalizer. A multipathtime-discrete channel can be seen as a convolutional encoder with code rate 1.Thereby the received signal can be "decoded" using an equalizer as the inner de-coder. A typical Turbo equalizer is a scheme with a SISO-equalizer as the innerdecoder and a SISO-decoder as the outer decoder. These modules, which areseparated with an interleaver/deinterleaver then process the same set of receiveddata in an iterative way until a certain stop criterion is reached. This is usually asuccessful CRC check, a LLR magnitude check or a maximum number of allowediterations. When the iterations are stopped the decoder finally outputs an estima-tion of the transmitted block of data. Comparing the Turbo equalization schemein Figure 3.4 and the decoding part of the SCCC example in Figure 3.3 will givea better understanding of the similarities between the concepts.

3.2 An Overview of Turbo Equalizers 21

3.2 An Overview of Turbo Equalizers

The Turbo equalization approach was first proposed by C. Douillard et al. in [23]and later further developed in articles such as [16] and [12]. The SISO-equalizersand SISO-decoders used in the mentioned papers are based on the suboptimalSOVA and Max-Log-MAP algorithms [42] instead of the MAP algorithm, due tothe very high complexity of the MAP algorithm. Unfortunately these algorithmsare still too complex when multiple receiving antennas and/or higher order mod-ulations are used. The complexity of these algorithms also increase exponentiallywith the length of the channel impulse response. To further reduce the Turboequalization complexity filter-based equalization solutions can be used instead.One of the early suggestions is a joint equalization-decoding approach based onDFE and convolutional coding proposed by Ariyavistakul and Li [13]. Anotheris a multiuser filter-based Code Division Multiple Access (CDMA) detector pro-posed in [55] by Wang et al. where a SISO LMMSE equalizer is used instead of aMAP equalizer. In these solutions the linear filter coefficients are updated everytime one symbol is processed. A solution with lower complexity than the earliersuggestions was proposed by Glavieux et al. in [28].

The Turbo equalization research took a new phase around the time the articles[50], [49] and [48] were published. In [50] R. Koetter et al. explain the fundamentalsof the Turbo equalization principles thoroughly and show that Turbo equalizersbased on the MAP-criterion outperforms all other Turbo equalizers in convergenceand BER. But they also note that in certain conditions the performance of theLMMSE based Turbo equalizers approach the MAP-based ones. The article [49]introduce some new linear filtering-based Turbo equalization methods. They sug-gest two approximative LMMSE based methods and one DFE based method. Theapproximative methods give a significant reduction in complexity by updating fil-ter coefficients more sparsely instead of updating at each detected symbol as inthe exact LMMSE equalizer used in [55]. They present a complexity comparisonof different receivers and they describe a hybrid approach which utilize the two ap-proximative LMMSE based methods. They show that it is possible to achieve thesame performance as the exact LMMSE equalizer based Turbo equalizer by usingthe hybrid method. Another interesting conclusion is that the DFE approach doesnot show satisfactory results. In the paper [48] with focus on the LMMSE basedTurbo equalizers, the exact LMMSE algorithm and the suggested approximativeLMMSE algorithms are described in detail. The algorithms are also extendedto general signal constellations. Tüchler et al. also show that the approximativeLMMSE-based Turbo equalizers gives very large complexity reductions while stillperforming relatively well compared to the exact LMMSE and MAP based Turboequalizers. It has also been proven that several previous linear soft interferencecancellation based Turbo equalizers, e.g. [28], could be viewed as approximationsof the solutions presented by Tüchler et al.

An interesting instrument which can be used for optimizing parameters andalgorithms in Turbo equalization is Extrinsic Information Transfer (EXIT)-charts.


In the article [31] Hanso et al. conclude, "Future iterative receiver research is ex-pected to rely on EXIT-chart-based design principles for the sake of performingclose to the capacity limits, using the principles outlined in [54], [53] and stimu-lating the research community to aspire for achieving near-capacity performanceover dispersive, fading wireless channels at the lowest possible complexity and de-lay.". In EXIT-charts the LLR convergence is plotted on graphs for estimating thebehavior of different algorithms or settings. Some examples where EXIT-chartshave been used are presented in [49] and [20].

A frequency domain LMMSE Turbo equalizer can be used since it can save com-putational complexity. The complexity gain compared with time domain equal-izers depends on block length, ISI channel impulse response length and LMMSEfilter length. According to [47] there is no significant difference in performancecompared to time domain based equalizers but a drawback with frequency domainalgorithms is that for equalizing properly they require a Guard Interval (GI) orextended filtering for removing Inter Block Interference (IBI) [45].

In [22] dos Santos A. F. et al. propose a Turbo equalizer incorporating a Turbodecoder. Their proposal include a special solution for reducing complexity. Usu-ally one or more Turbo decoding iterations are performed at each Turbo equal-ization iteration. In their paper they suggest that only one single convolutionaldecoder, of the two convolutional decoders inside a Turbo decoder, is executed ineach Turbo equalization iteration. Thereby two Turbo equalization iterations areneeded to complete one Turbo decoding iteration since only a half Turbo decodingis performed after equalization is preformed. The advantage with this approachis reduced complexity by allowing more executed equalization steps compared tothe number of decoding steps. One requirement for utilizing this advantage is theusage of an equalizer with low complexity, which is possible in the case of a lowcomplexity LMMSE equalizer.

Since retransmission combing will be used in the implementation the subjectis a part of the literature study. Except relevant 3GPP documents other paperswere studied and one of them is [14] where Assimi et al. describe different HARQretransmission methods and show how EXIT charts can be used for interpretingthe performance of the different methods. In another paper Takeda et al. describean implementation of a frequency domain LMMSE based DS-CDMA Turbo equal-izer where retransmission combing is evaluated [44]. They use Chase Combiningand conclude by simulation results that throughput performance is improved whencombining retransmissions and Turbo equalization. Another article [46] briefly de-scribes an interesting implementation where Chase Combining is used on HSUPA.They suggest diversity combining of retransmissions in the equalizer instead ofbit LLR level combining before decoding. Each retransmission is basically seen asan extra receiver antenna. The results show significant reduction in Block ErrorRate (BLER), especially in higher order modulations.

An equalizer often utilize channel estimates derived from pilot symbols trans-

3.2 An Overview of Turbo Equalizers 23

mitted together with data symbols or in separate control channels. When Turboequalization is used the extra knowledge about the transmitted information afterdecoding can be used for improving the channel estimates at each iteration. Thishas been widely studied and in [37] several proposals are presented for iterativelyimproving the channel knowledge.


Chapter 4

Algorithm Description

Different mentioned publications in Chapter 3 are showing that LMMSE-basedTurbo equalizers perform well at a reasonable level of computational complexity.Most proposals for time-domain LMMSE-based Turbo equalization receivers havea similar base structure. A time-domain LMMSE-based Turbo equalization al-gorithm with basic features has therefore been chosen for implementation in thesimulator. The implemented Turbo equalizer can thereby easily be extended withadditional features from different proposals. The main references used in the fol-lowing algorithm derivations are [48] and [58]. The simulation environment isdescribed in Chapter 5.

The equalization and decoding modules use soft values as input and soft valuesas output in the following descriptions. Figure 4.1 gives a brief overview of theinformation flow and notations used in the described algorithm. In the first sectionof this chapter some definitions needed for the algorithm descriptions are made.The following sections in this chapter will follow the chain of modules in Figure 4.1.In Section 4.2 the equalizer is derived. In Section 4.3 the descrambling and de-spreading process is described while Section 4.4 derives the soft demodulation. InSection 4.5 deinterleaving, physical channel concatenation, rate dematching andcode block segmentation are briefly described. In Section 4.6 the Turbo decodingprocess is explained. In Section 4.7 the code block concatenation, rate match-ing, physical channel segmentation and interleaving are described. Section 4.8describes the soft modulation performed and in Section 4.9 the calculations fromsymbol statistics to chip statistics are presented. The HARQ functionality is pre-sented in Section 4.10.

Figure 4.2 where four E-DCH Dedicated Physical Data Channels (E-DPDCHs)and two Turbo decoders are used illustrates a more detailed overview of Figure 4.1.The figure can be compared with Figure 2.7 on page 16 where a non-iterativereception is illustrated.

25

26 Algorithm Description

Output ofbit decisions

yi

di

dic

i

xk,n

xk,n L(bk,n,q)

vk,n

L(rb,z)

L(rb,z)L(bk,n,q)

Input fromchannel

SoftModulation

SoftDemodulation

Interleaver ,HARQ &

Rate Matching

Descrambling &Despreading

Deinterleaver ,HARQ Combining &

Rate Dematching

Chip Level SISOLMMSE Equalizer

Spreading & ScramblingChip Mean &

Covariance Calculation

SISO TurboDecoder

Figure 4.1: Simplified overview of chosen Turbo equalization algorithm. Seedetailed signal flow in Figure 4.2.

4.1 Some Definitions4.1.1 OperatorsThe following operators are defined and used in the algorithm derivations. Theoperator E{·} is the expectation over the Probability Density Function (PDF),taking the a priori information into consideration. The covariance operator isgiven by Cov{x,y} , E{xyH} − E{x}E{yH}.

4.1.2 LLR ValuesTurbo equalization is based on iteratively exchanging probabilities between theequalizer and decoder. When working with probabilities of binary values it isconvenient to work with LLRs. The LLR for a binary variable b is defined as

L(b) , lnP{b = 0}P{b = 1} (4.1)

and is often denoted as the "soft" value of a bit or simply soft-bit. The sign of L(b)is the "hard" value of the bit b, it is often called hard-bit. A positive value of L(b)gives decision +1, or the binary value 0. A negative value gives decision -1, or abinary 1. The magnitude of |L(b)| represents the reliability of the decision. Thespecial case when P(b = 0 ) = P(b = 1 ) = 1/2 results in the LLR value L(b) = 0 .

4.1.3 Probabilistic DefinitionsSome probabilistic definitions important for understanding the Turbo principle arepresented:

4.1 Some Definitions 27

Channel inputs

Despreading & Descrambling

Chip Level SISO LMMSE Equalizer

Channel estimator

Channel estimator

HARQ & Rate MatchingRate Dematching & HARQ Combining

Physical Channel Concatenation

Physical Channel Segmentation

SISO Turbodecoder

Spreading & ScramblingChip Mean &

Covariance Calculation


SISO Turbodecoder



CRC Check

Deinter -leaver

Deinter -leaver

SoftModu -lation

Inter-leaver

Inter-leaver

SoftModu -lation

SoftModu -lation

SoftDemod -ulation

SoftModu -lation

SoftDemod -ulation

SoftDemod -ulation

Deinter -leaver

SoftDemod -ulation

Deinter -leaver

Inter-leaver

Inter-leaver

Square rootSquare root

Figure 4.2: An example overview of a HSPA uplink reception scheme utilizingTurbo equalization.


A Priori Information is probability information associated with a bit bi prioran equalization or decoding step begins. The a priori information should originatefrom another source than the received sequence or the code constraints.

Extrinsic Information is probability information associated with a bit biprovided solely by the processing in an equalizer or a decoder. The extrinsic in-formation is derived by processing all other received bits in a block except theactual bit bi and all other a priori probabilities except the one associated with theactual bit bi . In a decoder the extrinsic information is possible to extract sincethe memory in the encoder has introduced dependency among bits. By using thisdependency, statistics about the probability of the actual bit bi can be gainedfrom the surrounding bits. It is also possible to extract extrinsic information fromequalization in the same manner since a dispersive discrete channel can be seen asa convolutional encoder with code rate 1.

Observation Information is probability information of the received signal.

A Posteriori Information is probability information associated with a bit biwhen all available sources of information about the bit is taken into account. Thiscan be a priori information, extrinsic information and observation information.

4.2 Chip Level SISO LMMSE EqualizerThe equalizer module is used for equalizing the received signal from the two re-ceiver antennas by also incorporating a priori information, i.e. some statisticalknowledge of the chips about to be estimated. The a priori information shouldcome from a source other than the received signal. Inputs to the equalizer arethereby the received signal from the two receiver antennas, the statistics di rep-resenting the expectation values of the chips based on a priori information, thestatistics ci representing the covariances of the chips based on a priori informationand the channel estimates for both antennas. In this thesis the channel impulseresponses are assumed to be known at the receiver and they are thereby not esti-mated. The equalizer finally outputs estimated chips di.

The transmitted signal includes the E-DPDCHs, E-DPCCH and DPCCH.Scaling factors, spreading codes, I/Q-mapping and symbols are in the followingderivations marked with ed, ec and c respectively for separating the variables fordifferent physical channels. The symbols and spreading codes for E-DPDCHs arewritten without ed. The transmitted signal from a UE can then be written as

di =K∑k=1

βed,kqed,kak,ixk,i div Sk + βecqecaec,ixec,i div Sec + βcqcac,ixc,i div Sc (4.2)

where di denote the transmitted chip number i. K is number of utilized phys-ical data channels. βed,k is the used gain factor and qed,k the I/Q-mapping for

4.2 Chip Level SISO LMMSE Equalizer 29

physical data channel number k. ak,i is the product of channel specific chan-nelization and user specific scrambling codes for physical data channel number kand chip number i. xk,n represent symbol number n modulated in physical datachannel number k. xk,n ∈ S where S = {α1, α2, ..., α2Q} represents the 2Q-arysignal alphabet. A symbol αr in the signal alphabet corresponds to the bit patternsr , {sr,1, sr,q, ..., sr,Q}. The bit vector representing symbol xk,n modulated inthe transmitter is defined as bk,n , {bk,n,1, bk,n,q, ..., bk,n,Q}. i div Sk is the integerdivision of i by Sk . The Sk used in the integer division denotes spreading factorfor physical data channel number k. βecqecaec,ixec,i div Sec and βcqcac,ixc,i div Sc

represents the contribution of the control channels.

yi1

di

dic

i

xk,n

vk,n

yi2

di

noise

noise

Channel 2

Channel 1

Chip level SISOLMMSE equalizer

Chip mean & covariance calculation

Square root

Square root

Square root

Figure 4.3: SISO LMMSE Equalizer with two receiver antennas.

Figure 4.3 illustrates equalization using two antennas. The received signal isoversampled with λ samples per chip in the receiver. The received signal in theantenna with index α can then be modeled by

yαi

=L∑l=0

hαl di−l + nαi (4.3)

where yαi

, [yαi (λ − 1), ..., yαi (0)]T is the received signal column vector of size λnumber of samples per chip, representing sampled values during chip period i.hαl , [hαl (λ − 1), ..., hαl (0)]T is the sampled channel coefficients column vector ofsize λ. The total revered discrete channel impulse response of length L + 1 chipscan be written as [hαL

T , ...,hα0T ]T . nαi , [nαi (λ − 1), ..., nαi (0)]T represents the

column vector of sampled received noise during chip period i. The channel coef-ficients hαl include the convolution of the transmitter and receiver pulse shapingfilters and the received noise samples nαi include the receiver pulse shaping filter.

The following definitions are made to simplify the derivation of the LMMSEequalizer


yαi , [yαi+F

T , ...,yαi−F

T ]T (4.4)

nαi , [nαi+FT , ...,nαi−F

T ]T (4.5)

di , [di+F , ..., di−F−L]T (4.6)

where F specifies the length in chips of the causal and non-causal parts of theLMMSE filter. The filter length used in simulations is given in Section 5.2.

The (2F + 1 )λ× (2F + 1 + L) channel convolution matrix for antenna α isdefined as

Hα ,

hα0 · · · hαL

hα0 · · · hαL. . .

hα0 · · · hαL

. (4.7)

To further simplify the notation the received signal vector yi, channel matrixH, received noise vector ni, and Equation 4.3 can in a two antenna configurationα = 1 , 2 be written as:

yi =[y1i

y2i

](4.8)

H =[H1

H2

](4.9)

ni =[n1i

n2i

](4.10)

yi = Hdi + ni (4.11)

The equalization algorithm is based on MMSE estimation for obtaining chipestimates di from the received signal. It can be shown [39] that the Mean SquareError (MSE), E{|di − di|2}, is minimized when

di = E{di}+ (Cov{yi,yi}−1Cov{yi, di})H(yi − E{yi}). (4.12)

If the noise samples ni are assumed to have zero mean, the noise samples niand transmitted chips di are assumed to be uncorrelated and the transmitted chipsdi are assumed to be independent, the following simplifications can be done

E{yi} = HE{di} (4.13)


Cov{yi, di} = Cov{Hdi, di}︸︷︷︸Cov{di,dj}=0 ∀ i,j,i 6=j

+Cov{ni, di}︸︷︷︸=0

(4.14)

= Cov{di, di}h = cih

Cov{yi,yi} = Cov{Hdi,Hdi}︸︷︷︸Cov{di,dj}=0 ∀ i,j,i 6=j

+Cov{Hdi,ni}︸︷︷︸=0

+Cov{ni,Hdi}︸︷︷︸=0

+Cov{ni,ni}

(4.15)= HCiHH + N

where covariance matrix Ci is defined as diag([ci+F , ..., ci−F−L]T ). The scalar ciis defined as Cov{di, di}. The vector h is the column number F+1 in the channelconvolution matrix H. N is the noise autocorrelation matrix further described inAppendix A.

By using the simplifications above, using a bar notation for the operator E{·}according to di = E{di} and defining Ri , HCiHH + N, the estimate di can bewritten as

di = di + (ciR−1i h)H(yi − yi) (4.16)

= di + wHi (yi − yi)

yi , Hdi (4.17)

The vector wi , ciR−1i h can be seen as a linear filter applied to the difference

yi−yi, where yi is the reconstruction of the received signal based on chip probabil-ities achieved from the decoder extrinsic information and the channel informationused in the equalization. The vector wi with the size 2 (2F + 1 )λ is in Equation4.16 a time varying vector which in expanded form can be written as

wi = ci(HCiHH + N)−1h = ciR−1i h. (4.18)

Equation 4.18 represents the so called optimal LMMSE equalization weights.di and ci in Equation 4.16 and 4.18 are a priori information to the equalizer.They are computed using extrinsic LLR values L(rb,z) derived from the decoder,see Figure 4.1. The decoder output consist of extra knowledge of the equalizedsymbols in previous Turbo equalization iteration and this information is meant tohelp the equalizer to improve the chip estimations through di and ci in currentiteration. In the special case when no a priori information is available, as in thefirst iteration of Turbo equalization or in standard Linear Minimum Mean SquareError Chip Equalization (LMMSE-CE), the a priori information for all i is set todi = 0 and ci = σ2

d. σ2d represents the chip power and is defined as


σ2d ,

K∑k=1

β2ed,k + β2

ec + β2c . (4.19)

where β2ed,k, β2

ec and β2c represents power scaling factors applied to the respective

physical channel.

When no a priori information is available, denoted as NA, the filter coefficientswi are constant over the equalized block of chips according to

wNA = wi|di=0,ci=σ2d, ∀ i = σ2

d(σ2dHHH + N)−1h = σ2

dRNA−1h. (4.20)

When a priori information is incorporated into the derived equalization algo-rithm 4.16 at the second or higher Turbo equalization iterations the computationalcomplexity is high due to the matrix Ri changes and needs to be inverted at es-timation of each chip. The matrix changes due to the chip covariance statisticsci+F , ..., ci−F−L inside the matrix Ri changes at estimation of each single chip i.There are some adaptive methods to do inverse matrix updating since succeedingmatrices have similarities. However further simplifications are desirable for a lowcomplexity implementation. An approximative LMMSE equalization method pro-posed in [48] is therefore used where an average chip covariance value is used overthe whole equalized block of chips.

c ≈ 1BN

BN∑j=1

ci (4.21)

where BN is the block size in chips. By doing this computational complexitycan be reduced since the matrix inversion in Equation 4.18 does not need to beupdated at estimation of each chip. The equalization process described in thissection is performed on each slot. Thereby the equalization block size is set to asingle slot, 2560 chips, in the chosen algorithm. A block size of one TTI wouldbe more convenient for Turbo equalization in HSPA since decoding is performedwhen a whole TTI is received. A HSPA 2 ms TTI spans over 3 slots and if theslots are equalized separately the chip estimates di from 3 equalizations processesare concatenated for each TTI. The equalization block size of a single slot is cho-sen considering the transmission power which can be changed due to slot basedpower control. If the equalization block size instead is TTI based the change oftransmitted power between slots would give erroneously scaled estimates using theapproximative equalization method mentioned above since it utilizes a single con-stant chip covariance over the whole equalized block. The drawback of slot basedblock size is that zero-padding is needed before and after each equalized block dueto the size of the filter sliding window. The padded causal zeros could be replacedwith information from the previous slot but still some performance degradationcan be expected in the transitions between the slots inside the TTI when equaliz-ing blocks in the size of a single slot compared to equalizing a TTI based block size.


The approximative equalization method has shown to perform very well com-pared to the optimal method, except at high number of Turbo equalization itera-tions [49]. The approximative method performs well especially when the channelvector h is stationary over the equalized block [57]. When the approximativemethod is used the equalization filter weights will be constant during equalizationof each block of chips according to

wconst = c(cHHH + N)−1h = cR−1h (4.22)

and the chips can be estimated by

di = di + wHconst(yi − yi). (4.23)

To successfully utilize Turbo equalization it is important to avoid positive feed-back when information is iterated between the LMMSE equalizer and the Turbodecoder. This can be solved in the equalizer by not taking the a priori informationfor current chip number i into account, di = 0, while estimating chip number i.The chip estimation can then be written as

di = 0 + wHconst(yi −Hdi + hdi) (4.24)

= wHconst(yi − yi + hdi)

where the vector hdi is added for eliminating the contribution of di in Hdi.

Equation 4.23 is an unbiased estimate under slow varying channel conditionsas claimed in [58]. But the chip estimate di in Equation 4.24 becomes biased,E{di − di} 6= 0, after the modification and may require correction. In [57] it issuggested that the correction of the LMMSE algorithm can be done by minimizingthe mean square error under the constraint that the equalized response is unity,wHh = 1 , resulting in scaling of the chip estimate by a factor (chHR−1h)−1.Correctly scaled symbol estimates are achieved by using the equalizer weight

w = R−1hhHR−1h . (4.25)

Details about the scaling can be found in [27] and [57]. After applying the biascorrection term on Equation 4.24 the resulting expression for chip estimation isgiven by

di = di + wH(yi − yi). (4.26)

Equation 4.26 is the resulting chip estimate and it is possible to place di outsidethe parenthesis since the filter weights were gained under the constraint wHh = 1 .


4.3 Descrambling & Despreading

Here the chip estimates, di, are despread to symbols, xk,n. The estimated chipnumber i can be written similarly to Equation 4.2 on page 28

di =K∑k=1

βed,kqed,kak,ixk,i div Sk + βecqecaec,ixec,i div Sec + βcqcac,ixc,i div Sc + wi

(4.27)except the variable wi representing receiver noise and interference after equaliza-tion. After despreading and descrambling the symbol estimates for physical datachannel k, k = 1, ...,K, can be written as

xk,n = q∗ed,k

(n+1)Sk−1∑i=nSk

dia∗k,i = βed,kSkxk,n +Wk,n. (4.28)

where the variable Wk,n represents noise and interference after despreading. Theinterference in Wk,n includes ICI from other data channels and control channels.The received symbol estimates xk,n are scaled with the spreading factor Sk andbeta factor βed,k compared to transmitted symbols xk,n. This is due to despreadingand amplification at transmission.

4.4 Soft Demodulation

Each symbol xk,n is here soft demodulated to extrinsic LLRs L(bk,n,q) represent-ing probabilities for corresponding bits. The q in L(bk,n,q) is the bit number insymbol n.

For demodulating estimated symbols the PDFs p(xk,n | xk,n = αr) = p(xk,n |bk,n = sr), r = 1, 2, ..., 2Q are assumed to be gaussian with mean E{xk,n | xk,n =βed,kSkαr} = βed,kSkαr and noise plus interference variance σ2

n. According to [58]one can write the symbol level noise and interference variance after despreadingoperation as

σ2n , E{W 2

k,n} = Sk

hHR−1h(4.29)

where the impairment matrix is defined as R , R − chhH [58].

When BPSK modulation is used the estimated symbols can be demodulatedto LLR values using the following equations

4.5 Deinterleaver, HARQ Combining & Rate Dematching 35

L(bk,n,1) , ln

(p(xk,n | xk,n = +1)p(xk,n | xk,n = −1)

)(4.30)

= ln

e− 1σ2n

(xk,n−βed,kSk)2

e− 1σ2n

(xk,n+βed,kSk)2

= 1σ2n

((xk,n + βed,kSk)2 − (xk,n − βed,kSk)2)

= 4βed,kSkσ2n

xk,n

where L(bk,n,1) is defined as the LLR extrinsic information from the Equalizer. Asseen in Equation 4.30 the soft demodulation to LLRs for BPSK modulated symbolsis simply performed through a scaling. This scaling is important since the inputLLRs need to be properly scaled when processed by the decoder in order to achievecorrectly scaled decoder output extrinsic LLRs. L(bk,n,1) can after inserting 4.29into 4.30 be written as

L(bk,n,1) = 4βed,khHR−1hxk,n (4.31)

When transmitting with 4-PAM modulated symbols similar equations as the onesabove are used for mapping one symbol to two bit LLRs.

4.5 Deinterleaver, HARQ Combining & Rate De-matching

In this step the streams of LLRs representing each physical data channel k are sep-arately deinterleaved and they are after deinterleaving concatenated to one blockof LLRs. This stream of LLRs is rate matched to the correct number of encodedbits expected at the following Turbo decoding. Retransmission combining is alsoperformed here if a retransmission is received. The resulting stream of LLRs issplit into separate code blocks of LLRs, L(rb,z), according to the segmentationprocedure in the standard. Index b denotes code block number and index z bitnumber in code block. If only one encoder is used at transmission no segmentationis performed.

4.6 SISO Turbo DecoderAs seen in Figure 4.4 the LLR code bit estimates L(rb,z) obtained from the equal-ization extrinsic information are fed into the Turbo decoder. The output fromthe decoder, after a desired number of turbo decoding iterations, are coded bitextrinsic LLRs L(rb,z) and decoded data bit decisions. Decoded data bit decisions


from all code blocks are at the end of each Turbo decoding process concatenatedand sent to a CRC check for detection if the TTI is decoded without any errors. Ifthis is the case an ACK signal is generated and the Turbo equalization iterationsare stopped. If the TTI is not successfully decoded the Turbo equalizer continuesthe iterations by processing the coded bit extrinsic LLRs L(rb,z).


L(rb,z)

L(rb,z)SISO Turbo

decoder

Figure 4.4: SISO Max-Log-MAP Turbo decoder.

The Turbo decoder used in the simulations is for complexity reasons a SISOMax-Log-MAP Turbo decoder and the interested reader is referred to literature[38] for details.

4.7 Interleaver, HARQ & Rate MatchingThe extrinsic LLR output values L(rb,z) from the SISO Turbo decoder are in thecode block concatenation put together to a single stream of LLR values. Thenrate matching is performed as shown in Figure 4.2, followed by physical channelsegmentation. When the LLR values are separated to physical data channelseach physical data channel stream is interleaved in the same pattern as the bit-interleaver used in the transmitter. We define the resulting LLRs as L(bk,n,q)where k represents physical data channel number, n the symbol number and q thebit number in symbol n.

4.8 Soft ModulationThe LLRs L(bk,n,q) arrives in separate physical data channel streams which areseparately soft modulated to estimates of the transmitted symbols xk,n and theircovariances Cov{xk,n, xk,n} according to

xk,n , E {xk,n} =∑αrεS

αr · P{xk,n = αr} (4.32)

vk,n , Cov {xk,n, xk,n} =(∑αrεS

|αr|2 · P{xk,n = αr}

)− |xk,n|2 (4.33)

4.8 Soft Modulation 37

Table 4.1: Symbol alphabet BPSK

r 1 2sr,1 0 1αr +1 -1

Table 4.2: Symbol alphabet 4-PAM

r 1 2 3 4sr,1sr,2 01 00 10 11αr +1.3416 +0.4472 -0.4472 -1.3416

P{xk,n = αr} =Q∏q=1

P{bk,n,q = sr,q} (4.34)

Since the bit values arriving to the soft modulator are given in LLR format theyneed to be converted to bit probabilities using

P{bk,n,q = sr,q} = 12 + sr,q ·

tanh (L(bk,n,q)/2)2 (4.35)

where

sr,q ,

{+1 if sr,q = 0−1 if sr,q = 1.

(4.36)

Using the equations together with the symbol alphabet given in Table 4.1 forBPSK and Table 4.2 for 4-PAM, the bit LLRs to symbol statistics operations canbe summarized in Table 4.3.

Table 4.3: Conversion from L(bk,n,q) toxk,n , E {xk,n} and vk,n , Cov {xk,n, xk,n}

BPSK:xk,n = tanh (L(bk,n,1)/2)vk,n = 1− |xk,n|24-PAM:γ1 , tanh (L(bk,n,1)/2)γ2 , tanh (L(bk,n,2)/2)xk,n = (0.4472/2) · γ1 · (1 + γ2) + (1.3416/2) · γ1 · (1− γ2)vk,n =

(0.44722/2

)· (1 + γ2) +

(1.34162/2

)· (1− γ2)− |xk,n|2


4.9 Spreading & Scrambling, Chip Mean & Co-variance Calculation

In this module the input statistics xk,n and vk,n are spread with physical datachannel specific spreading codes and summed up for achieving chip statistics, rep-resenting the chips which the Turbo equalizer is trying to estimate. The modulethereby output chip means E {di} and chip covariances Cov{di, di} based on the apriori information. These are the statistical values which are supposed to help theequalizer to improve the chip estimations at the beginning of next Turbo equal-ization iteration.

The chip statistics can be derived by

di , E {di} =K∑k=1

βed,kqed,kak,ixk,i div Sk +βecqecaec,ixec,i div Sec +βcqcac,ixc,i div Sc

(4.37)

ci , Cov{di, di} =K∑k=1

β2ed,kvk,i div Sk + β2

ec + β2c (4.38)

Here ci is defined as the chip covariance and it is supposed to be equivalent withEquation 4.19 when no a priori information is present and thereby the estimatedsymbol covariances vk,i div Sk = 1. In Equation 4.37 βecqecaec,ixec,i div Sec andβcqcac,ixc,i div Sc represents the contribution of the control channels where the truecontrol channel symbols are used instead of estimated ones. This is for minimizingthe effect of the control channel under the simulations.

The chip statistics di and ci are then used in the equalizer as a priori informa-tion when updating the filter weights. The di chip statistics are not oversampledand convolved with any pulse shaping filter at this stage since this is handled bythe oversampled channel coefficients which include the transmission and receptionpulse shaping filters, for example in Equation 4.17.

4.10 Retransmission HandlingThis section explains the HARQ transmission functionality which spans over thewhole Turbo equalization process and does not describe a single module.

The HARQ method used in this study is Incremental Redundancy (IR). Theretransmitted packets include different sets of parity bits from the 1/3 Turboencoder and the combing is not trivial when incorporating Turbo equalization.Storing the values from the first Turbo equalization iteration do not make anydifference compared to normal equalization and decoding retransmission combi-nation, except the current received packet which could be Turbo equalized andadded to the previous stored LLR values. The benefit is that the values stored are

4.10 Retransmission Handling 39

not converged, if erroneously converged values are stored it could negatively affectthe following retransmission combinations. If Turbo equalized values are storedafter the last Turbo equalization iteration they might be erroneously convergedbut are on the other hand very helpful if they are approaching correct bit values.The later option with storing fully Turbo equalized values has been implemented.A simplified overview of retransmission combining when two Turbo decoders andthree HARQ transmissions are used can be seen in Figure 4.5.


y(1)

Input fromchannel

y(2)

y(3)

Interleaver 3

Interleaver 2

Interleaver 1

Deinterleaver 3

Deinterleaver 2

Deinterleaver 1




HARQ & RateMatching

HARQ Combining &Rate Dematching

SISO Turbodecoder

SISO Turbodecoder

Figure 4.5: A simplified overview of HARQ transmission combining when twoTurbo decoders and three HARQ transmissions are used.

When the soft bit buffer for current HARQ process is empty and the firstpacket y(1) is received, normal Turbo equalization is done. When NACK signalis received after the last Turbo equalization iteration the soft bit buffer is storedand a retransmission is requested 8 subframes later, if 2 ms TTI is used. Whenthe next packet y(2) for the HARQ process is received it is equalized and com-bined with the stored information in the soft bit buffer. Then the combined LLRsare decoded. The decreased code rate due to packet combination provides morereliable decoding. If NACK is signalled again after the last Turbo equalizationiteration a new retransmission is signalled and received 8 subframes later. y(3)is then equalized and its output is combined with the previous stored soft bits,followed by decoding. This continues until the maximal number of retransmissionsis reached.


Chapter 5

Algorithm Evaluation

5.1 Simulation EnvironmentThe simulations have been performed using IT++, which is an open source C++library with classes and functions for mathematics, signal processing and commu-nication routines.

5.2 Simulation Setup and ParametersAs earlier mentioned only a single user is considered in the simulations. The onlyinterference is the user’s own self-interference introduced by the dispersive chan-nel. In the simulator two channelization codes with SF 2 and two channelizationcodes with SF 4 are used for all simulation setups listed in Table 5.1. The controlchannels E-DPCCH and DPCCH, with spreading factors of 256, are also includedin the transmitted signal. The relative power of all control channels is 8% and therelative power of all data channels is 92% of the total transmission power.

With a chip rate of 3.84 Mcps and selecting a spreading factor of 2 or 4, symbolrates of 1280 and 640 symbols/slot are achieved. This gives 1.92 Msymbols/s whena spreading factor of 2 is used and 0.96 Msymbols/s when a spreading factor of4 is used. Applying 4-PAM modulation to the channelization codes used in thesimulations results in a total peak data rate of 11.52 Mbit/s. This throughput isonly achievable when all parity bits are punctured, resulting in a code rate of 1.Usually the transmission data rate is lower than the peak rate since at least someparity bits are needed for reliable communication.

Channel estimation is not performed in simulations and it is assumed that thechannel is known. The Turbo encoder is based on 1/3 rate PCCC and the Max-Log-MAP Turbo decoder performs 8 decoding iterations if nothing else is stated.The LMMSE equalizer filter length F is set to 40, giving a total sliding windowof N = 2F + 1 = 81 chips. The equalizer channel impulse response length L is

41

42 Algorithm Evaluation

Table 5.1: Simulation parameters

Simulation parameter SetupBPSK6 PAM12 PAM22 S-BPSK6

Modulation BPSK 4PAM 4PAM BPSKTransport Block Size (bits) 6000 12000 22000 6000

Code Rate 0.52 0.52 0.96 0.52TPC on on on off

Max # HARQ Transmissions 4 4 4 1Nrof RX Antennas 2 2 2 1

set to 30 chips in all simulations. The equalizer parameters have been estimatedthrough test simulations performed with Pedestrian B channel model. A filtersample space of λ = 2 samples per chip is used in all simulations. Using a filtersample space of λ = 4 has also been tested and results showed similar performanceas the ones with λ = 2. In the simulations both 1 and 2 receiver antennas are usedand the number of antennas can be set with the variable ∆. These parametersgive a total filter length of Nλ∆ = 324 filter taps when 2 antennas are used and162 filter taps when 1 antenna is used. Up to 4 transmissions have been used insimulations incorporating HARQ retransmissions.

When 1 iteration is stated in the figures of the simulation results it indicatesthat the received signal has only been equalized (without a priori information)and decoded once, resulting in a standard Linear Minimum Mean Square ErrorChip Equalization (LMMSE-CE) reception. In the second or more iterations theequalizer uses a priori information. The a priori information is obtained afterprocessing Turbo decoder extrinsic information from the previous iteration. Thenumber of simulated radio frames is 3000 and thereby the number of data blocks15000 in all simulations.

The performance of the simulations is evaluated in terms of throughput for aparticular transport format, that is, a particular modulation and coding rate. Thethroughput is plotted against the signal-to-noise ratio Ec/N0 per antenna, whereEc is the received chip-stream energy and N0 is noise.

The simulation setup PAM22 is used for evaluating the Turbo equalization per-formance as close to the peak rate as possible. The maximum throughput is here11 Mbit/s and a code rate of 0.96 is used. Simulation setup PAM12 is used forevaluating the effect on Turbo equalization when the Turbo decoder uses a lowercode rate. The highest code rate is here 0.52. The simulation setup BPSK6 isused for evaluating the Turbo equalization performance with BPSK modulation.S-BPSK6 simulations run the Turbo equalizer without TPC, without HARQ re-transmissions and with only a single receive antenna for studying the effect when

5.2 Simulation Setup and Parameters 43

the system is as simple as possible.

0 5 10 150

0.1

0.2

0.3

0.4

Relative Delay [Chips]

Rela

tive M

ean P

ow

er

TU (typical urban) channel tap placement

0 5 10 150

0.2

0.4

0.6

0.8

1


Rela

tive M

ean P

ow

er

PedB (Pedestrian B) channel tap placement

0 5 10 150

0.2

0.4

0.6

0.8

1


Rela

tive M

ean P

ow

er

PedA (Pedestrian A) channel tap placement

Figure 5.1: Original tap placement of channels used in simulations. For exactvalues used in simulations see Appendix B.

The channel models used in the simulations are the 3GPP TU (Typical Urban),International Telecommunication Union (ITU) Pedestrian A and ITU PedestrianB. The UE speed is 3 kmph in all simulations if nothing else is stated and thecarrier frequency is assumed to be 2 GHz. TU and Pedestrian B are classified asheavily dispersive while Pedestrian A is a lightly dispersive channel. The exacttap placements are illustrated in Figure 5.1 where the x-axis represents tap delayin number of chips. As the chip rate is fixed in HSPA the delay for one chip isapproximately 0.26 µs. In simulations the channel taps are moved to the closest1/4 chip space since a channel sampling resolution of a 1/4 chip is used. Themodified tap delay values used in the simulations are given in Appendix B.


5.3 Simulation Results and Analysis

5.3.1 Performance in Lightly Dispersive Channels

The Pedestrian A channel is a channel model with low time-dispersion. Figure 5.2shows simulation performances through the Pedestrian A channel with the setupBPSK6 and shows only a maximum gain of 0.3 dB. Figure 5.3 shows simulationperformances through a Pedestrian A channel with the setup PAM22 and showsonly a maximum gain of 0.1 dB. There is not much iterative gain from Turboequalization when it is applied on transmissions sent through lightly dispersivechannels. This can be explained by the channel taps in Pedestrian A channelwhich usually only have a single strong tap. As there are no other strong taps thedispersion is small resulting in less ICI. Possibly the gain from using a LMMSEequalizer with known channel parameters and two receiver antennas is good enoughfor compensating for the ICI in this lightly dispersive channel.

-10 -8 -6 -4 -2 0 20

0.5

1

1.5

2

2.5

3

Thro

ughput (M

bps)

Average received Ec/N

0 (dB)

Iteration 1 (LMMSE-CE)

Iteration 2

Iteration 3

Iteration 4

Iteration 5

Figure 5.2: Turbo equalization iterative gain when simulation setup BPSK6 isused in Pedestrian A channel.

5.3 Simulation Results and Analysis 45

-4 -2 0 2 4 6 8 10 12 140

2

4

6

8

10

12

Thro

ughput (M

bps)


0 (dB)


Iteration 2

Iteration 3

Iteration 4

Iteration 5

Figure 5.3: Turbo equalization iterative gain when simulation setup PAM22 isused in Pedestrian A channel.


5.3.2 Performance in Heavily Dispersive ChannelsSimulation setup PAM22 is used in Figure 5.4 where simulations are performedin Pedestrian B channel. At higher Ec/N0 values the gain is about 0.25 dB andat lower Ec/N0 values where a couple of retransmissions have been received thegain is 0.5 dB. Figure 5.5 shows results from setup PAM12 simulated in Pedes-trian B channel, here up to 0.35 dB gain is achieved at higher Ec/N0 values. InFigure 5.6 simulations with setup BPSK6 is performed in Pedestrian B channel.Here an approximative gain of 0.35 dB is noticed in the higher throughput ranges.In Figure 5.10 showing results from simulations under the S-BPSK6 setup, where1 antenna is used and transmissions are done without TPC and retransmissions,gains of 0.8 dB is obtained with only 3 Turbo equalization iterations. In Figure 5.8where an other transport block size have been used the gain is close to 1 dB.

Simulation results from TU channel and simulation setup PAM22 are shown inFigure 5.7. The Turbo equalization performance at higher Ec/N0 values are lessthan 0.1 dB in TU channel. At lower Ec/N0 values, where a couple of retransmis-sions have occurred, the gain is 0.15 dB.

The results from simulation setup PAM22 simulated in the heavily dispersivechannels Pedestrian B and TU can be compared with the Pedestrian A perfor-mance presented in Figure 5.3, where the gain is very small. Comparison betweenPedestrian A channel and a heavily dispersive channel can also be done with resultsfrom Figure 5.2 and Figure 5.6 where setup BPSK6 has been used.

5.3.3 Decoding AlgorithmA simulation with S-BPSK6 (except transport block size = 10000, code rate 0.87)setup has been performed for comparison of different Turbo decoding algorithms.Solely the Max-Log-MAP algorithm has been used in all other simulations andthese simulations have been performed for investigating if a more complex decodingalgorithm could generate better results. As described before the Max-Log-MAPis an approximation of the MAP algorithm. Using the optimal method would becomputationally too complex so the Log-MAP algorithm, which is an extensionof the Max-Log-MAP algorithm, has been used for comparison. In Figure 5.8the simulation results show that it is only a negligible Turbo equalization iterativegain over Max-Log-MAP algorithm when using the Log-MAP algorithm. Running3 iterations in the Pedestrian B channel resulted in up to 1 dB gain when usingboth decoding algorithms. An overall performance gain of approximately 0.1 dBis noticed when comparing Log-MAP and Max-Log-MAP algorithms.

5.3.4 Code RateIn this comparison simulations in Pedestrian B channel are used. Looking at Fig-ure 5.5 showing simulation with setup PAM12 (code rate 0.52) and Figure 5.4showing simulation with setup PAM22 (code rate 0.96) the gain is not much largerin the lower code rate case as it might be expected. This can be explained by the


-2 0 2 4 6 8 10 12 14 16 180

2

4

6

8

10

12

Thro

ughput (M

bps)


0 (dB)


Iteration 2

Iteration 3

Iteration 4

Iteration 5

Figure 5.4: Turbo equalization iterative gain when simulation setup PAM22 isused in Pedestrian B channel.


-6 -4 -2 0 2 4 60

1

2

3

4

5

6

Thro

ughput (M

bps)


0 (dB)


Iteration 2

Iteration 3

Iteration 4

Iteration 5

Figure 5.5: Turbo equalization iterative gain when simulation setup PAM12 isused in Pedestrian B channel.


-12 -10 -8 -6 -4 -2 00

0.5

1

1.5

2

2.5

3

Thro

ughput (M

bps)


0 (dB)


Iteration 2

Iteration 3

Iteration 4

Iteration 5

Figure 5.6: Turbo equalization iterative gain when simulation setup BPSK6 isused in Pedestrian B channel.


-4 -2 0 2 4 6 8 10 12 140

1

2

3

4

5

6

7

8

9

10

Thro

ughput (M

bps)


0 (dB)


Iteration 2

Iteration 3

Iteration 4

Iteration 5

Figure 5.7: Turbo equalization iterative gain when simulation setup PAM22 isused in TU channel. Except a transport block size of 20000 bits has been usedinstead of a transport block size of 22000 bits, for achieving a code rate of 0.87.


6 8 10 12 14 16 18 20 220.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Thro

ughput (M

bps)


0 (dB)

Iteration 1 (using Max-Log-MAP)

Iteration 3 (using Max-Log-MAP)

Iteration 1 (using Log-MAP)

Iteration 3 (using Log-MAP)

Figure 5.8: Compare Log-MAP and Max-Log-MAP Turbo decoders when usingTurbo equalization with Pedestrian B channel and simulation setup S-BPSK6.Except a transport block size of 10000 bits has been used instead of a transport

block size of 12000 bits, for achieving a code rate of 0.87.


fact that when only a single iteration (simple LMMSE-CE reception and decoding)has been run, the strong error correction capability of a Turbo decoder, utilizinga low code rate, has already corrected most of the errors. At higher data ratesthe gain in PAM22 is approximately 0.25 dB compared to 0.35 dB in the PAM12case. At lower Ec/N0 values the gain in PAM22 setup is as high as 0.5 dB whilethe gain stays at 0.18 dB in the PAM12 case. At these Ec/N0 values several re-transmissions have been received.

Simulations done with different coding rates are compared in chapter "Compar-ative Study of Turbo equalizers" of the book "Turbo Coding, Turbo equalizationand Space-Time Coding" written by Hanzo et al. [32]. Their results show varyingperformance depending on chosen code rate or decoding algorithm and it seemsto be hard to see any correlation between used code rate and performance.

-3 -2 -1 0 1 2 3 40

0.5

1

1.5

2

2.5

Thro

ughput (M

bps)


0 (dB)

Iteration 3 (using 8 internal Turbo decoding iterations)



Figure 5.9: Different combinations of internal Turbo decoder iterations andTurbo equalization iterations. A different setup with 1 receiver antenna, 4PAMmodulation, ETFCS=20000, no retransmissions and no TPC has been used in

Pedestrian B channel.


5.3.5 Turbo Equalization and Turbo Decoding IterationsThe number of Turbo equalization iterations and the number Turbo decoding it-erations have been evaluated by simulations. First the performance depending onthe number of Turbo equalization iterations is described and in these simulations8 Turbo decoding iterations have been performed in each Turbo equalization iter-ation.

As seen in most figures of the simulation results the Turbo equalization gain isbiggest between the curves representing the first and second iterations. In follow-ing iterations the gain for each iterative step is reduced. This behavior is notablein most simulations but in Figure 5.10 where iterations up to number 7 is pre-sented it is clearly visible that most part of the total gain is achieved at iteration3. A lot of computation is needed for reaching iteration 7 though the gain is min-imal. This extra computational effort is probably not worth the small increase inperformance. The simulation results in this study indicate that it would not benecessary to continue above 3 iterations.

According to some papers the number of internal Turbo decoding iterationsshould be kept low at each Turbo equalization iteration, e.g. [41]. In [41] theauthors recommended one Turbo decoding iteration at each Turbo equalization it-eration. An article which also considers Turbo equalization incorporating a Turbodecoder running few iteration is [22]. In the article, which is briefly describedin previous chapters, it is concluded that complexity is reduced and prematureconvergence of extrinsic information is avoided if the number of Turbo decodingiterations is kept low.

Turbo equalization simulations have been performed with different combina-tions of internal Turbo decoder iterations and Turbo equalization iterations. Asseen in Figure 5.9 the configuration providing the best performance is the setuprunning 8 internal Turbo decoding iterations in each iteration of Turbo equal-ization. Turbo equalization is defined as TEQ in the figure. Other simulationsresulting in the same conclusion has been performed within this thesis but thefigures are not included here. In contrast to the mentioned papers the results ofthis study show the necessity of multiple internal Turbo decoding iterations forthe implemented algorithm. One also need to consider that in the articles [41] and[22] the authors use a modified decoding structure of the two single componentcodes inside the Turbo decoder for avoiding convergence.

5.3.6 UE VelocityIn Figures 5.10 and 5.11 simulations are performed in the Pedestrian B channelusing setup S-BPSK6 and the UE velocities 3 kmph and 30 kmph. The Turboequalization performance gain is almost identical in both UE velocities, even if theresulting throughput differs between them. The increased speed which results ina faster fading channel does not seem to affect the achievable gain when using theapproximative Turbo equalization method which only updates the equalizing filter


once every slot. A UE velocity of 120 kmph has also been simulated in the sameconditions and the results show that the Turbo equalization gain is retained.

-1 0 1 2 3 4 5 60

0.5

1

1.5

2

2.5

3

Thro

ughput (M

bps)


0 (dB)


Iteration 2

Iteration 3

Iteration 7

Figure 5.10: Turbo equalization iterative gain when simulation setup S-BPSK6used in Pedestrian B(3 kmph) channel.

5.3.7 Other DiscussionsRetransmission, TPC and 2 receiving antennas have been used in the simulationsperformed with setups BPSK6, PAM12 and PAM22. In simulations with setupS-BPSK6 these functionalities are disabled. When comparing the figures of sim-ulations with these functionalities enabled with setup S-BPSK6, e.g. comparingFigure 5.6 with Figure 5.10, one can see that the gain of the Turbo equalizer isobvious less. The retransmissions would hardly have any role in this gain degra-dation. TPC could have some affect since the transmission power is not constantover a TTI and the slot mean chip amplitudes are fluctuating between each slot. Itcould possibly disturb the derived Turbo equalization algorithm. TPC also lowersthe required Ec/N0 for the same throughput, resulting in more noise than ISI,which can effect the performance. The most likely reason for Turbo equalizationgain loss is the 2 receiving antennas which by antenna diversity already very ef-


1 2 3 4 5 6 7 80.5

1

1.5

2

2.5

3

Thro

ughput (M

bps)


0 (dB)


Iteration 2

Iteration 3

Iteration 7

Figure 5.11: Turbo equalization iterative gain when simulation setup S-BPSK6 isused in Pedestrian B(30 kmph) channel.


fectively mitigate much of the interference. There is simply less interference leftto cancel out by the Turbo equalization algorithms.

Other factors which could possibly affect the performance is that no extensivesimulations have been performed for determining the optimal filter length in chipsand channel sampling length. The parameters have been calibrated with simu-lations running simple LMMSE-CE in Pedestrian B channel. These values havelater been used in the rest of the simulations regardless of the channel type andconfiguration used.

Chapter 6

Conclusions and Remarks

A literature survey has been done on Turbo equalization and a low complexityLMMSE based Turbo equalizer has been implemented in a HSPA uplink simula-tor. The algorithm has been extended to multiple receiver antennas, oversampling,4-PAMmodulation and retransmission handling. Simulations have been performedin lightly and heavily dispersive channels to analyze the performance of the algo-rithm.

6.1 ConclusionsAccording to the achieved results from simulations in lightly dispersive channelsthe Turbo equalizer gain is very small. It can be explained by the fact that Turboequalization is performed for reducing ICI and in a lightly dispersive channel theICI is less severe compared to heavily dispersive channels.

The Turbo equalization performance in heavily dispersive channels shows upto 0.5 dB gain. Simulations using 1 receiving antenna, having TPC disabled andnot using retransmissions have been performed to evaluate a more simple commu-nication link. The achievable gain then reached up to 1 dB and the single receiverantenna can be the major reason for the increase in gain. This can still not beconfirmed without further simulations.

Simulations also show that the additional gain after 3 Turbo equalization iter-ations is very small and that further iterations thereby are computationally costineffective. According to simulations comparing the usage of the more complexLog-MAP decoder with the Max-Log-MAP decoder there is no significant gain.The effect of different code rates has been evaluated but results are hard to inter-pret even if lower code rate showed a small gain in overall. The simulations alsoshow that the number of internal Turbo decoding iterations should be kept highusing the implemented algorithm.

57

58 Conclusions and Remarks

The implemented Turbo equalization algorithm did not give significant gaincompared to simple LMMSE-CE and comparing the results with other referencesis difficult due to the different used algorithms, wireless systems and transmissionsetups. In general many studied proposals present better results with 2 dB gain ormore but usually in these cases the transmission bit rate is lower and the equalizeris only utilizing one receiver antenna [58], [44]. Some papers have mentioned thepoor Turbo equalization gain when equalizing a single transmitted stream withtwo receiving antennas [36]. Another reason why the study doesn’t show as largegain as expected might be that the LMMSE equalizer is assumed to know thereal channel coefficients. If estimated channel coefficients are used in the LMMSEequalizer the Turbo decoder feedback might contribute to an improved overallTurbo equalization gain. More simulations are needed for concluding the approachand suggestions for further work are given in the next section.

6.2 Further WorkThe performance of the implemented Turbo equalizer does not advocate an appli-cation in a real system. Further studies are necessary to determine whether theTurbo equalization is useful together with HSPA uplink.

• Channel Estimation and Noise Variance EstimationThe most important continuation to the performed work in this thesis isthe addition of algorithms for channel estimation, which is for example donein [58]. The Turbo equalization gain is expected to increase when chan-nel estimation is used since the decoder extrinsic information will be evenmore useful for the inferior equalization caused by imperfect channel esti-mations. The channel estimation will though affect yi, the reconstructionof the received signal in the equalizer, negatively and modifications of theequalization algorithm might be needed. When channel estimates are usedin Turbo equalization the extrinsic information from the decoder could alsobe used for iteratively improving the channel estimates at each iteration. In[37] some adaptive channel estimation algorithms for Turbo Equalization arepresented.

• Hybrid and Optimal LMMSE AlgorithmsSince optimal Turbo equalization methods have high computational com-plexity approximative methods like the one presented in this thesis are used.These approximative methods can have varying performance depending ondifferent parameters such as LLR magnitudes, SINR, code rate and numberof Turbo equalization iterations. One way to deal with this problem is touse hybrid methods with switched algorithms like the one presented in [49].EXIT-charts could be used for comparing different algorithms when devel-oping these hybrid methods. One approach could also be to evaluate theoptimal LMMSE algorithm since the approximative algorithms could be farto simplified for achieving significant gain.

6.2 Further Work 59

• DemodulationA way to increase the performance of the algorithm could also be more de-tailed demodulation. The bit probabilities derived from the decoder extrinsicinformation can be incorporated in the demodulation as described in [48].

• Turbo DecoderA Turbo decoder approach which looks promising is the decoding of eachconstituent RSC decoder separately as proposed in [22]. The benefits areclaimed to be complexity reduction in certain scenarios and avoidance ofpremature converging of extrinsic information.

• Equalization Block LengthThe equalization is performed once every slot in the implemented algorithm.Since one 2 ms TTI consists of three slots in the uplink HSPA standard,decoding is done of all information from three equalized slots. It would beinteresting to investigate the effect of equalizing a whole 2 ms TTI at onceand compare to the method used where one slot is split into multiple partswhich are equalized separately.

60 Conclusions and Remarks

Appendix A

Noise Correlation Matrix

Due to oversampling and RRC reception filter the resulting noise nαi is not a whiteGaussian process. The RRC filter colors the noise and the noise autocovariancesquare matrix Nα of size (2F + 1 )λ× (2F + 1 )λ is used in the LMMSE algo-rithms. In the following time-continuous derivation w(t) represents white noise,hRRC(t) the real-valued RRC-filter and n(t) the received noise at time instant t.

n(t) = hRRC(t) ? w(t) =∞∫−∞

hRRC(t− τ)e(τ)dτ (A.1)

E{n(t1)n∗(t2)} = E{∞∫−∞

hRRC(t1 − τ1)w(τ1)dτ1∞∫−∞

hRRC(t2 − τ2)w∗(τ2)dτ2} =

(A.2)

=∞∫−∞

∞∫−∞

hRRC(t1 − τ1)hRRC(t2 − τ2)E{w(τ1)w∗(τ2)}︸︷︷︸σ2wδ(τ1−τ2)

dτ1dτ2 =

= σ2w

∞∫−∞

hRRC(t1 − τ1)hRRC(t2 − τ1)dτ1 =

= σ2w

∞∫−∞

hRRC(t1 − t2 + τ)hRRC(τ)dτ = σ2wr(t1 − t2)

where r(t) is the autocorrelation of the RRC-filter hRRC(t) and σ2w is the noise

power. Since hRRC(t) is a symmetric function hRRC(t) = hRRC(−t) it can beshown that

61

62 Noise Correlation Matrix

r(t) =∞∫−∞

hRRC(t+τ)hRRC(τ)dτ =∞∫−∞

hRRC(t−τ)hRRC(τ)dτ = (hRRC?hRRC)(t).

(A.3)The convolution (hRRC?hRRC)(t) can in frequency domain be written asHRRC(ω)·HRRC(ω) and since the relation between RRC frequency response, HRRC(ω), andRaised Cosine (RC) frequency response, HRC(ω), can be written as

HRC(ω) = HRRC(ω) ·HRRC(ω) (A.4)

the autocorrelation r(t) equals a RC-filter.

The oversampled noise correlation matrix with two receiver antennas can thenbe written as

N =[N1 00 N2

](A.5)

where Nα = Cov{nαi ,nαi } is the diagonal symmetric noise correlation matrixrepresenting antenna number α. The zero matrices 0 in the two antenna rep-resentation corresponds to uncorrelated noise between antennas, Cov{nki ,nli} =0,∀ k, l, k 6= l.

Element in row m and column n in Nα is given by

{Nα}m,n = E{nαi [m]nαi [n]} = (σαw)2r[n−m] (A.6)

where r[τ ] is the sampled RC-filter, sampled at same rate as the noise vector. Theequality E{nαi [m]nαi [n]} = (σαw)2r[n −m] is valid for all i and α since the sameRRC filter is used on each chip and at reception of both antennas.

Appendix B

Used Propagation Channels

The channel models used in the simulations are modified, channel taps are movedto the closest 1/4 chip space since a sampling resolution of a 1/4 chip is used.

63

64 Used Propagation Channels

Table B.1: Propagation Conditions for Multi-Path FadingEnvironments

Modified Modified ModifiedITU Pedestrian A ITU Pedestrian B Typical Urban (TU)

Speed 3km/h Speed 3km/h Speed 3km/hRelative Relative Relative Relative Relative Relative

Delay Mean Power Delay Mean Power Delay Mean Power[ns] [dB] [ns] [dB] [ns] [dB]0 0 0 0 0 -5.7

130 -9.7 195 -0.9 195 -7.6195 -19.2 780 -4.9 520 -5.4390 -22.8 1170 -8.0 650 -11.5

2275 -7.8 910 -13.43705 -23.9 1235 -16.3

1300 -141365 -17.41560 -16.01625 -19.81820 -18.51885 -22.11950 -22.62015 -23.52145 -24.3

Appendix C

LLR Distribution BetweenIterations

In Figure C.1 the extrinsic LLR distribution of coded bits for each Turbo equaliza-tion iteration is illustrated with simulation setup PAM22. A subframe transmittedthrough Pedestrian B channel is received. The highly uncertain LLRs in the firstiteration slowly diverge in each iterative stage and in iteration number 5 there aretwo clearly separated distributions corresponding to ones and zeros. The CRCcheck here generates an ACK, meaning that the transmitted block of data is re-ceived and decoded without any errors. In iteration 5 the LLRs representing onesand zeros are symmetrically distributed around the Y-axis, but at each of thedistributions on both sides there is a noticeable shape with two peaks instead ofone. This could possibly be explained by the use of different spreading factors ondifferent symbols or by the 4-PAM demodulation algorithm used. The algorithmused in the decoder is a Max-Log-MAP decoder approximating the MAP algo-rithm and could thereby also affect the output LLRs of the coded bits.

65

66 LLR Distribution Between Iterations

-100 0 1000

0.1

0.2

0.3

0.4Iteration 1

-100 0 1000

0.1

0.2

0.3

0.4Iteration 2

-100 0 1000

0.1

0.2

0.3

0.4Iteration 3

-100 0 1000

0.1

0.2

0.3

0.4Iteration 4

-100 0 1000

0.1

0.2

0.3

0.4Iteration 5 (ack)

Figure C.1: Extrinsic LLR distribution after code block concatenation and ratematching.

Bibliography

[1] 3GPP technical specification 25.808 (FDD enhanced uplink, physical layer as-pects), version: 6.0.0 release 6, 2005. http://www.3gpp.org/ftp/Specs/html-info/25-series.htm.

[2] 3GPP technical specification 25.201 (physical layer - general description),version: 8.1.0 release 8, 2008. http://www.3gpp.org/ftp/Specs/html-info/25-series.htm.

[3] 3GPP technical specification 25.101 (user equipment UE radiotransmission and reception FDD), version: 8.6.0 release 8, 2009.http://www.3gpp.org/ftp/Specs/html-info/25-series.htm.

[4] 3GPP technical specification 25.104 (base station BS radio trans-mission and reception FDD), version: 8.6.0 release 8, 2009.http://www.3gpp.org/ftp/Specs/html-info/25-series.htm.

[5] 3GPP technical specification 25.211 (physical channels and mapping of trans-port channels onto physical channels FDD), version: 9.0.0 release 9, 2009.http://www.3gpp.org/ftp/Specs/html-info/25-series.htm.

[6] 3GPP technical specification 25.212 (multiplexing and channel coding FDD),version: 8.5.0 release 8, 2009. http://www.3gpp.org/ftp/Specs/html-info/25-series.htm.

[7] 3GPP technical specification 25.213 (spreading and modulation FDD), ver-sion: 8.4.0 release 8, 2009. http://www.3gpp.org/ftp/Specs/html-info/25-series.htm.

[8] 3GPP technical specification 25.214 (physical layer procedures FDD), ver-sion: 8.5.0 release 8, 2009. http://www.3gpp.org/ftp/Specs/html-info/25-series.htm.

[9] 3GPP technical specification 25.306 (UE radio access capabilities), ver-sion: 8.7.0 release 8, 2009. http://www.3gpp.org/ftp/Specs/html-info/25-series.htm.

[10] LLC 3G Americas. Q&A HSPA+. http://www.3gamericas.org/index.cfm?fuseaction=page&pageid=1086. visited 2010-01-15.

67

68 Bibliography

[11] 3GPP. 3GPP - specifications. http://www.3gpp.org/specifications.

[12] Anastasopoulos A. and Chugg K.M. Iterative Equalization/Decoding of TCMfor Frequency-selective Fading Channels. Signals, Systems and computers,1997. Conference Record of the Thirty-First Asilomar Conference, Nov 1997.

[13] S. Ariyavisitakul and Y. Li. Joint Coding and Decision Feedback Equaliza-tion for Broadband Wireless Channels. IEEE Journal on Selected Areas inCommunications, pages 1670–1678, Dec 1998.

[14] A. N. Assimi, C. Poulliat, and I. Fijalkow. Packet Combining for Turbo-diversity in HARQ Systems with Integrated Turbo-equalization. Turbo Codesand Related Topics, 2008 5th International Symposium on, pages 61–66, Sep2008.

[15] G. Battail. Pondération Des Symboles Décodés par l’Algorithme de Viterbi.Annales des Télécommunications, 42:31–38, Jan 1987.

[16] G. Bauch and V. Franz. A Comparison of Soft-In/Soft-Out Algorithms forTurbo-Detection. In in Proc. Intern. Conf. on Telecomm, pages 259–263,1998.

[17] S. Benedetto and G. Montorsi. Serial Concatenation of Block and Convolu-tional Codes. Elctron. Lett., May 1996. p. 887-888.

[18] C. Berrou, A. Glavieux, and P. Thitimajshina, editors. Near Shannon LimitError-correcting Coding and Decoding: Turbo-codes., volume 2 of Communi-cations, 1993. ICC 93. Geneva. Technical Program, Conference Record, IEEEInternational Conference on, May 1993. p. 1064-1070.

[19] S. Buzzi, M. Lops, and H. V. Poor, editors. Code-aided Interference Suppres-sion for DS/CDMA Overlay Systems, Proceedings of the IEEE, Mar 2002. p.394-435.

[20] X. Cheng, C.-X. Wang, D. Yuan, and H.-H. Chen. A Novel Iterative Methodfor Turbo Equalization. Wireless Communications and Networking Confer-ence, 2007. IEEE, pages 488–492, Mar 2007.

[21] E. Dahlman, S. Parkvall, J. Sköld, and P. Beming. 3G Evolution - HSPA andLTE for Mobile Broadband. Academic Press, 2nd edition, 2008.

[22] A. F. dos Santos, W. Rave, and G. Fettweis. A Low-Complexity Schedulingfor Turbo Equalization with Turbo Decoding. IEEE Vehicular TechnologyConference VTC2007-Spring, 22:2160–2164, Apr 2007.

[23] C. Douillard, M. Jezequel, C. Berrou, A. Picart, P. Didier, and A. Glavieux.Iterative Correction of Inter-symbol Interference: Turbo-Equalization. Proc.IEEE Int. Conf. on Communications, 6:507–511, Oct 1995.

Bibliography 69

[24] L. Fety, D. Zanatta Filho, and M. Terre. A Comparison of Chip Rate MMSEand Symbol Rate MMSE in Multiuser Uplink Long Code DS-CDMA. SignalProcessing Advances in Wireless Communications, 2004 IEEE 5th Workshop,pages 497–501, Jul 2004.

[25] G. D. Forney and D. J. Costello, editors. Channel Coding: The Road toChannel Capacity, volume 95 of Proceedings of the IEEE, Jun 2007. p. 1150-1177.

[26] The UMTS Forum. Global WCDMA and HSPA subscriptions.http://www.umts-forum.org/. visited 2009-11-05.

[27] G. Giannakis, Y. Hua, P. Stoica, and L. Tong. Signal Processing Advances InWireless And Mobile Communication - Trends In Single-user And Multi-userSystems. Prentice-Hall International, Upper Saddle River, NJ, USA, 2001.

[28] A. Glavieux, C. Laot, and J. Labat. Turbo Equalization Over a FrequencySelective Channel. In Proc. 1st Symp. Turbo Codes, pages 96–102, 1997.

[29] J. Hagenauer, editor. The Turbo Principle: Tutorial Introduction and Stateof the Art, International Symp. on Turbo Codes, Brest, France, Sep 1997. p.1-11.

[30] J. Hagenauer and P. Hoeher. A Viterbi Algorithm with Soft-decision Out-puts and its Applications. IEEE Global Communications Conference, Globe-com’89, Dallas, Texas, pages 4711–17, Nov 1989.

[31] L. Hanzo, J. P. Woodard, and P. Robertson, editors. Turbo Decoding andDetection for Wireless Applications, volume 95 of Proceedings of the IEEE,Jun 2007. p. 1178-1200.

[32] L. Hanzo, B. L. Yeap, and T. H. Liew. Turbo Coding, Turbo Equalizationand Space-Time Coding. Wiley, New York, NY, USA, 2002.

[33] S. Haykin. Adaptive Filter Theory. Prentice-Hall International, Upper SaddleRiver, NJ, USA, 1986.

[34] G. D. Forney Jr. Concatenated Codes. MIT Press, Cambridge, MA, USA,1966.

[35] W. Koch and A. Baier. Optimum and Sub-optimum Detection of Coded DataDisturbed by Time-varying Inter-symbol Interference. Proc. IEEE GLOBE-COM, pages 1679–1684, Dec 1990.

[36] M. Lampinen and V. Haikola. HSDPAMIMO Performance with Turbo Equal-izer. Personal, Indoor and Mobile Radio Communications, 2006 IEEE 17thInternational Symposium on, pages 1–5, Sep 2006.

[37] R. Otnes and M. Tüchler. Soft Iterative Channel Estimation for Turbo Equal-ization: Comparison of Channel Estimation Algorithms. In in Proc. IEEEIntern. Conf. on Communication Systems, pages 1858–1862. IEEE, 2002.

70 Bibliography

[38] S. Papaharalabos, P. Sweeney, and B. G. Evans. SISO Algorithms Based onMax-Log-MAP and Log-MAP Turbo Decoding. Communications, IET, pages49–54, Feb 2007.

[39] H. Poor. An Introduction to Signal Detection and Esitmation. Springer, NewYork, NY, USA, 1994.

[40] J. G. Proakis. Digital Communications. Mc Graw Hill, Singapore, 4th edition,2001.

[41] D. Raphaeli and Y. Zarai. Combined Turbo Equalization and Turbo Decod-ing. In Proc. Global Telecommunications Conf., pages 639–641, Nov 1997.

[42] P. Robertson, P. Hoeher, and E. Villebrun. Optimal and Sub-optimal Max-imum A Posteriori Algorithms for Turbo Decoding. European Trans. onTelecommunications, pages 119–125, Mar 1997.

[43] B. Sklar. A Primer on Turbo Code Concepts. Communications Magazine,IEEE, 35:94–102, 1997.

[44] K. Takeda and F. Adachi. HARQ Throughput Performance of MulticodeDSCDMA with MMSE Turbo Equalization. Vehicular Technology Confer-ence, 2007. VTC2007-Spring. IEEE 65th, pages 1603–1607, Apr 2007.

[45] K. Takeda, H. Tomeba, and F. Adachi. Iterative Overlap FDE for DS-CDMAwithout GI. Vehicular Technology Conference, 2006. VTC-2006 Fall. 2006IEEE 64th, pages 1–5, Sep 2006.

[46] M. Et Tolba, S. Saoudi, R. Visoz, and T. Ait-Idir. Chip-Level HARQ ChaseCombining for HSUPA. Research Letters in Communications, vol. 2009, Ar-ticle ID 230276, 2009.

[47] M. Tüchler and J. Hagenauer, editors. Turbo Equalization Using FrequencyDomain Equalizers, Proc. Allerton Conf., Monticello, IL, Oct 2000. p. 1234-1243.

[48] M. Tüchler, R. Koetter, and A. C. Singer. Minimum Mean Squared ErrorEqualization Using A Priori Information. IEEE Transactions of Signal Pro-cessing, 50:673–683, Mar 2002.

[49] M. Tüchler, R. Koetter, and A. C. Singer. Turbo Equalization: Principlesand New Results. IEEE Transactions on Communications, 50:754–767, May2002.

[50] M. Tüchler, R. Koetter, and A. C. Singer. Turbo Equalization. Signal Pro-cessing Magazine, IEEE, 21:67–80, Jan 2004.

[51] M. Upamanyu. Fundamentals of Digital Communication. Cambridge Univer-sity Press, Cambridge, 1st edition, 2008.

[52] B. Walke. UMTS : The Fundamentals. Wiley, West Sussex, England, 2003.

Bibliography 71

[53] J. Wang, S. X. Ng, A. Wolfgang, L.-L. Yang, S. Chen, and L. Hanzo, editors.Near-capacity Three-stage MMSE Turbo Equalization Using Irregular Convo-lutional Codes, Int. Symp. Turbo Codes (ISTCŠ06) in Connection With the6th International ITG-Conf. Source and Channel Coding, Munich, Germany,Apr 2006.

[54] J. Wang, L.-L. Yang, and L. Hanzo, editors. Combined Serially ConcatenatedCodes and MMSE Equalisation: An EXIT Chart Aided Perspective, 64thIEEE Vehicular Technology Conf. (VTC), Sep 2006.

[55] X. Wang and H. V. Poor. Iterative (Turbo) Soft Interference Cancellationand Decoding for Coded CDMA. IEEE Trans. on Communications, pages1046–1061, Jul 1999.

[56] T. Wu and T. Tsai. Successive Interference Cancelers for Multimedia Multi-code DS-CDMA Systems Over Frequency-selective Fading Channels. Infor-mation Theory, IEEE Transactions, pages 2260–2282, May 2009.

[57] J. Zhang, T. Bhatt, and G. Mandyam. Efficient Linear Equalization for HighData Rate Downlink CDMA Signaling. Signals, Systems and Computers,2003. Conference Record of the Thirty-Seventh Asilomar Conference., 1:141–145, Nov 2003.

[58] J. Zhang, H. Nguyen, and G. Mandyam. LMMSE-based Iterative and TurboEqualization Methods for CDMA Downlink Channels. Signal Processing Ad-vances in Wireless Communications, 2005 IEEE 6th Workshop, pages 231–235, Jun 2005.

Documents

Turbo Equalization for HSPA