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Multicarrier Modulation andCoding for Multichannel Systems

PL FRENGERDepartment of Information TheoryChalmers University of Technology

S-412 96 Sweden

Submitted to the School of Electrical and Computer Engineering,Chalmers University of Technology, in partial fulfilment of the requirements

for the degree of Licentiate of Engineering

Technical report no. 258LISBN 91-7197-445-8

Gteborg, February 1997

GOTEBOR

G

CHALM

ER

STE

KNISKAHO

GSKOLA

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In this thesis decision directed coherent detectors for single- and multicar-rier systems employing an MMSE channel estimation technique is pre-

sented. The detectors are designed for Rayleigh fading channels andDQPSK or -DQPSK modulation and exploit knowledge of the fading

process correlation. Pilot symbols are not used and differential encoding isneeded to resolve phase ambiguities due to decision errors. Analytical and

simulated results are presented. The detectors have significantly lower biterror probability than a traditional differential detector and do not suffer

from the problem of an irreducable bit error floor.

Further more, a Parallel Combinatory OFDM (PC-OFDM) system is pre-

sented. The PC-OFDM system uses only a subset of the available sub-carri-ers in each symbol interval. A bit mapping procedure is proposed using the

Johnson association scheme to choose which sub-carriers to use and -PSK modulation is used on these sub-carriers. The PC-OFDM scheme can

be designed to have a higher spectral efficiency, lower bit error probability,

and lower peak-to-average power ratio than ordinary OFDM systems. Ana-lytical and simulated results are presented for the AWGN channel as well as

simulated results for the Ricean fading channel. The PC-OFDM system ishowever not as robust against fading as an ordinary OFDM system.

4

M

ABSTRACT

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The use of Rate Compatible Punctured Convolutional codes (RCPC-codes)

for rate matching in multichannel systems is also presented. A DS-CDMAsystem is used for evaluating purposes. The RCPC-codes are shown to pro-

vide a flexible and efficient coding scheme which is superior compared torepetition encoding schemes.

Keywords: Multicarrier modulation, OFDM, Channel estimation, Decisiondirected coherent detection, Parallel combinatory signaling, RCPC-codes,

rate matching, multichannel systems, multi-code DS-CDMA.

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iii

ABSTRACT i

CONTENTS iii

ACKNOWLEDGMENTS vii

1 INTRODUCTION 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Short Introduction to OFDM . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Applications of OFDMOFDM Techniques

1.3 Multi-Code DS-CDMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.5 Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.7 Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

CONTENTS

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2 DECISION DIRECTED COHERENT DETECTION IN

MULTICARRIER SYSTEMS 11

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2.2 System and Channel Models . . . . . . . . . . . . . . . . . . . . . . . . . 12Single-Carrier System

Multicarrier System

2.3 Decision Directed Channel Estimation . . . . . . . . . . . . . . . . . 16

Single-Carrier SystemScalar Solution for the Multicarrier System

Vector Solution for the Multicarrier System

2.4 Bit Error Probability and Estimation Error Analysis . . . . . . . 23Bit Error Probability

Estimation Error Variance

2.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Results for the Single-Carrier System

Results for the Multicarrier System

2.6 Chapter Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Appendix 2A: Channel Correlation Function. . . . . . . . . . . . . 35

3 A PARALLEL COMBINATORY OFDM SYSTEM 37

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.2 System and Channel Models . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.3 Bandwidth Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.4 Bit Mapping Procedure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40Selecting the Sub-Carriers

Positions of the PSK Symbols

3.5 Bit Error Probability in AWGN . . . . . . . . . . . . . . . . . . . . . . . 443.6 Numerical Results on AWGN Channels . . . . . . . . . . . . . . . . 46

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3.7 BER Performance on Ricean Fading Channels . . . . . . . . . . . 49

3.8 Chapter Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51Appendix 3A: Probability Density andDistribution Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4 RATE MATCHING IN MULTICHANNEL SYSTEMSUSING RCPC-CODES 53

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.2 RCPC-Codes for Rate Matching . . . . . . . . . . . . . . . . . . . . . . 54

4.3 System and Channel Description . . . . . . . . . . . . . . . . . . . . . . 56

4.4 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56Downlink

Uplink

Multipath Channel

4.5 Comparison to Repetition Encoding . . . . . . . . . . . . . . . . . . . 61

4.6 Chapter Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5 CONCLUSIONS AND FUTURE WORK 65

5.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

BIBLIOGRAPHY 69

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vii

I have had the enormous privilege to have prof. Arne Svensson as my super-visor. His support has simply been invaluable. I think he knows how grateful

I am for everything, so Ill just say thanks.

I am also deeply indebted to all my dear colleagues, former and present, at

the department of Information Theory. Special thanks to all of you for mak-ing this a great place to work in. Thanks in particular to my room neighbor

Tony Ottosson for his never-ending enthusiasm. Thanks also to ThomasEriksson for being a lousy badminton player and for all fruitful discussions

in the coffee room. Thanks to Lars Kollberg who has helped my computer insickness and in health. Thanks also to Tobias Ringstrm for being the

department hacker.

A huge thank you to all my friends for distracting me and to my family forencouraging me. At last, but not least, thanks to sa-Karin for always being

around.

I could never have done this without all of you. Once again, thanks.

The work presented in Chapter 4 has been performed in the framework ofthe project ACTS AC090 FRAMES, which is partly funded by the European

Community.

Pl Frenger

ACKNOWLEDGMENTS

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CHAPTER

1.1 BACKGROUNDDigital modulation is the process of mapping digital information (bits) to onewave form out of a set of possible wave forms that are suitable for transmis-

sion over the available medium. The medium may be a radio channel or a cable

of some kind. The modulated signal may be an electromagnetic wave, or car-rier, where the bits affect the phase, amplitude, or frequency of the transmittedsignal.

The design of a digital communication system is influenced by a number offactors such as the technology available, the type of service aimed for (e.g.

speech, data, facsimile, video, images, etc.), the acceptable cost of the system,

the channel characteristics, new ideas in research, regulations, and politics, to

name but a few. The great complexity and the fast development in this field arewhat makes this area so exiting. One strong trend today towards future digitalcommunication systems is the demand for higher data rates and systems capa-

ble of supporting many different types of services with different bit error prob-ability and delay requirements. The aim of this thesis is to contribute to the

development of future communication systems.

INTRODUCTION

1

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SHORT INTRODUCTION TO OFDM

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1.2 SHORT INTRODUCTION TO OFDMThis short introduction to OFDM is not intended to give an extensive over-view but rather to provide some perspective, to the work presented in thisthesis. Good overviews may be found in e.g. [5], [17], [59], [77], [47]. A

multicarrier modulation system is simply a system using more than one car-rier for transmission. If the transmission of the individual sub-carriers is

coordinated properly we can design systems with some benefits compared

to single-carrier systems.

Multicarrier modulation (MCM) is no longer a novel technique. Theidea of transmitting data in parallel on multiple carrier dates back at leastforty years [5]. The sub-carriers in the earliest multicarrier systems did not

overlap in frequency and were separated using band-pass filtering. Earlypapers describing a multicarrier system with orthogonal sub-carriers over-

lapping in frequency were published by Chang in 1966 [9] and by Saltzbergin 1967 [58]. These systems use infinitely long symbols that are strictly

band limited and each sub-carrier overlaps only its two nearest frequency

neighbors. The orthogonality between the overlapping sub-carriers is main-tained by a time offset, or staggering, of the in-phase and quadrature-phasecomponents called Staggered Quadrature Amplitude Modulation (SQAM).

These systems are a special form of multicarrier systems called OrthogonalFrequency Division Multiplexing (OFDM) systems. In 1971 Weinstein and

Ebert [76] described an OFDM system using the Fast Fourier Transform(FFT) to generate the orthogonal wave forms. The data symbols are pro-

cessed in the transmitter by the inverse FFT and by the FFT in the receiver.The symbols are time-limited and all sub-carriers overlap each other in the

frequency domain. The use of the FFT makes it possible to design OFDM

systems with a large number of sub-carriers and low implementation com-plexity. Since OFDM systems transmit data in parallel they have longer

symbol intervals, reducing the sensitivity to impulse noise, and the fre-quency overlapping gives a system with high spectral efficiency. OFDM

systems are however more sensitive to synchronization errors and nonlineardistortions than single-carrier systems [61].

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The long symbols also reduce the problem of Inter Symbol Interference

(ISI). When an OFDM signal passes through a time dispersive channel thereceived signal will suffer from intersymbol interference. However if we

insert a Cyclic Prefix (CP) [5], longer than the length of the channel impulseresponse, all ISI will be removed by deleting the CP before the FFT in the

receiver. The CP is also necessary to avoid inter-channel interference (ICI)caused by the transient effects of the channel. Further more, the CP accounts

for the channel memory and forces the linear convolution performed by thechannel to look like a cyclic convolution. This elegant solution of inserting a

CP enables that channel equalization may be performed by a simple multi-plication after the FFT in the receiver since multiplication is the dual opera-

tion to cyclic convolution when using the DFT. The cost of using a CP is a

reduction in data rate and a loss of power and in many cases it is better toendure some ISI and use a shorter CP or to use a short CP together with a

time domain equalizer [72], [16], [35].

Applications of OFDMMulticarrier systems are being proposed and tested for wireless data trans-

mission in applications as HDTV [73], [13], [22], [78], cellular mobile tele-

phony and PCS [20], [56], [54]. The European DAB-system is yet anotherexample of a successful use of multicarrier modulation [81], [21]. The pop-

ularity of OFDM for broadcasting applications is due to several factors. Oneis the ability to avoid transmitting on certain frequencies, that might be

occupied by existing analogue systems, by e.g. inserting zeros on the associ-ated sub-carriers before the IFFT in the transmitter. Another reason is the

easy design of Single Frequency Networks (SFN). As long as signals fromdifferent transmitters arrive with time differences less than the length of the

cyclic prefix, the intersymbol interference may be removed in the same wayas multipath ISI.

Multicarrier modulation is also widely used in Asymmetric Digital Sub-scriber Lines (ADSL) [65] and High bit rate Digital Subscriber Lines

(HDSL) [10], [12] systems, often under the name Discrete Multi-Tone(DMT) modulation. In systems like these, multicarrier solutions provide the

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possibility of assigning different number of bits and different power to the

carriers. Hence sub-carriers with high Signal to Noise Ratios (SNR) areassigned more bits and power and poorer sub-carriers are assigned less. The

optimum1 solution to this bit and power allocation problem is known as thewater-pouring solution [40], [11].

OFDM Techniques

To perform channel equalization by a multiplication in the frequency

domain we need something to multiply with. This is the problem of channelestimation and several solutions are proposed. If we use differential encod-

ing we may perform differential channel estimation, as in [60], assumingthat the channel is constant over two consecutive symbol intervals. This

technique is simple but not as effective as coherent detection using explicitchannel estimation and will lead to a high bit error probability floor if the

channel is changing too fast. Other more efficient channel estimators basedon the use of pilot symbols are proposed in [59], [34], [71]. The use of a

decision directed Least Mean Square (LMS) algorithm is proposed in [57]and a decision directed MMSE solution is proposed in [26] and described in

Chapter 2 of this thesis.

The peek to average power ratio of the OFDM signal grows linearly withthe number of sub-carriers and as the number of sub-carriers increase the

amplitude distribution of the transmitted signal tends to be Gaussian. Linearamplifiers must be used to avoid intermodulation distortion and this makes

OFDM signals difficult to amplify. The problem of designing such amplifi-ers is addressed in e.g. [7], [36]. Other solutions are the use of clipping to

reduce the peak power [50], various coding schemes [66], [37], [79], predis-tortion [6], [4], and selective scrambling [19]. The Parallel Combinatory

OFDM (PC-OFDM) system proposed in [27] and described in Chapter 3has, as one of its benefits, a reduction in the peak to average power ratio.

1. In the sense of maximizing the bit rate for a certain bit error probability under the con-straint that the total available power is limited.

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MULTI-CODE DS-CDMA

5

Synchronization problems in OFDM systems have attained much inter-

est since the synchronization requirements are tighter than for single-carriersystems. To attain frame synchronization, methods have been proposed

using the inherent redundancy of the cyclic prefix of an OFDM signal [59].Frame synchronization methods using pilot carriers [75], as well as decision

directed [41] approaches, are also proposed. In [14] a carrier frequency syn-chronization method using the CP is proposed.

The pulse form used in an OFDM system determines its spectral proper-ties. In [76] a smooth roll-off windowing of the CP is proposed. For finite

length pulses the optimum1 shapes are derived in [74] for OFDM systemsusing offset QAM. Time-limited raised cosine pulses together with a certain

time overlap is employed in [45].

1.3 MULTI-CODE DS-CDMAInstead of using orthogonal carriers we may use spreading codes for parallel

data transmission. The codes may be Walsh [55] or Gold sequences [69] orsome other suitable sequences. With this change of basis functions we

obtain a system called multi-code direct-sequence code division multiple

access (multi-code DS-CDMA) which is very similar to OFDM. BothOFDM systems and multi-code DS-CDMA systems may be seen as special

cases of a more general class of multi-pulse Pulse Amplitude Modulation(multi-pulse PAM) systems [43]. Alternatively we may view both systems

as multichannel systems where a channel corresponds to a carrier in theOFDM case and a code in the multi-code DS-CDMA case. Multi-code DS-

CDMA systems are strong candidates for future personal communicationsystems. Aspects of data rate matching in general multichannel systems

using multi-code DS-CDMA systems as an example are examined in Chap-ter 4.

1. In the sense of minimizing the out-of-band energy under the constraints of zero ISIand ICI for a given length.

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OUTLINE

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1.4 OUTLINEThe outline of this thesis is as follows. Chapter 2 deals with decisiondirected coherent detection and channel estimation in multicarrier systems.In Chapter 3 a Parallel Combinatory OFDM system is presented and Chap-

ter 4 deals with data rate matching in multichannel systems using RateCompatible Punctured Convolutional codes (RCPC-codes). Some conclu-

sions are drawn in Chapter 5 together with a discussion on future work. A

longer outline of the Chapters 2-4 follows below.

Novel coherent detectors for DQPSK and -DQPSK on Rayleigh fad-ing channels are presented in Chapter 2. The detectors are based on decisiondirected minimum mean square error (MMSE) channel estimation. The pro-

posed detectors may be used in both single-carrier and multicarrier systems.Analytical results in form of expressions for channel estimation error vari-

ance and bit error probability, both with and without diversity, are derived.The MMSE based detector has a significantly lower irreducible bit error

probability floor compared to a conventional differential detector. For most

practical applications the error floor of the MMSE based detector is negligi-ble. Simulated results are presented to verify the analysis and to justify theapproximations made.

A parallel combinatory OFDM system (PC-OFDM) is described inChapter 3. The proposed system is able to obtain a higher bandwidth effi-

ciency than an ordinary OFDM system. The bit error rate performance isanalyzed and simulated. On a Gaussian channel the PC-OFDM system can

obtain lower bit error rates than ordinary OFDM. In some cases we can atthe same time increase the bandwidth efficiency compared to an ordinary

OFDM system. Further, the peak to mean power ratio of the PC-OFDM sys-

tem is lower than for OFDM, which reduces the problem of designing linearpower amplifiers.

Rate Compatible Punctured Convolutional codes (RCPC-codes) are pro-posed for rate matching in multichannel multiple access systems in Chapter

4. The bit error rate performance of a multi-code direct sequence code divi-sion multiple-access (DS-CDMA) based system using RCPC-codes is used

4

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CONTRIBUTIONS

7

to evaluate the proposed rate matching scheme. Comparison with repetition

encoding is also made. The RCPC-codes outperform the repetition codesand can provide a larger span of available channel coding rates. We show

that RCPC-codes provide a flexible coding scheme suitable for futuremobile radio communication systems.

1.5 CONTRIBUTIONSThe main contributions in this thesis may be summarized as follows

A decision directed MMSE channel estimator for single- and multi-

carrier systems. This work was presented in parts at the IEEE Vehic-ular Technology Conference, Atlanta, USA, April 28-May 1, 1996

[25] and at the RVK seminar, Lule and Kiruna, Sweden, June 3-6,1996, [24]. This work is also submitted to IEEE Transactions on

Vehicular Technology [26].

A parallel combinatory OFDM scheme. This work was presented atthe IEEE Personal, Indoor and Mobile Communications Confer-

ence, Taipei, Taiwan, October 15-18, 1996 [27].

A proposal of the use of RCPC-codes for rate matching in a multi-

code DS-CDMA systems. This work will be presented at the IEEEVehicular Technology Conference, Phoenix, USA, May 5-7, 1997

[28].

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ACRONYMS

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1.6 ACRONYMSThe fields of communication- and information theory are overwhelmed byacronyms. Often, but not always, these acronyms have an obvious interpre-tation. However, the same letter combination may mean something com-

pletely different to someone familiar to a different field. Listed below are theacronyms that appear in this thesis together with the interpretation used

here.

ASDL Asymmetric Digital Subscriber Line.

AWGN Additive White Gaussian Noise.BER Bit Error Rate.

BPSK Binary Phase Shift Keying.CDMA Code Division Multiple-Access.

CMFB Cosine Modulated Filter Banks.CP Cyclic Prefix.

DAB Digital Audio Broadcasting.

DFT Discrete Fourier Transform.DMT Discrete Multi-Tone.

DQPSK Differential Quadri-Phase Shift Keying.DS-CDMA Direct Sequence Code Division Multiple-Access.

FDMA Frequency Division Multiple-Access.FFT Fast Fourier Transform.

FIR Finite Impulse Response.HDSL High bit rate Digital Subscriber Line.

HDTV High Definition Tele-Vision.IDFT Inverse Discrete Fourier Transform.

IFFT Inverse Fast Fourier Transform.ICI Inter-Channel Interference.

ISI InterSymbol Interference.LMMSE Linear Minimum Mean Square Error.

LMS Least Mean Square.

MCM MultiCarrier Modulation.ML Maximum Likelihood.

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ACRONYMS

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MMSE Minimum Mean Square Error.

NBC Natural Binary Code.OFDM Orthogonal Frequency Division Multiplexing.

PAM Pulse Amplitude Modulation.PC-OFDM Parallel Combinatory Orthogonal Frequency Division

Multiplexing.PCS Personal Communication System.

PSK Phase Shift Keying.QPSK Quadri-Phase Shift Keying.

RAKE Not really an acronym. Refers to a receiver structure usinga tapped delay line collecting signal energy from many

received signal paths in a fashion somewhat analogous to

an ordinary garden rake.RC Raised Cosine.

RCPC Rate Compatible Punctured Convolutional.RS-code Reed Solomon code.

SFN Single Frequency Network.SNR Signal to Noise Ratio.

SQAM Staggered Quadrature Amplitude Modulation.TDMA Time Division Multiplexing.

-DQPSK Differential Quadri-Phase Shift Keying with phase incre-ments 45, 135, -45 or, -135 degrees.

4

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CHAPTER

2.1 INTRODUCTIONThis chapter describes coherent detection in single- and multicarrier systemson Rayleigh fading channels. Using the correlation of the channel fading pro-

cess we design accurate channel estimators needed for coherent detection.

Differential detection of DQPSK and -DQPSK is widely used todayfor radio communication in both single-carrier and multicarrier systems world-wide. Both the north American and the Japanese digital cellular mobile tele-

phone systems are examples of single-carrier systems using -DQPSK [3].The Japanese system uses a traditional differential detector combined with

diversity reception to obtain acceptable performance on a fading channel [1],

[2]. The European DAB-system uses DQPSK and applies differential channel

equalization to avoid explicit channel estimation [81]. In systems like the onesmentioned above there is a need for the performance enhancement given bycoherent detection compared with differential detection. The drawbacks with

differential detection are the irreducible error probability obtained due to fad-ing and the degraded performance compared to ideal coherent detection.

Coherent detection, though, requires an accurate carrier phase reference. Ingeneral, known pilot symbols need to be inserted periodically in the data

stream to enable channel estimation needed for a coherent detector on a fading

4

4

DECISION DIRECTEDCOHERENT DETECTION INMULTICARRIER SYSTEMS

2

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SYSTEM AND CHANNEL MODELS

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channel [8], [18], [71]. These symbols increase both the bandwidth and the

required signal to noise ratio for a given bit error probability.Here we propose to use previously made decisions instead of pilot sym-

bols for DQPSK. Thus we derive a decision directed coherent detector thatcan be used in both single-carrier and multicarrier systems. Initially only

one known symbol on each carrier is needed in the transmission. However,differential encoding is still needed, since carrier phase estimation with

decision directed techniques in QPSK always lead to a 90 degree phaseambiguity due to decision errors.

The outline of this chapter is as follows. In Section 2.2 the system andchannel models used in this chapter for the single-carrier and multicarrier

systems are presented. Section 2.3 describes the actual decision directed

channel estimation procedure proposed here. Then follows in Section 2.4 abit error probability analysis of the proposed detectors on fading channels.

Results with and without diversity are obtained for both the single-carriersystem as well as for the multicarrier system. In Section 2.5 numerical

results are presented and discussed. To justify the approximations made inthe analysis, simulated results are also presented. The chapter is then sum-

marized in Section 2.6.

2.2 SYSTEM AND CHANNEL MODELSIn this chapter we assume Gray encoded DQPSK but the method also works

for -DQPSK. We will use upper-case letters for the multicarrier systemand lower-case letters for the single-carrier system whenever there is a need

to distinguish between them. The transmitted symbolon sub-carrier at time for the multi-

carrier system and at time for the single-

carrier system is given according to Table 2.1. Here is the symbol

period, is the transmitted amplitude and is the imaginary unit. Note thatfor the multicarrier system we may choose to do the differential encoding

both in the time domain, between consecutive symbols on the same sub-car-rier or in the frequency domain between sub-carriers. We have in this chap-

4

Cn k, A jA A jA,,,{ } n kTck A jA A jA,,,{ } kT

T

A j

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ter chosen to make the differential encoding in the time domain for the

multicarrier system to enable easy comparison between the two systems.Differential encoding in the frequency domain is a topic for future research.

Single-Carrier System

We assume a flat fading channel model for the single-carrier system. Theimpulse response is

(2.1)

where is the Dirac impulse function, is the channel delay which is

assumed to be known and perfectly compensated for and denotes a sam-ple from a correlated complex Gaussian random process with zero mean.

The auto correlation of the fading process is

, (2.2)

where is the zeroth order Bessel function of the first kind, is the

maximum Doppler frequency, is expected value of and the asterix

denotes complex conjugate. This is the same model for a mobile radio Ray-leigh fading channel as used in e.g. [1] and [15] and is by far the most usedmodel. It is frequently referred to as Jakes model [38]. At the output of the

receiver filter we obtain at time the received value

, (2.3)

where the noise sequence is a complex uncorrelated Gaussian ran-dom processes with zero mean and variance .

Table 2.1 Gray encoding used in this paper

Bit Pattern 00 01 10 11

Multi -

carrier

Single-

Carrier

Cn k, = Cn k 1, jCn k 1, jCn k 1, Cn k 1,

ck = ck 1 jc k 1 jck 1 ck 1

gk t( ) hk t k( )=

t( ) khk

hk{ }

k E hkhk k [ ] J0 2k fdT( )= =

J0 ( ) fdE x[ ] x

kT

rk ckhk wk+=

wk{ }

w

2

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Multicarrier System

For the multicarrier system we model the channel as a time varying FIR-fil-ter of length where each tap is assumed constant during at least one mul-ticarrier symbol. Hence the channel impulse response at time index is

, (2.4)

where is the attenuation and is the delay of the th path. It is

assumed throughout this paper that . Each tap is indepen-dently modeled as random variable with Rayleigh distributed amplitude and

uniformly distributed phase and a correlation function according to Jakesmodel. We will for simplicity assume that the power delay profile is uni-

form, i.e. all channel taps are random variables with the same variance. Themulticarrier system used in this chapter is an Orthogonal Frequency Divi-

sion Multiplexing (OFDM) system but the method will work for other mul-

ticarrier systems providing that the correlation between the received valueson different sub-carriers is known. Assuming rectangular pulse shaping theth transmitted OFDM symbol can be expressed in complex base-band

notation as

. (2.5)

where is the sum of the symbol time and the cyclic prefix length

and is the total number of carriers. The cyclic prefix is inserted by thetransmitter in order to remove the intersymbol interference (ISI) and inter-

channel interference (ICI) that would otherwise cause degradation to thesystem performance [5]. The received signal is obtained by a convolu-

tion between the transmitted signal and the channel impulse responseas depicted in Fig. 2.1.a. When the number of sub-channels is

L

k

gk t( ) hi k, t i k,( )i 0=

L 1

=

hi k, i k, i

i k, iTs Nc=

k

sk t( )1Ts

--------- Cn k, ej2 n

Ts-----t

n 0=

Nc 1

; t kT k 1+( )T{ , }

0 ; otherwise

=

T Ts Tc pNc

rk t( )

sk t( )hk t( ) Nc

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15

large each sub-channel will have a narrow bandwidth and we can approxi-

mately say that the fading on each sub-channel is flat. The transmitted datasymbols on sub-carrier at time index will then be affected by the chan-

nel by a scaling of amplitude and a phase rotation. It is straightforward toshow [60] that after the DFT in the receiver we have

, (2.6)

where is the received value of the th OFDM symbol at the th sub-

channel (see Fig. 2.1.b). is the channel gain and is complex

additive white Gaussian noise with zero mean and variance . By com-paring (2.6) and (2.3) we see that the equations are almost equivalent, onlydiffering in the presence of a frequency subscript index for the multicar-

rier system. For the channel model in Fig. 2.1.b the channel gain iscorrelated both in time and in frequency. The correlation function is

defined as

, (2.7)

where is the frequency distance and is the time distance. It is shown

in Appendix 2A that for the channel with a uniform power delay profileequation (2.7) evaluates to

. (2.8)

n k

Rn k, Cn k, Hn k, Wn k,+=

Rn k, k n

Hn k, Wn k,

W2

n

Hn k,n k,

n k, E Hn k, Hn n k k+,+[ ]=

n k

n k, J0 2 fdTto tk( )1L---

nLNc

-------------- sin

nNc

----------- sin

--------------------- ejn L 1( ) Nc=

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DECISION DIRECTED CHANNEL ESTIMATION

16

2.3 DECISION DIRECTED CHANNELESTIMATION

In the single-carrier and the multicarrier systems we end up with almost thesame equations at the receiver. In order to make a coherent decision onwhich symbols were transmitted we need to know the channel gain or

for the single-carrier and multicarrier system respectively. We maymake use of our knowledge of the channel correlation function given in

(2.2) for the single-carrier system and in (2.8) for the multicarrier case aswell as all previously detected symbols. We will start our development with

the single-carrier system and then generalize the procedure to the multicar-rier case in two steps.

Single-Carrier System

Assuming the data symbols are all known for , we introduce a

scaled received sample

. (2.9)

Figure 2.1 (a) The multicarrier channel model viewed in the time domain and (b)the multicarrier channel model viewed in the frequency domain.

.

.

.

.

.

.

MultipathFrequency Selective

Rayleigh FadingChannel

Flat FadingChannel

Flat FadingChannel

Flat FadingChannel

(a) (b)

CNc 1 k,

C1 k,

C0 k,R0 k,

R1 k,

RNc 1 k,

sk t( ) rk t( )

hkHn k,

cl{ } l k

Q

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53

CHAPTER

4.1 INTRODUCTIONA future mobile communication system must provide services with both highand low bit rates with various quality requirements. In many applications e.g.

speech and video we might want the system to provide time varying data rates

as well. To allow many users to share a common channel we may divide thechannel into sub-channels in the time, frequency or code domain. One suchsub-channel may be a time slot in a TDMA based system, a certain frequency

range in an FDMA based system or a specific code in a CDMA system. It isalso possible to design a hybrid multiple-access system consisting of compo-

nents from different multiple-access techniques. This multichannel approach

provides a flexible and efficient way of solving the multiple rate problem. The

users with the lower data rates are assigned one sub-channel, and users withhigher data rates are assigned several sub-channels. In such a system there is aneed for a flexible channel coding scheme to allow different error protection

for different services, and to match the source data rate to a multiple of thebasic channel data rate which is provided by the multiple-access system [51].

RCPC-codes have attained some interest in recent publications [31], [32],[29] [30], [33], [44], [23]. We show in this paper that RCPC-codes can provide

the large number of different channel coding rates needed for future mobilecommunication services. An important feature of RCPC-codes is that the same

RATE MATCHING INMULTICHANNEL SYSTEMS

USING RCPC-CODES

4

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RCPC-CODES FOR RATE MATCHING

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decoder can be used for all different code rates, which reduces the receiver

complexity. Whenever multiple data rates are provided by assigning multi-ple slots, carriers or codes to one user, we will have large steps in the possi-

ble channel data rates provided by the system. RCPC-codes can fill this gapand provide a flexible and efficient method for source data rate matching.

The outline of this Chapter is as follows. In Section 4.2 RCPC-codes andtheir use for rate matching purposes are briefly described. In Section 4.3 a

multi-code DS-CDMA based system used for evaluating the proposed ratematching scheme is described together with the channel models used. Sec-

tion 4.4 contains numerical results for a downlink and an uplink scenario. InSection 4.5 we compare the RCPC rate matching scheme with a repetition

encoding scheme, and the Chapter is summarized in Section 4.6.

4.2 RCPC-CODES FOR RATE MATCHINGRCPC-codes consist of a convolutional mother code with rate and

a puncturing matrix , with rows and columns. The puncturing matrixconsists of zeros and ones, where a zero denotes that the code symbol is not

transmitted. By designing a large set of puncturing matrices we can easily

change the resulting code rate. Generally, from a mother code of rate ,we obtain a family of codes with the rates

. (4.1)

By introducing a rate compatibility restriction on the puncturing matriceswe can change the channel coding rate during transmission and thus easilyobtain a system with unequal error protection properties [31]. In Fig. 4.1 we

show an example of the rate matching in a communication system based onmultiple channels (time slots, frequency bands or codes) for variable data

rate. Each channel is assumed to transmit 20 kbit/s. We assume a mothercode of rate = 1/4, and that the puncturing matrix contains = 8 col-

umns. By varying the channel coding rate and the number of channels usedwe obtain a large number of source data rates supported by the system. All

r 1 n=

P n p

1 n

r pnp------, p

np 1--------------- , , p

p 1+------------=

r P p

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possible combinations of coding rates and the number of channels used are

marked with circles in Fig. 4.1. Note that the source data rate 80 kbit/s issupported by using 5 to 16 channels with channel coder rates 1/4, 4/15, 2/7,

4/13, 1/3, 4/11, 4/10, 4/9, 1/2, 4/7, 2/3, 4/5 and 8/9 respectively, and thusallowing different error protection for different services.

One advantage of the RCPC codes is that the same Viterbi decoder canbe used for all different puncturing matrixes thus giving a receiver with low

complexity. An alternative way to perform rate matching is to have a higherrate convolutional encoder concatenated with a repetition encoder that sim-

ply repeats some of the bits before transmission. The repeated bits are com-bined before Viterbi decoding in the receiver. For a given constraint length

of the convolutional mother code these two approaches have equal computa-

tional complexity.

Figure 4.1 Rate matching with RCPC-codes. All possible combinations ofencoder rates and the number of channels used are marked with circles.

0.3 0.4 0.5 0.6 0.7 0.8 0.90

10

20

30

40

50

60

70

80

So

urceDataRate[kbit/s]

Channel Encoder Rate

1 Channel

2 Channels

3 Channels

4 Channels

5 Channels

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SYSTEM AND CHANNEL DESCRIPTION

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4.3 SYSTEM AND CHANNEL DESCRIPTIONFor purposes of evaluating the rate matching properties of the RCPC-codesa multi-code DS-CDMA system is chosen. The spreading is done usingorthogonal Gold codes [69] of length 128. In this chapter we use QPSK

modulation where the same spreading sequence were used for I- and Q-spreading. We have simulated the bit error rate for both a situation where all

users are synchronized as well as the case when the users are asynchronous.

This corresponds to a downlink and an uplink scenario, respectively. We

have used both a single path correlated Rayleigh fading channel as well as afive path correlated Rayleigh fading channel with equally strong and inde-pendent paths. The fading processes are generated according to Jakes model

[38] with a normalized Doppler frequency (the Doppler frequencymultiplied with the symbol duration) of 0.1. An interleaver of 50 50 sym-bols were used and all simulations were performed until at least 2000 errorsoccurred. We assume perfect channel estimation and synchronization and

we use single user detectors in the receiver. The RCPC-code used has a con-

straint length of 5 and the generating polynomials were 46, 72, 56 and 66 inoctal notation. The puncturing matrices are chosen according to Table I of[29]. In the sequel denotes the transmitted energy per information bit.

4.4 NUMERICAL RESULTSFirst we show results for a single path Rayleigh fading channel in Fig. 4.2 toFig. 4.5 and then follow results for a multipath fading channel with five

independent and equally strong Rayleigh fading paths in Fig. 4.6. A com-parison between RCPC-codes and repetition codes is shown in Fig. 4.7.

Downlink

We start with the case where all spreading sequences are transmitted syn-

chronously. In Fig. 4.2 we see the simulated bit error rate results for differ-ent puncturing of the rate 1/4 convolutional mother code as a function of

fdTs

Eb

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57

. All curves use 64 of the 128 available orthogonal Gold codes. Wethus have to accept lower data rate in order to lower the channel encoder

rate. We see that there is little difference in bit error rate performance whengoing from = 1/4 to = 1/3. We also see that we obtain reasonable quality

for coding rates < 2/3. Due to the interference between the spreadingcodes caused by the relatively fast fading we obtain an error floor at a bit

error rate of approximately 10-4.When choosing to use a low rate channel code we must allocate more

spreading codes to the users in order to keep the effective data rate constant.If we assume that the users want to communicate with 80 kbit/s and that one

spreading code can carry a bit rate of 20 kbit/s we can achieve this by

assigning 4 spreading codes to all users and use no channel coding ( = 1).Other alternatives are of course to use equal to 1/2 or 1/4 and assign 8 or

Figure 4.2 Simulated bit error rate for different channel encoder rates, , as afunction of in dB with 64 orthogonal Gold codes of length 128. Thenormalized Doppler frequency is 0.1. Interleaver size is 50 50 symbols.Downlink scenario.

0 5 10 15 20

104

103

102

101

100

q

q

q

q

q

q

q

q

q

q q

vv

v

v

v

v

v

v

v

v

v

ww

w

w

w

w

w

w

w

w

w

x xx

x

x

x

x

x

x

x

x

ss s

ss

s

s

s

s

s

s

v

w

x

s r= 8/9

r= 4/5r= 2/3r= 4/7r= 1/2r= 4/10r= 1/3r= 1/4

Eb/N0 [dB]

BER

rEb N0

Eb N0

r r

r

rr

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see the simulated bit error rate when using 64 of the available 128 spreading

sequences. The bit error rate is degraded compared to the situation where allusers are synchronous due to the increased interference between the users.

We see that the coding is efficient in counteracting the degrading effects of

multiple access interference. The bit error rate performance for the channelencoders with the highest rate in Fig. 4.4 is far to poor for most applications.Still the loss in bit error rate performance when going from channel encoder

rate = 1/4 to = 1/3 is reasonably low.In Fig. 4.5 the 8 asynchronous users all transmit at a data rate of 80 kbit/

s in the same fashion as described previously for Fig. 4.3. Once again we seethat although the puncturing reduces the multiple access interference we

still gain in performance when choosing a lower rate puncturing scheme.

Figure 4.4 Simulated bit error rate as a function of in dB for channelencoder rates ranging from = 8/9 (top) to 1/4 (bottom) with 64 orthogonal Goldcodes of length 128. The normalized Doppler frequency is 0.1. Interleaver size is50 50 symbols. Uplink scenario.

0 5 10 15 20 25 3010

3

102

101

100

4/13

r = 8/9

Eb/N0 [dB]

BER

4/5

2/3

4/7

1/2

4/94/10

4/11

1/3

2/7

4/15

1/4

Eb N0r

r r

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Multipath Channel

In Fig. 4.6 we use a multipath fading channel model with five equally strongRayleigh fading paths. All users are assumed to be synchronous and share

the same channel (downlink scenario). Out of the 128 available spreadingsequences 64 are used for all curves in Fig. 4.6. The tap delays are uni-

formly distributed over one symbol duration. We use a five finger RAKE inthe receiver and perform maximum ratio combining of the RAKE finger

output values. We assume perfect channel knowledge in terms of pathdelays and fading gains. We see that the RAKE receiver obtains a substan-

tial diversity gain giving lower bit error rates for low .

Figure 4.5 Simulated bit error rates for different as a function of thechannel encoder rate, . with orthogonal Gold codes of length 128. The sourcedata rate is 80 kbit/s. The normalized Doppler frequency is 0.1. Interleaver size is50 50 symbols. Uplink scenario.

0.2 0.3 0.4 0.5 0.6 0.7 0.8

102

101

100

Eb/N0 = 10 dB

15 dB

20 dB

25 dB

30 dB

Channel encoder rate, r

B

ER

Eb N0r

Eb N0

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4.5 COMPARISON TO REPETITION ENCODINGAn alternative to RCPC-codes is to use a fixed convolutional code and con-

catenate it with a simple repetition code where some bits are transmittedtwice for rate matching purposes (c.f. IS-95 [70]). For comparison we showin Fig. 4.7 the simulated bit error rate results of RCPC-codes, based on a

rate 1/4 convolutional mother code, punctured to the rates 4/9, 1/3 and 4/15(solid lines). Also shown in Fig. 4.7 are the results of a rate 1/2 convolu-

tional code that is repetition encoded to the same rates (dashed lines). The

channel used is a single path correlated Rayleigh fading channel as

described earlier. Both mother codes have a constraint length of 5 and thegenerator polynomials used for the repetition mother code are 46 and 72 in

Figure 4.6 Simulated bit error rate for different channel encoder rates, , as afunction of in dB on a five path channel with 64 orthogonal Gold codes oflength 128. The normalized Doppler frequency is 0.1. Interleaver size is 50 50symbols. Downlink scenario.

Eb/N0 [dB]

B

ER

0 2 4 6 8 10 1210

4

103

102

101

100

q

q

q

q

q

q

q

vv

v

v

v

v

v

ww

ww

w

w

w

x xx

x

x

xx

s s s ss s s

v

w

x

s r = 8/9

r = 4/5r = 2/3r = 4/7r = 1/2r = 4/10r = 1/3r = 1/4

rEb N0

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62

octal notation [46]. The curves in Fig. 4.7 marked with circles correspond to

the case where the used rate is , that is the used rate is closer to the rateof the repetition mother code than the rate of the RCPC mother code

. The number of repeated bits is less than the number of puncturedbits for this case. Marked with cross signs are the curves with rate

where we are closest in rate to the RCPC mother code and marked withfilled diamonds are the curves corresponding to the rate , where

the same number of bits are punctured or repeated. We see that the RCPC-codes outperform the repetition codes for all rates 1/2 > > 1/4. Also we

note that when using repetition codes we can not provide coding rateshigher than the rate of the repetition mother code and that the rate of the rep-

etition mother code must be low enough to provide reasonably good perfor-

mance. Given the facts that the computational complexities of both schemesare equal, that the repetition scheme is less flexible in providing a large span

Figure 4.7 Simulated bit error rate for RCPC-codes (solid) and repetition codes(dashed) for channel encoder rates = 4/9, 1/3 and 4/15 with 64 orthogonal Goldcodes of length 128. The normalized Doppler frequency is 0.1. Interleaver size is50 50 symbols. Downlink scenario.

4 91 2( )

1 4( )4 15

r 1 3=

r

10 12 14 16 18 20

104

103

102

x

x

x

x

xx

x

x

x

x

x x

Eb/N0 [dB]

BER

x r = 1/3r = 4/15

r = 4/9

r

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CHAPTER SUMMARY

63

of coding rates compared to RCPC-codes and that the RCPC-codes show

better performance we conclude that puncturing is superior to repetition forthe purposes of rate matching.

4.6 CHAPTER SUMMARYThe use of RCPC-codes for rate matching in multi-channel systems is pro-posed and analyzed. RCPC-codes are shown capable of providing a flexible

and efficient coding scheme for multi-rate multiple access systems. Simula-tions are performed using a multi-code DC-CDMA system. RCPC-codes

provide lower bit error probability and a larger span of available codingrates than a scheme bases on repetition encoding.

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CHAPTER

5.1 CONCLUSIONSIn Chapter 2 decision directed coherent detectors for single-carrier and multi-carrier systems based on a minimum mean square error channel estimation and

decision feedback are presented. The MMSE based detector does not suffer

from the problem of an irreducible bit error probability floor. The single-car-rier system can use the correlation in time between the received values and themulticarrier system can lower the bit error rate performance further by utiliz-

ing the correlation between the different sub-carriers. The performances of theproposed detectors are analyzed under the assumption that all previous deci-

sions are correct and the differential decoding is not taken into account. Simu-

lations are performed to study the effects of error propagation and differential

decoding in the detector when decisions are used in channel estimation. Weassume perfect knowledge of the channel correlation function and the additivewhite Gaussian noise power. For the single-carrier system this means that the

normalized Doppler frequency is perfectly known and for the multicarrier sys-tem we need the additional knowledge of the number of independent taps on

the channel. The sensitivity to parameter errors is small, at least for small Dop-pler and small predictor orders. The ML detector for the single-carrier system

on this channel is derived independently in [15]. Due to some differences inthe implemented channel models, the results are not directly comparable. It

CONCLUSIONSAND FUTURE WORK

5

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seems, however, that our detector is equally good as the ML detector for

small SNR values and moderate Doppler frequencies, while the ML detectorshows a significant improvement for large SNR values and Doppler frequen-

cies. It should be noted that the ML detector is more complex, since it sam-ples faster than the symbol rate. A decision directed coherent detector for

16-QAM based on the same principles as those described in Chapter 2 isfound in [49]. Using 16-QAM the channel estimator coefficients will be data

dependent.In Chapter 3 we show that the PC-OFDM system can be designed to

have higher bandwidth efficiency and at the same time lower peak to meanpower ratio than ordinary OFDM. On a Gaussian channel the bit error prob-

ability of PC-OFDM is in some cases less than the BER for ordinary OFDM

for high values. Since OFDM is more robust against impulse noisethan a single-carrier system due to the long symbol interval this would moti-

vate the use of PC-OFDM on channels with AWGN and impulse noise. Asan example of such a channel we can mention communications on high volt-

age power lines that suffer from Gaussian noise due to partial discharges tothe surrounding air and impulse disturbances due to switching on and off

electrical machinery. On fading channels the use of PC-OFDM can only bemotivated by its higher bandwidth efficiency and reduced peak to mean

power ratio. The bit error rate will be higher for the PC-OFDM system com-pared to an ordinary OFDM system.

We show in Chapter 4 that RCPC-codes provide a flexible codingscheme for multi-rate multiple access systems. The same Viterbi decoder is

used for all rates which allow a simple implementation. RCPC-codes canprovide a larger span of channel coding rates compared to repetition encod-

ing. The bit error rate performance of RCPC-codes is lower than that of rep-etition encoding schemes of the same complexity. Further more, we show

that the additional interference, caused by lowering the code rate and usingmore spreading codes to maintain the effective data rate, is compensated for

by the larger coding gain provided.

Eb

N0

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FUTURE WORK

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5.2 FUTURE WORKIn Chapter 2 we assume that the correlation function of the process is knownas well as the channel noise variance. Further investigations are needed toshow exactly how estimation errors in these parameters will effect the per-

formance of the MMSE based detector. Differential encoding in the fre-quency domain instead of in the time domain is also a topic for future

research. Another interesting problem is how to combine the good proper-

ties of decision directed schemes and pilot based schemes for channel esti-

mation in the best way. By using very few pilots it is possible to avoid thedifferential encoding of the data since the pilots will then resolve the phaseambiguities. Also the decision directed approach described in Chapter 2 has

poorer bit error probabilities on the sub-carriers at the frequency edgeswhere the number of frequency neighbors is smaller. Inserting pilots in

these regions might help to reduce the error propagation and thus lower theerror variance of the channel estimator.

Further studies are needed to find a suitable coding scheme for the PC-

OFDM system described in Chapter 3. One solution using an RS-code todecode all bits in one PC-OFDM symbol is proposed in [62]. If however thePSK-modulated bits are much fewer than the parallel combinatory bits the

RS-code will not be able to correct errors due to a wrong detection of sub-carriers in the receiver. Longer RS-codes with code words spanning over

several PC-OFDM symbols may be preferred instead. An alternative solu-tion to PC-OFDM might be to design a block code with elements in the field

GF(M) and codewords of length having as low weight as possible. Thecode elements can be mapped on the carriers using ( -1)-PSK modulation

for the nonzero elements and transmitting a zero carrier for the zero ele-

ments of the codeword. This is a topic for further investigations. It is inter-esting to note that the PC-OFDM system actually performs better than a

system using a water-pouring bit and power allocation scheme on anAWGN channel where all sub-carriers are equal. Simulation results not pre-

sented in this thesis show that this advantage of the PC-OFDM system ismaintained on channels with non-constant transfer function [27]. The bit

NtotM

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and power allocation from the water-pouring scheme is kept unchanged

and parallel combinatory signaling is used independently on all carriers hav-ing the same number of bits. This solution is somewhat lumbering but actu-

ally achieves better result than the already excellent results of the water-pouring scheme. Further studies in this direction are also topics for future

research.Future work related to the work presented in Chapter 4 is to find RCPC-

codes for large constraint length and low rates and to find puncturingschemes optimized for specific channels. Codes with larger constraint

lengths are needed to enhance the BER performance and codes with lowerrates are needed to provide a larger span of available data rates and to ensure

low enough BER performances for services sensitive to errors.

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