Loop Qualification for VDSL2

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Loop Qualification for VDSL2

MATTIAS ERNELLI

Masters Degree Project

Stockholm, Sweden April 2008

XR-EE-KT 2008:3


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Acknowledgements

This master thesis project was carried out at the Fixed Networks departmentat Telenor AB in Stockholm 2007. I would like to thank PerOdling and PerOla Borjesson at The Faculty of Engineering LTH, at the University of Lundfor their academic support regarding the theoretical part of the project. Their

comments and input regarding the outline of the report has been very helpfuland made me focus on the more important aspects of my work.I also want to thank Miguel Berg and Per-Erik Eriksson at the Ericsson signal

processing department for their support and input regarding various standardsrelated issues.

My colleagues at the Telenor Network department Fredrik Tingsborg andThomas Rahm for letting me use the DSL lab and helping me with the equip-ment.

And finally my wife Karin for her patience during late evenings and neverending promises that the report will soon be finished.

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Abstract

Broadband access technology is rapidly developed due to higher bandwidthdemand. One of the driving factors is triple play, where Internet access, IPTVand IP telephony is delivered over the same shared medium. Digital SubscriberLine (DSL) technology has been the fastest growing access technology. DSL uses

the local telephone loop between the Central Office (CO) and the Customer tocarry data traffic. The twisted pair copper cable can carry information at amuch higher data rate than the Public Switched Telephone Network (PSTN).

The next generation of mainstream copper access technology will use VDSL2transmission. VDSL2 uses the same basic modulation as ADSL, ADSL2 andADSL2+, which is Discrete Multitone modulation, based on the same codingand modulation parameters as ADSL2+ but uses frequencies up to 30 MHz.The capacity of a VDSL2 connection is very dependant on the signal conditionof the local loop and differs between individual pairs in a single binder. Looppre-qualification is very important so that an upgrade to VDSL2 is only offeredto those subscribers that will actually achieve a higher data rate, and also thatupgrades is not prohibited for customers that has a potential capacity gain.

The ADSL2/ADSL2+ standard defines a loop diagnostics mode where the

central office equipment, DSLAM, and customer-premises equipment, DSL Mo-dem, performs a similar test sequence as the training sequence performed whenthe link is activated. The loop characteristic parameters such as attenuationand noise level is then available for analysis. This masters degree thesis projectevaluates the ADSL2+ built in loop diagnostics function to se if it can be usedas a loop qualification method for high-speed data service such as VDSL2.

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Contents

Abbreviations and Acronyms . . . . . . . . . . . . . . . . . . . . . . . 6

1 Introduction 7

1.1 Outline of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . 71.1.1 Overview to DSL technology and its applications . . . . . 71.1.2 Communications theory . . . . . . . . . . . . . . . . . . . 71.1.3 Capacity estimation of the local loop . . . . . . . . . . . . 71.1.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2 Overview of DSL technology . . . . . . . . . . . . . . . . . . . . . 81.2.1 Digital communication over PSTN . . . . . . . . . . . . . 81.2.2 The Digital Subscriber Loop . . . . . . . . . . . . . . . . 8

1.3 Communication systems theory . . . . . . . . . . . . . . . . . . . 91.3.1 Digital Communication systems . . . . . . . . . . . . . . . 91.3.2 The Additive White Gaussian Noise channel . . . . . . . 101.3.3 Probability of error in the AWGN channel . . . . . . . . . 111.3.4 Probability of error for M-ary PAM . . . . . . . . . . . . 121.3.5 Quadrature Amplitude Modulation . . . . . . . . . . . . . 151.3.6 Probability of symbol error in QAM . . . . . . . . . . . . 161.3.7 Error performance of QAM . . . . . . . . . . . . . . . . . 16

1.4 Coding and error correction . . . . . . . . . . . . . . . . . . . . . 18

1.4.1 Trellis code . . . . . . . . . . . . . . . . . . . . . . . . . . 181.4.2 Forward Error Correction . . . . . . . . . . . . . . . . . . 18

1.5 Channel equalisation and Inter Symbol Interference . . . . . . . . 181.5.1 Inter Symbol Interference . . . . . . . . . . . . . . . . . . 191.5.2 Channel equalisation . . . . . . . . . . . . . . . . . . . . . 191.5.3 Decision Feedback Equalization . . . . . . . . . . . . . . . 20

1.6 Discrete Multitone Modulation . . . . . . . . . . . . . . . . . . . 201.6.1 DMT Implementation using Fast Fourier Transform . . . 201.6.2 The benefits of using DMT in DSL transmission . . . . . 211.6.3 Cyclic extension and ISI . . . . . . . . . . . . . . . . . . . 241.6.4 Time domain equalization . . . . . . . . . . . . . . . . . . 24

2 Modelling the local loop 25

2.1 The local loop distribution network . . . . . . . . . . . . . . . . . 252.1.1 The topology of the loop plant . . . . . . . . . . . . . . . 25

2.2 Transmission line characterisation . . . . . . . . . . . . . . . . . . 272.2.1 ABCD model of the transmission line . . . . . . . . . . . 272.2.2 The Telegraphers equations . . . . . . . . . . . . . . . . . 28

2.3 Distributed RLCG parameters . . . . . . . . . . . . . . . . . . . 312.3.1 Measurement Procedure . . . . . . . . . . . . . . . . . . . 322.3.2 Cable models . . . . . . . . . . . . . . . . . . . . . . . . . 322.3.3 The MAR model . . . . . . . . . . . . . . . . . . . . . . . 332.3.4 MAR model . . . . . . . . . . . . . . . . . . . . . . . . . . 332.3.5 BT vs. the MAR model . . . . . . . . . . . . . . . . . . . 34

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2.4 Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 342.4.1 Background noise . . . . . . . . . . . . . . . . . . . . . . . 342.4.2 Crosstalk noise . . . . . . . . . . . . . . . . . . . . . . . . 342.4.3 FEXT Modelling . . . . . . . . . . . . . . . . . . . . . . . 372.4.4 Radio Frequency Ingress . . . . . . . . . . . . . . . . . . . 372.4.5 Impulse noise . . . . . . . . . . . . . . . . . . . . . . . . . 38

3 Loop measurement 39

3.1 Channel characterisation . . . . . . . . . . . . . . . . . . . . . . . 393.1.1 Single Ended Line Testing . . . . . . . . . . . . . . . . . . 393.1.2 Dual Ended Line Testing . . . . . . . . . . . . . . . . . . 393.1.3 ADSL2 Training sequence . . . . . . . . . . . . . . . . . . 393.1.4 ADSL2+ training sequence . . . . . . . . . . . . . . . . . 413.1.5 Loop Diagnostics mode . . . . . . . . . . . . . . . . . . . 413.1.6 Loop diagnostic parameters . . . . . . . . . . . . . . . . . 423.1.7 Reference measurements . . . . . . . . . . . . . . . . . . . 433.1.8 Noise reference measurement . . . . . . . . . . . . . . . . 463.1.9 Noise level accuracy . . . . . . . . . . . . . . . . . . . . . 473.1.10 Noise level correction . . . . . . . . . . . . . . . . . . . . . 47

3.1.11 Measuring the Modem Background Noise . . . . . . . . . 473.1.12 Measuring the line background noise . . . . . . . . . . . . 48

4 Channel capacity estimation 51

4.1 Fitting the Loop channel model . . . . . . . . . . . . . . . . . . . 514.1.1 Fitting the cable model . . . . . . . . . . . . . . . . . . . 514.1.2 Error analysis of the cable model . . . . . . . . . . . . . . 524.1.3 Further analysis of the model error . . . . . . . . . . . . . 544.1.4 Results from fitting the optimized cable model to simula-

tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.1.5 Correctness of the optimized model . . . . . . . . . . . . . 564.1.6 Importance of cable model optimization . . . . . . . . . . 58

4.2 Fitting the noise model . . . . . . . . . . . . . . . . . . . . . . . 584.2.1 Validity of the Noise Model . . . . . . . . . . . . . . . . . 604.3 Channel capacity estimation . . . . . . . . . . . . . . . . . . . . . 60

4.3.1 Calculating the attainable rate . . . . . . . . . . . . . . . 614.3.2 VDSL2 profiles . . . . . . . . . . . . . . . . . . . . . . . . 624.3.3 VDSL2 band plans . . . . . . . . . . . . . . . . . . . . . . 62

5 Implementation 64

5.1 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645.1.1 DELT measurements . . . . . . . . . . . . . . . . . . . . . 645.1.2 HLOG/HLIN measurement correction . . . . . . . . . . . 645.1.3 QLN measurement correction . . . . . . . . . . . . . . . . 64

5.2 Fitting the loop model . . . . . . . . . . . . . . . . . . . . . . . . 64

5.2.1 The FTW xDSL simulation tool . . . . . . . . . . . . . . 645.2.2 Fitting the cable model . . . . . . . . . . . . . . . . . . . 655.2.3 Fitting the Noise model . . . . . . . . . . . . . . . . . . . 65

5.3 Calculating the attainable rate . . . . . . . . . . . . . . . . . . . 65

6 Results 67

6.1 Lab measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 676.1.1 Test set-up . . . . . . . . . . . . . . . . . . . . . . . . . . 676.1.2 QLN measurement . . . . . . . . . . . . . . . . . . . . . . 676.1.3 VDSL2 estimation . . . . . . . . . . . . . . . . . . . . . . 696.1.4 VDSL2 measurements . . . . . . . . . . . . . . . . . . . . 69

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6.1.5 Deviations between real and calculated rate . . . . . . . . 696.2 Field measurements . . . . . . . . . . . . . . . . . . . . . . . . . 70

6.2.1 Capacity results . . . . . . . . . . . . . . . . . . . . . . . 706.2.2 Model dep endency . . . . . . . . . . . . . . . . . . . . . . 71

7 Conclusions 73

7.1 Further work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 737.1.1 Improving the DELT results . . . . . . . . . . . . . . . . . 737.1.2 VDSL2 DELT . . . . . . . . . . . . . . . . . . . . . . . . 737.1.3 Measuring background noise . . . . . . . . . . . . . . . . . 747.1.4 Estimating the loop topology . . . . . . . . . . . . . . . . 74

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Abbreviations and Acronyms

2B1Q Coding method used in ISDN, equvivalent to PAM-4 modulationADSL Asymmetric Digital Subscriber Line transmissionADSL2 Next generation ADSL where several optional features is mandatoryADSL2+ Improvement over ADSL2 by extending the tranmission band to 2.2MHz

AFE Analog Front End, performs gain adjustment and ADCATM Asynchronous Transfer ModeAWGN Additive White Gaussaian Noise, common noise model in digital communica-

tionBER Bit Error RateCO Central Office, where the telecom operator aggerages all subscriber loopsDELT Dual Ended Line Testing, loop test method which uses active equipment in

booth endsDFE Decision Feedback EqualizerDMT Discrete Multitone, a modulation methodDSL Digital Subscriber Line, technology that uses the telephone local loop for data

transmission.DSLAM Digital Subscriber Line Access Multiplexer, equipment used to connect multiple

lines in the CO.FDM Frequency Division Multiplexing, transmission scheme to provide channel sep-

aration by using different frequenciesFEC Forward Error CorrectionFEXT Far-End Crosstalk.FFT Fast Fourier Transform, an effiecient algorithm to perform a Discrete Fourier

Transform.HDSL High bitrate Digital Subscriber Line.IFFT Inverse Fast Fourier Transform.IL Insertion Loss, the increased loss in a transmission system by inserting a cable

or device in the signal path.INP Impulse Noise Protection.

IPTV Digital TV transmission using IP networks.ISDN Integrated Services Digital Network.ISI Inter Symbol Interference.NEXT Near-End Crosstalk.OFDM Orthogonal frequency division multiplexingPAM Pulse Amplitude ModulationPOTS Plain Old Telephone Service, basic analog voice grade telephone service.PSD Power Spectral DensityPSTN Public Switched Telephone NetworkQAM Quadrature Amplitude ModulationQLN Quiet Line NoiseRFI Radio Frequency IngressRS Reed Solomon error correction codeSNR Signal to Noise RatioUTP Unshielded Twisted Pair, the type of cable used in subscriber loopsVDSL Very high speed Digital Subscriber Line, uses booth single carrier QAM and

DMTVDSL2 Next generation VDSL technology, uses DMT and FDM.

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Chapter 1

Introduction

1.1 Outline of the thesis

1.1.1 Overview to DSL technology and its applications

The report is arranged as follows. First this introduction section that explainsthe concept of DSL and gives a short background to the history and evolutionof DSL technology.

1.1.2 Communications theory

Then follows an introduction to communication systems theory covering thosetopics that is relevant to Discrete Multitone (DMT) modulation and the prin-ciple of DMT modulation is explained.

1.1.3 Capacity estimation of the local loop

The main topic of this project, capacity estimation of the twisted pair local loopfor VDSL2 is studied, which covers

The electrical characteristics of the UTP transmission line. Models for simulating signal transmission over UTP. The various sources of disturbance and crosstalk. The established model for FEXT, far end crosstalk. Channel characterisation through loop diagnostics. Qualification of the loop diagnostics result

Fitting the UTP channel model to measurements Stability and correctness of fitted model Capacity and rate calculation of the modelled channel

1.1.4 Results

Then the established method to estimate the capacity of the local loop is testedin a lab setup. Finally the results from example loops from the Telenor networkis presented.

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1.2 Overview of DSL technology

1.2.1 Digital communication over PSTN

Digital Subscriber Line, DSL, technology is an access technology that uses thehigher capacity of the twisted pair (TP) local loop that connects the Subscriberto the PSTN (Public Switched Telephone Network). The PSTN, originallydesigned for voice communication, can only transmit signals in a narrow fre-quency band, wide enough to reproduce spoken language with minor impair-ments. When frequency division multiplexing was introduced on long distanceinterconnects, each channel was band limited to a frequency range of 300 to3400 Hz. Later when the PSTN went digital, the sampling frequency of 8 kHz,and 8-bits of resolution established the upper limit for data communicationover PSTN to 64 kbit/s. During the massive growth of Internet users duringthe 90s, analogue modem technology achieved the capacity of 56 kbit/s in thedownstream direction, utilising the all-digital connection between the InternetService Provider (ISP) modem pool and Central Office (CO) equipment.

1.2.2 The Digital Subscriber Loop

By installing communication equipment in the central office, the higher band-width and signal to noise ratio of the local loop compared to the limited capacityof the PSTN, can be utilised. The local loop becomes a Digital Subscriber Loop.

Integrated Services Digital Network

Basic Rate Integrated Services Digital Network (ISDN) uses two binary, onequaternary (2B1Q) modulation with a symbol rate of 80 kbaud providing asymmetric line rate of 160 kbit/s that carries two 64 kbit B-channels and one16 kbit D-channel. Duplex communication is achieved by echo cancellation.

High bitrate Digital Subscriber Line

High bitrate Digital Subscriber Line (HDSL) uses 2B1Q or Carrierless Ampli-tude Phase (CAP). The data rate when using 2B1Q modulation is either 784,1168 or 2320 kbit/s depending on if 1, 2 or 3 lines are bonded together. Sin-gle pair HDSL (SHDSL) provides symmetric data rate from 192 to 2304 kbit/susing one pair or up two 4608 kbit/s using two pairs.

Asymmetric Digital Subscriber Line

Asymmetric Digital Subscriber Line (ADSL) was the first mainstream broad-band access technology deployed. ADSL uses Discrete Multitone (DMT) mod-ulation with 256 carriers, each using a bandwidth of 4.3125 kHz thus operatingup to 1104 kHz. Each carrier uses Quadrature Amplitude Modulation (QAM)

and can transmit from to 1 to 15 bits of data per symbol (8 bits/carrier in earlyimplementations). The symbol rate is 4000 baud/s, which provides a maximumuncoded line rate from 7.168 Mbit/s to 13.4 Mbit/s, if frequency division multi-plexing is used for duplexing. The first 32 tones are used for upstream data andPOTS. Thus providing 25 upstream carriers capable of transmitting 800 kbit to1.5 Mbit uncoded line rate. Trellis coded modulation is optional.

ADSL uses Asynchronous Transfer Mode (ATM) as frame bearer. Variousdata services is mapped in to ATM Private Virtual Channels (PVCs). Theoverhead by using the ATM frame structure reduces the effective payload byabout 10%.

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1011 1011

Transmitter Channel Receiver

Detects messageDistorts signalEncodes message

MessageSignal Signal Message

Noise

Figure 1.1: Basic communication system

ADSL2

ADSL2 is an enhancement over ADSL. In ADSL2 a QAM-constellation size

of 15 bits and trellis coding is mandatory. ADSL2 also supports an increasedupstream band using up to tone 64, thus extending the upstream data rate to3 Mbit/s on the expense of a reduced downstream rate.

ADSL2+

ADSL2+ improves the data rate even more by using 512 subcarriers. Thetransmission band is extended up to 2.208 MHz and the maximum downstreamdata rate is 24 Mbit/s.

VDSL2

VDSL2 is the latest broadband access technology. VDSL2 extends the transmis-

sion band up to 30 MHz. For DSL transmission on subscriber loops 8.5 MHz,12 MHz or 17 MHz profiles are provided. Where the 8.5 MHz and 12 MHz istargeted for deployment in the Central Office. VDSL2 uses the same modulationas ADSL2/ADSL2+. For the profiles up to 12 MHz, transmission is divided intwo downstream bands, DS1 and DS2 and up to three upstream bands US0,US1 and US2. The bidirectional data rate on VDSL2 ranges from 50 MBit/s to150 Mbit/s depending on selected transmission profile and the conditions on thelocal loop. The later, which is the most important factor regarding successfulVDSL2 deployment is what will be the main focus on in this project.

1.3 Communication systems theory

1.3.1 Digital Communication systems

The basic principle of a digital communication system is to transmit a messagefrom a source to a user over a physical medium, a channel. By representing theinformation being transmitted with a discrete set of symbols, e.g. digitally codedinformation, a communications system can be designed for data transmissionwith a very low probability of error. Digital Communication theory coversthe problem of achieving error free communication as close as possible to thetheoretical capacity of a given channel. Figure 1.1 shows the basic scenario fora communication system.

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matched filter or correlation-type demodulator in the receiver converts the re-ceived waveformr(t) into anNdimensional vector r(t). for instance QAM usestwo orthogonal carriers, each modulated by M-ary Pulse Amplitude Modulation(PAM) signals in which case the detected signal is a two dimensional vector rep-resentingMQAM= m1 m2 possible symbols.The AWGN channel is a sufficient model for DMT transmission as we will see

later, since each narrowband DMT channel is closely approximated with theAWGN model.

1.3.3 Probability of error in the AWGN channel

With the presence of noise on a communication channel, the probability oferror becomes non-zero. The signal received over an AWGN channel is givenby Equation (1.4) that consists of the transmitted symbol waveform and anadditive noise component. For a system with binary modulation, e.g. antipodalsignalling with M = 2, the signal consists of s1 = gT(t) and s2 =gT(t),wheregT(t) is an arbitrary pulse with energy s. Which in the case of antipodalsignalling is the same as energy per bit b. The received signal from the matchedfilter or correlation-type demodulator is then

r=

s+ n ifs1 is transmitted

s+ n ifs2 is transmitted (1.5)

The optimum detector, given that both signals are equiprobable is then

s=

s1 ifr 0s2 ifr


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r0

s s

Figure 1.2: Conditional PDFs of antipodal signals

The area of (1.9) in the interval where r < 0 is equal to the symbol errorprobability for symbols transmitted usings1. As well as the area of (1.9) wherer

0 is equal to the error probability for symbols transmitted using s2. Theprobability of error when transmitting symbol s1 is then

P(e|s1) = 0

1N0

e (r

s)

2

N0 dr (1.11)

= 1

2

2sN0

ex2

2 dx (1.12)

=Q

2sN0

(1.13)

WhereQ(x) is related to the Gaussian error function by

Q(x) = 1 (x) (1.14)= 1 1

2

x

eu2

2 du (1.15)

= 1

2

x

eu2

2 du (1.16)

Where (1.16) is identified in (1.12). There exists no closed form for Q(x)so the integral has to be solved numerically. Q(x) is equal to the probabilitythat the outcome of a random variable with normal distribution, zero mean andvariance 1, is larger than x.

Q(x) = P(X > x), X N(0, 1) (1.17)

1.3.4 Probability of error for M-ary PAM

In M-ary PAM, Mdifferent levels of the signal waveform is used to represent asymbol. When the channel transfer function is unity, affected by white Gaussiannoise and all Msymbols are equally probable, then the optimal constellationfor M-ary PAM is shown in Figure 1.3.

The signal points is evenly spread with distanced in between, symmetricallyaround 0. The average energy per symbol, given all symbols is equiprobable is

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0av av

ddd d d d d

Figure 1.3: Signal constellation for M-ary PAM, (M= 8)

av = 1

M

M

m=1

m= g

M

M

m=1

A2m (1.18)

Whereg is the energy of the signal waveform gT(t) andAmis the amplitudescale of the signal waveform used for each symbol. Each symbol is transmittedusing the signal

sm(t) = AmgT(t) (1.19)

With the energy

m= A2mg (1.20)

When the signal amplitude is symmetric around 0, Am is then

Am= (2m M 1), m= 1, 2,...,M (1.21)The energy per symbol given by (1.18) becomes

av = gM

Mm=1

(2m M 1)2 =g(M2 1)/3 (1.22)

The detection of M-ary PAM symbols consists of dividing the received sig-nal level using M 1 thresholds, placed in the midpoint between two symbolamplitude levels, as shown in Figure 1.4.

In the detector, each threshold interval Ti1 r Ti maps to a correspond-ing symbol sm for symbols m = 2,...,M 1. Except for the symbols at s1 andsM, e.g. the left and rightmost symbols in the Figure 1.4. For those symbols

the detector maps

s=

sM ifr TM1s1 ifr < T1

(1.23)

Where the thresholds Tm, m= 1, 2,...,M is equal to

Tm= (Am+ 1)2g = (2m M)2g (1.24)

The probability of error for symbols sm, m= 2, 3,...,M 1 is then twice ashigh as for binary PAM with the same distance between the symbol points, ascan be seen in Figure 1.5

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0s3

s2

s1

s4

s5

s6

s7

s8

T3

T2

T1

T4

T5

T6

T7

Figure 1.4: Detector thresholds for M-ary PAM, (M= 8)

0s3

s2

s1

s4

s5

s6

s7

s8

T3

T2

T1

T4

T5

T6

T7

Figure 1.5: Conditional PDF of received signal fors3, error area marked in grey

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k bits

k/2 bits

PAM

PAM

k/2 bits

DET

DET

sn

cos(ct)

sin(ct)

cos(ct)

sin(ct)

k bits

k/2 bits

k/2 bits

Figure 1.6: Principle of a QAM transmission system

The distance between two signal points d = 2

g gives the symbol errorprobability as

Pe,sm = 1 g/N0g/N0

1

er2

2 dr,m= 2,...,M 1 (1.25)

=

g/N0

1

er2

2 dr+

g/N0

1

er2

2 dr (1.26)

= 2

g/N0

1

er2

2 dr (1.27)

= 2Q

2gN0

(1.28)

Since the detection of the two symbolss1, sMhas the error probability given

by (1.13), the symbol error probability for M-ary PAM becomes

Pe =(M 2)

M 2Q

2gN0

+

2

MQ

2gN0

=

2(M 1)M

Q

2gN0

(1.29)

With SNR expressed using average energy per symbol, as given in (1.22),the probability of symbol error is

Pe,PAM =2(M 1)

M Q

3av

(M2 1)N0

(1.30)

1.3.5 Quadrature Amplitude ModulationQAM is a modulation method where usually two baseband PAM signals mod-ulates two sinusoidal carrier signals. The two carrier signals have the samefrequency fc but are separated in phase by 90 degrees. In the detector, thereceived signal is correlated with two signals with the same frequency as thecarrier signal in the modulator, the two signals in the detector is also separatedin phase by 90 degrees. Figure 1.6 shows the principle of a QAM transmissionsystem.

The two QAM modulated signals represents a 2 dimensional symbol spacedivided in M regions. The smallest constellation is QAM-4 where each symbolis located in one of the 4 quadrants of the symbol space. A QAM constellation

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QAM-4

even

QAM-8

odd

QAM-16

even

QAM-32

odd

Figure 1.7: QAM constellations used in ADSL/VDSL2

can be either odd or even. Even constellations consists of two orthogonal M-aryPAM signals and odd constellations consists of one M-ary and one orthogonalN-ary PAM signal. Even constellations are usually always square. Odd con-stellations can be rectangular, or symmetrical. Figure 1.7 shows some examplesof the QAM constellations used in DMT ADSL/VDSL, that is symmetrical forboth odd and even sizes. For rectangular constellations, an M-ary QAM symbolis represented by the signal

s(t) =Xn gT(t)cos(2fct) Yn gT(t)sin(2fct), 0 t T (1.31)WhereXnand Yn maps to one of the points in the M-ary QAM constellation

and gT is the transmitter signal waveform. fc is the center frequency of thecarrier.

1.3.6 Probability of symbol error in QAMSince the two carriers in a QAM system is orthogonal, the transmission of twoM-ary PAM signals over an AWGN channel can be seen as two independentuses of the channel. Both signals is affected by the channel transfer functionH(f) and additive noise N0/2. The probability of a QAM symbol error is theprobability that either one of the two detected M-ary PAM symbols is erroneous.

For square constellations, the probability of a symbol error is the same forboth M-ary PAM signals. WithPe for M-ary PAM given by Equation (1.30),the probability for a QAM-M symbol error using a square constellation becomes

Pe,QAMeven = 2 Pe,PAM = 4(

M

1)

M Q 3av

(M 1)N0 (1.32)and for odd constellations it is bounded by

Pe,QAModd


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0 5 10 15 20 25 30 35 40 45 50 55 608

7

6

5

4

3

2

1

0

SNR [dB]

log10

Pe

QAM4

QAM16

QAM64

QAM256

QAM1K

QAM4K

QAM16K

Figure 1.8: Symbol error rate for even QAM as a function of SNR

Table 1.1: SNR requirement for symbol error rate 107

QAM SNR Gapsize [dB] [dB]

4 14.5 9.7616 21.6 9.8864 27.9 9.92

256 34.0 9.941024 40.0 9.954-K 46.1 9.9516-K 52.1 9.96

C=W log2(1 + SN R) = W log2(1 + PN0W

)[bits/s] (1.34)

Where W is the bandwidth of the signal being transmitted in [Hz], anddetected using an optimal detector. This is often referred to as the Shannoncapacity. Equation (1.34) can also be expressed in [bits/Hz] if the received

signal and noise level varies with frequency

b(f) = log2(1 + S(f)

N(f)) = log2(1 + SN R(f))[bits/Hz] (1.35)

The channel capacity when using QAM transmission without coding dependson the error rate accepted. Figure 1.8 shows the symbol error rate as a functionof SNR.

The target error rate for ADSL/VDSL is 107 according to the standard.Table 1.1 shows the required SNR for different QAM constellations to achievethat error rate. The SNR Gap is also given which is the difference in dB betweenthe channel capacity for a given SNR according to (1.35) and the required SNR

17


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for QAM, which asymptotically goes to 9.96 dB. SNR Gap is usually denotedusing .

When evaluating the performance of a transmission system, the term erroredsecond is usually used. An errored second is one or more errors within onesecond of channel use. If a symbol error occurs, one or more bits of informationwill be corrupt, but it will be counted as one errored second. The bit error

rate is of interest when block coding is used to improve the performance of thecommunication system.

1.4 Coding and error correction

1.4.1 Trellis code

Trellis code is used in ADSL2+/VDSL2 to improve the coding efficiency withoutincreasing the bandwidth. Trellis codes uses detection of several symbols trans-mitted sequentially or in parallel (by using larger constellations) to improve thedetection. The data rate is increased by adding a convolutional code. By usinga maximum likelihood decoder, e.g. a viterbi decoder, the received sequence is

compared to all possible sequences and the most probable is selected.A 4-D 16-state Trellis Code is used in ADSL2, ADSL2+ and VDSL2 toobtain an asymptotic coding gain of about 4.5 dB [4]. That is, for a given SNRthe coding Gap can be reduced from 10 dB to about 5.5 dB, and still maintaina symbol error probability of 107.

1.4.2 Forward Error Correction

Apart from improving the coding gain by using Trellis coded modulation, anouter Reed Solomon (RS) Forward Error Corretion (FEC) block code is also usedin ADSL2+/VDSL2. The outer block code is usually combined with a blockinterleaver to dilute the data in one coded block over several DMT symbols.Thus make the transmission more immune to wide band noise impulses, which

occur intermittently and contains much more energy than the stationary noisepresent on the channel. Different combinations of RS parity check words andinterleave depth provide an INP (Impulse Noise Protection) value that measuresthe number of lost DMT symbols that can be fully recovered.

FEC coding also provides an additional coding gain to the trellis code. TheRS code in ADSL2+/VDSL2 uses GF(256) with the number of redundancyoctets between 0 and 16. The error correction capability, without using erasures,is R/2, where R is the number of redundancy octets per FEC codeword. Thesize of an RS codeword in ADSL2/ADSL2+ and VDSL2 ranges from 32 to 255.The largest protection is given by the FEC configuration (n, k) = (32, 16) whichhas an overhead of 50%. It can correct 8 erroneous octets out of 32 transmittedoctets.

1.5 Channel equalisation and Inter Symbol In-terference

The AWGN channel is a simplified model of a transmission system. Very few realcommunication channels share the properties of an AWGN channel, unless onlya fraction of the channel capacity is utilised. All practical channels introducessome sort of distortion that affects the shape of the signal gT(t) being trans-mitted. If the channel transfer function C(f) is not considered in the detector,not all of the available energy in the received signal r(t) will be recovered, thus

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0 1 2 3 4 5 61

0.5

0

0.5

1

0 1 2 3 4 5 61

0.5

0

0.5

1

0 1 2 3 4 5 61

0.5

0

0.5

1

0 1 2 3 4 5 61

0.5

0

0.5

1

Figure 1.9: Effects of ISI when transmission rate increases

optimal performance will not be the case. Apart from suboptimal detection,another effect from the channel transfer function is Inter Symbol Interference.

1.5.1 Inter Symbol Interference

Inter Symbol Interference (ISI) is caused by different propagation time for dif-ferent frequencies e.g. the phase delay is not a linear function of the frequency.

Both causes dispersion in which the energy of the transmitted symbol is spreadout in the time domain. If the duration of the transmitted signalgT(t) is TS,then the duration of the received signal r(t) isTS+ TD. The time dispersion TDis the duration of the impulse from the channel. IfTD 0 the signal energy inthe symbol received att = T0 will contain energy from the symbol transmittedat t = T0 TS, and thus reduce the average signal energy in the demodulatedsignal and the result is lower average SNR than a channel without ISI wouldhave. Figure 1.9 shows the effects of increasing ISI for 6 consecutive symbolswhen the transmission rate is increased.

ISI is mitigated by either using a channel equaliser that shortens the channelimpulse response or by the use of Decision Feedback Equalisation. Both methodsuse an estimation of the channel transfer function that is usually determined byanalysing a known training sequence sent by the transmitter prior start of data

transmission.

1.5.2 Channel equalisation

With the estimated channel transfer function given as G(f) a simple channelequalisation is performed by using a Zero Forcing Equalizer (ZFE). The idealZFE is simply the inverse of the channel transfer function

F(f) = 1

G(f)(1.36)

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The drawback of the ZFE is that noise is not accounted for. The ZFE filtermay amplify noise to such an extent that the error performance is degraded. Theperformance is much better when using a minimum mean square error (MMSE)Equalizer that optimizes the receiver filter based on error performance.

1.5.3 Decision Feedback Equalization

Decision Feedback Equalization (DFE) is a non-linear ISI mitigation methodwhere the residual of the previously transmitted symbol is subtracted from thecurrently received signal. DFE requires that the receiver knows the channelimpulse response from some training sequence. The drawback of DFE is that ifan incorrectly detected symbol is fed back into the detector, the performance willbe severely degraded and the detector can lock up and generate long sequencesof incorrect decisions. The Tomlinson-Harashima precoding applies the decisionfeedback in the transmitter by feeding back the transmitted symbol through aninverse channel response function, thus transmitting an ISI cancellation signal.The performance is then improved over the ZFE since noise is not enhanced,but if the channel transfer function contains zeroes, the inverse channel functionmay be unstable.

1.6 Discrete Multitone Modulation

Much of the problems regarding channel equalisation, ISI, and efficient modu-lation when the SNR varies with frequency, is solved by using DMT. The basicconcept of DMT is to divide the transmission spectrum into N equally sizedchannels occupying the same bandwidth f. DMT is basically the same asorthogonal frequency division multiplexing (OFDM) with the difference that inDMT each subchannel uses a QAM constellation size that is adapted for theSNR condition for that particular channel. In conventional OFDM all subchan-nels usually uses the same modulation parameters.

The generic multi carrier modulator consists ofN orthogonal sub-carriers,each separated by f. Mathematically, a set of functions represents an or-thonormal basis if

m(t)n(t)dt= mn, where mn =

1 m= n0 m =n (1.37)

This is satisfied by the basis function

n(t) =ej2nft (1.38)

This is also the same principle as Frequency Division Multiplexing, althoughapplied within a single channel.

1.6.1 DMT Implementation using Fast Fourier TransformDMT and OFDM is usually implemented using Inverse Fast Fourier Transform(IFFT) in the transmitter and Fast Fourier Transform (FFT) in the receiver.FFT/IFFT is a widely studied algorithm for which various efficient implemen-tations exists both in software and hardware designs. With the basis functionfor each carrier given by Equation (1.38), modulation is performed by mappingbinary data onto QAM constellations represented by a complex number. Eachone of the Nsubcarriers uses a QAM constellation determined by the SNR forthat subcarrier, based on a target error rate. The modulated subcarrier is thengiven by

20


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n(t) = (Xn+ jYn) ej2nft (1.39)Where X is the real part of the constellation and Y the imaginary part.

X and Y maps into a QAM constellation as shown in Figure 1.7. With themodulated carrier given by (1.39) a DMT modulator can be implemented usingIFFT. In ADSL and VDSL2, the modulation of one DMT symbol carrying Ncarriers is defined as

xn =2N1i=0

ej2ni2N Zi, for n = 0 to 2N 1 (1.40)

Where Zi, i = 0,...,N carries the QAM constellation mapped onto eachcarrier, and

Zi = conj(Z2Ni), fori= N+ 1 to 2N 1Z0= 0 andZNbeing real. The resultxn is a sequence of real values that can

be transmitted over an analogue channel using a digital to analogue converter.In the receiver, after the analogue to digital converter, the sequence is reversed

and the complex values Zi, i= 0,...,Nis reconstructed by the FFT transformand the encoded data is detected usingNparallel QAM detectors.

1.6.2 The benefits of using DMT in DSL transmission

DMT enables the possibility to adjust the modulation and data rate to a channelwhere the SNR varies with frequency. On long telephone loops the difference inattenuation between the low frequency part of the signal and the high frequencypart can differ as much as 90 dB. Also the noise, which mainly consists ofcrosstalk from adjacent lines, changes with frequency. The result is a channelwhere the capacity, expressed in bits/Hz bandwidth changes with frequency.Figure 1.10 shows the attenuation, received signal, receiver noise, and resulting

SNR for a typical DSL channel. In the lower frequency band, the SNR is limitedby the crosstalk from other disturbers. In the upper part the attenuation of theloop brings the received signal below the noise floor.

Waterfill bit allocation

In most communication systems, transmitter power is a limiting factor. Also,the Power Spectral Density (PSD) of the transmitted signal may not exceed thelimits determined by the transmitter PSD mask. To efficiently utilise a channelgiven those constraints, the energy has to be distributed over all subcarriersin an optimum way. The number of bits subcarriern can transmit, per Hz ofbandwidth, with a given signal to noise ratio (SNR) and gap is

bn = 12

log2(1 + S N Rn

) (1.41)

With QAM modulation, each subchannel transmits two orthogonal, inde-pendently modulated signals, thus the capacity per subchannel is

bn = log2(1 +S N Rn

) (1.42)

Given the transmitted energy n, the receiver noise PSD 2n, the channelgaingn, usually between 0 and 1 since all passive channels attenuate the signal,the number of bits each subchannel can carry is

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0 276 552 828 1104 1380 1656 1932 2208160

140

120

100

80

60

40

20

Frequency [kHz]

[dB]

|H(f)|2

S(f)

N(f)

0 276 552 828 1104 1380 1656 1932 22080

10

20

30

40

50

60

SNR(f)[dB]

Frequency [kHz]

Figure 1.10: Characteristics of 3 km long DSL loop

bn = log2(1 +n gn

2n)[bits] (1.43)

and the total number of bits per transmitted symbol, the sum of all Nsubchannels is

b= Nn=1bn[bits] (1.44)

To maximize the expression in Equation (1.44), given an output power con-straint Nn=1n, the waterfill algorithm solves that problem by maintainingthe relation

n+ 2n

gn=K (1.45)

Where the constant level K is the sum of /gn and n. Figure 1.11 illus-trates the waterfill analogy, where the level K represents the waterline if theavailable energy was poured as water into the subchannels. The depth ofeach subchannel is the inverse SNR scaled by the coding gap. Where high SNRsubchannels will receive more energy than low SNR subchannels. Subchannelswhere SNR minus coding Gap is negative, will not receive any energy at all.

The Waterfill algorithm iteratively removes unusable subchannels. The resultis that energy is distributed between the subchannels capable of transmittinginformation, in a way that maximizes the capacity.

Usually the number of bits per subchannel given by Equation (1.42) requiresrounding since the encoder/decoder can only work with fixed sized constella-tions. The integer constraint on the number of bits per subchannel results in asaw tooth shaped energy level for a channel with monotonically decreasing SNR,which is illustrated in Figure 1.12. Therefore the transmitter PSD mask allowsfor the extra energy required when rounding towards larger bit constellations

22


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0 10 20 30 40 505

0

5

10

15

20x 10

3

ImpulseResponse

t [s]

Figure 1.13: Impulse response of a 2 km 0.5 mm cable, simulated using thePE05 mar cable model

1.6.3 Cyclic extension and ISI

DMT uses a low symbol rate, since each DMT symbol carries Nparallel sub-channels simultaneously. ISI can then be mitigated by introducing a guard pe-riod between each transmitted symbol. In OFDM and DMT the guard periodconsists of a cyclic prefix. The transmitted symbol consists of the 2N 1 sam-ples from the IFFT transform prepended with the last Ksamples. WhereK in

ADSL is 4/642N. The symbol rate in ADSL2 are 4000 data symbols per second.The transmitter sends one sync symbol after 68 data symbols, thus requiringthe symbol rate to be increased to 69/68 4000 = 4059 symbols per second. Thecyclic prefix causes the transmitter to use a sampling rate that is (1+4/64) mul-tiplied with the symbol rate times twice the number of subcarriers. This causesthe subcarriers to be separated by f= (1 + 4/64) 4000 69/68 = 4.3125kH z.The cyclic prefix also causes the transmitted symbol to be periodic so the re-ceiver FFT can reconstruct the original constellation points Zi, i= 0,...,N.

1.6.4 Time domain equalization

The cyclic prefix reduces the impact of the channel impulse response from theprevious transmitted symbol. For ADSL2+ the cyclic prefix introduced canhandle impulse responses with a duration of (4/64) 2N = 64 samples, whichcorresponds to 64/fs= 64/2.208 106 = 30s.

The simulated impulse response of a 2 km 0.5 mm twisted pair copper cableis shown in Figure 1.13. For longer loops the duration of the impulse responsefrom the loop may exceed the guard interval introduced by the cyclic prefix.

The solution is to use a Time Domain Equalizer, TEQ that shortens theimpulse response of the channel to fit within the guard interval.

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Chapter 2

Modelling the local loop

The upper capacity limit of a channel is determined by its signal to noise ra-tio over all frequencies used for communication and its given by the Shannoncapacity

C= f2

f1

log2(1 + S(f)N(f)

)df (2.1)

Estimating the capacity of the twisted pair local loop is then equal to deter-mine the signal attenuation over all frequencies used in a modulation scheme aswell as estimating the noise power over the same frequency range.

2.1 The local loop distribution network

Each telephone subscriber is connected to the Central Office by a twisted paircopper cable. The use of a twisted pair instead of a single wire with a commonground was early discovered to give a better performance when it comes to

noise immunity. By injecting the signal into the cable using an unbalancedto balanced circuit, and receiving the differential signal and convert it frombalanced to unbalanced, common mode induced disturbances and crosstalk iscancelled out. Figure 2.1 shows the principle of a twisted pair transmission line.The upper pair shows how common mode noise ingress is cancelled by the use ofdifferential signalling. The lower pair shows how continous crosstalk coupling iscancelled out by the alternating polarity due to the twists. The level of crosstalkimmunity between individual pairs in a multi pair binder is very dependent onthe twist ratio. In the optimum case, all pairs should have unique twist ratios,but that is not possible for practical reasons. The twisted pair copper cableusually consists of polyethylene insulated copper wire of approximately 0.5 mmdiameter.

2.1.1 The topology of the loop plant

The local loop plant topology is shown in Figure 2.2. The central office in adense populated area can serve 10,000 to 20,000 customers. The distributionof the subscriber loop is carried in segments of feeder cable. The feeder cableclosest to the CO carries hundreds or thousands of pairs, while the more remotesegments consist of 100 pair binders or less. For long loops, thicker cable isused on the more distant segments to keep loop resistance under a certain limit.Therefore a mixture of cable gauges can be expected for longer loops.

25


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+

-

VS

ZS

V1

+

-V2

+

-

I1

I2

ZL

[A B

C D

]Source LoadTwo port network

Figure 2.3: Two-port network model

2.2 Transmission line characterisation

Transmission lines is characterised by its frequency dependant attenuation and

phase delay, the later causing propagation time dispersion. The electrical prop-erties of the transmission line is often described by a two-port linear circuitusing ABCD parameters in matrix form.

2.2.1 ABCD model of the transmission line

The following relation defines the ABCD model between the input voltage V1,input current I1, output voltage V2 and output current I2

V1I1

=

A BC D

V2I2

=

V2I2

(2.2)

The parameters A,B, Cand D is defined by the following relations

Open load voltage ratio

A= V1V2

I2=0

(2.3)

Shorted load impedance

B= V1I2

V2=0

(2.4)

Open load admittance

C= I1V2

I2=0

(2.5)

Shorted load current ratio

D= I1I2

V2=0

(2.6)

The ABCD parameters is also frequency dependant and complex, since thevoltages and currents is complex and frequency dependant. The ratio

T(f) = V2(f)

V1(f) =

V2(f)

A(f)V2(f) + B(f)I2(f)=

1

A(f) + B(f) I2(f)V2(f)

(2.7)

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V(x)

+

-V(x+

dx)

+

-

I(x) I(x+dx)

G dx

R dx L dx

C dx

Figure 2.4: Incremental section of a transmission line

is related to the transfer function H(f) between input voltage VS with in-ternal impedanceZSand output voltage V2= VL across load ZL.

H(f) = VL(f)

VS(f) = V

L(f)V2(f)

V2(f)VS(f)

= Z1

Z1+ ZS T(f) (2.8)

Where Z1 = V1/I1 is the input impedance to the network. The transferfunction depends on the source and load impedances. According to circuit the-ory, the maximum power transfer occurs when the source and load impedanceis the conjugate of each other. As we will see, the impedance of a twisted pairtransmission line is dominated by the real part{Z1} and is more or less con-stant above 300 kHz. Therefore transmission lines is usually terminated by realimpedances, e.g. simple resistors where R = ZL= ZS= {Z0}whereZ0 is theaverage real part of the characteristic input impedance over the frequency rangeused for signal transmission. Z0is given by the solution of the transmission linedifferential equation that we will look at next.

One property of two-port representation of transmission lines using ABCDmatrices is that multiple cascaded line segments can be modelled by multiplyingthe two-port ABCD matrix for each line segment. For example, the characteris-tics of a loop consisting ofNline segments, each with a two-port representationn can be calculated as

= 1 2... N (2.9)Where 1 is the two port model of the first line segment, 2 the second

and so on starting from the source. The order of multiplication is important.A single homogeneous line segment is symmetrical, but the cascade of multi-ple line segments with different characteristics has different two-port behaviourdepending on which end the source and load is connected.

2.2.2 The Telegraphers equations

The two-port characterization of a transmission line and its corresponding ABCDparameters is derived by looking at an incremental line segment, as shown inFigure 2.4

The current and voltage over the incremental line segment is related by thefollowing pair of differential equations

28


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dVdx

= (R +jL)I(x, ) (2.10)

dIdx

= (G +jC)V(x, ) (2.11)

I and V are dependant on time and distance x. j represents first derivativewith respect to time. R,L,C and G are frequency dependant, and should bewritten as R(f), L(f), C(f) and G(f), but are considered constant for a givenfrequency in a homogeneous transmission line segment. The solution to (2.10)and (2.11) is the following equivalent set of second-order differential equations

d2V

dx2 =2V(x, ) (2.12)

d2I

dx2 =2I(x, ) (2.13)

Which is identified as a wave solution where the propagation constant isexpressed as

= +j=

(R +j L)(G +jC) = ZY (2.14)This is a frequency dependant constant, since R, L, C and G is frequency

dependant. The solutions to the differential equations is a sum of positive andnegative going waves, which vary with position according toex . The real partofis the attenuation constant, which represents the loss in the transmissionline. The imaginary part, represents phase constant. The phase constantrelates the wavelength with the phase velocity for each frequency componentof the signal. When the phase constant varies with frequency, different fre-quency components travel along the transmission line with different velocity,thus spreading the signal in time. This causes time dispersion and is one of thesources for ISI, Inter Symbol Interference as discussed in section 1.5.1.

When DMT transmission is used, the time dispersion caused by the trans-mission line is not a major issue, since the cyclic prefix separates two consecutivesymbols in time. The attenuation on the other hand is the largest impairment forDSL communication. The signal amplitude is attenuated as ex. Even thoughsubscriber loops uses heavier gauge on the remote sections on long loops, theskin effect causes attenuation to increase with frequency, which we will se laterin section 2.3.

The solution in (2.12) and (2.13) can be modelled as the sum of two oppositegoing voltage/current waves

V(x) = V+0

ex + V0

ex (2.15)

I(x) = I+0 ex + I0 ex (2.16)If any of these two solutions is inserted into the appropriate first order volt-

age/current equations in (2.10) or (2.11), the ratio of the positive-going voltageto the positive-going current, or the (negative) negative-going voltage to thenegative-going current, is equal to the characteristic impedance of the transmis-sion line according to

Z0= V+0

I+0= V

0

I0=

R +jL

=

R +jL

G +jC =

Z

Y (2.17)

29


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A uniform segment of a transmission line of length d, e.g. one where theRLCG parameters is constant along the line for a certain frequency, has thesolution

VL= V(d) = V+0 ed + V0 ed (2.18)

IL= I(d) =I+0 ed + I0 ed (2.19)Since V+0 is related to I

+0 and V

0 is related toI

0 by Z0, given in (2.17),

the Equation (2.19) can be written as

IL =V+0

Z0ed V

0

Z0ed (2.20)

And thus V+0 and V0 is expressed as

V+0 =1

2(VL+ IL Z0)ed (2.21)

V0 = 1

2 (VL IL Z0)ed (2.22)The solution above solves the boundary condition for Equation (2.18) when

d= 0 as

V(0) =V+0 + V0 (2.23)

= 1

2(VL+ Z0 IL)ed +1

2(VL Z0 IL)ed (2.24)

=VLcosh(d) + Z0ILsinh(d) (2.25)

Similarly the solution to I(0) becomes

I(0) =I+0 + I0 (2.26)

=1

2(IL+

1

Z0VL)e

d +1

2(IL 1

Z0VL)e

d (2.27)

=ILcosh(d) + 1

Z0VLsinh(d) (2.28)

This is identified as the ABCD parameters in the relation given in (2.2),thus the A,B,C and D two-port representation of a transmission line withdistributed parameters R,L,C,G becomes

A BC D

= cosh(d) Z0sinh(d)1Z0 sinh(d) cosh(d)

(2.29)

Whereis a function of the frequency dependantR, L, C,Gparameters andis given in (2.14)

The transfer function can then be calculated directly from the ABCD pa-rameters using

H(f) = VL(f)

VS(f) =

ZLA ZL+ B+ CZSZL+ D ZS (2.30)

But more common is the use ofTIL(f), insertion loss (IL), since it is the in-sertion of the cable between sender and receiver that results in signal loss, not

30


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the impedance matching source and load impedance. Given a transfer functionH(f) the insertion loss is given by

TIL = H(f) ZL+ ZSZL

(2.31)

If for example the two-port element is described by a unity matrix (1 0

0 1

)the insertion loss becomes

TIL = H(f) ZL+ ZSZL

= ZL

ZL+ ZS fracZL+ ZSZL = 1 (2.32)

While the transfer function is

H(f) = ZL

ZL+ ZS TIL = ZL

ZL+ ZS(2.33)

Which is the generated power divided between source and load impedance,and when the line is terminated with its characteristic impedance, it results in6 dB loss of signal power in the source impedance.

2.3 Distributed RLCG parameters

The twisted pair transmission line consist of two polyethylene (PE) insulatedcopper cables twisted together. The diameter of the copper cable varies between0.4 mm and 0.91 mm. With thicker cables resulting in lower DC resistance permeter. The theoretical electrical properties [5] of a two-wire transmission linein terms of its distributed RLCG parameters, given its copper core diameter aand the distance between the conductors D is

L=

cosh1(D

2a

) [H/m] (2.34)

C=

cosh1(D/2a) [F/m] (2.35)

G=

cosh1(D/2a) [S/m] (2.36)

R= 1

a

f c

c[/m] (2.37)

These equations is normally not useful when considering real twisted paircables. The proximity effect causes the surface current to be non-uniform, whichaffects both inductance L and resistance R. Also the twists along the cablecauses the distanceDbetween the pairs to vary. In the equations above it is onlyR that is frequency dependant. R increases with the square root of frequency.

The increase in resistance with frequency is caused by the Skin effect, whichoccur due to Eddy currents induced in the copper core which forces the currentin the wire to travel along its circumference, thus the effective conducting areaof the cross section of the wire is decreased. The skin effect affects both theResistance as well the Inductance. C and G is normally considered constant,and G is usually neglected. Allthough conductance does increase with highfrequencies so for wide band DSL transmission, such as VDSL2 it must betaken in account. In practice all four RLCG parameters is frequency dependantwhich makes the equations above unsuitable to model a twisted pair cable usingDSL transmission.

31


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To properly model the characteristics of a twisted pair transmission line, thefrequency dependant RLCG parameters is best established through measure-ments.

2.3.1 Measurement Procedure

When measuring twisted pair cable characteristics, the measurement proce-dure consists of measuring the open circuit impedance ZOC and short circuitimpedance ZSC for a cable of length l. The characteristic impedance is thencalculated as [2]

Z0=

ZOCZSC (2.38)And the propagation constant is derived from

=1

ltanh1

ZSCZOC

(2.39)

The relation

=

(R +jL)(G +jC) (2.40)

Z0=

R +jL

G +j C (2.41)

Leads to the following relation

R= {Z0} = {R +jL} (2.42)L=

1

{Z0} = 1

{R +jL} (2.43)

G= {

Z0 } = {G +jC} (2.44)C=

1

{

Z0} = 1

{G +jC} (2.45)

Cable measurements is performed on a cable of length l = 10m for fre-quencies below f = 2M Hz. For measurements between f = 2MHz andf= 30M Hz, a cable of length l= 1mis used.

2.3.2 Cable models

The resultingR, L, Cand Gvalues derived from measurements is then fitted intoa parameterised smooth curve. Several empirical cable models exist and one ofthe more popular is the BT model. In the BT model [6] the primary parametersare given by fitting the following curves to the measured cable impedance

R(f) = 11

4

r4oc+acf2+ 1

4

r4os+asf2(2.46)

Equation (2.46) models the frequency dependence of a steel enforced copperwire. This model is also referred to as BT#1. For plain copper wires (BT#0),the expression is simplified

R(f) = 4

r4oc+ ac f2 (2.47)

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Which shows that R is proportional to

f when f >, which is alsoshown in Equation (2.37).

Inductance is modelled according to the BT model as

L(f) = l0+ lxb

1 + xb(2.48)

xb = ( ffm

)b (2.49)

Wherel0 and l are the low frequency and high frequency inductance, b isa parameter chosen to fit the transition between low and high frequencies in themeasured inductance values.

Even though C(f) is more or less constant and G(f) usually negligible forf 10M Hz.C(f) and G(f) is given by the BT model as

C(f) = c+ c0 fce (2.50)

G(f) = g0 fge (2.51)Where c is the contact capacitance and c0 and ce is used to fit the mea-

surements. g0 andge are constants chosen to fit the measurements.

2.3.3 The MAR model

Musson [7] pointed out that the established BT model for cable simulationslacked physical significance. All practical models are empirical in the sense thatthey fit smooth curves onto measurements. What Musson emphasized was thatR and jL is the real and imaginary part of a physical impedance and thusmust be related by the Hilbert transform, which origin is that an effect cannot

precede its cause. Any model whereR and jL as well as G and jC is notrelated by the Hilbert transform, is not guaranteed to have a causal time domainbehaviour, which is also shown in [8].

2.3.4 MAR model

Musson suggested that the measured cable parameters should be fitted accordingto a model in whichRandjLis related by the Hilbert transform, the suggestedmodel is the MAR1 [7] model with the following parameters

ZS=jL+ R0(1

4+

3

4

1 +

as(s + b)

s + c ) (2.52)

YP =Cf(j+ tan) =j C1MHz (jf 106)2 (2.53)

Where

L= High frequency inductance per km.R0= DC resistance per km.

s= 4107jf

342R0103 =j

f447.6R0

a= Proximity factor for skin effectb and c are skin effect shape coefficients= Shunt capacity loss angleCf =

C1MHz

(f106)2

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Table 2.1: Residential Background Noise Power [dBm/Hz]

Location 8-100 kHz 100-500 kHz 500 kHz - 2 MHz1 -150 -148 -1332 -136 -153 -146

The MAR1 model has been simplified in the MAR2 model where b, andc isfixed to b = 2, c= 2.765.

2.3.5 BT vs. the MAR model

Both cable models are empirical in the sense that they fit smooth curves onto measured cable parameters. Mussons argument for using the MAR modelis that by maintaining the relation between the real and imaginary part ofZSand YP by the Hilbert transform, the resulting model parameters will be lesssensitive to measurement noise. According to Musson, it is essential in Max-

imum Likelihood estimation that one establish the set of possible parametersto estimate. Modelling R and L independent of each other is not possible ina physical sense, and should not be allowed by the model. Although the BTmodel do resemble real cable measurements the main argument for using theMAR model is that it is Causal which makes it possible to manufacture testequipment that realises the standardised models.

2.4 Noise

The capacity of a communication channel, according to (1.34), is a function ofthe ratio between signal and noise at the receiver. In the preceding sections wehave focused on the attenuation of the signal when transmitted over the twisted

pair copper cable. The noise at the receiver end consists of thermal noise fromthe receiver electrical circuit and various induced signals in the copper pair. Thethermal noise in the receiver circuit can be calculated from Equation (1.2) andis -174 dBm/Hz in room temperature, but it also depends on the design of theanalogue front end.

2.4.1 Background noise

The thermal noise is usually much weaker than the background noise inducedinto the copper pair. Some measurements have been performed. In [3] a studymade by Bellcore at two locations in New Jersey is mentioned. The resultof those measurements is listed in table 2.1. Based on the results from theBellcore study, the background noise level on twisted pair telephone loops has

been assumed to be -140 dBm/Hz. For most DSL installations, crosstalk fromadjacent lines is the dominating noise source, but the background noise levelsets the capacity limit for long loops.

2.4.2 Crosstalk noise

Crosstalk noise arises in DSL because the individual copper pairs in a binderradiates energy electromagnetically. The field surrounding wire i, couples tosurrounding wires j, through mutual inductance denoted by Mij and couplingcapacitance denoted by Eij , which is illustrated in Figure 2.5.

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Pair 1 wire 1

Pair 1 wire 2

Pair 2 wire 3

Pair 2 wire 4

E13

E24

E14

E23

M13

M24

M23

M14

Figure 2.5: Distributed mutual coupling between twisted pairs

The balanced transmission mode of the signal as well as the twisting of thecable pair mitigates electromagnetic coupling. The balanced signal transmis-sion suppresses common mode noise signals induced in the cable from externaldisturbers, such as radio waves and electrical equipment. By twisting the cable,induced balanced signals is supposed to cancel itself out along the cable. Unfor-tunately twisted pair cables are not perfectly homogeneous. RLCG parametersdiffer along the cable, so the coupling varies between the twists. Also the indi-vidual pairs move around along the binder, which alters the inter pair couplingeven more.

The frequency dependant coupling function between pair 2 to pair 1, X21(f)can be found by a generalisation of a two port model. The induced noise, atposition x along the cable, is then given by

N1(f, x) = X21 2jf V2(f, x) (2.54)Where X

21is a generalised coupling function, determined by all M and E

parameters for the two pairs. N1 is the induced voltage on pair 1 and V2 isthe voltage in the disturbing pair 2 at position x. The factor 2jf representsthe time derivative of the disturbing voltage, since the inductive and capacitivecoupling only transmits alternating current/voltage.

Equation (2.54) gives the induced noise voltage along the cable binder be-tween two individual pairs. The resulting noise signal at the end of the cableis characterised as either Near End Cross Talk (NEXT) or Far end Cross Talk(FEXT). NEXT arises in the receiver at the disturbed pair, originating fromthe transmitter on the disturbing pair in the same end. FEXT is the receivednoise from a disturbing pair originating from a transmitter in the far end of thecable. Figure 2.6 and Figure 2.7 illustrates the difference between FEXT and

NEXT.NEXT is mainly a problem in DSL transmission techniques where the same

spectrum is shared between upstream and downstream traffic, through echocancellation or time division multiplexing. NEXT also occur between spectrallyincompatible modulation techniques where the upstream and downstream spec-trum overlap. VDSL2 is spectrally compatible with ADSL2+ and uses frequencydivision multiplexing so when estimating crosstalk noise we will only considerFEXT.

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Pair 2

Transmitter

Pair 1

Receiver

Figure 2.6: Inter pair coupling causing NEXT

Pair 2

Transmitter

Pair 1

Receiver

Figure 2.7: Inter pair coupling causing FEXT

Pair 2

Transmitter

S2

(f)

Pair 1

Receiver

dx

H2(f,x)

H1(f,d-x)

X21(f)

Figure 2.8: Model of the signal coupling along the cable causing FEXT

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2.4.3 FEXT Modelling

Figure 2.8 show how the signals contributing to FEXT is coupled between twoadjacent pairs along the cable binder. Since the signal in the disturbing pair2 is attenuated along the cable, the energy transferred through the couplingfunctionX21(f) is a function of transmitter energy S2(f), cable attenuation upto x given by H2(f, x). The induced signal in pair 1 then travels further downthe cable and is attenuated according to H1(f, d x) for the remaining sectionof twisted pair cable. The total FEXT contribution from pair 2 to pair 1 is thengiven by

F(f, d) =

d0

X21 2j f V2(f) T2(f, x) T1(f, d x) dx (2.55)

WhereT1and T2is the insertion transfer function of the line up to the pointof coupling and from that point onward to the far-end receiver respectively.Taking the squared magnitude of the crosstalk, since it is viewed as noise andassuming that both pairs are terminated by its own characteristic impedance,and also assuming that pair 1 and pair 2 has the same RLCG characteristics,Equation (2.55) can be rewritten as

|F(f, d)|2 = (42f2) |X21(f)|2 |V2(f)|2 d0

e2ddx (2.56)

= (42f2) |X21(f)|2 |V2(f)|2 d e2d (2.57)FEXT increases with the square of frequency of the transmitted signal.

When considering a multi-pair cable binder, each individual pair to pair cou-pling functionXij(f), varies significantly with frequency, but the sum of severalcross talkers can be approximated as

SFEXT(f) = kFEXT f2

d p |H(f, d)|2

S2(f) (2.58)Which is also the empirical FEXT model accepted by ETSI [9]. d is the

length of the cable in meter, p is a meter to feet conversion factor (1/0.3048).|H(f, d)|2 is the magnitude of the cable transfer function. S2(f) is the PSD ofthe disturber. The factor kfext is given by

kFEXT = (N

49)0.6 8 1020 (2.59)

Where N is the number of disturbers in the same binder. The calculatedSFEXT(f) according to the model corresponds to a 1% worst case value. Themodel is normally used for design purposes and simulation, thereby focus onmodelling the 1% worst case.When estimating the performance for VDSL2 based on noise measurementsfrom ADSL2+ and ADSL&2 disturberskFEXTwill be estimated by fitting themodel onto measured noise PSD.

2.4.4 Radio Frequency Ingress

External interference such as RF signals and impulse noise is not considered inthis study. The sensitivity to Radio Frequency Ingress (RFI) for a given copperpair depends on how well the pair is balanced. However, balance changes withfrequency so a copper pair that shows no signs of RFI in the ADSL2+ band maycontain severe RFI in the VDSL2 frequency range. Table 2.2 lists the frequencyranges used by HAM radio that could interfere with VDSL2 [13].

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Table 2.2: International HF amateur radio bands

Band start Band stop(kHz) (kHz)1 810 2 0003 500 3 800

7 000 7 10010 100 10 15014 000 14 35018 068 18 16821 000 21 45024 890 24 99028 000 29 100

2.4.5 Impulse noise

Impulse noise is defined as non-stationary noise injected into the local loop ei-

ther from an external disturber or as crosstalk between electrical wires in closeproximity to the telephone cable binder. It can also originate from phones ring-ing in adjacent pairs in the binder. The characteristics of impulse noise is ashort-duration, high amplitude wideband signal that occurs intermittently. Im-pulse noise usually have a duration of 10-100 s but can be up to 2-3 ms, thusaffecting multiple DMT symbols. The most efficient method to mitigate impulsenoise is Forward Error Correction (FEC) and interleaving. In the ADSL2+ stan-dard [10] impulse noise protection is specified by the number of DMT symbolsthat can be recovered and is given by

IN P = (S D) 12 R

NFEC(2.60)

Where Impulse Noise Protection I N Pis the number of DMT symbols thatcan be recovered by the error correction. D is the interleaver depth in numberof Reed Solomon (RS) FEC codewords. R is the number of redundancy octetsper RS FEC codeword. NFEC is the size of the RS FEC codeword. Sis givenby

S=8 NFEC

L (2.61)

WhereLis the number of bits transmitted by each DMT frame. As Equation(2.61) shows, when the transmission rate increases, e.g. the number if bitstransmitted in each DMT frame increases, the data transmission becomes morevulnerable to impulse noise. VDSL2 increases the data rate by a factor of 3or 4 depending on the selected profile but uses the same FEC configuration

as ADSL2. To maintain the same impulse noise protection larger interleavememory is used.

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Chapter 3

Loop measurement

3.1 Channel characterisation

Characterisation of the local loop is vital to successful DSL deployment. Several

methods of loop characterisation exist. First there is capacity estimation basedon calculations using key parameters such as loop length and topology as input.Those parameters are sometimes based upon installation data where the typeof copper cable and distance is known, or by open loop measurements whereconductance and capacitance between the cables in a pair is measured. Usinginformation about the local loop, coarse capacity estimations can be made usingthe models presented so far.

3.1.1 Single Ended Line Testing

Single Ended Line Testing (SELT), is based on Time Domain Reflectometry(TDR). During a TDR measurement, a pulse is transmitted from one end ofthe pair, usually the CO side. If the pair is not properly terminated, either

by leaving the remote end unconnected, e.g. open ended, or with a telephonehandset on hook, the injected pulse will be reflected back. By measuring thepropagation time and the attenuation of individual frequencies in the trans-mitted pulse. The gathered data can be used to calculate the loop length,attenuation and cable parameters. If the quiet line noise is measured in the COend, a rough estimate of the attainable data rate can be calculated. SELT mea-surements is very useful when it comes to fault diagnostics where the DSLAMand Modem fails to establish a connection, for example if the cable is broken orincorrectly patched.

3.1.2 Dual Ended Line Testing

Loop characterisation using Dual Ended Line Testing, DELT, requires activeequipment in both ends of the loop. Traditionally such measurements requiresa technician to go to the remote location and connect measurement equipmentand perform the measurement between the remote end and the central office,where remote controlled equipment is already present. Such measurements hasonly been affordable when qualifying leased lines for DSL access in the past.

3.1.3 ADSL2 Training sequence

In the ADSL2 standard Dual Ended Line Testing functionality is built into themodem and DSLAM. DELT is performed as part of the initialisation/training

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Table 3.1: ADSL2/2+ training sequence

Training phase1 Handshake procedures2 Channel Discovery3 Transceiver Training4 Channel Analysis5 Exchange

sequence if either the ATU-C or ATU-R requests DELT procedure to be entered.During a normal training sequence the following steps is performed:

Handshake procedure

In phase 1, the ATU-R (modem transceiver) and ATU-C (DSLAM transceiver)detects each other and agree on a transmission mode. From here on we assumethat both ATU-R and ATU-C agree on G.993.2 (ADSL2+) there are schemesto fall back, when line conditions are severe, and try lower levels of transmissionmodes. The initial handshake is carried out using the G.994.1 standard [12]. Itis also in phase 1 that a decision to initiate loop diagnostics mode is taken.

Channel Discovery

In phase 2, the channel is discovered. Here both ATUs may perform coarsetiming recovery and perform channel probing to determine a power cutbackbased on hook status. The ATU-R can also choose a proper subcarrier fortiming reference. Channel discovery is initiated with QUIET state on bothtransceivers. During the QUIET state both receivers measure the Quiet LineNoise (QLN) over a minimum of 512 DMT symbols ( 128 ms). Then chan-nel discovery is carried out by sending the COMB test signal. The COMBsignal consists of repeatedly transmitted multi tone-symbols with 16 active car-riers in the downstream direction and 5-10 carriers in upstream (Depending ontransmission mode). The carriers is chosen not to interfere with underlyingPOTS service. The carriers is modulated with a 4-QAM constellation and car-ries random data from a pseudo random bit sequence (PRBS) of length 511 fordownstream and 63 for upstream. The mapping of PRBS bits to each real andimaginary part of each modulated carrier follows the same scheme as for theREVERB symbol.

At the end of channel discovery, Both transceivers agrees on a power cutbacklevel (PCB) on both upstream/downstream to avoid saturation of the receiveranalouge front end (AFE) in each end. This is necessary for very short loops.

Transceiver Training

Phase 3, Transceiver Training. First the REVERB signal is transmitted. TheREVERB signal is generated using the same PRBS as used for the COMB signalbut now all DMT downstream carriers and upstream carriers are modulated.The signal level used is also reduced from the NOMPSD level to REFPSDwhich is NOMPSD - PCB as determined during the channel discovery phase.The REVERB signal is stationary, e.g. it does not change between symbols.That way both receivers can train their Automatic Gain Controller and TimeDomain Equalisers. After the REVERB signal, the ATU-C sends the pilottone C-TREF. it consists of a single tone symbol where the subcarrier chosen

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by the ATU-R to be used for pilot modulates the 4-QAM {0,0} constellationpoint. Also during phase 3, both transceivers are given opportunity to transmita vendor proprietary echo cancellation training signal.

After phase 3 both transmitters now enable the cyclic prefix on all DMTsymbols transmitted.

Channel Analysis

Phase 4, channel analysis phase. During the channel analysis phase both transceiversstransmit the MEDLEY symbol, which is generated using the same PRBS as theREVERB symbol except that the PRBS is not restarted between each symbol.The duration of the PRBS is 511 bits downstream and 63 bits upstream soeach symbol generated will shift the PRBS sequence by 1 bit. The MEDLEYstate always lasts for a multiple of 512 symbols so all subcarriers will have gonethrough the same 4-QAM constellation sequence, although at different points intime. The receiving ATU aggregates the signal level on each subcarrier, duringthe entire MEDLEY sequence so the received aggregated signal will accuratelyindicate the loop attenuation on a per carrier sense.

After the channel analysis phase, both ATUs calculate the optimum trans-

mitter configuration for the other end using proprietary bin loading algorithms.

Exchange

After the Channel Analysis phase, both ATUs exchange transmission relatedparameters to configure the ATU on the other end in terms of tone order, bitconstellation and gain scaling for each carrier, as well as performance relatedparameters such as total aggregate transmit power and SNR margin.

3.1.4 ADSL2+ training sequence

ADSL2+ uses the same training sequence as ADSL2 except that in ADSL2+ theDMT symbol used for downstream communication uses 512 subcarriers insteadof 256, which means that the PRBS used for the REVERB and MEDLEYwill be repeated once during each generated DMT symbol. Also the REFPSDlevel used for downstream transmission is limited by the ADSL2+ transmitspectral mask, which depends on the operation mode and is specified in thecorresponding annex in [11]. In the channel analysis phase, the measured PSDof the received signal is not only a function of the loop attenuation but the loopattenuation and transmit PSD.

3.1.5 Loop Diagnostics mode

ADSL2 and ADSL2+ offer a built in diagnostics mode with the purpose ofanalysing the local loop to identify sources of various impairments such as

crosstalk, RFI, bridged taps, impedance mismatch or bad connections. The loopdiagnostics mode is entered from the G.994.1 initialisation 3.1.3. During loop di-agnostics mode the same sequence is performed as during initialisation/trainingup to the MEDLEY state. Each variable length state have a fixed duration,equal to the maximum duration of the same state during initialisation, exceptfor the QUIET state which has a longer duration during Loop Diagnostics thanthe maximum duration during training. After the C-EXCHMARKER and R-EXCHMARKER, which starts the Exchange phase during normal initialisation,loop diagnostics specific states is entered. During the loop diagnostics specificstates, the transceives in both ends exchange the loop characteristics parametersthat has been measured.

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Table 3.2: Parameters determined during Initialisation and Loop Diagnosticsmode

Hlin(i f) Channel Characteristics per subcarrier, linearX+ jYHlog(i f) Channel Characteristics per subcarrier, 20 log10(|X+ jY|)QLN(i

f) Quiet Line Noise per subcarrier, [dBm/Hz]

SN R(i f) Signal-to-Noise Ratio per subcarrierLATN Loop AttenuationSATN Signal AttenuationSNRM Signal-to-Noise Ratio MarginATTNDR Attainable Net Data RateACTATP Actual Aggregate transmit power (far-end)

3.1.6 Loop diagnostic parameters

Table 3.2 lists the parameters determined during training/initialisation andLoop diagnostics mode.

Hlin is given by

Hlin(i f) =X+ jY =scale/215 (a(i) +jb(i))/215 (3.1)Wherescale is a 16 bit unsigned integer, a and b are 16 bit signed integers.

The range of Hlin is -2 to 2 for the real and imaginary part and accommodatesfor a dynamic range of +6 dB to -90 dB. This is necessary since short loopscan result in signal levels above 0 dB. The resolution of Hlin decreases with thereceived signal level.

Hlog is calculated as

Hlog(i f) = 20 log10|H(i f)| = 6 m(i)/10 (3.2)Where

|H(f)

|is the magnitude of the loop attenuation for a given frequency.

m(i) is represented by a 10 bit unsigned integer which gives Hlog a dynamicrange of +6 dB to -96.2 dB in 0.1 dB steps. The resolution of Hlog is con-stant over the whole parameter range. The receiving end calculates Hlog(f)and Hlin(f) during the transmission of at least 256 REVERB symbols. Apartfrom measurement noise, the aggregated measurement over multiple symbolsincreases the resolution of the measured attenuation. In [2] a linear relationshipbetween the accuracy of the estimated channel gain and number of trainingsymbols is given. With 256 measurements the accuracy of the estimated gain isimproved by 24 dB over the noise. The limiting factor when measuring atten-uation on long loops will be the resolution of the Analog to Digital Converter(ADC).

QLN in dBm/Hz is given by

QLN(i f) = 23 n(i)/2 (3.3)Where n(i) is an 8 bit unsigned integer. This data format supports a QLN(f)

granularity of 0.5 dB and a dynamic range of -23 to -150 dBm/Hz. QLN is mea-sured during the QUIET state over at least 256 DMT symbols during initialisa-tion and at least 1 second (4000 DMT symbols) during Loop Diagnostics mode.QLN(f) represents the estimation of the variance of the narrowband noise in thecentre of each subcarrier, which is given by 2n. The variance of that estimation,assuming that the noise is Gaussian is then [2]

var(2n) = 2

L 4n (3.4)

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The estimated QLN has a Std. deviation of

2/L 2n which expressed indB becomes 10 log10(1 +

2/L)dB per sigma point. For a measurement length

of 256 symbols this equals a std deviation of 0.36 dB. For a 99.7% confidence upto 1.02 dB of error in QLN measurement must be expected. In Loop diagnosticsmode, the error is reduced to 0.28 dB when QLN is measured over 4000 symbols,which is below the 0.5 dB granularity of the QLN parameter.

SNR is measured during the MEDLEY state and is defined as

SN R(i f) = 32 + snr(i)/2[dB] (3.5)WhereS N R(i) is an unsigned 8 bit integer which results in a granularity of

0.5 dB and SNR dynamic range of -32 to 95 dB.LATN is the average Loop Attenuation over all subcarriers and is given by:

LATN[dB] = 10 log10 1N SC

i= 0NSC1|H(i f)|2| (3.6)

Where NSC is the number of used subcarriers used. In diagnostics mode,H is the HLIN parameter measured during the REVERB state. During normalinitialisation, H is taken from HLOG parameters converted to linear scale.

SATN is the difference in dB between the aggregated transmitted power(NOMACTP lowered by the power cutback PCB) and aggregated receivedpower. LATN and SATN can be used to verify the Hlog and HLin parame-ters as we will see later.

ATTNDR is the estimated attainable data rate determined from the sum

ATTNDR= (

NSC1i=0

[log2(1 + 10(SNR(i)TARSNRM)/10)]) 4000 (3.7)

Where the Gap is 9.75 dB which corresponds to a 4-QAM modulated signalwith a Bit Error Rate (BER) equal to 107 and TARNSNRM is the target SNR

margin per subcarrier, usually 6 dB. This capacity estimation does not takein account any bin loading algorithm and is a coarse estimate. The log2 valueshall be within [0..BIMAX] where BIMAX is the maximum number of bits percarrier, which for ADSL2/2+ is 15 and shall be rounded to the nearest integer.

ACTATP is an estimate of the total power delivered into the loop from thetransmitter at the point of insertion (tip and ring), it should take into accountthe transmit filter function when calculating the aggregate transmit power asa function of NOMATP (Nominal aggregate transmit power) lowered by thepower cutback.

3.1.7 Reference measurements

When measuring the characteristics of the local loop using DELT, initial ref-

erence measurements are necessary. By connecting a DSL modem directly tothe DSLAM using at short (few meters) cable a reference measurement on the0-loop can be performed. Figure 3.1 shows the result of DELT HLIN measure-ments over a 0-loop on two modems using different chipsets, connected to twoDSLAMs using different chipsets.

The reported LATN (Loop attenuation) is shown together with each mea-surement. As the graph shows, the reported HLINpsds values do not conformvery well to the 0-loop where the Texas chipset is used. With the Connexantchipset in the CO, minor effects from impedance mismatch can be visible. Theoffset between the reported LATN (loop attenuation) and HLIN can be cor-rected for by using the relation in (3.6). For the Texas chipset, a correction for

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0 276 552 828 1104 1380 1656 1932 220860

50

40

30

20

10

0

10

Frequency [kHz]

20

log10

|Hlin

(f)|[dB]

Hlin

, CO:Connexant, RE:Texas , LATN:0.5 dB

Hlin

, CO:Connexant, RE:Broadcom, LATN:3.0 dB

Hlin

, CO:Broadcom , RE:Texas , LATN:0.5 dB

Hlin

, CO:Broadcom , RE:Broadcom, LATN:1.5 dB

Figure 3.1: Reference measurements on 0-loop between different vendors

the transmit PSD mask must be applied, since the measured HLIN is not re-ported according to [10]. In section 8.12.3.1 it is stated that the reported H(f)should be equal to U2/U1 whereU1 is the received signal without the loop andU2 the received signal with the loop in-between CO and RE. With a 0-loopinserted,H(f) should be unity for all frequencies. The level of conformance inthe implementation of DELT varies between vendors and firmware releases. Tobe able to use the DELT measurements in loop qualification, it is necessary to

adjust the reportedHlin andHlog values according to the reported overall loopattenuation LATN. The adjustedH(f) for the 0-loop measurement is shownin Figure 3.2.

The reported loop attenuation and the actual graph for HLIN do not trulyreflect the 0-loop even with the correction applied. Effects of the transmitfilters, receive filters and eventual gain adjustments and adaptive hybrids is notproperly compensated for by the ATU-C and ATU-R.

When fitting the cable model to the measured loop characteristics functionH(f), the model will only be optimized in the

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Loop Qualification for VDSL2