This paper describes the unique performance evaluation results of a Gigabit Digital
Subscriber Line modem that provides Multi-user-interference-free communication, by incorporating
Super Orthogonal Complete Complementary spreading into the existing xDSL modem architecture.
The GDSL modem was tested under practical crosstalk conditions, using the Network Interface, Power,
and Protection (NIPP) Committee MIMO Crosstalk Model. It was found that the GDSL modem
provides acceptable bit error rate performance for a fully loaded system, even for very short twisted
pairs. A unique observation from these performance evaluation tests is than the non-linear behaviour of
NEXT and FEXT creates an orthogonality distortion effect on the correlation properties of the SOCC
code family.http://www.saiee.org.za/DirectoryDisplay/DirectoryCMSPages.aspx?name=Publications#id=1588&dirname=ARJ&dirid=337am2018Electrical, Electronic and Computer Engineerin

Linde, Louis P.

Van Wyk, J.H. (Jacques Herman)

SAIEE Africa Research Journal

UPSpace at the University of Pretoria

Vol.108 (4) December 2017SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS144PERFORMANCE EVALUATION OF A GIGABIT DSL MODEMUSING SUPER ORTHOGONAL COMPLETE COMPLEMENTARYCODES UNDER PRACTICAL CROSSTALK CONDITIONSJ.H. van Wyk∗ and L.P. Linde†∗ Department of Electrical, Electronic & Computer Engineering, University of Pretoria, South Africa,0002. E-mail: jhvanwyk@up.ac.za† Department of Electrical, Electronic & Computer Engineering, University of Pretoria, South Africa,0002. E-mail: lplinde@ieee.orgAbstract: This paper describes the unique performance evaluation results of a Gigabit DigitalSubscriber Line modem that provides Multi-user-interference-free communication, by incorporatingSuper Orthogonal Complete Complementary spreading into the existing xDSL modem architecture.The GDSL modem was tested under practical crosstalk conditions, using the Network Interface, Power,and Protection (NIPP) Committee MIMO Crosstalk Model. It was found that the GDSL modemprovides acceptable bit error rate performance for a fully loaded system, even for very short twistedpairs. A unique observation from these performance evaluation tests is than the non-linear behaviour ofNEXT and FEXT creates an orthogonality distortion effect on the correlation properties of the SOCCcode family.Keywords: Gigabit Digital Subscriber Line (GDSL), Super Complete Complementary (SOCC),MUI-free, Performance evaluation, MIMO crosstalk, FEXT, NEXT, crosstalk1. INTRODUCTIONIn this paper we present the unique performance evaluationresults of a Gigabit Digital Suscriber Line (GDSL)modem that was developed and described in [1], wherea ”‘spreading block”’ (SB) is added to the existingDSL architecture, using Super Orthogonal CompleteComplementary (SOCC) spreading codes to createa Multi-user Interference (MUI) free environment, evenin the presence of severe FEXT crosstalk (very short loops).In Section 2 the proposed system architecture is brieflydescribed from [1]. In Section 3 the channel modeling,NEXT and FEXT crosstalk environment and the NIPPMIMO Crosstalk model is provided. In Section 4 theperformance evaluation results is provided and discussed.Finally a conclusion of this paper is provided in Section 5.2. PROPOSED SYSTEM ARCHITECTUREThe proposed GDSL system architecture was described ina previous paper [1], but is repeated here for completeness.Figure 1 shows the GDSL transmitter [2], based onDiscrete Multi-Tone (DMT), with the proposed SOCCspreader highlighted. Figure 2 shows the correspondingGDSL receiver. With a subchannel spacing of 51.75 kHz(12×4.3125 kHz) and using a 4096 FFT structure, a totalsystem bandwidth of 211.968 MHz is required. Thisbandwidth is suggested for future G.fast systems [3].During modem initialization the channel attenuation andbackground noise is determined. For our simulations,Figure 1: GDSL Transmitter with proposed SOCC Spreader(highlighted) [Taken from [1]]Figure 2: GDSL Receiver with proposed SOCC Despreader(highlighted) [Taken from [1]]a theoretical approach, based on two-port networks willbe used, as discussed in Section 3. Figure 3 shows thePower spectral densities of the pilot tones (in this example-60dBm/Hz), the channel attenuation (shown in dB tocompare profile with that of received tones), the receivedtones, the background noise, 99% worst case NEXT noiselevel and 99% worst case FEXT noise levels for differentcoupling lengths d, for 200m of 0.5mm twisted pair.Copyright c©2004 IEEE: An earlier version of this paper was first published in AFRICON ’04, 15-17 September 2004, Gaborone, BotswanaVol.108 (4) December 2017 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 145Figure 3: Power spectral density of pilot tones, channelattenuation (in dB), received tones, background noise, 99% worstcase NEXT noise level and 99% worst case FEXT noise levelsfor different coupling lengths.3. CHANNEL AND CROSSTALK ENVIRONMENT3.1 Channel modelingLocal loops usually consist of several sections of cable withdifferent lengths and wire gauges, with or without bridgedtaps, and terminated with resistive impedance. Two-portnetworks, and specifically ABCD matrixes can be used torepresent each segment or section of a line. By multiplyingthe ABCD matrixes of each segment, an ABCD matrixis obtained which represents the complete line [2]. For a200m 0.5mm twisted-pair, the obtained channel attenuationis shown in Figure 4. A practical xDSL modem will obtaina SNR profile of the channel. This is referred to as themeasured SNR (SNRmeas). To allow for performancevariations and a target uncoded BER of 10−7, a SNRperformance margin of Γ = 10 dB is added to SNRmeasto obtain SNRused [2], which is used by the modem. Apractical example, with a VDSL 30a profile bypass policy,averaged over 518 FFT blocks (10 ms) is shown in Figure4.3.2 NEXT and FEXT modelingThe transfer function for a 99% worst-case NEXT channelcan be expressed as [2]:|HNEXT,99(f)|2 = xn · f1.5 (1)and the PSD as:PSDNEXT = PSDDis · |HNEXT,99(f)|2 (2)where xn = 8.814 · 10−14 and f is the frequency [Hz].FEXT is dependent on the characteristics of the line. Theoriginal signal at the transmitter (of a disturber) will beFigure 4: SNRmeas and SNRused for a 200m 0.5mm twistedcopper pairattenuated due to the inherent propagation loss of the line.In a real network, FEXT is not just a function of thecrosstalk in the cable, but also of the cable topology [2],i.e.|HFEXT,99(f)|2 = xn · l · |Hins(f)|2 · f2 (3)and the PSD as:PSDFEXT = PSDDis · |HFEXT,99(f)|2 (4)where xn = 2.625 · 10−16, l is the length of the disturbingline [m], Hins(f) is the insertion loss for the line underconsideration, | · |2 is the modulus-squared function, and fis the frequency [Hz].In Figure 5 a comparison is shown between NEXT,FEXT (l=0m), FEXT (l=100m) and FEXT (l=200m). ItFigure 5: NEXT and FEXT Crosstalk couplingshould be noted that FEXT approaches NEXT as the linelength decreases (with the coupling length equal to theVol.108 (4) December 2017SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS146Figure 6: NEXT and FEXT Crosstalk coupling comparison for200m 0.5mm twisted pair for different coupling lengthsline length). In Figure 6 a comparison is shown betweenNEXT, FEXT (d=10m), FEXT (d=100m) and FEXT(d=200m), for a 200m 0.5mm twisted-pair.In ADSL systems, where the line length was still relativelylong (the so called ’last-mile’), NEXT was eliminated byusing a FDD approach, using different sub-channels forupstream and downstream transmission. One approachto control crosstalk was to control certain transmissionparameters such as tone power levels. These ”spectrummanagement” restrictions are conservatively designed sothat 99% of all operational cases operate properly. FEXThad PSD levels close to or below the noise level due tolarge line attenuation, specifically at higher frequencies.With VDSL / VDSL2 the FEXT from other VDSL systems(often called ’self-FEXT’) is the major performanceconstraining factor, especially as the loop length becomesshorter. As the line attenuation decreases for shorterloops, FEXT noise starts to approach the same levels asNEXT noise. NEXT is usually avoided by using a FDDapproach (upstream and downstream bands in separatefrequency bands) or a TDD (sending upstream packets anddownstream packets after each other) approach.FEXT remains a problem for the FDD approach - a solutionwas to apply dynamic spectral management (DSM) Level1. DSM Level 2 performs spectrum balancing jointlyacross multiple lines to mitigate crosstalk, while DSMLevel 3 applies Vectored DSL to effectively removecrosstalk. Vectored DSL makes use of pre-coding indownstream transmission and makes use of Multi-UserDetection (MUD) interference cancellation in upstreamtransmission [4]. For the GDSL modem, SOCC spreadingis used to mitigate the effect of crosstalk (MUI).Figure 7: Illustration of NEXT and FEXT interferenceConsider Figure 7. In order to determine how SOCCspreading will perform under NEXT and FEXT conditions,the disturbing signal (including background noise, NEXTinterferer and or FEXT interferer) should be considered.It is equivalent to determining the Interference noise.Consider the case of sending information downstream forUser i. If TxDOWN has a power spectrum of SDOWN (f),the transmitter’s received version at the downstreamreceiver (RxDOWN ) will be SDOWN (f). | Hins(f) |2,basically an attenuated version of the transmitter’sspectrum. The interfering received signal from User(s)j will be a power sum of NEXT and FEXT terms [5],each respectively of the form SUP (f).NEXT (f) andSDOWN (f).FEXT (f). If No/2 is the background noise,the Interference noise will be:Nint =N02+(NjNdis)0.6Sjup(f).NEXT (f)+(NjNdis)0.6Sjdown(f).FEXT (f) (5)for all Users j, where Nj is the number of similar disturbersfrom Users j and Ndis is the total number of disturbers.During modem initialization the channel attenuation profileis determined and synchronized between the GTU-C andGTU-R. Since both receivers of User i have knowledge ofthe channel, the 1-tap decision feedback equalizer (DFE)can remove the effect of insertion loss. This is equivalent todividing the received signal by | Hins(f) |2. The equalizedInterference noise then becomes:Nint =N02∣∣Hiins(f)∣∣2+(NjNdis)0.6 Sjup(f).NEXT (f)∣∣Hiins(f)∣∣2 (6)+(NjNdis)0.6Sjdown(f).FEXT (f)∣∣Hiins(f)∣∣2where Nj is the number of similar disturbers from Users jand Ndis is the total number of disturbers.Vol.108 (4) December 2017 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 147From Figure 6, NEXT and FEXT (for short loops)provide the most detrimental (crosstalk) effect for currentxDSL systems. It can be observed that the crosstalkcoupling is relatively high (where a higher negative dBvalue means lower coupling and vice versa) for higherfrequencies.3.3 MIMO Crosstalk ModelIn 2009 the Network Interface, Power, and Protection(NIPP) Committee: Network Access Interfaces (NAI)Subcommittee conducted a study [6] that provided astochastic model for a MIMO (FEXT) coupling channel forDSL transmission systems. From this report ”The modelwas derived using a statistical analysis of measurements ofingress energy into pairs of a cable, from other pairs in thesame cable, using an actual loop plant. The probabilitydensity function (PDF) of the model is asymmetric,meaning that the crosstalk coupling from line (or pair) 1to 2 is different from the crosstalk coupling from line 2 to1. The difference seems to vary between 0 dB to 3 dB. TheMIMO crosstalk model is also based on a 99% worst casemodel for single or multiple binders of up to 25 pairs each(up to 100 pairs total), 0.4mm or 0.5mm cable type. Thetransfer function for the MIMO FEXT model is given as:HFEXT (f) = |HFEXT,99(f)| .ejϕ(f). 10XdB20 (7)where f is the frequency [Hz], d is the coupling length [m],HFEXT,99 is the 99% worst-case crosstalk coupling modelin linear scale, ϕ(f) is the phase of the crosstalk channeltransfer function and XdB is the amplitude offset of thecrosstalk transfer function [dB], relative to the amplitude ofthe 99% worst case model. The phase ϕ(f) is equal to thephase of the direct channel transfer function plus an offset:ϕ(f) = tan−1(imag (Hins(f))real (Hins(f)))+ ϕ0 (8)where the phase offset ϕ0 is a uniformly distributedrandom variable over the range [0, 2π].” An interestingobservation from the practical measurements was ”...itis also clear that the phase of the crosstalk channel hasthe same slope as the phase of the direct channel”. Thus,the crosstalk channels are only affected by the amplitudeXdB(f). Also note that ”...the amplitude offset XdB(f)can be considered to be independent of the frequency”.Thus, the frequency variation of the amplitude offset isignored and approximated by XdB .For this study a standard 100x100 matrix of XdB(representing a 100-pair cable with four 25-pair binders)will be used [6]. Row 70 (Pair i=70 as desired channel)had the worst profile and was used for the MIMO channelprofiling. Xi,j vs. Pair j (only for the worse 64 cases)are shown in Table 1. Although the MIMO model wasderived for FEXT, it is also applicable to NEXT, as Xi,j isthe crosstalk coupling between pairs i and j. HNEXT (f)and HFEXT (f, d) is thus defined as:HNEXT (f) = HNEXT,99(f) · 10XdB20 (9)HFEXT (f, d) = HFEXT,99(f, d) · 10XdB20 (10)4. PERFORMANCE EVALUATION RESULTSBit error rate (BER) analysis was first performed onthe GDSL modem for QPSK, 16-QAM and 64-QAMmodulation, with frequency spreading Lfsp = 64, asshown in Figure 8. It should be observed that spreadingdoes not affect the BER performance of the system. The−10 −5 0 5 10 15 2010−710−610−510−410−310−210−1100EbNoBERQPSK (theoretical)16−QAM (theoretical)32−QAM (theoretical)64−QAM (theoretical)GDSL QPSK (FS64)GDSL 16−QAM (FS64)GDSL 32−QAM (FS64)GDSL 64−QAM (FS64)Figure 8: BER for GDSL system with Lfsp = 64 frequencyspreading.Figure 9: BER for a QPSK system for different NEXT coupledusers, operating in the lowest frequency Resource BlockGDSL system was tested for different users using only99% worse case NEXT coupling, with operation in thelowest frequency resource block (RB), as shown in Figure9, and in the highest frequency RB, as shown in Figure10 (’4 Users’ mean that there is the desired user and 3Vol.108 (4) December 2017SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS148Figure 10: BER for a QPSK system for different NEXT coupledusers, operating in the highest frequency Resource BlockFigure 11: BER for a 64 users QPSK system, comparing NEXTand FEXT (l=10m,100m and 200m respectively) for the highfrequency RB.Figure 12: BER for a QPSK system for different NEXT coupledusers, with practical MIMO model, operating in the lowestfrequency Resource BlockFigure 13: BER for a QPSK system for different NEXT coupledusers, with practical MIMO model, operating in the highestfrequency Resource BlockFigure 14: BER for a 64 users QPSK system, with practicalMIMO model, comparing NEXT and FEXT (l=10m, 100m and200m respectively) for the high frequency RB.other NEXT coupled users). It can be observed that theperformance for up to 16 users are still acceptable, but forup to 64 users the performance deteriorates. In Figure 11a 64 users QPSK system is used to compare NEXT andFEXT (l=10m, 100m or 200m respectively). The systemperformance is acceptable for line lengths of more than100m, provided that NEXT is not present.In Section 3.3 a more practical MIMO Crosstalk model isexplained. If crosstalk coupling attenuation values XdB ofTable 1 are also taken into consideration, the performancefor low - and high frequency RBs are shown in Figures 12and 13. It can be observed that the performance for up to64 users are still acceptable. In Figure 14 a 64 users QPSKsystem is used to compare NEXT and FEXT (l=10m, 100mor 200m respectively) when practical crosstalk couplingattenuation (XdB) values are taken into account. Thesystem performance is acceptable, even for FEXT at veryVol.108 (4) December 2017 SOUTH AFRICAN INSTITUTE OF ELECTRICAL ENGINEERS 149Table 1: Crosstalk coupling Xi,j(dB) for i=70 (worst-case)Pair j => 54 70 68 55 69 72 73 63 74 610.26 0 -1.07 -2.26 -5.56 -7.36 -7.79 -7.87 -8.4 -8.98Pair j => 77 39 65 96 27 99 34 81 66 87-10.41 -11.01 -12.06 -12.79 -12.96 -13.43 -13.51 -13.51 -13.54 -14.36Pair j => 84 75 71 59 35 85 45 36 79 26-14.88 -14.98 -15.09 -15.34 -15.99 -16.63 -17.09 -17.3 -17.42 -17.71Pair j => 20 8 19 91 32 82 6 44 76 98-17.92 -18.22 -18.22 -18.27 -18.83 -19.1 -19.56 -19.98 -19.99 -20.3Pair j => 9 80 48 1 62 23 43 46 24 95-20.49 -20.61 -20.75 -21.12 -21.19 -21.34 -21.59 -22.21 -22.7 -22.73Pair j => 52 58 5 78 3 33 64 28 13 97-23.03 -23.19 -23.37 -23.44 -24.27 -24.92 -24.96 -24.98 -25.03 -25.4Pair j => 10 90 31 57-25.43 -26.25 -26.4 -26.56short lengths or even NEXT. A unique observation fromthese performance tests is than the non-linear behaviourof NEXT and FEXT creates an orthogonality distortioneffect on the correlation properties of the SOCC codefamily. The attenuation level of the relevant NEXT/FEXTfunction also plays a role in further amplifying this effect.This is evident when comparing Figure 9 and Figure 10,using Figure 6 to determine the degree of non-linearity (thegradient of the respective crosstalk functions at low andhigh frequencies). Orthogonal codes thus do not functionwell under high gradient changes over the spreading lengthof codes.5. CONCLUSIONIn this paper the unique performance evaluation of a GDSLmodem using SOCC spreading, operating within a practicalNEXT/FEXT (MIMO) channel, was described. It wasfound that the original 99% worst case NEXT and FEXTmodels are too conservative towards practical systems, asindicated in Section 3.3. Using the practically measuredMIMO model, the GDSL system shows acceptable BERperformance for a fully loaded system (64 users) under allNEXT/FEXT conditions.REFERENCES[1] van Wyk JH, Linde LP. Design of a Gigabit DSLmodem using Super Orthogonal Complete Comple-mentary Codes. Trans. Emerging Tel. Tech. (2016).Published online in Wiley Online Library (Availablehttp://wileyonlinelibrary.com). DOI: 10.1002/ett.3071.[2] Starr T, Cioffi JM, Silverman PJ. UnderstandingDigital Subscriber Line Technology. Prentice Hall.1999. ISBN 0-13-780545-4.[3] ITU-T. 2014. Fast access to subscriber terminals(G.fast) - Physical layer specification. Available:https://www.itu.int/rec/T-REC-G.9701/en.[4] Leung C, Huberman S, Ho-Van K, Le-Ngoc T.Vectored DSL: Potential, Implementation Issues andChallenges. IEEE Communications & Tutorials Q42013. 15 (4). pp. 1907-1923.[5] Galli S, Kerpez K. Methods of summing crosstalk frommized sources - Part I: Theoretical Analysis. IEEETrans. Commun., 50 (3), pp. 453461.[6] ATIS, Multiple-input Multiple-output Crosstalk Chan-nel Model. NIPP-NAI-2009-014R3, Tech. Rep., 2009.

Performance evaluation of a Gigabit DSL modem using super orthogonal complete complementary codes under practical crosstalk conditions

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