Multi· Tone Transmission
`for
`Asymmetric Digital Subscriber Lines (ADSL)
`
`Kamran Sistanizadeh (Bellcore), Peter S. Chow (Stanford University), and John M. Cioffi (Amati Corporation)
`
`Bell core
`MRE-2K-250, 445 South Street, Morristown, NJ 07960-1910.
`Tel: (201)-829-5130, Fax: (201)-829-5976
`loops are extracted from the canonical loopsC6l that are at the extreme
`range of the non-loaded loop plant.
`
`ABSTRACT
`
`fer
`technique
`is a pctentially viable
`transmission
`Multi-Tone
`application on Asymmetrical Digital Subscriber Lines (ADSL). This
`paper presents the results of a preliminary study on the performance of
`an ideal Discrete Multi-Tone (DMT) signaling technique for a 1.6 Mb/s
`ADSL. The performance margins using
`single-tone 16-point
`Quadrature Amplitude Modulation (QAM) with an ideal Decision
`Feedback Equalization (DFE) are also presented. The feedforward filter
`of the DFE is a quarter-baud spaced Fractionally Spaced Equalizer
`(FSE). The interference is assumed to be the sum of far-end crosstalk
`(FEXT) and additive white Gaussian noise (A WGN). The subscriber
`loops are assumed to be in a plant environment where the maximum
`resistance does not exceed 1300 ohms. The projected performance of
`an ideal DMT with a sampling rate of 1.024 MHz and 256-subchannel
`segmentation offers potential margin enhancement up to 3 dB over a
`quarter baud-spaced FSE-based 16-QAM signaling.
`
`1. Introduction
`
`Asymmetric Digital Subscriber Line (ADSL) is a digital transpon
`technology that could provide high-bandwidth services on existing
`non-loaded subscriber loops. Although the data rate has not been
`established yet, the prevailing consensus is that initial ADSL system
`will transport 1.544 Mb/s from the network towards the customer on a
`single twisted-pair telephone line up to 18 kft. Thus, POTS and high
`rate services would be provided on the same loop.
`ADSL is an access technology that is intended to serve residential
`customers, enabling such potential services as: VCR-quality video on
`demand, video browsing, information services, CD-quality music,
`interactive games, home shopping, and cther multi-media applications.
`Non-residential applications might include computer-aided design,
`remotely conducted educational sessions, and database services.
`
`Because of the asymmetric nature of the high-bandwidth service (from
`the CO to the customer), the loop plant characteristics, the noise
`environment, and the existence of analog POTS, the transmission
`technique and the transceiver architecture for ADSL will be distinctly
`different from predecesscr Basic Rate DSL£ 1l and High-rate DSL
`(HDSL)l2l technologies.
`
`technologies:
`transmission
`three contending
`there are
`Presently,
`(QAM),! 31 Carrierless
`Amplitude Modulation
`Quadrature
`Amplitude/Phase modulation (CAP),! 41 and the Discrete Multi-Tone
`(DMT)!5l technique. A comprehensive assessment of various trade-offs
`for each of these techniques is currently being carried out through
`ANSI-Tl E 1.4 Standards Committee deliberations.
`
`This paper is a computer analysis of the performance margin of two of
`the transmission techniques: uncoded single-tone 16-point QAM and
`ideal DMT. The QAM receiver is based on an ideal Decision Feedback
`Equalization (DFE) with finite length feedforward Fractionally Spaced
`Equalizer (FSE). The interference is assumed to be the sum of far-end
`crosstalk (FEXT) and additive white Gaussian noise (AWGN). The test
`
`0-7803-0950-2/93/$3.00© l 993IEEE
`
`756
`
`Such issues as functionality, programmability, flexibility, and control
`channel implementation of DMT have been discussed by Cioffi, et al. !71
`More elaborate results have also been presented on the performance of
`DMT in the presence of impulse noise.C81 The underlying theoretical
`analysis for DMT is delineated in a TIEl.4 Technical Contribution,C9l
`and the ideal DFE-based QAM transceiver is discussed by Sistanizadeh
`in a GLOBECOM'90 paper. [!OJ
`
`For a Bit Error Rate (BER) of 10-7
`, the performance margin of an
`uncoded DMT-based system can be computed from the knowledge of
`the overall system signal to noise ratio (SNR), the number of bits per
`blcck, and the number of used sub-channels (see Sectioo 2, the
`Appendix, and Reference [9] for details).
`
`For the uncoded QAM system, the performance index, defined by the
`average SNR at the detector output of the in-phase channel (with
`perfect post-cursor ISI cancellation), is calculated from:!IOJ
`[ C&1)top1 ~I+ (fia1)topt ~d 2
`(SNR)1-op1 = --''----------=-(cid:173)
`[ 1 - <&1 )f opt ~1 - <!iaY op• !1 l
`
`where subscripts (I) and (Q) refer to in-phase and quadrature-phase
`channels respectively, and (f) denotes the transpose operation. The
`performance margin for a BER of 10-7 and a 16-QAM rectangular
`constellatioo
`can
`be
`approximated
`byY IJ
`ti.QAM-mor1i• =IO log10 (SNR)1-opt - 21.5 dB.
`
`The organization of this paper is as follows. Section 2 briefly describes
`the system principles and delineates the computational algorithm for the
`performance margin. Section 3 discusses the loop plant environment,
`FEXT model, QAM transceiver structure, and the DMT simulation
`parameters. Section 4 presents the computer analyses results. Section 5
`is a summary of results. Finally, a derivation of the DMT margin
`expression is presented in the Appendix.
`
`2. Discrete Multi-Tone (DMT) System
`
`2.1 The System Principles
`
`The underlying idea is to divide the channel spectrum into several sub(cid:173)
`channels (i.e., frequency bands) and transmit and receive data
`separately in each sub-channel. This is generically depicted in Figure I.
`The transmit spectrum for each sub-channel is assumed to have
`identical energy spectral density, as illustrated in Figure 2. The block
`diagram of the proposed transceiver is shown in Figure 3. The operation
`of the transceiver is described as follows.
`
`The input bit stream at the rate of R bits/sec is buffered into blccks of
`boMT = R ToMT bits, where ToMT dencxes the DMT symbol period. The
`DMT symbol rate is denoted by frymbol-DMT = - 1
`- . The buffered bits
`ToMr
`are shared by several sub-channels. The bit allocation strategy follows
`an optimization criterion based on the achievable signal to noise ratio
`M
`such that: boMT =I: bi. Each of the bi bits are mapped into a complex
`
`j;l
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`

`DMT sub-symbol Xi.t. where j and k dencxe the sub-channel and the
`buffer time index respectively. The set ri. sub-symbols for each sub(cid:173)
`channel fonns the QAM constellation cl that sub-channel. For a sub(cid:173)
`channel with an allocated bi bits, there should exist 2•1 unique sub(cid:173)
`symbols.
`
`The IFFr maps the M complex sub-symbols into 2M real time domain
`samples x1 k ( i - l,2, ... ,2M ). This set of 2M real samples constitute the
`k-th DMT 'transmitted symbol. These Xi.k's are passed through a Parallel
`to Serial (P/S) device, and applied to a Digital to Analog Convener
`(DAC) with sampling rate of: !._,i,,-DMT = ..,.2M . The low-passed
`'DMT
`output of the DAC is the transmitted wavefoon x(t) on the channel.
`
`The channels of interest are the highly dispersive and lossy subscriber
`loqis. When the number of sub-channels is sufficiently large, the
`channel transfer function, H(j), can be approximated by a set of
`ri. width
`contiguous rectangular sub-channel
`transfer functions
`. I H(/,) 12
`f
`1
`. h
`J,.,,.p/•-DMT
`- -
`Hz and wit
`center- requency gam
`1
`Tow
`2M
`U•l,2, . .,M). With such an approximation, the channel can be
`decomposed into a set of discrete-time, parallel, independent, ISi-free
`sub-channels with gains I H(f;) 1 2• It can be shown that with large M,
`the noise ccxnponents on each sub-channel are independent if the noise
`is Gaussian.P 2l Thus, each independent sub-channel can be deccxied
`separately using a memoryless detectcr (i.e., without equalization).
`
`The operation of the receiver proceeds as the reverse cl the transmit
`operation: low-pass filtering of the received signal y(t), analog to digital
`conversion, serial to parallel fcrmation, FFr processing on the 2M
`samples, and buffering/deccxiing to generate data at the rate of R
`bits/sec.
`
`The IFFr is an energy invariant crthogooal transfa:matioo. That is:
`M
`2M
`1: I Xi.J 2 =1: x.·.k 2
`• The mean-squared value of the X1,1: is called the
`i=l
`i=l
`sub-symbol energy and is dencxed by E1; thus, the sub-symbol power is
`£.
`defined by P1 = - 1
`- . Therefore, the texal transmit energy and power
`TvMT
`denoted by E'"'"' and P,,.,,., can be expressed by:
`
`(I)
`
`The energy per sub-channel can be related to the number ri. square
`QAM signal constellations by:
`
`(2)
`
`where L is the number of symbols in the constellation, and d is the
`distance between two adjacent symbols in each dimension. For
`example, with 16-QAM rectangular constellation using 4 symbols in
`each dimension L=l6. d=2, and Ei .. 10. For a sufficiently large M, the
`signal to noise ratio on each sub-channel can be written as:
`
`SNRj.M-DMT
`
`Eil Hil 2
`2
`0
`j-No;,,
`
`)=I, ···,M
`
`(3)
`
`The total number of bits that can be allocated to all the sub-channels is
`expressed as:
`
`M
`bow = :t, bi = log2
`i=I
`
`{ M (
`II
`J=l
`
`1 +
`
`SNRj,M-DMTj}
`r
`DMT
`
`(4)
`
`An average DMT signal to noise ratio fer the overall system can be
`defined by SNRDMT such that:
`
`Thus:
`
`(6)
`
`(7)
`
`Assuming that "+ 1" and "· l" are negligible, the average SNR can be
`written as:
`
`Then from equation (6), the margin can be calculated by:
`
`/J.DMT-mar1in = )Q)og!O
`
`SNRM-DMT
`bDMT
`2 M -1
`
`[
`
`- 9.8
`
`(8)
`
`(9)
`
`Equation (9) is used for performance evaluatioo study of the DMT
`system.
`
`2.2 Computational Algorithm for Performance Margin
`
`Equation (9) expresses achievable margin through the average channel
`signal to noise ratio (SNRM-DMr). the optimal number of used sub(cid:173)
`channels (M), and the desired number of bits per block (bDMT ).
`For a given channel, sampling rate, and the number of allowed sub(cid:173)
`channels (NJ, an NxN "sorted sub-channel TTUJtrix" can be computed as:
`
`SNR1,1-0MT
`SNR1,2-0MT
`SNR1,J-oMT
`
`SNR2.1-om
`SNR2,2-om
`SNR 2.H>MT
`
`SNR3,l-DMT
`SNR i.2-l>MT
`SNR3,H>MT
`
`SNRN.1-DMT
`SNRN,2-DMT
`SNRN,l-DMT
`
`(10)
`
`SNR 1.cii-1roMT SNR 2,rii-1>-DMT SNR 3,CN-1)-DMT
`SNR1:N-0MT
`SNRzN-DMT
`SNR3,N-DMT
`
`... SNR rii>.<N-1)-DMT
`SNRN,N-DMT
`
`where _!he elements of each row are the signal to noise ratio fer each of
`the N
`sub-channels
`listed
`in
`the descending
`crder
`(i.e.,
`SNRk,M-DMT > SNRk+l,M-oMT). The value of the used-subchannels
`ccrresponds to the row number (i.e., the first row corresponds to M-1,
`and the secood row corresponds to M-2, etc). Nae that the effects of
`bridged-taps or gauge changes on the subscriber loops is exhibited in
`this matrix by the variation of SNR with respect to the position of the
`center frequency of the sub-channels. That is, the SNR on a sub-channel
`is not necessarily a monotonically decreasing function of its center
`frequency (i.e., a higher center frequency might suppcrt a larger SNR
`than a lower center frequency).
`
`The lower diagonal portion of the above matrix forms the "used sub(cid:173)
`channel matrix", where the M-th row has M associated largest sub(cid:173)
`channels. Next, equation (8) is applied to each row to calculate an
`average SNR for a given M. Finally, the optimal channel SNR is the
`maximum of the computed SNR:
`
`where, for a BER of 10-7
`approximated[9l by:
`
`r DMT = 9.8dB +/J.oMT-margin
`
`• the unccxied SNR Gap, r DMT·
`
`is
`
`The optimal number of sub-channels is M, the index associated with
`SNRM-DMT·
`
`(5)
`
`3. Computer Simulation Framework
`
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`3.1 Loop Plant Environment
`
`A set of five loops from the 1983 Loqi survey,r131 as shown in Figure 5,
`are used for simulation studies. These loops have also been prqmsed as
`test loq>s for perfcrmance studies of various ADSL transceiver
`architectures in TlEl.4 Standards Committee.l6l Each loop is identified
`by a number as depicted in the loq> make-up diagram (to the left of the
`"CO" in the Figures). In the simulation studies, an extra set of three
`loq>s are added to the canonical loops: 12 kft of 24-AWG (loop #16),
`18 kft of 24-A WG (loop #17), and 9 kft of 26-A WG (loq> #18). These
`loqis are quite lossy and dispersive. For example, at 70° F, the pulse
`height loss of 18-kft, 24-A WG is about 61 dB at a carrier frequency of
`250 kHz with 16-QAM signaling.
`
`3.2 FEXT and A WGN Models
`
`The coupling path for the generation of FEXT is dependent on the loss
`characteristics of the disturbing loop and the loss coupling function
`according to:
`
`2
`
`k I / 2
`
`2 =I Hdistwbing(f,1)1
`I HFEXr(/)1
`where I Hdisturbin1 (f,l)I
`is the magnitude of the disturbing loop loss
`function. The coupling constant k, for 1 % equal level 49 disturber
`crosstalk, is assumed to be 8x10-20 (with I in feet and /in Hz), where I
`is the length of the coupling path. Since the focus of the present study
`is to evaluate the effects of FEXT and the additive white Gaussian
`noise, the effects of NEXT from other systems are not considered in
`this study.
`
`The AWGN level is set at -140 dBm/Hz. This is equivalent to
`a2 AWGN = 10-1
`' V 2 per Hz across a 100-ohm termination, or 4x10-12
`Watts across 400-kHz of bandwidth.
`
`3.3 QAM ADSL Transceiver Structure
`
`The single-tone QAM ADSL system uses 16-point QAM for signaling
`at a nominal rate of 1.6 Mb/s. This rate is 56 kb/s above 1.544 Mb/sand
`can accommodate sufficient overhead. The symbols are extracted from
`a rectangular constellation with 4 symbolic levels of± 3, ± 1 on each
`dimension. The source and load impedances are assumed to be 100-
`ohrn resistive at 70° F, with the resulting transmit power of 20 dBm at
`the source. The transmit and receive lowpass filters are 10-th order
`Butterworth with the 3-dB corner frequency at 200 kHz. The carrier
`frequency, fc, is determined by: !c = f,wardband + A-dB where f,.,,rdband
`(i.e., the frequency band from DC to the lower 3-dB point of the
`bandpass filter) is a simulation parameter in the range of 20 to 110 kHz.
`
`A detailed description of the simulated QAM receiver can be found in a
`previous paper by the author.l10J As illustrated in Figure 4, the in-phase,
`quadrature-phase, and cross-coupled
`feedforward
`filters
`(FFF),
`respectively denoted by R 11 , R 22 , R 12 , and R21 are designed to
`minimize the sum of the pre-cursor ISi and the additive noise at the
`input to the slicer. The optimal tap weights of the FFFs are obtained
`through minimization of the mean-squared error (MSE) at the output of
`the FFFs (in the absence of post-cursor ISi). A quarter baud-spaced
`Fractionally Spaced Equalizer (FSE) is used for pre-cursor equalization.
`A 41-tap FSE is assumed for the feedforward and cross-coupled filters.
`The pulse response of each loop is assumed to have a span of 15 pre(cid:173)
`cursor and 60 post-cursor bauds with respect to its cursor.
`
`3.4 DMT Simulation Parameters
`
`For DMT margin computation, the transmit power is also assumed to be
`20 dBm at the source with 100-ohrn terminations. It is assumed that the
`sampling rate is 1.024 MHz, and the channel is decomposable into 256
`sub-channels. That is each sub-channel occupies 2 kHz of channel
`bandwidth. With such an arrangement, the maximum sub-channel
`center frequency is at 256x2 = 512 kHz. Thus, searching for cptimum
`sub-channels is conducted at carrier frequencies of f; = 2 i kHz for
`i = 1 , · · · , N=256. Furthermore, it is also assumed that the power is
`equally divided amongst the used sub-channels, and the discarded sub(cid:173)
`channels do not have any energy. This is an important assumption since
`
`758
`
`the resulting transmit spectrum will not be uniform across the channel
`bandwidth.
`4. Computational Results
`
`The results of the DMT margin computations are tabulated in Table 1
`for the case where all sub-channels are allowed to be used (i.e.,
`f; = 1 , · · · , 256). Ncte that the computed DMT margin is sufficiently
`high even with loq> #1. Table 2 tabulates the results of the margins for
`bcth 16-QAM and DMT for three values of guardbands: 20, 50, and
`100 kHz. For the QAM study, the guardband refers to the lower 3-dB
`point of the band-pass filter that determines the region of channel
`spectrum usage. For the case of DMT with 2-kHz sub-channel
`bandwidth, 20, 50, and 100 kHz refer to excluding the first 10, 25, and
`50 lower sub-channels from usage for bit distribution. This sub-channel
`exclusion scenario imposes a severe penalty on the perfcrmance of the
`DMT. However, since the inclusion of POTS and a "reverse control
`channel" has not been investigated, the sub-channel exclusion strategy
`as a preliminary simulation approach is deemed to be a judicious
`method for comparison with a QAM system.
`
`The last three columns of Table 2 show the relative enhancement of an
`ideal DMT over 16-QAM. The tabulated results indicate that generally,
`for a given guardband, DMT has a higher margin than QAM across the
`loq>s. This enhancement is more evident at lower guardbands where
`only the first IO sub-channels form the exclusion region. As the
`guardband increases, the ftexibility of DMT in energy distribution
`weakens, and thus the relative advantage of DMT decreases.
`It is instructive to remark oo the following points:
`
`1. A higher sampling rate is conjectured to improve the theoretical
`performance for certain loops.
`
`2.
`
`In the DMT margin computations, the loop transfer function did
`not include any low-pass or band-pass filters associated with any
`segment of the system.
`
`3. By excluding a number of sub-channels in the lower channel
`spectrum (i.e., utilizing a brickwall type exclusion region), some
`of the inherent advantages of DMT are discarded. That is, at the
`critical low frequency region where the channel gains are higher,
`the ability of DMT to vary the bit distribution is weakened.
`
`4. The number of channel pre-cursors in the equalization of the
`QAM channel was set at 60 (i.e., 15 bauds with T/4-FSE), and the
`number of post-cursors was set at 240 (i.e., 60 bauds with T/4-
`FSE). The size of these two parameters are quite significant when
`the guardband is below 40 kHz.
`
`5.
`
`It was observed that the so-called "Narrow-Band" channel
`modeil11J for a QAM system is valid at guardbands above 40 kHz
`with IO-th order Butterworth filters. For guardbands below 40-
`kHz, four channel pulse responses should be computed: in-phase,
`quadrature-phase, and two cross-coupled channels (in-phase to
`quadrature-phase and quadrature-phase to in-phase).
`
`5. Conclusions
`
`The projected performance of an ideal DMT with a sampling rate of
`1.024 MHz
`and 256-subchannel
`segmentation offers margin
`enhancement up to 3 dB over a quarter baud-spaced FSE-based 16-
`QAM signaling. However, more studies need to be performed to
`determine how well this analytically demonstrated enhancement can be
`achieved with a non-ideal DMT transceiver. For example, more
`sophisticated analyses and simulation studies which take into account
`effects such as finite length and finite precision filtering, intersymbol
`interference between subchannels, and adaptation residual error are in
`order.
`
`6. Appendix: Margin in the Presence of FEXT &A WGN
`
`Dencte the transmit power by Pr and the load termination by RL. The
`energy per block can be defined as: Pr RL. Define Mas the "number of
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`

`used sub-channels." To keep the transmit power constant, the energy
`per used sub-channel defined by a is: a= ~ (Pr RL). It is this energy
`per used sub-channel that determines the QAM constellatico:
`
`Define 11 as the energy density per used-subchannel per Hz:
`
`a
`Tl= -
`IV
`
`1
`energy I Hz I sub-channel, !:lf = - -
`Tsymbol
`
`Define the SNR/sub-channel as:
`
`(A-1)
`
`(A-2)
`
`(A-3)
`
`loop transfer function at center frequency f;,
`the
`is
`where H;
`ol-FEXT =Tl kFEXT ii Hj 2 ff,
`or= o;_FEXT + o;_AWGN•
`and
`Of-AWGN = 2 oiwaN· The factor of 2 in the previous expression
`accommodates white noise per 2-dimensional QAM symbol per sub(cid:173)
`channel. Therefore equation (A-3) can be written as:
`
`SNR;,M-DMT = kFEXT l
`{
`
`2 oiwaN
`f;2 + - - - - - - - -1
`ll HI 2
`_!__ (PrRL) k
`M
`FEXT
`!:lf
`
`11
`
`}-l
`
`Define the parameter ~ as:
`
`2 oiwaN (f).f)
`~ = -kF_E_xr_l (_P_r_R_L_)
`
`Thus, equation (A-4) can be expressed as:
`
`__ l_
`SNR;,M-DMT- kFEXT I
`
`j-1
`2 ~ [
`
`f; + I H;I 2
`
`(A-4)
`
`(A-5)
`
`(A-6)
`
`The overall system SNRvMr can be approximated by the geometric
`mean of the sub-channel SNRs defined by:l9l
`
`M
`n
`
`J~l
`
`(A-7)
`
`1
`-
`SNRvMr=-k I
`FEXT
`
`1 t
`l
`1"~
`J:+ IH 1;1 2
`where Ji; and I Hi,j 2 are corresponding frequency and insertion loss fer
`SNRii,M-DMT• and SNRi;,M-DMI. for j= 1,2, ···,Mare the_M largest
`SNRs fer a given M within a N sub-channels (i.e., i•l,2, ... ,N) ordered
`such that:
`
`SNR \M-DMT > SNR 2;,M-DMT > SNR\M-DMT > · · · > SNRM1,M-DMT
`
`(A-8)
`
`3. K. Sistanizadeh, "Petformance Evaluatico of 16/64-QAM ADSL
`Transceivers in the Presence ci Self-FEXT," TlEl.4/91-117.
`
`4. M. Sorbara, J. J. Werner, and N. A. Zervos, "Carrierless AM/PM,"
`TlEl.4/90-154.
`
`5. P.S. Chow, et al., "Preliminary Feasibility Study of a Multi-Carrier
`Transmission System for the Proposed ADSL Data Service,"
`Tl El .4190-211.
`
`6. K. Sistanizadeh, "Proposed Canonical Loops for ADSL and their
`Loss Characteristics," Tl El .4191-116.
`
`7. J. Cioffi, et al., "A Comparison of Multi-Carrier and Single-Carrier
`Modulatioo for ADSL," Tl El .4/91-123.
`
`8. P. S. Chow, et al., "Performance of Multicarrier with DSL Impulse
`Noise," TlEl.4191-159.
`
`9. J.M. Cioffi, "A Multicarrier Primer," TlEl.4191-157.
`
`10. K. Sistanizadeh, "Analysis and Petformance Evaluation Studies of
`HDSL using QAM and PAM with Ideal DFE within a CSA,"
`Prcceedings of IEEE GLOBECOM'90 Conference, pp.1172-1176.
`
`11. Digital Communications, J. G. Proakis, Second Edition, McGraw(cid:173)
`Hill Book Company.
`
`12. Information Theory and Reliable Communication, Chapter 8, R.
`G. Gallager, John Wiley & Sons, Inc., 1968.
`
`13. Bellcore Database for 1983 Loop Survey.
`
`Loop#
`
`Margin dB
`
`I
`
`2
`
`3
`
`4
`
`6
`
`12-Jcft,24AWG
`
`18-kft.24-A WG
`
`9-kft.26-A WG
`
`8.7
`
`11.8
`
`12.4
`
`16.S
`
`14.9
`
`25.S
`
`19.8
`
`26.7
`
`Table 1. DMI' Margins with No Sub-Channel Exclusion
`
`16-QAM
`Margin dB
`
`Guardband
`kHz
`
`DMT
`Margin dB
`
`Margin Enhancement
`dB
`
`Excluded Sub-Channels
`Number
`
`Excluded Sub-Channels
`Number
`
`Loop
`
`20
`
`so
`
`100
`
`1-10
`
`1-25
`
`I-SO
`
`1-10
`
`1-25
`
`I-SO
`
`kHz
`
`kHz
`
`kHz
`
`I
`
`2.7
`
`0.6
`
`-4.6
`
`2.6
`
`Finally, the margin is calculated by:
`
`'1vMT-mar1in =-10 log10 [ kFEXT1] - 10 log10[ 2bDllrlM - l] -
`
`(A-9)
`
`~ #i log10 [Ji/+ I Zij 2]-9.8 dB
`
`REFERENCES
`
`l. "Integrated Services Digital Network
`Interface," ANSI-Tl.601, 1991.
`
`(ISDN)-Basic Access
`
`for High-Bit-Rate Digital Subscriber
`2. "Generic Requirements
`Lines," Bellcore TA-NWT-001210, Issue l, October 1991.
`
`759
`
`2
`
`3
`
`4
`
`6
`
`8.2
`
`7.6
`
`11.2
`
`7.6
`
`12kft.24
`
`23.S
`
`S.3
`
`8.5
`
`8.9
`
`13.8
`
`11.3
`
`1.7
`
`4.9
`
`4.9
`
`10.9
`
`6.6
`
`-2.4
`
`-1.6
`
`6.S
`
`0.8
`
`19.1
`
`24.0
`
`22.4
`
`4.0
`
`S.3
`
`9.9
`s.s
`21.2
`
`-3.5
`
`0.7
`
`0.0
`
`6.S
`
`-0.7
`
`19.7
`
`18kft,24
`
`15.5
`
`13.7
`
`10.6
`
`17.S
`
`14.9
`
`11.0
`
`9kft,26
`
`22.7
`
`22.0
`
`20.6
`
`2S.3
`
`23.5
`
`20.9
`
`0.3
`
`1.3
`
`2.6
`
`3.7
`
`0.5
`
`2.0
`
`2.6
`
`I.I
`
`0.9
`
`-0.4
`
`1.0
`
`I.I
`
`1.2
`
`1.2
`
`1.5
`
`I.I
`
`3.1
`
`1.6
`
`0.0
`
`-1.5
`
`0.6
`
`0.4
`
`0.3
`
`Table 2. 16-QAM and DMI' Margins
`
`CSCO-1033
`Cisco v. TQ Delta, IPR2016-01020
`Page 4 of 5
`
`

`

`Loop fl:
`
`Loop'2:
`
`co
`
`co
`
`/,
`
`/,
`
`/,
`
`j,
`
`/,
`
`/,
`
`j,
`
`Frequency
`
`Figure l. Qiannel Spectrum Decomposition to Sub-Oumnel Spectra
`
`I
`
`/,
`
`/,
`
`/,
`
`j,
`
`Figure 2. Transmit Energy Spectral Density
`
`Frequency
`
`Loop13:
`
`Loopf4:
`
`16SOO'
`
`26AWO
`
`ISOO'
`
`24AWO
`
`13SOO'
`
`26AWO
`
`lSOO'
`
`ID
`
`24AWG
`3000'
`24AWO
`
`SOO'
`
`24AWG
`
`1000'
`
`SOO'
`
`1000'
`24AWG 22AWG 24AWG
`1000'
`(JOO()'
`lSOO'
`24AWG 24AWG 22AWG
`
`24AWG
`lSOO'
`
`ID
`
`3000' -
`
`ID
`
`26AWG
`
`SOO'
`
`SOO'
`
`7SOO'
`
`26AWG
`
`- 7SOO'
`
`co
`
`26AWO
`
`4SOO'
`
`2000'
`
`24AWO
`
`22AWG
`
`t:::;:
`
`j,
`
`J,
`
`'"
`
`Noile
`
`Rec:eiveSipll
`y(/)
`
`co
`
`Loopf6:
`
`4SOO'
`
`26AWG
`
`12000'
`
`24AWG
`
`24AWG 24AWG
`1000'
`
`24AWG
`
`Note:
`
`1) AWG means American Wire Gauge
`2) Distacea ""' in feet('): 1000' • .3048 km
`
`Tnm1111il
`s·
`
`l'lpre 5. Configuration of Teat Loops
`
`-2ain(Co1,1-H!)
`
`2M Time·Oomlill Sanplea M QAM Symbol•
`
`Figure 3. DMT Tra11J1ceiver Block Diagram
`
`FEX'T+A'WGN
`
`FEX'T+A'WGN
`
`~ T
`
`Tnm1111it
`lJ'F
`
`ADSL
`
`Figure 4. QAM Tra11J1ceiver Block Diagram
`
`flpn 6. FEXl' simulation model
`
`760
`
`CSCO-1033
`Cisco v. TQ Delta, IPR2016-01020
`Page 5 of 5
`
`