IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS. VOL. 9. NO. 6, AUGUST 1991
`
`A Discrete Multitone Transceiver System for HDSL
`Applications
`
`895
`
`Jacky S. Chow, Student Member, IEEE, Jeny C . Tu, Student Member, IEEE,
`and John M. Cioffi, Senior Member, IEEE
`
`Abstract-A discrete multitone (DMT) transceiver design for
`high-bit-rate digital subscriber line (HDSL) access is presented
`and analyzed. The DMT transmitter and receiver structure and
`algorithms are detailed, and the computational requirements
`of DMT for HDSL are estimated. We find that at a sampling
`rate of 640 kHz, using an appropriate combination of a short
`FIR equalizer and a length-512 DMT system, 1.6 Mb/s data
`transmission is possible within the CSA at an error rate of lo-’
`on a single twisted pair. We also show significant performance
`margin can be achieved when two coordinated twisted pairs are
`used to deliver a total data rate of 1.6 Mb/s. We conclude that,
`in terms of a performance-per-computation figure of merit, the
`DMT system is an excellent candidate for HDSL implementa-
`tion.
`
`I. INTRODUCTION
`ULTITONE modulation methods use an optimized
`
`M frequency division allocation of energy and bits to
`
`maximize the reliably achievable data rates that can be
`transmitted over bandlimited communication channels.
`These systems are easily described because they use fre-
`quency division multiplexing to transport a single-input
`data stream on several carriers within the usable fre-
`quency band of the channel. The simplicity of multitone
`methods accounts for their use in some of the earliest data
`transmission modems, such as the Collin’s Kineplex mo-
`dems of 1957 [ l]. While the simplicity and appeal of mul-
`titone modulation has existed for decades, it is only very
`recently that their optimal performance has been proven
`theoretically (see [2], [3]) and demonstrated in practice
`with recent products, such as Telebit’s Trailblazer mo-
`dems [4] or NEC’s multitone voiceband and groupband
`modems [5]. These highest-performance products are sold
`at only a fraction of the cost of comparable performance
`single-channel or QAM modems.
`The excellent high-performance/cost tradeoff of multi-
`tone modulation also makes it a strong candidate for the
`transceiver implementation for high-bit-rate digital sub-
`scriber lines (HDSL), a 1.6 Mb/s digital subscriber ser-
`vice on twisted-pair channels of up to two miles. This
`paper presents a multitone modulation structure that is of
`
`Manuscript received November 14, 1990; revised May 17, 1991. This
`work was supported in part by a gift from Bell Communications and by a
`contract with the University Technology Transfer Institute.
`The authors are with the Information Systems Laboratory, Department
`of Electrical Engineering, Stanford University, Stanford, CA 94305.
`IEEE Log Number 9 102 134.
`
`particularly high performance and low cost for the HDSL
`application. We generally find that, even on worst-case
`channels, a 1.6 Mb/s (1.536 Mb/s user data plus 64 kb/s
`control channel) data rate is achievable at an error rate of
`lo-’ on a single twisted pair (with 6 dB margin). Fur-
`thermore, we find that the described multitone system ex-
`hibits excellent margins (nearly 18 dB) for the so-called
`dual-duplex option of providing 1.6 Mb/s on two coor-
`dinated twisted pairs. I
`The intersymbol interference, crosstalk, and attenua-
`tion of 24-gauge and/or 26-gauge twisted pair is particu-
`larly severe within the two-mile camer serving area (CSA)
`requirements, as we discuss in Section TI. Section I1 also
`briefly examines and reviews theoretically and practically
`achievable maximum data rates for HDSL. Equalization
`and coding methods have to be carefully applied in the
`HDSL application to render the high transported data rates
`reliable. In the approach presented, a particularly effec-
`tive combination of a small amount of time-domain equal-
`ization and of a larger amount of multitone modulation is
`used to transmit the data reliably. The equalizer is used
`to shorten the effective response length of the data chan-
`nel, while the multitone modulation is used to mitigate
`the remaining intersymbol interference and the effects of
`crosstalk, as is described in Section 111. The multicarrier
`system is fully adaptive, employing both an adaptive al-
`gorithm for update of the adaptive filters and also a spe-
`cial channel identification procedure that is used to ini-
`tialize and update
`the
`transmitter bit allocation
`to
`frequency-indexed subchannels. This relatively simple
`procedure is essential for maximizing performance. We
`also estimate the complexity in terms of the number of
`arithmetic operations in Section 111 and illustrate that the
`multitone transceiver can be implemented with program-
`mable signal processors, although those processors may
`need to be custom designed for lowest cost.
`The performance in achievable data rate of the multi-
`carrier system is analyzed and characterized in Section IV
`as a function of input power, channel characteristic, num-
`ber of tones or carriers, sampling rate, noise margins, and
`crosstalk.
`
`‘We note that results in this paper use channel models with less atten-
`uation than those of previous studies in [6]-[9]. based on measured line
`results of several industrial sources.
`
`0733-8716/91/0800-0895$01.00 0 1991 IEEE
`
`

`
`896
`
`IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL 9. NO 6 AUGUST 1441
`
`11. SUBSCRIBER LOOP CHARACTERIZATION
`AND
`MODELING
`In any study of HDSL transceivers, the channel models
`are critical to specification of performance. We outline in
`detail the HDSL channel models used throughout the study
`of DMT HDSL transceivers. We note that performance
`projections based on different channel models can lead to
`erroneous claims and comparisons. A detailed tutorial on
`HDSL technologies is presented by Lechleider in this is-
`sue [IO].
`
`A . CSA Loop Characteristics
`The carrier serving area (CSA) is an identifiable subset
`of the current subscriber loop population in the U.S., and
`our HDSL study is restricted to loops that satisfy minimal
`CSA requirements. The CSA consists of mainly 24- and
`26-gauge twisted pair, with lengths on 24-gauge wire to
`12 kft and on 26-gauge wire to 9 kft. CSA loops can also
`contain bridge taps of limited length; a complete specifi-
`cation of the CSA appears in [I I]. Impairments in the
`CSA data transmission channel include:
`intersymbol interference (ISI),
`crosstalk noise coupled from adjacent loops within
`the same cable bundle,
`impulsive noise (caused by switching transients,
`lightning, and other electrical machinery),
`echo noise resulting from the combination of imper-
`fect hybrids and gauge changes on the line as well as sig-
`nals reflected from bridged taps,
`electronics noise (such as quantization noise in ana-
`log-to-digital converters (ADC) and thermal noise in the
`analog portion of the transmitter and receiver), and
`inductive noise at 60 Hz and its harmonics caused by
`nearby power lines.
`We consider a set of representative CSA channels, pro-
`vided by Bell Communications Research [ 121, that have
`the respective loop cable arrangements illustrated in Fig.
`1. We use a letter designation (A-H) on these channels
`for reference. These channels are generally representative
`of some of the worst, in terms of channel impulse re-
`sponse, expected to be found within the CSA limits. In
`general, longer wire length, smaller wire size, and pres-
`ence of more and longer bridge taps results in poorer
`achievable data rates. We also note that on-premises wir-
`ing is often impossible to characterize statistically, so a 6
`dB margin is imposed upon the performance of any HDSL
`transceiver to ensure that IO-' error rate is maintained
`[13]. In all loop models in this paper, we include this 6
`dB margin simply by increasing loop attenuation for the
`loops in Fig. I by 6 dB (see also Footnote I).
`
`B. Channel Modeling
`A line simulation program, based on standard trans-
`mission line modeling and a standard set of twisted-pair
`characteristics, was used to generate an impulse response
`for each of the channels in Fig. 1. The effect of the cou-
`pling transformer at each end of the loop termination was
`
`Channel 25
`
`1778'124 190/24
`
`Channel 29
`O 11112'/2'r
`B
`
`l80/22
`
`Channel23 AY6L24
`180/26
`c
`1786/26
`6514126
`Channel 2h
`D-
`
`Channel 21 I
`E
`
`14012
`11643'124
`Channel 210
`800122
`08100'/26 ' '
`Channel 27
`12000/24
`G-
`
`Channel 16
`n -
`Fig. I . CSA channels: length (in ft.)/gauge
`
`9000'126
`
`included by adding a double-pole double-zero highpass
`digital filter with a cutoff frequency of 300 Hz. These
`characteristics were found to be in near exact agreement
`with those provided by separate programs at various in-
`dustrial groups working in the HDSL field [ 141, [ 121. One
`such time-domain impulse response is shown in Fig. 2 for
`Channel H .
`
`Crosstalk noise coupled from adjacent wire pairs in the
`cable bundle is the dominant noise impairment in CSA
`loops. Various characterizations have been proposed [ 151,
`[ 161, and we will use [ 151, which models crosstalk noise
`as near end crosstalk (NEXT) with the following transfer
`function:
`>I2 = KNEXTf 3'2
`(1)
`IHNEXT(f
`where KNEXT is the coupling coefficient. Since far end
`crosstalk noise is attenuated by the channel, the resulting
`noise power is negligible compared to near end crosstalk.
`Hence, we will only consider NEXT. The coupling coef-
`ficient K N E X T for a 50-pair cable was empirically deter-
`[17].
`mined to be approximately
`To model the effects of residual echo after cancellation,
`we note that a typical CSA loop attenuation is on the order
`of 24 dB, and a good echo canceller can presumably re-
`duce the echo to a level of 30-40 dB below the received
`signal. Assuming an average input power of 10 mW (10
`dBm), this translates into -44 to -54 dBm of total echo
`noise power across the two-sided bandwidth of 640 kHz,
`which corresponds to a noise power spectral density of
`to 6.22 x
`6.22 x IO-"
`mW/Hz. This residual
`echo noise is assumed to be additive white Gaussian noise
`(AWGN), and we fix this AWGN to have a power spectral
`density of - 110 dBm/Hz for subsequent analysis and
`simulation. The electronics noise, as mentioned earlier,
`is typically on the order of -140 to -170 dBm/Hz [6]
`and is thus, by comparison to echo noise, negligible. Of
`course, crosstalk noise is larger than either echo or elec-
`tronics noise.
`While impulsive noise is more difficult to characterize,
`some [ 181 have attempted to model its effect. Impulsive
`noise usually consists of millivolt pulses (say, up to 40
`mV) that last a few ps to 1000 ps.
`Inductive noise can be modeled as a fixed noise level
`at 60 Hz, but the highpass filter simulating the trans-
`formers eliminates the inductive noise.
`I ) Pole-Zero Modeling: To facilitate simulation of
`CSA loops for performance analysis, we constructed a
`pole-zero (ZIR) model for each channel impulse response
`
`__
`
`7
`
`

`
`CHOW er al.: A DISCRETE MULTITONE TRANSCEIVER SYSTEM
`
`897
`
`0’035
`~ -
`0.03
`
`-
`
`0.025
`
`0.02
`
`~
`
`-
`
`0.015
`
`-
`0.01
`
`0.005
`
`-
`
`0 -
`
`-0.005 ‘
`
`TABLE I
`CAPACITY A N D FLAT INPUT C A P A C I T Y FOR CSA LOOPS, 800 KHZ KATE A N D
`WITH 6 DB MARGIN ( I N MB/s)
`
`- Bellcore line simulation
`- - - - Pole-Zero Model
`
`Capacity with 6 dB
`Margin
`
`Flat Input Capacity with 6 dB
`Margin
`
`Channel
`
`Crosstalk
`Bound
`
`11 dBm
`Power
`
`OdBm
`Power
`
`1 0 d B m
`Power
`
`17 dBm
`Power
`
`2.42
`2.39
`2.32
`2.31
`2.26
`2.29
`2.19
`2.14
`
`2.30
`2.27
`2.20
`2.19
`2.14
`2.17
`2.07
`2.02
`
`1.87
`1.85
`1.78
`1.77
`1.72
`1.75
`1.65
`1.60
`
`2.29
`2.27
`2.19
`2.19
`2.13
`2.16
`2.06
`2.01
`
`2.40
`2.37
`2.30
`2.29
`2.24
`2.27
`2.16
`2.11
`
`150
`100
`50
`200
`Fig. 2. Impulse response of a CSA loop.
`
`at various sampling rates, using standard system identifi-
`cation tools. An impulse response obtained for Channel
`H is compared to the impulse response generated by a
`pole-zero model in Fig. 2. Since the pole-zero model
`closely approximates the true response, the use of pole-
`zero models for subsequent studies is justified.
`The number of poles and zeroes varies with different
`CSA channels, but they all fall into the same range: 5-8
`zeroes, and 6-12 poles. For future reference, assume the
`number of zeroes for a particular channel is equal to U ,
`and the number of poles is equal to L - 1. We also found
`that most of the CSA channels are not minimum phase,
`i.e., some of the zeroes from the pole-zero models lie out-
`side the unit circle in the z-plane.
`
`C. Capacity
`The capacity of these loops with the aforementioned
`models is computed in [6], at the sampling rates of 400
`and 800 kHz. As explained later in Section IV-A and [6],
`a sampling rate of 400 kHz is not sufficient to maximize
`the HDSL transceiver performance on most CSA chan-
`nels shown in Fig. 1 as well as the capacity with a flat
`input spectrum (called “flat input capacity” in Table I)
`at 800 kHz sampling rate. The two columns under “Ca-
`pacity” list the capacity using the optimal transmit power
`distribution [6], and represent the best data rates that can
`be achieved with an 800 kHz sampling rate. “Crosstalk
`Bound” assumes crosstalk noise is the only noise impair-
`ment (and, thus, ignores the contribution of AWGN),
`while “11 dBm Power” includes the effect of AWGN
`with 11 dBm transmit input power. The three columns
`under “Flat Input Capacity” do not optimize transmit
`power distribution; instead, a flat input power spectral
`density is assumed. The effects of near end crosstalk, 6
`dB margin, and AWGN are included for the calculation,
`and the maximum achievable data rate based on the flat
`input power spectrum are shown for three different input
`powers: 1, 10, and 50 mW (0, 10, and 17 dBm, respec-
`tively). Notice that, with a sufficiently high input power
`(10 dBm or above), the penalty in achievable data rate
`
`(10 dBm or above), the penalty in achievable data rate
`without optimizing the transmit power distribution be-
`comes negligible. Thus, we will assume a flat input power
`spectrum is used, and this will simplify analysis and sim-
`ulation. Also, this allays any practical concern about loop-
`to-loop energy spectrum variation.
`We can infer from this table that 1.6 Mb/s can be re-
`liably transmitted over most CSA channels. However, an
`excellent transceiver design is required to accomplish this
`goal on either a single pair or on two coordinated pairs
`with a large performance margin such as 12 dB. Even with
`only a 6 dB performance margin on two pairs, 800 kb/s
`is 35-50% of capacity and more than a trivial receiver is
`required. On the other hand, a data rate of 160 kb/s on
`CSA channels (as in the case of basic rate ISDN) is well
`below the fundamental limits (although it may be a little
`more difficult on longer (18 kft) channels). Thus, one
`would not expect that a simple receiver used for basic rate
`ISDN would necessarily be good for use in HDSL.
`
`111. THE DISCRETE MULTITONE TRANSCEIVER
`This investigation focuses on a discrete multitone
`(DMT) transceiver for HDSL. We briefly describe the
`modulation and demodulation processes and the major
`system components. We also accurately compute com-
`putational requirements for the DMT HDSL transceiver
`using Motorola’s 56000 DSP as a representative host for
`implementation. A system using multiple Motorola 56000
`DSP’s has been used to implement the described DMT
`transceiver in real-time at Stanford University.
`
`A. System Description
`A simplified illustration of the DMT transmitter, re-
`ceiver, and channel appears in Fig. 3. The basic concept
`is to use frequency division modulation to divide the
`transmission system into a set of frequency-indexed sub-
`channels that appear to be modulated and demodulated
`independently. With a careful allocation of bits and trans-
`mit power to the subchannels, it is well known [2], [3]
`that such a system is capable of performing at the highest
`theoretical limits and that no other system can exceed its
`
`--
`
`II !I
`
`I
`
`-
`
`

`
`! xn+l
`
`89 8
`
`I
`
`PQ
`
`Noise n,
`I
`
`Channel
`
`IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS. VOL. 9, NO. 6. AUGUST 1991
`. . . , yN - I , with p,*. The noise at the channel output pres-
`ently includes only additive white Gaussian noise; we will
`generalize to the crosstalking case as this development
`proceeds.
`Because of the finite number of subchannels, a cyclic
`prefix (CP) of the transmitted signal samples f k is needed
`once for every transmitted block of bits. The CP prefixes
`the block of transmitted samples f o , * . . , f N - by the
`(repeated) samples, f N - ,, *
`We denote the cor-
`, f N -
`responding time indexes at the beginning of the block by
`k = - v, - U + 1,
`, -1. When v + 1 is the length
`of the channel impulse response in sample periods, then
`the successive blocks of transmitted data do not interfere
`with each other, and one can write (see [3]) that
`f, = IH,Ix, + n,
`
`*
`
`Fig. 3 . Simplified illustration of DMT transceiver and channel
`
`performance. There are now at least three commercial
`19.2 kb/s voiceband modems, marketed by three differ-
`ent companies, that use DMT to attain excellent perfor-
`mance. This section describes a DMT system for HDSL.
`The system in Fig. 3 is presumed to be sampled (digi-
`tized) at a rate that is at least twice as high as any signal
`frequency, so that sampling theory arguments apply and
`the discrete-time system is equivalent to the actual con-
`tinuous-time system. A block of input bits is divided into
`N subsymbols, x,, n = 0, * . * , N - 1, that are indepen-
`dently modulated by N-dimensional sampled-sinusoid
`modulating vectors p,, and then summed to form an
`N-dimensional block of modulated transmit signal sam-
`ples f k , k = 0, * . . , N - 1. The nth modulating vector
`is given by:
`
`~n = [ P ~ . o Pn.1
`
`* Pr1.N- I]
`
`*
`
`*
`
`(2)
`
`where
`
`the inverse discrete Fourier transform (IDFT) vector. To
`ensure a real-valued transmit signal, f k = 'SZ(fk), it is nec-
`essary that we impose the constraint on the subsymbols
`that (* denotes complex conjugate, '$3 denotes real part)
`n = 1, . *
`(4)
`, N - 1.
`x, = xi-,l
`It is convenient to think of DMT as consisting of N / 2
`quadrature amplitude modulation (QAM) channels. In
`practice, of course, the modulation is done digitally and
`no explicit use of any carrier modulation frequencies or
`modulators is required. The channel output samples yk are
`found by the sum of the convolution of the modulated
`transmit samples, f k , with the sampled channel impulse
`response hk and the additive noise nk,
`
`*
`
`The impulse response hk is assumed to be of finite length,
`and can be described by the v + 1 samples ho,
`, h,.
`h k D k . In the receiver, the
`Its D-transform is h(D) =
`corresponding demodulation is accomplished by taking the
`inner product of the corresponding N channel outputs, yo,
`
`*
`
`(6)
`
`where
`H = h
`n
`0
`
`+ h e-J(2*/N)n + h2e-J(2n/N)n + . . .
`1
`
`
`In practice, the modulation and demodulation process-
`ing is implemented with fast Fourier transform (FFT) al-
`gorithms that require significantly less computations than
`would occur in the direct implementation shown in Fig.
`3. We discuss specific computational requirements in Sec-
`tion 111-C.
`A trellis code [19] of coding gain y can be applied to
`each subchannel so that the energy allocated to this chan-
`nel will sustain a greater number of bits than in the ab-
`sence of the applied trellis code. The number of bits can
`be approximated by
`
`6, = log, (1 + T) SNR,
`
`where l? = 10 dB - y for a bit error rate of lo-' [20]. If
`no code is used, y = 0 dB and r = 10 dB. The signal-
`to-noise ratio on the nth subchannel is denoted by SNR,
`and is computed by
`
`(9)
`
`where ex = E ( x , ( ~ is the signal energy of the nth subsym-
`bo1 and o2 is the corresponding white noise energy. In
`practice with HDSL, the dominant noise is crosstalk
`noise, which is not white, so that o 2 -+ ai, a subchannel-
`dependent noise energy. When N is chosen sufficiently
`large, the noise on each of the subchannels will be ap-
`proximately white within the occupied frequency band and
`will be uncorrelated with the noise on any of the other
`subchannels. In order to compute the bit allocation out-
`lined by (8), the channel characteristic must be known at
`the transmitter, which is achieved as described in Section
`111-A-3. The energy allocation is approximated by a flat
`
`

`
`CHOW PI al.: A DISCRETE MULTITONE TRANSCEIVER SYSTEM
`
`(M-bit frames)
`
`a Inverse -+
`Length-N
`
`Coset-Encoder
`and
`Modulation
`plus Tone Shuffle:+
`
`FFI -
`
`-
`
`DAC
`and
`Transmit Filter
`(S = 640 kHz)
`
`899
`
`-
`
`Line
`Interface --c
`Unit
`
`*Tap
`Cyclic Prefix
`(parallel,serlal~
`
`transmit energy spectrum, so that E , is not a function of
`the frequency index n. Our studies have found that very
`little is lost in using this flat energy distribution in the
`HDSL application. The poorest subchannels carry only
`dummy data and are simply ignored by the receiver. This
`flat transmit spectrum has the effect of rendering the
`crosstalk power spectrum from any DMT HDSL trans-
`mitter constant in practice.
`1) The DMT HDSL Transmitter: A specific embodi-
`ment of the HDSL transmitter is illustrated in block dia-
`gram form in Fig. 4. In the specific implementation of the
`system that we study, v is always limited (through equal-
`ization, as discussed later) to a maximum of 8, and later
`in Section IV-A-3) and 4), we fix the sampling rate S to
`be equal to 640 kHz and N = 5 12.
`For a single twisted pair to carry R = 1.6 Mb/s (the
`single-duplex option), the input data bit stream is parsed
`into M-bit blocks, where M = (N + u ) R / S = 1300. These
`bits are then transformed into (a maximum of) N/2 =
`256 QAM subsymbols that are then applied to a trellis
`encoder. The trellis coder sequentially processes the fre-
`quency-indexed subsymbols to avoid the large latency and
`memory requirement that would occur with multiple trel-
`lis encoders. This process requires that the subchannel in-
`dexes be “shuffled” to avoid any minor correlation be-
`tween the noise on adjacent frequency subchannels. The
`output of the trellis encoder is then modulated, as de-
`scribed earlier, through the use of an N = 512 inverse
`FFT. Finally, an eight-sample cyclic prefix is placed in
`the beginning of the corresponding block of modulated
`transmit samples, and the extended block of N + v sam-
`ples is then applied to the channel through the digital-to-
`analog converter (DAC) and line-interface unit. The sam-
`pling rate is 640 kHz, which leaves the 256 subchannels
`effectively separated by 1.25 kHz. This corresponds to a
`block symbol period of 5 12 + 8 = 520 samples or 812.5
`ps. Eight samples is considerably shorter than most HDSL
`channel impulse responses at 640 kHz. An unusual and
`simple equalizer is used in the receiver to contain inter-
`symbol interference to eight samples, or impulse-re-
`sponse length to nine samples.
`For the so-called dual-duplex option with two twisted
`pairs, the 1300-bit blocks are parsed into the 512 QAM
`subchannels that exist on both of the channels. There are
`then two IFFT’s, two DAC’s, and two line-interface units.
`
`However, only one trellis code is necessary with this op-
`tion with respect to the single-duplex option. This im-
`proves the performance margin but increases the cost of
`the dual-duplex option. If a sufficient margin can be ob-
`tained using the single-pair solution (called “single-du-
`plex”), then it is preferable from a cost standpoint.
`2) The DMT HDSL Receiver: A block diagram of the
`general DMT HDSL receiver appears in Fig. 5, and a
`specific receiver that corresponds to the specific transmit-
`ter of Fig. 4 is shown in Fig. 6. This receiver structure is
`a slight variation of the original receiver proposed in [7].
`Both receiver structures achieve the same performance but
`the one in Fig. 6 results in lower complexity.
`An actual HDSL channel response is of significant du-
`ration in practice, and we can model its polynomial-frac-
`tion D-transform
`
`In practice, we identify this infinite-impulse-response
`model, &D), by choosing a(D) and p(D) to minimize the
`mean square error between this model and the channel
`output. Using this method, the crosstalk noise also affects
`the settings for a(D) and p(D). Due to the nonminimum
`phase nature of a(D), the use of an IIR equalizer 1 /h(D)
`to eliminate IS1 results in unstable filter. A short, fixed
`L-tap feedforward equalizer is thus used to process the
`sampled channel output yk sequentially. This equalizer
`does not remove intersymbol interference completely, but
`rather confines the impulse response so that its length is
`approximately U + 1 sample periods or less. By setting
`the equalizer to p(D), we will have a minimum mean
`square error approximation of an additive white noise
`channel with impulse response characterized by a(D),
`which has a response length of U + 1 sample periods or
`less. The last N samples of the N + U samples that cor-
`respond to the transmit block are extracted from the
`equalizer output. An N-point FFT is performed on the
`equalizer output. The FFT outputs, z,, (n = 0, 1, . *
`* ,
`N - l), are multiplied by N complex, 1-tap adaptive fil-
`, N - l) so that a common
`ters, w,, (n = 0, 1, *
`decision device can be used to estimate the subsymbols
`on each of the subchannels. The initial tap setting for w,
`
`1
`
`

`
`900
`
`I
`
`I
`
`-
`
`
`
`Extension
`
`L Tap
`
`?"
`
`I
`
`op''onal
`
`Fig. 5. Block diagram of the receiver.
`
`I
`
`Fig. 6. Specific block diagram of a DMT HDSL receiver
`
`w, = An-',
`
`n = 0, 1,
`
`. , N - 1
`
`(11)
`
`is:
`
`where
`
`N - I
`A, =
`
`k = O
`
`ake-J'2"/N'k"
`
`,
`
`n = 0 , 1, *
`
` , N - 1
`
`.
`
`-
`
`(12)
`
`the FFT of a(D). The resulting output data
`U , = w,z,, n = 0, 1,
`(13)
`, N - 1
`can then be decoded, which in the case of an applied trel-
`lis code requires a Viterbi decoder as shown. The symbol
`decisions are used (in the coded case) only to derive an
`error signal, so that the adaptive updating mechanism can
`be used to allow for slight channel variation. The corre-
`sponding error is
`n = 0, 1, . . , N - 1.
`e,, = d,, - U,,
`(14)
`Standard LMS algorithm can be used for updating,
`w, +- w, + 2 p n e n 5 ,
`. , N - 1
`n = 0 , 1,
`(15)
`where p, is the stepsize for each subchannel, and can be
`adjusted independently to optimize the rate of conver-
`gence.
`Since ak and uk are real, A, = A;-,, and z, = zi-,,, so
`that (13)-(15) are computed only through n = N/2.
`3) Channel Identijication and Initialization Protocol:
`As the DMT transmitter requires knowledge (either di-
`rectly, or indirectly through knowing the bit allocation b,)
`of the channel, the channel impulse response and crosstalk
`noise spectrum must be estimated during initialization.
`The more accurate the initial estimate, the more reliable
`the transmission with DMT. Accuracy requirements are
`significantly mitigated by the adaptive filters in the re-
`
`IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS. VOL 9. NO. 6. AUGUST 1991
`
`ceiver in practice, but are still important. (We note that
`decision feedback approaches that employ Tomlinson
`precoding [21], 1221 also need to know the channel at the
`transmit side and require an even greater accuracy than
`DMT [8], even when an adaptive feedfonvard section is
`used in the DFE receiver.) Rather than pursue channel
`identification in detail (see, for example, [23]-[25] for
`details), we will briefly summarize the basic steps in the
`initialization protocol. The complete startup time (includ-
`ing channel identification, SNR calculation, and bit and
`energy allocation) is less than one second.
`1) After receiving a request for transmission signal,
`some loopback and test patterns are exchanged, followed
`by timing and synchronization patterns.
`2) A predefined pseudorandom sequence is sent from
`the transmitter to the receiver for spectral estimation. A
`pole-zero model for the channel is derived from the re-
`ceived training pattern using a least-squares fit.
`3) Based on the result of the above channel spectral
`estimation, the receiver sets the tap values for the equal-
`izer at the pole settings of the pole-zero model, then com-
`putes the SNR for each frequency-indexed subchannel,
`and finally computes the transmit bit and energy alloca-
`tion across the frequency band.
`4) The bit assignments are sent to the transmitter in a
`reliable fashion.
`5) For bidirectional transmission, the above steps are
`repeated for the other direction.
`6) After frame synchronization and start commands are
`exchanged, the DMT transceiver system is ready for ac-
`tual data transmission.
`We have not considered the implementation of echo
`cancellation in this paper. We note that low-computation/
`high-performance echo cancellation is possible with DMT
`(see [26]).
`
`B. Transmit Power Level
`As shown in Section IV-A, we can improve perfor-
`mance by increasing the average input power. However,
`due to physical constraints, only a certain range of aver-
`age input power level is feasible. As a result, maximum
`average input power or energy is a common constraint
`that is usually imposed at the input of the channel (or
`equivalently, at the output of the transmitter).
`1) Transmit Power Adjustment: We have assumed an
`average energy constraint of E, per transmitted subsym-
`bol, before adding the cyclic prefix. The IFFT and FFT
`do not change the energy of a block of data, so the energy
`constraint specified at the output of the IFFT in the trans-
`mitter is the same as at the input of the IFFT, i.e., the
`total average energy per block at the input of the IFFT is
`limited to NE,. However, the total average energy of a
`v-sample cyclic prefix is not necessarily equal to VE,. We
`will thus briefly investigate the impact of the cyclic ex-
`tension samples to the average energy constraint.
`The real and imaginary parts of the noise variance after
`the FFT in the receiver are, in general, unequal for any
`
`

`
`CHOW er a/.: A DISCRETE MULTITONE TRANSCEIVER SYSTEM
`
`specific frequency band due to the correlated, non-i.i.d.
`crosstalk noise at the input to the FFT. This inequality of
`variance is more profound at smaller blocklength (larger
`than 4), and the difference between the real and imaginary
`noise variance gradually diminishes as longer blocklength
`is used. As blocklength approaches infinity, the difference
`becomes zero. To optimize bit error rate throughout the
`subchannels, we would then need to assign unequal signal
`energy on the real and imaginary part of each frequency
`band. A fairly tight bound for the average energy of a
`block of N + v samples (after cyclic extension) is derived
`in the Appendix.
`However, as the blocklength increases, the difference
`between the real and imaginary noise variance becomes
`insignificant, and we can simply assign equal energy on
`the real and imaginary parts of each corresponding fre-
`quency band without any noticeable performance degra-
`dation. In this case, as derived in the Appendix, each
`sample at the output of the IFFT has the same average
`energy
`Consequently, the v-sample cyclic prefix does
`not change the energy constraint.
`
`C. Computation Requirements
`In this section, we describe the computational require-
`ments to implement the DMT transceiver. The computa-
`tional complexity includes only the functions that are
`unique to DMT; those functions that are common to both
`DMT and conventional single-carrier transceivers are not
`included.
`The following are the assumptions in computing the to-
`tal complexity.
`Complexity is measured in terms Of inillions of in-
`structions per second (MIPS).
`The sampling rate is equal to 640 kkz. We choose
`this number because, as Section IV-A shows, further in-
`crease in sampling rate does not significantly increase the
`throughput but does increase the cost substantially.
`A real addition, a real multiplication, or a real mul-
`tiplication followed by a real addition (multiply-accu-
`mulate) is counted as one instruction; a complex multi-
`plication is counted as four instructions.
`The number of required instructions to compute an
`N-point real-input FFT (or, equivalently, N-point real
`output IFFT) is assumed to be N logz N, where N is less
`than or equal to 128. Otherwise, the number of instruc-
`tions is equal to 1.5N logz N (N is a power of 2).
`Computations required in synchronization, timing
`recovery, decision block, and codingldecoding are not in-
`since these components are ‘‘“On
`‘luded9
`to Other
`schemes s