7.3 DMT Physical Layer Standard

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Discrete multitone transmission (DMT) is the only worldwide standard for ADSL, and VDSL transmission using DMT is the most efficient of the high-performance transmission methods that allow a transmission system to perform near the fundamental limit known as capacity [6]. For difficult transmission lines, there is no other cost-effective high-performance alternative presently, and VDSL has the most difficult transmission environment of all DSLs. Variants of DMT for wireless transmission (known as OFDM) have also come into strong use in the areas of wireless local area networks (IEEE 802.11(a), [8]), wireless broadband access (IEEE 802.16 [20]), as well as digital terrestrial television (HDTV and digital TV) and radio broadcast [21] in most of the world. All are known to also be particularly difficult transmission problems. The standardized VDSL DMT method is a natural extension of the method used for ADSL and backward compatible with it, as described in Section 7.3.1. Section 7.3.2 describes the " zipper " duplexing method that is also called "digital duplexing ," which is an enhancement to the original DMT method that allows the upstream and downstream transmissions to be compactly placed in the limited transmission bandwidth of a telephone line. Section 7.3.4 investigates initialization.

7.3.1 Basic Multicarrier Concept

The basic multicarrier transmission concept of dividing a transmission band into a large number of subcarriers and adaptively allocating fractions of total energy and data rate to each to match an individual line characteristic is explained in [6]. It is this adaptive loading feature that sets multicarrier methods in a higher league of performance than other DSL transmission methods. VDSL presents a highly variable transmission environment with bandwidths that can vary from a few MHz to nearly 20 MHz, with intervening radio interference in several narrow bands, with huge spectrum notching effects from bridged taps, and with a variety of crosstalking situations. VDSL is undoubtedly the most difficult and highly variable transmission problem yet faced by DSL engineers . Multicarrier transmission is the most practical method to meet that challenge.

The first challenge for VDSL is interoperability with existing ADSL. One of the applications for VDSL is simply a speed extension of ADSL, meaning that it is possible for an existing ADSL customer to have that service provided by a new ONU in his neighborhood that is VDSL ready. A VDSL modem in the ONU that will interoperate with that existing ADSL modem is highly desirable so that no extra labor or purchases are necessary at the customer's premises should that customer elect to keep his current ADSL service for a period of time before electing to move to VDSL to increase the speeds of his ADSL service. Similarly, an existing ADSL customer may elect to purchase a VDSL modem (or may have one from a previous residence or business address) and then need to interoperate with an existing ADSL CO modem. Thus, a requirement for incremental DSL roll out to higher speeds and increasing use of fiber is that VDSL interoperate with existing ADSL, meaning the lower 256-down/32-up DMT tones of an ADSL modem, must also be implemented by an interoperating VDSL modem. For this reason, the DMT VDSL standard [17] uses the same tone spacing of 4.3125kHz that was used in ADSL. The VDSL standard allows for the DMT VDSL modem to use numbers of tones of 256, 512, 1024, 2048, and 4096 or,2 ^{n + 8} , n = 0,1,2,3,4 in either an asymmetrical or symmetrical allocation. Support of 2048 tones is considered a default for full compliance with other VDSL modems, but interoperation with smaller numbers of tones is illustrated in Figure 7.12.

Figure 7.12. Interoperability diagram for standardized DMT modems of increasing speeds.

From Figure 7.12, one can determine upon close inspection that the modem (ONU or customer premises) with the smallest number of DMT tones then dictates the maximum that can be used (in either an upstream or downstream direction). Such elimination of superfluous tones can occur naturally during training, or may be selectively programmed during special initialization exchanges, with the latter usually the preferred implementation.

We now proceed to characterize some details of the DMT VDSL standard.

Cyclic Extension : The cyclic extension [6] size for DMT VDSL is optionally programmable to sizes m x 2 ^{n + 1} , where m is an integer. The modem must be able to implement at least the default of 20 x 2 ^{n + 1} = 40 x 2 ⁿ for the case of n = 0 , which corresponds to interoperability with ADSL. ^[7] Longer cyclic prefixes on shorter channels might allow some additional performance-enhancing features to be added for DMT VDSL that are not implemented in ADSL, which are described more in Section 7.3.2.

^[7] Actually, in this case, the cyclic prefix is reduced by 8 samples if the synchronization symbol of ADSL is to be inserted every 69 symbols or 17 ms.

Encoder : The constellation encoder for DMT VDSL and tone-ordering procedures are identical to those of ADSL standards [6], although implemented perhaps over a larger set of tones for VDSL. There are two such ordering procedures inherited from ADSL.

Pilot : The pilot of ADSL has been made optional and generalized in VDSL. In early ADSL, the pilot was always sent downstream on tone number 64 (276 kHz). In VDSL, the VTU-R can decide to use a pilot on any (or no) tone in initialization. If a pilot is used, the 00 point in the standardized 4-point QAM constellation on that selected tone is sent in all symbols. The synchronization symbol of ADSL has been eliminated in VDSL, except when interoperating with an ADSL modem.

Timing Advance : The VTU-R is capable of changing the symbol boundary of the downstream DMT symbol it receives by a programmable amount, which is communicated during initialization to the VTU-O modem. This is also a new feature for VDSL that is used for implementation of digital duplexing as described in Section 7.3.2.

Power Back Off (PBO) : PBO has been studied by standards groups as a way to prevent upstream FEXT from a customer closer to an ONU from acting as a large noise for a VDSL customer further away. The basic problem is that the closer user could operate at a higher data rate or with better performance than is necessary or fair to other customers. Various methods for reducing the disparity among lines vary from introducing a flat PBO at all frequencies as a function of measured received signal (see [16]) to spectrally shaped methods. Two of the shaping methods are:

1. Reference noise method force all upstream transmissions to have an FEXT of common spectral shape (and thus harm)

2. Reference length method force all upstream transmissions to have an FEXT the same as that of a nominal "reference" length VDSL line.

These two methods, particularly (b), seem to have won favor with standards groups, but the area is still debated at the time of writing. A method making use of actual line measurements in [24] was introduced for future spectrum management and essentially eliminates the PBO issue, but it came after VDSL standards had entered final voting and could not then be standardized. Chapter 11 shows several far superior methods in dynamic spectrum management (DSM).

Express Swapping : The standardized bit swapping of ADSL is mandatory also in VDSL [6]. However, VDSL also offers a highly robust and high-speed optional capability of altering the bit distribution all at once (instead of one tone at a time as in the older bit swapping). This is known as express swapping . The additional commands are described in the VDSL standards documents [17] and in Chapter 3. Express swapping allows the new bit table to be sent in one command and protected by a CRC check. If correctly received, all tones are replaced with the new bit distribution at an immediately succeeding point specified in the commands and protocol. This allows a system to react very quickly to abrupt transients caused by excitation of crosstalkers or RF interferers, or perhaps an off-hook line change in splitterless operation. It also can enable advanced spectrum management features that may occur in the future (see Chapter 11).

7.3.2 Digital Duplexing

This subsection describes digital duplexing, which is a method for minimizing bandwidth loss in separating downstream and upstream DMT VDSL transmissions. Originally, this method was introduced by Isaksson, Sjoberg, Nilsson, Mesdagh, and others in a series of papers that refer to the method as "Zipper" in [22] and [2932]. General principles, as well as some simple examples, illustrate how digital duplexing works and why it saves precious bandwidth in VDSL. This description is intended for readers familiar with basic DMT, although a brief DMT review is included with emphasis on DMT features that are enhanced with digital duplexing. Thus, readers can use their DMT knowledge and the examples and explanations of this section to understand the relationship of the cyclic suffix to the cyclic prefix, and thus consequently to comprehend the benefits of symbol-rate loop timing and to appreciate the use of windows without intermodulation loss.

Excess bandwidth is a term used to quantify the additional dimensionality necessary to implement a practical transmission system. The excess-bandwidth concept is well understood in the theory of intersymbol interference where various transmit pulse shapes are indexed by their percentage excess bandwidth. In standardized and implemented DMT designs for ADSL, for instance, the symbol rate is 4000 Hz while the tone width is 4312.5 Hz, rendering the excess bandwidth (.3125/4) = 7.8%. In ADSL, additional bandwidth is lost in the transition band between upstream and downstream signals when these signals are frequency-division duplexed. In VDSL, this additional bandwidth loss is zeroed through an innovation [22] known here as digital duplexing, which particularly involves the use of a "cyclic suffix" in addition to the well-known "cyclic prefix" of standardized DMT ADSL. This subsection begins with a review of basic DMT and of its enhancement through the use of the cyclic suffix, including a numerical example that illustrates symbol-rate loop timing. This discussion illustrates why the time-domain overhead is all that is necessary to allow full use of the entire bandwidth without frequency guard bands in a very attractive and practical implementation.

This section proceeds to investigate crosstalk issues both when other VDSL lines are synchronized and not synchronized. Windowing and its use to mitigate crosstalk into other DSLs or G.pnt are also discussed, as are conversion-device requirements.

This section then continues specifically to use a second example that compares a proposed analog duplexing plan for VDSL with the use of digital duplexing in a second proposal. In particular, 4.5 MHz of excess bandwidth is necessary in the analog duplexing whereas only the equivalent of 1.3 MHz is necessary with the more advanced digital duplexing. The difference in bandwidth loss of 3 MHz accounts for at least a 612 Mbps total data rate advantage for digital duplexing in the example, which provides a realistic illustration of the merit of digital duplexing.

Basic DMT

Figure 7.13 illustrates a basic DMT system for the case of baseband transmission in DSL [2], showing a transmitter, a receiver, and a channel with impulse response characterized by a phase delay D and a response length n in sample periods. N/2 tones are modulated by QAM-like two-dimensional input symbols (with appropriate N -tone conjugate symmetry in frequency) so that an N -point Inverse Fast Fourier Transform (IFFT) produces a corresponding real baseband time-domain output signal of N real samples.

Figure 7.13. Basic DMT transmission system.

For basic DMT, the last L = n of these samples are repeated at the beginning of the symbol (packet of samples) of transmitted samples so that N + L samples are transmitted, leading to a time-domain loss of transmission time that is ^L / _N . This ratio is the excess bandwidth. The minimum size for L = n is the channel impulse response duration (in sampling periods) for basic DMT (later for digitally duplexed DMT, L will be the total length for all prefix/suffix extensions and thus greater than n ). Sometimes DMT systems use receiver equalizers [6] to reduce the channel impulse response length and thus decrease n . Such equalizers are common in ADSL. The objective is to have small excess bandwidth by decreasing the ratio ⁿ / _N . In both DMT ADSL and VDSL, the excess bandwidth is 7.8 percent.

The IFFT of the DMT transmitter implements the equation

where x _k , k = 0,, N 1 are the N successive time-domain transmitter outputs (the prefix is a trivial repeat of last n ). The values X _n are the two-dimensional modulated inputs that are derived from standard QAM constellations (with the number of bits carried on each "tone" adaptively determined by loading as in [6] and stored in the b _n , g _n tables at both ends). To produce a real time-domain output, in the ubiquitous case that N is an even number. In ADSL, N = 512, while in VDSL, N = 512 2 ^{n + 1} , n = 0,1,2,3,4. One symbol of N + n samples is transmitted every T seconds for a sampling rate of N + ^L / _T With ¹ / _T = 4000 Hz in ADSL and VDSL, the sampling rates are 2.208 MHz and up to 35.328 MHz, respectively, leading to a cyclic prefix length of n = L = 40 samples in ADSL and a cyclic-extension length of up to L = 640 samples in VDSL. The extension length in VDSL also includes the cyclic suffix to be later addressed.

When the cyclic extension length is equal to or greater than the impulse-response length of the channel ( L

where the reindexing of time is tacit and really means samples corresponding to times k = L + 1 ,, L + N in the receiver. The receiver must know the symbol alignment and cannot execute the FFT at any arbitrary phase of the symbol clock. If the receiver were to be somehow offset in timing phase, then time-domain samples from another adjacent symbol would enter the FFT input, displacing some corresponding time-domain samples from the current symbol. For instance, suppose the FFT executed m sample times too late, then the output would be

where u _k are samples from the next symbol that are unwanted and act as a disturbance to this symbol. Furthermore, m samples from the current symbol were lost (and the rest offset in phase). Thus,

where E _n is a distortion term that includes the combined effects of u _k , the missing terms , y _k, and the timing offset in the symbol boundary. E _n = 0 only (in general) when the correct symbol alignment is used by the receiver FFT. DMT systems easily ensure proper phase alignment through the insertion of various training and synchronization patterns that allow extraction of correct symbol boundary.

It is important to note that the FFT of any other signal with the same N might also have such distortion unless the symbol boundaries of that signal and the DMT signal were coincident. In the later case of time coincidence , the FFT output is simply the sum of the two signals' independent FFTs. Indeed the receiver would have no way of distinguishing the two signals and would simply see them as the sum in the time-coincident case.

The second signal could be the oppositely directed signal leaking through the imperfect hybrid in VDSL. If the transmitted and received symbols are aligned in time and frequency-division duplexing is used, tones are zeroed in one direction if used in the other. Then, the sum at the FFT output is simply either the upstream or the downstream signal, depending on the duplexing choice for the set of indices n. No zeroed tones are necessary between upstream and downstream frequency bands as that is simply a waste of good undistorted DMT bandwidth. No analog filtering is necessarythe IFFT, cyclic-prefix, and the FFT do all the work if the system is fortunate enough to have the time coincidence of the two DMT signals traveling in opposite directions. The establishment of time coincidence of the symbols at both ends of the loop is the job of the cyclic suffix, which the next subsection addresses. In other words, the FFT works on any DMT signal of symbol size N samples, regardless of source or direction as long as the symbol is correctly positioned in time with respect to the FFT. This separation is not easily possible unless the DMT signals are alignedthus VDSL DMT systems ensure this alignment through a cyclic suffix to be subsequently described.

Table 7.7 provides a comparison and summary of DMT use in ADSL and in VDSL. Note that DMT VDSL uses digital frequency-division multiplexing (FDM) and spans at most sixteen times the bandwidth of ADSL at its highest bandwidth use. This full bandwidth form is actually optional and the default values are shown in parenthesis on the right, with the default actually being exactly one-half the full.

Cyclic Suffix

The cyclic suffix is appended to the end of a DMT symbol (the opposite side of the cyclic prefix) and could repeat for instance the first 2 D samples of the DMT symbol (not counting the prefix samples) at the end as in Figure 7.14, where D is the phase delay in the channel (phase delay or absolute delay, not group delay, which is related to n ). A symbol is then of length N + L . The value for L must be sufficiently large that it is possible to align the DMT symbols, transmit and receive, at both ends of the transmission line. Clearly, alignment at one end of a loop-timed line ^[8] is relatively easy in that the line terminal (LT) need only wait until an upstream DMT symbol has been received before transmitting its downstream DMT symbols in alignment on subsequent boundaries. Such single-end alignment is often used by some designers to simplify various portions of an ADSL implementation. The alignment is not necessary unless digital duplexing is used. However, alignment at one end almost surely forces misalignment of the symbol boundary at the VTU-R as in Figure 7.14.

^[8] Loop-timing of the sample clock means that the NT (VTU-R) uses the derived sample clock from the downstream signal as a source for the upstream sample clock in DMT.

Figure 7.14. DMT symbol alignment without cyclic suffix.

Table 7.7. Comparison of DMT for ADSL and VDSL.

	ADSL	VDSL (default)
FFT Size	512	8192 (4096)
# of tones	256	4096 (2048)
Cyclic ext length	L = v = 40	L = 640 v + D
Sampling rate	2.208 MHz	35.328 (17.664) MHz
Bandwidth	1.104 MHz	17.664 (8.832) MHz
Duplexing	Analog FDM	Digital FDM
Tone width	4.3125 kHz	4.3125 kHz
Excess bandwidth	86 kHz (prefix) +40 kHz (filters)	1.3 MHz (650 kHz) (no filters)
The 40kHz EB in ADSL is only if it's a true FDD systemecho cancellation doesn't have this penalty, even if the spectra are overlapped .

In Figure 7.14, let us suppose that N = 10, n = 2, and that the channel phase delay or overall delay is D = 3. The reader can imagine a master time clock and that the LT begins transmitting a prefixed DMT symbol at time sample 0 of that master clock. The first two samples at times 0 and 1 are the cyclic prefix samples and are followed by 10 samples of the DMT symbol at times 2 through 11. See the vertical line at the left in Figure 7.14 that denotes the time axis (increasing time going down). In the second line from the left in Figure 7.14, the downstream (ds) symbol and prefix are shown on the scale of the timeline. At the receiver, all samples undergo an absolute delay of 3 samples (in addition to the dispersion of n = 2 samples about that average delay of 3). Thus, the cyclic prefix's first sample appears in the VTU-R at time 3 of the master clock, and the DMT symbol then exists from time 3 to time 14 as in the third vertical line from the left in Figure 7.14. The samples used by the receiver for the FFT are samples 5 through 14, whereas samples 3 and 4 are discarded because they also contain remnants from a previous DMT symbol. The LT has DMT symbol alignment in Figure 7.14, so that it also received the upstream prefix first sample at time 0 and continued to receive the corresponding samples of the upstream DMT symbol until time 11. Thus, the DMT symbols are aligned at the LT. However, in order for the upstream DMT symbol to arrive at this time, it had to begin at time 3 in the VTU-R (fourth vertical line from the left in Figure 7.14). Thus, the upstream symbol transmitted by the VTU-R occurs in the VTU-R at times 3 through 8 of the reader's master clock. Clearly the DMT symbols are not aligned at the VTU-R even though they are aligned at the VTU-O.

In Figure 7.15, a cyclic suffix of 6 samples is now appended to DMT symbols in both directions, making the total symbol length now 18 samples in duration (thus slowing the symbol rate or using excess bandwidth indirectly). The LT remains aligned in both directions and transmits the downstream DMT symbol from master-clock times 017. These samples arrive at the NT at times 320 of the master clock, with valid times for the receiver FFT now being 514, 615, , 1120. Each of these windows of 10 successive receiver points carry the same information from the transmitter and differ at the FFT output by a trivial phase rotation on each tone that can easily be removed. The upstream symbol now transmits corresponding valid DMT symbols from time 1 to time 8, also 09, 110, and the last valid upstream symbol is time 514. At the VTU-R, the first downstream valid symbol boundary from samples 514 and the last upstream valid symbol boundary, also at samples 514, are coincident in time. Thus, the receiver's FFT can correctly find both LT and VTU-R transmit signals by executing at sample times 514 without distortion of or interference between tones. At this time only (for cyclic suffix length 6), the receiver FFT and IFFT can be executed in perfect alignment, and thus, downstream and upstream signals are perfectly separated. This DMT system in Figure 7.15 has symbol-rate loop timing, and, thus, a single FFT can be used at each end to extract both upstream and downstream signals without distortion. (There is still an IFFT also present for the opposite-direction transmitter.) This loop is now digitally duplexed.

Figure 7.15. DMT symbol alignment at both LT and NT through use of suffix.

Note the cyclic suffix has length double the channel delay (or equivalently was equal to the round-trip delay) in the example. More generally, one can see that from Figure 7.15 that VTU-R symbol alignment will occur when the equivalent of time 5, which is generally , n + D , is equal to the time Equivalently, L _suf = 2 D . In fact, any

is sufficient with those cyclic suffix lengths that exceed 2 D just allowing more valid choices for the FFT boundary in the VTU-R. For instance, if the designer had chosen a cyclic suffix length of 7 in our example, then valid receiver FFT intervals would have been both 514 and 615. This condition can be halved using the timing advance method in the next subsection.

Timing Advance at LT

Figure 7.16 shows a method to reduce the required cyclic suffix length by one-half to L _suf D samples. The two symbols now align at both ends at time samples 211, and the cyclic suffix length is reduced to 3 in the specific example of Figure 7.16. Thus, for VDSL with timing advance, the total length of channel impulse-response length must be less than 18 m s (the same requirement as if there were no digital duplexing), which easily is achieved with significant extra samples for the suffix in practice. In VDSL, the proposal for L is 640 when N = 8192. The delays of even severe VDSL channels are almost always such that the phase delay D plus the channel impulse-response length n are much less than the 18 m s cyclic extension length (if not, a time equalizer can be used, see [6]). One notes that the use of the timing advance causes the transmitters and receivers at both ends to all be operational at the same phase in the absolute time measured by the master clock.

Figure 7.16. Illustration of cyclic suffix and LT timing advance.

Digital duplexing thus achieves complete isolation of downstream and upstream transmission with no frequency guard bandthere is, however, the 7.8 percent cyclic extension penalty (which is equivalent to 1.3 MHz loss in bandwidth in full VDSL and 650 kHz loss in the default or "lite" VDSL). Thus, it is not correct, nor appropriate, to place frequency guard bands in studies of DMT performance in VDSL. Some papers on this subject have reached misleading conclusions due to the unnecessary inclusion of guard bands for DMT digital duplexing.

Digital duplexing in concept allows arbitrary assignment of upstream and downstream DMT tones, which with FDM VDSL means these two sets of upstream and downstream tones are mutually exclusive. On the same line, there is no interference or analog filtering necessary to separate the signals, again because the cyclic suffix (for which the equivalent of 1.3 MHz of bandwidth has been paid or 650 kHz in default VDSL) allows full separation even between adjacent tones in opposite directions via the receiver's FFT. However, while theoretically optimum, one need not "zipper" the spectrum in extremely narrow bands, and instead upstream and downstream bands consisting of many tones may be assigned as described earlier. Some alternation between up and down frequencies is universally agreed as necessary for reasons of spectrum management and robustness, although groups differ on the number of such alternations , which will depend on assumed loop topologies.

Crosstalk

Analysis of NEXT between neighboring VDSL circuits needs to consider two possibilities: synchronization of VDSL lines and asynchronous VDSL lines. The first case of synchronous crosstalk is trivial to analyze and implement with FDM. Adjacent lines have exactly the same sampling clock frequency (but not necessarily the same symbol boundaries). There is no NEXT from other synchronized VDSLs with FDM as will be clear shortly. The second case of asynchronous self-VDSL NEXT is more interesting. In this case, the sidelobes of the modulation pulse shapes for each tone are of interest.

A single DMT tone consists of the sinusoidal component

where or 4.3125 kHz in ADSL and VDSL, and w _T ( t ) is a windowing function that is a rectangular window in ADSL but is more sophisticated and exploits digital-duplexing's extra cyclic suffix and cyclic prefix in VDSL. Figure 7.17 shows the relative spectrum of a single tone with respect to an adjacent tone for the rectangular window.

Figure 7.17. Magnitude of windowed sinusoid versus frequency. Note notches at DMT frequencies.

Note the notches in the crosstalker's spectrum at the DMT frequencies: all are integer multiples of f . Thus, the contribution of other VDSL NEXT will clearly be zero if all systems use the same clock for sampling, regardless of DMT symbol phase with respect to that clock. This is an inherent advantage of DMT systems with respect to themselves because it is entirely feasible that VDSL modems in the same ONU binder group could share the same clock and thus have no NEXT into one another at all. Indeed, this is a recommended option in [17]. When this occurs, performance enhancement occurs automatically.

When the sampling clocks are different, however, the more that sampling clocks of VDSL systems differ, the greater the deviation in frequency in Figure 7.17 from the nulls, allowing for a possibility of some NEXT. Studies of such NEXT for DMT digital duplexing are highly subjective and depend on assumptions of clock accuracy, number of crosstalkers with worst-case clock deviation, and the individual contribution to the NEXT transfer function of each of these corresponding worst-case crosstalkers. Nonetheless, reasonable implementation renders NEXT of little consequence between DMT systems.

If the VDSL PSD transmission level is S = -60 dBm/Hz, and the crosstalk coupling is approximated by ( m /49) ⁶ 10 ^-13 f ^1.5 for m crosstalkers the crosstalk PSD level is

The peak or sidelobes can be only 12 dB down with such rectangular windowing of the DMT signal, as in Figure 7.17. Asynchronous crosstalk may be such that especially with misaligned symbol boundaries, a really worst-case crosstalker could have its peak sidelobe aligned with the null of another tone (this is actually rare, but clearly represents a worst case). To confine this worst case, the following methods are used.

Windowing of Extra Suffix and Prefix

This section explains how windowing can be implemented without the consequence of intermodulation distortion when digital duplexing is used. Windowing in digitally duplexed DMT exploits the extra samples in the cyclic suffix and cyclic prefix beyond the minimum necessary. Because the cyclic extension is always fixed at L = 640 samples in VDSL, there are always many extra samples. Figure 7.18 shows the basic idea: the extra suffix samples are windowed as shown with the extra extension samples now being split between a suffix for the current block and a prefix for the next block. The two are smoothly connected by windowing, a simple operation of time-domain multiplication of each real sample by a real amplitude that is the window height. The smooth interconnection of the blocks allows for more rapid decay in the frequency domain of the PSD, which is good for crosstalk and other emissions purposes. A rectangular window will have the per tone (baseband) roll off function given by

Figure 7.18. Illustration of windowing in extra suffix/prefix samplessmooth connection of blocks without affecting necessary properties for digital duplexing.

or the so-called "sinc" function in frequency. Clearly, a smoother window could produce a more rapid decay with frequency. A logical and good choice is the so-called raised-cosine window. Let us suppose that the extra cyclic suffix contains 2 L ' +1 samples in duration, an odd number. ^[9] Then the raised cosine function has the following time-domain window (letting the sampling period be T ') with time zero being the first point in the extra cyclic suffix and the last sample being time 2L ' T ' and the center point thus L ' T ':

^[9] If even, just pretend it is one less and allow for two samples to be valid duplexing end points.

One notes the window achieves values 1 at the boundaries and is zero on the middle sample and follows a sampled sinusoidal curve in between. The points before time L ' T ' are part of the prefix of the current symbol, whereas the points after L ' T ' are part of the suffix of the last symbol.

The overall window (which is fixed at 1 in between) has Fourier transform (let , ignoring an insignificant phase term)

Larger a means faster roll-off with frequency. This function is improved with respect to the sinc function, especially a few tones away from an up/down boundary. Reasonable values of a corresponding to 100200 samples will lead to even the peaks of the NEXT sidelobes below 140 dBm/Hz at about 200 kHz spacing below 5 MHz. The reduction becomes particularly pronounced just a few tones away, and so at maximum, a very small loss may occur with asynchronous crosstalk. Thus, signals other than 4.3125kHz DMT see more crosstalk, but within 200 kHz of a frequency edge, such NEXT is negligible. This observation is most important for studies of interference into home LAN signals like G.pnt, which at present almost certainly will not use 4.3125 kHz spaced DMT.

Overlapped Transmitter Windows

Figure 7.19 shows overlapped windows in the suffix region. The smoothing function is still evident and some symmetrical windows (i.e., square-root cosine) have constant average power over the window and the effective length of the window above L ' can be doubled , leading to better sidelobe reduction. This overlapping requires an additional 2 L '+1 additions per symbol, a negligible increase in complexity.

Figure 7.19. Illustration of overlapped windowing.

Receiver Windowing

Receiver windowing can also be used to again filter the extra suffix and extra prefix region in the receiver, resulting in further reduction in sidelobes. Figure 7.20 shows the effect on VDSL NEXT for both the cases of a transmitter window and both a transmitter and receiver window. Note the combined windows has very low transmit spectrum (well below FEXT in a few tones) and below 140 dBm/Hz AWGN floor by forty tones. If it is desirable to further reduce VDSL NEXT to zero, an additional small complexity can be introduced as in the next subsection with the adaptive NEXT canceler.

Figure 7.20. PS = transmitter windowing (pulse shaping), and window here means receiver window. This simulation is for a 1000 m loop of .5 mm transmission line (24 gauge).

Adaptive NEXT Canceler for Digital Duplexing

Figure 7.21 illustrates an adaptive NEXT canceler and its operation near the boundary of up and down frequencies in a digitally duplexed system. Figure 7.21 is the downstream receiver, but a dual configuration exists for the upstream receiver. Note any small residual upstream VDSL NEXT left after windowing in the downstream tone n (or in tones less than n in frequency index) must be a function of the upstream signal extracted at frequencies n + 1, n + 2, at the FFT output. This function is a function of the frequency offsets between all the NEXTs and the VDSL signal. This timing-clock offset is usually fixed but can drift with time slowly. An adaptive filter can eliminate the NEXT as per standard noise cancellation methods [6]. A very small number of tones are required for the canceler per up/down edge if transmit windowing and receiver windowing are used. Adaptive noise cancellation can be used to make VDSL self-NEXT negligible with respect to the 140 dBm/Hz noise level. This allows full benefit of any FEXT reduction methods that may also be also in effect (note the NEXT is already below the FEXT even without the NEXT canceler, but reducing it below the noise floor anticipates a VDSL system's potential ability to eliminate or dramatically reduce FEXT). See, for instance, Chapter 11. Note this noise canceller is an early version of the per-tone equalizer concept in [37].

Figure 7.21. Adaptive noise canceler for elimination of VDSL self-NEXT in asynchronous VDSL operation. Shown for one upstream/downstream boundary tone (can be replicated for each up/down transition tone that has NEXT distortion with asynchronous VDSL NEXT). No canceler necessary if NEXT is synchronous.

7.3.3 DMT VDSL Framing

The DMT transmission format supports use of Reed-Solomon forward error correction (see [6]) and convolutional/ triangular interleaving. The RS code is the same as that used for ADSL with up to 16 bytes of overhead allowed per code word. There is no fixed relationship between symbol boundaries and code word boundaries, unlike ADSL.

Instead, any payload data rate that is an integer multiple of 64 kbps ( implying an even integer multiple of payload bytes on average per symbol) with dummy byte insertion where necessary and as described in [17] is allowed. Triangular interleaving that allows interleaving at a block length that is any integer sub-multiple of a code word length (in bytes) is allowed (ADSL forced the block size of the interleaver to be equal to the code word length). Given the high speeds of VDSL, the loss caused by dummy insertion is small, compared with the implementation advantage of decoupling symbol length from code word length. Triangular interleaving was described in [6] and again in [17], so it is not described here.

Latency can take on any value between 1 ms (fast buffer requirement) and 10 ms (slow buffer default) or more. The latency is determined according to code word, data rate, and interleave -depth parameter choices as in [17]. Fast and slow data are combined according to a frame format that no longer includes the synchronization symbol of ADSL and has updates of the fast and slow control bytes with respect to ADSL. Superframes are no longer restricted to just sixty-nine symbols as in ADSL.

Framing can be implemented as in Chapter 9 of [17] and need not be repeated here.

7.3.4 Initialization

An earlier text describes in detail the various aspects of training of a DMT modem [6]. The VDSL training procedure is described in [17] and compatible with the popular g.hs (g. 994) of ITU. The fundamental steps of training are the same as in [6] with the LT now being expected to set a timing advance and measure round-trip delay of signals so that the digital-duplexing becomes automatic. The length of cyclic prefix versus suffix and other detailed framing parameters are set through various initialization exchanges.

One feature of digital duplexing is that it does allow very simple echo cancellation if there is band overlap. With synchronized symbols, there is only one tap per tone to do full echo cancellation where that may be appropriate. However, the NEXT generated by overlapping bands at high frequencies might discourage one from trying unless NEXT cancellation (coordinated transmitters and receivers) can also be used, which would only be one tap per tone per significant crosstalker.

The reader is otherwise referred to [17] for more details.

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