11.4 Vectoring

   


11.4 Vectoring

Coordination within a common DSLAM or modem unit allows co-generation (or co- reception ) of multiple (preferably all) lines at the DSLAM. Such situations occur naturally as DSL evolves to remote/line terminals fed by fiber. In such DSLAMs at remote terminals, it is possible and feasible to coordinate signals because all or most of the lines are terminated on common equipment. In downstream transmission, joint generation of a vector of transmit signals over a common packet period is feasible (and possibly more cost-efficient than individual generation). This is the downstream broadcast vectored system of Figure 11.32. Vectored multiple access for upstream signals occurs at the receiver as in Figure 11.33.

Figure 11.32. Vector broadcast system for downstream DSL with cogeneration of transmit signals (but separate simple receivers).

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Figure 11.33. Vector multiple-access system for upstream DSL with coordinated reception but separated transmitters.

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For DSL, both vectored situations meet the condition for Ginis's QR zero-forcing GDFE when the upstream and downstream signals travel in different frequency bands when only FEXT is of concern. This condition is simply that the off-diagonal entries of H are much smaller than the diagonal entries. Section 11.4.1 discusses the multiple-access upstream problem briefly , whereas Section 11.4.2 discusses the broadcast downstream problem. When either end of the link can be coordinated at that same end, then NEXT can be canceled with a simple multidimensional echo canceler. Section 11.4.3 illustrates and discusses such Ethernet-in-the-first-mile (EFM) “like results, as well as DSL results.

11.4.1 Upstream Multiple Access

The vector upstream multiple-access DSL system of Figure 11.33 has typically M = 1 transmit lines per user but typically K = L has coordinated line receivers for reception. It is possible with some DSL systems (such as EFM) to have M = 2,4coordinated upstream transmitters also. It is also possible that only some of the lines in the DSLAM can be coordinated, or there are groups of lines that can be coordinated within each group , but not between groups. However, this subsection focuses on the case where K = L and M = 1 for purposes of illustration. Extensions then follow naturally by combining the concepts in Section 11.3 with those in this section where coordination is used among the various groups.

In this vectored upstream multiple-access DSL system, iterative water-filling generates the optimum vectored spectrum choice for all the upstream users, as first noted by Yu and Rhee [24]. [4] The vectored DSLAM thus determines the spectra for each of the individual separated users and communicates these spectra to individual upstream transmitters through some kind of control or back channel. The receiver is a GDFE with L sampled inputs from the lines. When DMT is used and all lines are synchronized (which is easy with the common DSLAM and less costly as well), the GDFE becomes a simple 2 x 2 or at most 4 x 4 GDFE on each tone where only the significant crosstalkers at that frequency are processed . Indeed with this small number of users, ML detection is easy, and the feedback section need not be implemented (and thus error propagation is avoided). Indeed, soft cancellation can be used to simplify the ML if desired. Furthermore, Ginis's QR simplification can be applied to derive the feedforward and channel(ML)/feedback coefficients directly from the channel matrix with essentially no loss in performance with respect to optimal. Ordering of the tones is not illustrated here, as it is often considered to be a proprietary secret of the manufacture ”here we just presume such an order exists. Only complexity of implementation depends on ordering.

[4] Cheng and Verdu [3] studied a non-vectored situation where all of the upstream users effectively were added together, in which case iterative water-filling reduces to their solution. However, Cheng and Verdu's solution does not apply to the vectored case (and their result of FDM being optimal no longer holds).

Figure 11.34 illustrates the exact receiver for the upstream case for each tone of a DMT system. The quantities G i,n are the gains for the tone of the user as determined by iterative water-filling. The structure for non-DMT systems is the same except that the various matrices become much larger. Rate regions for the different users can be derived from the iterative water-filling procedure by lowering the power for individual users and recomputing the rates of the other users, thus sketching an approximation to the rate regions . Individual rate requests of customers can then be evaluated for feasibility as a function of the rate region. Section 11.4.3 has some sample rate region plots.

Figure 11.34. Exact illustration for one tone (n) of GDFE upstream vector receiver.

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11.4.2 Downstream Broadcast

The vector broadcast DSL system of Figure 11.35 has typically M = L coordinated transmitters per user but typically has K = 1 receiver for each line. It is possible with some DSL systems (such as EFM) to have K = 2,4 coordinated receivers also. It is also possible that only some of the lines in the DSLAM can be coordinated, or there are groups of lines that can be coordinated within each group, but not between groups. However, this subsection focuses on the case where K = 1 and M = L .

Figure 11.35. Exact illustration for one tone (n) of GDFE downstream vector receiver.

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The optimum spectra for each broadcast user has been determined by Yu and Cioffi [25] and requires a two-step iteration consisting of

  1. Determining a worst-case noise autocorrelation matrix that has the same diagonal noises as the original downstream lines in terms of minimum mutual information (this involves solution of a generalized Lyapunov equation as noted in [25])

  2. Determining a GDFE for that noise autocorrelation that when implemented as a precoder maximizes rate sum and simultaneously diagonalizes the GDFE feedforward matrix ”this is a water-filling step

This solution will be essentially equal to that provided by Ginis Precoder, which is easier to compute when iterative water-filling is instead used to decide the spectra of each of the downstream signals. Thus the optimum algorithm, while slightly better, may require at least conceptually considerably more complexity for design for little gain with respect to the easily understood iterative water-filling.

Figure 11.35 illustrates each tone of the Ginis Precoded implementation of the downstream broadcast vectored DSL system. The receiver gains correspond to the diagonal inverses that occur in the QR factorization of the matrix H. Receiver implementation is particularly simple for each tone in this case. The precoding is such that simple slicing (in the absence of trellis or turbo codes) is sufficient in each receiver. Rate regions can be computed in the same way previously described of executing several instances of iterative water-filling with individual users' powers reduced.

11.4.3 Examples

It is interesting to compute the performance of vectored systems in a few cases. Figure 11.36 illustrates the type of improvement possible in ADSL if each ADSL line in the binder used Level 2 coordination or vectoring with the existing ADSL frequency assignments. The lowest data rate versus range curve in the figure illustrates a theoretical upper bound on the performance of the best ADSL receivers today without vectoring nor coordination. The middle curve represents vectoring, whereas the upper two curves recognize that continued improvement after vectoring could occur by increasing the bit cap and using better (turbo or LDPC) codes. Note the level of improvement is quite large, basically a factor of 3 or more at all data rates.

Figure 11.37 repeats the vectoring exercise for VDSL and compares against theoretically best transmission when the current noncoordinated VDSL is used with both American (997) and European (998) band allocations . Again the data rate is symmetric and considerably higher than with no coordination.

Figure 11.37. Vectored VDSL data rates versus range.

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Figures 11.38 and 11.39 show the results of full vectoring (with NEXT cancellation) for potential short and longer line use of DMT VDSL with EFM. Also shown are results when vectoring is only used within groups of 4 lines.

Figure 11.38. Short line EFM/VDSL results with vectored DMT ”symmetric transmission over full band.

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Figure 11.39. Longer line EFM/VDSL results with vectored DMT ”symmetric transmission over full band.

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DSL Advances
DSL Advances
ISBN: 0130938106
EAN: 2147483647
Year: 2002
Pages: 154

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