Signal Processing - September 2017 - 158

W1

Q

+

X1[t ]

X1[t ]

~
Y1[t ]

Y1[t ]

H

f1 [t ]

+

X1[t ]

W2

H[t ]

Q

X2[t ]

X2[t ]

~
Y2[t ]

Y2[t ]

H

f2 [t ]

+

+

X2[t ]

F [t ]

YN [t ]
XN [t ]

~
YN [t ]

Fp [t ]

-

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H

fN [t ]

XN [t ]

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FIGURE 10. A two-stage LMS algorithm for adaptive crosstalk cancelation in the upstream G.fast.

In VDSL systems, which are based on the FDD scheme, the
channel coefficients are quantized at each user and transmitted
to the DP over the upstream channel. This increases the overhead and complicates the design, with a reduction of quality of
CSI for transmit precoding. G.fast's TDD duplexing scheme
makes it possible to exploit channel reciprocity to avoid the
complicated feedback protocol. This also enables the DP to
perform all CSI-related tasks. Using channel reciprocity, the
ud= H
u Tu , where H
uu
downstream channel can be estimated as H
is the estimated upstream channel. In practice, the transmit and
receive paths at the DP are not identical; hence, the estimated
downstream channel needs to be calibrated to compensate for
this mismatch. This calibration process is still in development
and has not yet received sufficient academic attention.

Adaptive crosstalk cancelation
The adaptation of a crosstalk canceler matrix to track the
channel dynamics is another important design consideration
for the G.fast system. In general, traditional adaptive algorithms designed for the VDSL system can be applied to the
G.fast system. However, these algorithms, and mainly the
LMS algorithm [61], become inefficient or converge very
slowly at higher frequencies because of the bad conditioning
of the input correlation matrix. At higher frequencies, the
received signal's covariance matrix is badly conditioned
because of the loss of diagonal dominance characteristics.
There is ongoing research on adaptive techniques for up stream transmissions.
An interesting new paper in [62] (the full version appeared
in [63]) presents a novel algorithm that can speed up the convergence of the LMS crosstalk canceler by preprocess158

ing the input-received signal with a judiciously designed
matrix-preprocessing matrix, as shown in Figure 10. The
proposed two-stage LMS algorithm first preprocesses
the input signal by multiplying it with a matrix Fp [t] and
then applies a standard LMS on the preprocessed signal that
updates another decoding matrix F [t]. The conventional
LMS is accelerated by updating the preprocessing matrix
(at carefully selected times) to also include the LMS
matrix Fp [t + 1] = Fp [t] F [t + 1] and LMS F [t] = I. The
paper shows that the updates of the preprocessing matrix
speed up the convergence of the LMS crosstalk canceler by
reducing the condition number of the correlation matrix at
the LMS input. Because the preprocessing matrix is not frequently updated, the complexity of the algorithm is approximately twice the complexity of the conventional LMS.
For the downstream, the TDD scheme in the G.fast facilitates a simpler approach to adaptive algorithms than the VDSL.
Using channel reciprocity, feedback from the users is no longer necessary. Instead, the adaptive algorithm can be carried
out solely in the upstream, and the resulting FEXT cancelation
matrix is guaranteed to also be a good precoding matrix for
the downlink.

Optimized crosstalk cancelation schemes
The performance of crosstalk cancelation techniques (as
described in the "Multichannel Crosstalk Cancelation
Techniques" section) depends mainly on the characteristics of
the DSL channel. Because the G.fast channel is not diagonally
dominant at higher frequencies, the crosstalk cancelation
schemes for the VDSL system are no longer optimal for most
of the G.fast channel bandwidth. We overview recent research

IEEE SIGNAL PROCESSING MAGAZINE

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September 2017

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Table of Contents for the Digital Edition of Signal Processing - September 2017
