Signal Processing - September 2017 - 147

X1
DMT
Encoder
(User 1)
XK

K Subcarriers

2K Samples
IFFT
User 1

Vectored Users
(Tone 1)
X1
Vectored Users
(Tone K )
XK

Y1
ADC

DAC

Precoder X~
1
(Tone 1) ~
XN
F1
Precoder X~
1
(Tone K ) ~
X
N
FK

X1
DMT
Encoder
(User N )
XK

Channel

FFT
(User 1)
YK

PerTone
FEQ

CPE 1
CPE N

IFFT
User N

Y1
DAC

ADC

FFT
(User 1)
YK

Vectored Transmit Processing at DP

PerTone
FEQ

Single-User Processing at Each CPE

FIGURE 6. A schematic diagram of vectored transmit processing in the downstream. At the DP, transmit signals for each user at each tone are collected as
a single vector, and a precoder is applied before transmission. There is no signal coordination among CPEs for joint receiver processing.

identical, the performance at the different frequency bins can
be significantly different.
The resulting vector channel model in the upstream is
y = Hx + w ,

(2)

where x is the vector of all transmitted symbols, H is the
N # N matrix of all (complex) channel gains at the considered frequency tone, and w represents the additional
noise and interference vector. Note that the diagonal elements of H correspond to the direct paths between the
CPEs and the DP, whereas the off-diagonal elements represent FEXT.
In the downstream, joint processing is performed before
the transmission. Thus, the channel structure remains the
same as in (2), but now x is the vector of symbols for
transmission over all the lines (after joint processing), and
y is the vector of all the samples received by the different
CPEs. Note that in TDD, the channel reciprocity dictates
that the channel matrix in the downstream is the matrix
transpose of the channel matrix in the upstream. But in
most cases, there are differences in amplitude and phase
between the transmission and reception circuits and filters at each end.
FEXT is currently the main limiting factor in DSL systems and plays an even more crucial role in the upcoming
G.fast technology. The various methods to cope with FEXT
are further described after the following discussion of channel models.

DSL channel models
Signal processing methods for a communication system
require an accurate characterization of the underlying transmission medium. For DSL technology, modeling twisted-pair

channels at higher frequencies has been an active field of
research for more than two decades as DSL standards have
evolved [3], [5], [6]. The resulting models are based on extensive measurement campaigns carried out by different laboratories and telecommunication companies to derive parametric
cable models [17]-[26].

Models for direct and crosstalk channels
The loss in signal strength transmitted over a cable depends on
the physics of the cable, which is implicitly captured in the
propagation constant c ^ f h and the loop length l. The cable
insertion loss is modeled as H ^ f, l h = e -lc^ f h, and most of the
measurement effort has been directed toward better characterization of c ^ f h .
Various empirical models are available for different
cable types over VDSL frequencies [19]-[22]. However, the
extrapolation of these models for G.fast frequencies deviates
from the actual measurements. Moreover, the G.fast system
incorporates different topologies for deployment using other
cable types, such as CAT5 and CAD55. In this context, the
treatment of the direct path (diagonal channel matrix elements) and the crosstalk paths (off-diagonal elements) is
quite different.
Parametric models for the direct channel have been developed for a few cable types and made available in the latest
International Telecommunications Union-Telecommunication
Standardization Sector (ITU-T) recommendation [3]. The
ITU-T model has been validated up to hundreds of megahertz
using the results of extensive cable measurement campaigns
on different cable types [27]. There is an ongoing effort to
improve the existing models and to derive models for other
cable types (e.g., the authors of [26] proposed a model for
the characteristic impedance and propagation constant of the
cables using fewer parameters).

IEEE SIGNAL PROCESSING MAGAZINE

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September 2017

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147
Table of Contents for the Digital Edition of Signal Processing - September 2017
