Signal Processing - September 2017 - 149

Diagonal
Dominance Parameter β (dB)

A diagonal-dominant channel ensures a well-conditioned
crosstalk channel matrix. Hence, most DSL-specific research
has used this feature in some way. Moreover, performance
analysis of various algorithms has used the aforementioned
metrics to bound performance. The diagonal-dominance parameter is depicted in Figure 8 using measurement data and
simulation results for the CAT5 cable at lengths of 100 and
400 m for binders with ten wires. Depending on the scenario,
the channels are diagonal dominant ( b is lower than 0 dB) up
to a frequency of 40-100 MHz. Thus, diagonal dominance
holds at these distances for all VDSL frequencies, but it does
not hold for many G.fast frequencies.

25
20
15
10
5
0
−5
−10
−15
−20
−25

Multichannel crosstalk cancelation techniques

80 100 120 140 160 180 200
Frequency (MHz)

Measurement (100 m)
Simulation (100 m)
Simulation (400 m)

FIGURE 8. The diagonal-dominance measure b as a function of frequency
using measurement [27] and simulation data for a binder with ten
lines of equal loop lengths of 100 m and 400 m. The VDSL frequencies
show strong diagonal dominance, whereas the G.fast channel at higher
frequency tones is not diagonally dominant.

3,000
Data Rate (Mb/s)

The various crosstalk cancelation methods available in the literature can be categorized by the coordination among users in
the binder. If no coordination is possible, the binder behaves
like an interference channel. Each receiver decodes its signal
independently in the presence of the interference from other
users. The advantage of these methods is that they can be
applied independently on each modem (without any coordination). Unfortunately, these techniques yield a relatively low
data rate for each user in the presence of crosstalk. This is
shown in Figure 9. It can be seen that the data rate without
crosstalk cancelation is just 20% (at 50 m) of what can be
achieved with full crosstalk cancelation.
The effect of crosstalk can be reduced using coordinated processing on signals. In the downstream, the multiuser
DSL binder behaves like a broadcast channel (BC) where a
single transmitter at the DP generates signals to geographically dispersed subscribers. This enables joint processing only at the transmitter side. The coordination of the
received signals is possible in an upstream multiple-access
channel (MAC) where a single receiver at the DP receives
signals from different users (see Figure 3). Joint processing
at both the transmit and receive side of the link requires
colocation of both the DP and customer premises modems,
which is possible only in the case of a bonded DSL system,
where a single (typically business) customer uses several
twisted pairs to achieve very high rates. In most DSL configurations, each customer has a single twisted pair, and
the customers are situated in different locations. Thus,
the DSL system is considered a MU-MIMO, and all the
research on MU-MIMOs developed for wireless systems
is applicable as well (see, for example, [33]-[36] and the
references therein).
However, as the rates of DSL systems, and in particular
of G.fast systems, are very high and the number of users
can be up to 100 served simultaneously by the same system,
most published algorithms for wireless communication are
not feasible, and the DSL community has turned to research
low-complexity algorithms. With the advent of vectored
transmission, there has been a surge of research interest in
transceiver design for crosstalk cancelation in DSL systems.
Various near-optimal receivers [9], [10], [12] have been
designed to perform crosstalk cancelation with relatively

2,500
2,000
1,500
1,000
500
0
50 100 150 200 250 300 350 400 450 500
Line Length (m)
MFB
SWP
Linear MMSE Canceler
ZF−GDFE Canceler
Linear ZF Canceler
No Cancelation
Approximate ZF First-Order Canceler

FIGURE 9. The average achievable user rate over the whole bandwidth of
212 MHz versus binder length. The binder is composed of ten users with
equal line lengths.

low complexity. Next, we discuss various crosstalk cancelation schemes for upstream and downstream transmission
(see the summary in Table 1).

Crosstalk cancelation in the upstream
Starting with the upstream, we first discuss theoretical performance
bounds and then present various crosstalk cancelation schemes.

MAC capacity and performance bounds
The capacity of the MAC was derived by Cover decades ago
[37]. This capacity is characterized through the achievable rate

IEEE SIGNAL PROCESSING MAGAZINE

September 2017

149

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