Signal Processing - September 2017 - 160

its own data rate. This results in suboptimal performance but
gives a low-complexity solution that can be readily implemented. Current research aims to find better algorithms to fill the
gap between the infeasible optimal solution and the simplified
ZF-IWF solution.

Design consideration for crosstalk cancelation schemes
The most important design issue in G.fast is the crosstalk cancelation scheme. As discussed in the "Multichannel Crosstalk
Cancelation Techniques" section, there is a performance/complexity tradeoff, where linear cancelers are simpler but lose in
terms of performance. We now discuss the choice of crosstalk
cancelers as regards their performance over standard channels. Performance is evaluated using measured channel [27]
as well as stochastic MIMO channel models with CAT5 cables
[3]. The measured channel contains data from a 0.5-mm cable

Data Rate (Mb/s)

1,400
1,200
1,000
800
600
400
200
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 11. The average achievable user rate over the whole bandwidth of

Data Rate Per User (Mb/s)

Spectral Efficiency (bits/s/Hz)

106 MHz versus binder length. The binder is composed of ten users, with
equal line lengths.

20
15
10
5
0

with ten pairs, each measuring 100 m. For the rate-reach plot,
we consider a simulated channel with two scenarios: the first
consists of ten lines, each of equal length, that range from 50
to 500 m; the second considers 15 lines with different line
lengths uniformly spaced from 50 to 400 m at intervals of
25 m. The lowest frequency was 2.2 MHz for both the
106-MHz and 212-MHz G.fast systems, which is defined in
the standard [3] for backwards compatibility with legacy
ADSL systems. The noise PSD was -140 dBm/Hz, and the
transmit PSD specification at each tone was taken from [78].
A bit cap of 12 bits per tone (i.e., 4,096 points for the QAM
densest constellation) was maintained, and an effective SNR
to Shannon gap of 10.75 dB was used.
The ITU-T standard [3] recommends linear crosstalk
cancelers for the G.fast 106-MHz system because the loss of
the linear scheme is marginal up to 106 MHz (see Figure 11).
The rate-reach in Figure 11 shows that the linear crosstalk
schemes are near optimal for 106 MHz. Note that at very high
frequency tones (above 90 MHz), the diagonal dominance is
not very strong, which degrades the performance of linear
schemes, as shown in Figure 12. However, at such high frequencies, the spectral efficiency is significantly lower because
of the signal attenuation, and therefore the overall loss in
data rate (computed over all tones) is marginal. The performance of the linear approximate inversion is significantly
degraded and is not recommended for G.fast. It can be seen
that the linear MMSE canceler performs marginally better
than the ZF at higher frequencies; however, the linear MMSE
is recommended, because it provides extra protection against
external noise and its complexity is almost identical to that of
the ZF. Recently, [79] presented an asymptotic analysis on the
performance of ZF receivers using the theory of large-dimensional random matrices for the G.fast system.
The G.fast channel up to 212 MHz is not diagonally
dominant, and the linear ZF scheme is no longer near
optimal for crosstalk cancelation (see Figure 13). Here,

60 80 100 120 140 160 180 200
Frequency (MHz)

ment [27] for a binder with ten lines of 100-m length.

160

2,500
2,000
1,500
1,000
500
0
50

100

150

200 250 300
Line Length (m)

350

400

MFB
SWP
ZF−GDFE Canceler
Linear MMSE Canceler
Linear ZF Canceler
No Cancelation
Approximate ZF First-Order Canceler

SWP
MFB
Linear MMSE Canceler
ZF−GDFE Canceler
Linear ZF Canceler
No Cancelation
Approximate ZF First-Order Canceler

FIGURE 12. The spectral efficiency performance using channel measure-

3,000

FIGURE 13. The achievable data rates of 15 users in a binder with
uniformly spaced line lengths. All users use the G.fast 212 MHz, with
various cancelers.

IEEE SIGNAL PROCESSING MAGAZINE

September 2017

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