Signal Processing - September 2017 - 143

41.6
41.7
41.8
41.9
42

Channel Gain

are simple and do not necessarily require transmit power
ers (also known as tones or frequency bins) [16]. As a result,
optimization. Even the matrix inversion required for linDMT effectively transforms a broadband frequency-selective
ear ZF crosstalk cancelation can be avoided through power
channel into many frequency-flat narrow-band channels, as
series expansion of the MIMO channel [12].
shown in Figure 1.
Simple least-mean-square (LMS)-based
The G.fast system has a wider tone
The recent xDSL standards
adaptive algorithms are very efficient and
width-exactly
12 times wider than asymuse a discrete multitone
converge quite rapidly for the diagonally
metric DSL (ADSL)/VDSL-to cover the
technique, which
dominant VDSL channels [13], [14].
higher bandwidth without increasing the
divides the transmission
At high G.fast frequencies, the crosstalk
number of tones. In the ADSL system,
frequency band into
K = 256 tones (over 2.2 MHz), VDSL conis significant, and the channel matrices are
no longer diagonal dominant. Thus, many
tains K = 4,096 tones (over 30 MHz), the
smaller subcarriers.
VDSL algorithms either fail or converge very
G.fast 106-MHz system has K = 2,048
slowly. Moreover, the adaptive schemes of the VDSL system
tones, and the G.fast 212-MHz profile increases the number of
are either not suitable or are no longer applicable in the TDDtones to K = 4,096. The DMT symbol also contains a cyclic
based G.fast system.
prefix (CP) that allows a tone separation of one symbol duration without any interference between tones, as long as the CP
Wireline discrete multitone technology
is longer than the channel memory (see, for example, [16]). The
Like any communication system, the performance of DSL
G.fast system has a typical CP length of L = 320 samples.
systems is limited by several types of impairments. In the folThe G.fast has a higher sampling frequency than the
lowing, we discuss the main ones and describe both tradiVDSL system, which operates at 70 million samples per
tional and novel techniques implemented by DSL systems
second (Msps). The sampling frequency of the G.fast 106to address them. We also discuss key distinguishing features
MHz profile is 212 Msps. To convert K data symbols into a
of G.fast technology and show how it differs from its predereal signal, 2K point inverse fast Fourier transform (IFFT)
cessor technologies.
is used. The resulting bandwidth is 106 MHz, and the tone
width is 51.75. Considering the CP, the resulting symbol rate
Thermal noise
is 48 KHz (exactly 12 times faster than ADSL/VDSL). The
All communication systems are inherently limited by thermal
G.fast 212-MHz system has the same symbol rate but a much
noise caused by the random movement of electrons in the syshigher sampling frequency rate (more than 400 Msps). A
tem. This additive noise is generally modeled as a random
typical DMT block diagram with G.fast parameters is shown
Gaussian signal that is independent of the transmit signal. The
in Figure 2.
effect of thermal noise cannot be completely avoided, and it
Another important advantage of the DMT is the ability to
sets an upper limit on communication performance, which is
use a different modulation at each tone. Thus, tones with a low
known as the channel capacity [15]. Attaining the channel
SNR will use small constellations, such as quadrature phasecapacity requires the implementation of powerful error corshift keying with two bits per tone. Tones with high SNRs
rection codes. Legacy DSL systems employ the relatively
simple Reed-Solomon (RS) codes as an outer code and trellis-coded modulation (TCM) as an inner code, with an inter0.9
leaver between them [5]. The combined RS-TCM coding
0.8
scheme was also chosen for the G.fast 106-MHz standard.
0.7
Capacity-approaching low-density parity-check (LDPC)
0.6
codes have also been proposed for the G.fast system. But the
0.5
design and implementation of an LDPC code with flexible
0.15
0.4
0.1
coding and modulation that can operate at the G.fast data rates
0.05
0.3
is an open research challenge. In most scenarios, however,
Zoomed
0
0.2
thermal noise is not the main limiting factor, and other impair0.1
ments must be considered.
0

Intersymbol interference and discrete
multitone modulation
Over wide bandwidths, the telephone channel is frequency
selective and exhibits frequency-dependent attenuation and
delay. This causes severe intersymbol interference (ISI),
where the communication symbols are prolonged and overlap
each other. To overcome this problem, the recent xDSL standards use a discrete multitone (DMT) technique, which
divides the transmission frequency band into smaller subcarri-

40 50 60 70
Frequency (MHz)

100

Frequency-Selective Channel
Frequency-Flat Subchannel

FIGURE 1. The frequency selectivity of the DSL channel is illustrated using
the channel gain of a 100-m CAD55 cable simulated for the G.fast 106-MHz
profile [3]. The figure shows how the use of 2,048 narrow-band tones of
51.75 KHz results in an almost frequency-flat channel at each tone.

IEEE SIGNAL PROCESSING MAGAZINE

September 2017

143

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