Signal Processing - September 2017 - 145

FEXT is thus the interference between upstream signals of
different pairs or between downstream signals of different
pairs [1]. The average FEXT power from the jth line to
the ith line can be described as
E 6 H ij 2@ = | fext f 2 d ij E 6 H jj 2@ ,

downstream, the transmitters are colocated, and it is possible to
preequalize signals and reduce the crosstalk. This coordinated
processing of the signals over all lines, referred to as vectoring [9], leads to an enormous rate increase in the DSL system.
A schematic diagram for vectored reception is shown in Figure 5, where the kth tone values Yk, i from all N users are collected to form the vector y k = 6Yk, 1, Yk, 2, f, Yk, N@T , which is used for
coordinated signal processing on all components at the DP. The
result of this processing can be fed to the conventional singleuser modem for demodulation and detection. In Figure 6, the
kth tone values X k, i from all N users are collected to form the
vector x k = 6X k, 1, X k, 2, f, X k, N@T , which is used for coordinated
transmit signal processing on all components at the DP.
In the following, we further describe vector processing,
and focus on a single frequency tone at a time. Hence, without any ambiguity, we drop the tone index from all quantities
until the section "Design Considerations and Challenges for
G.fast." Note that while the processing of all frequency bins is

(1)

where | fext is a constant whose value depends on the physical
properties of the copper cable, E 6 H jj @ denotes the attenuation of the disturber, f is the central frequency of the considered tone, and d ij is the coupling length between the victim
and distributer.
FEXT creates a linear dependence among the different
lines in the binder and hence calls for joint (vector) processing.
In the upstream, because modems are colocated at the DP, it
is possible to construct a vector that contains all the received
symbols over all lines (at a given tone) and then process them
together to reduce the effect of FEXT. On the other hand, in the

Single-User
Processing

External Interference
(Impulse Noise, RFI,
and so on)

Port 1

CPE 1
..
.
CPE i
...
CPE j
..
.

External Interference
(Impulse Noise, RFI, and so on)

Upstream (MAC)

Direct Path Hii
NEXT

Gij

FEXT Hij

Gji

FEXT Hji

Port i
NEXT

Fiber Line

Port j

Direct Path Hjj
Port N

CPE N
Downstream (BC)

Cable Binder

Joint Processing

Twisted Pairs (1-20)

Binder

9
1

18 3

5
13

11
7

20 12
20-Pair Binder Section

FIGURE 3. The FEXT and NEXT in a multipair DSL binder. The cross section of the cable binder is also shown to demonstrate how the twisted pairs are
enclosed in the binder. In the upstream, the DSL binder acts as a multiple access channel (MAC), whereas in the downstream it acts as a broadcast
channel (BC). Note that the CPEs are generally situated at different lengths from the DP. RFI: radio-frequency interference.
IEEE SIGNAL PROCESSING MAGAZINE

September 2017

145

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