ISSC 2004, Belfast, June 30 - July 2
Bandwidth, Spectral Efficiency and Capacity Variation in
Twisted-Pair Cable.
Chambers, P., Downing, C., * Baher, H.

School of Electronic and
Communications Engineering,
Dublin Institute of Technology,
Kevin Street, Dublin 8,
IRELAND.
E-mail: pchambers@dit.ie
* School of Electronic and
Communications Engineering,
Dublin Institute of Technology,
Kevin Street, Dublin 8,
IRELAND.
E-mail: * cdowning@dit.ie

School of Electronic and
Communications Engineering,
Dublin Institute of Technology,
Kevin Street, Dublin 8,
IRELAND.
E-mail:  hbaher@eircom.net
__________________________________________________________________________________________
Abstract –The capacity of a twisted-pair cable is limited by
crosstalk, bandwidth, interference and noise. A Multiple-Input/
Multiple-Output (MIMO) communications system is outlined in
which far end crosstalk (FEXT) is removed and the bandwidth
extended. Experimental results are presented which show a
significant potential increase in spectral efficiency compared with a
conventional connection over a bandwidth of 100 MHz.
Keywords – MIMO, SISO, bandwidth, spectral efficiency, twistedpair, capacity.
__________________________________________________________________________________________
I
INTRODUCTION
Before fibre optical systems the subscriber loop was
dominated by copper twisted-pair. Initially, the
copper twisted-pair was deemed inferior to the
optical fibre, from a technological point of view, but
persisted within the subscriber loop for financial
reasons. It is only in recent years that fibre optic
communication systems have gained any significant
place in the subscriber loop [9]. In the mean time,
many new experimental ideas and transmission
techniques have been tried with copper twisted-pair,
for example “xDSL” technology.
There is now a
growing belief that due to these new data
transmission techniques, such as improved coding
and crosstalk cancellation, that the data capacity of
copper twisted-pair may compete with what is
achievable using optical fibre [8]. From an economic
point of view this is very sound since fibre optic
systems still only exist in large cities. Previous work
by the authors [7] has shown that there is a
significant potential increase in spectral efficiency of
a multi-conductor communication system if it is
viewed as a multiple-input/multiple-output (MIMO)
channel. In this paper the bandwidth and spectral
efficiency of such a channel are considered in detail
and are supported by experimental results on a
bundle of twisted-pair telephone cables.
II
THE TWISTED-PAIR TELEPHONE
CABLE
With the demand for high-speed data communication
systems increasing, there is a growing interest in the
capacity limitations of twisted pair telephone cable.
The dominant source of performance degradation in
a bundle of twisted-pair telephone cables is far end
crosstalk (FEXT).
Figure 1: This is an illustration of far end crosstalk (FEXT)
between two adjacent twisted pair telephone lines. The
straight arrows represent the direction of the signal
propagation down the line.
FEXT propagates in the same direction as the signal
and is therefore detected at the receiver of any
adjacent line. It is the result of capacitive and
inductive coupling between adjacent telephone lines.
Conventional communication systems seek to
minimise FEXT by active crosstalk cancellation
methods [2], so that each cable can be viewed as a
single-input/single-output (SISO) system. However
with current active crosstalk cancellation methods,
there will still be a degree of FEXT coupling
between all adjacent telephone lines.
This is
especially true at higher frequencies where the extent
of crosstalk coupling is seen to increase.
III
COMMUNICATION SYSTEM MODELS
Shannon [1] proposed that the capacity, C , of an
information communication system is related to its
bandwidth, B , and its signal to noise ratio, SNR ,
by the following equation (1):
C
 log 2 (1  SNR)
B
(1)
(f ) 
h( f ) i i
 h( f )
2
(3)
2
i j
In the case where there are five telephone lines in a
cable, each being a SISO system, the crosstalk
voltage gain will be the sum of four gains due to the
neighbouring telephone lines. The capacity of five
twisted-pair SISO telephone cables can be derived
from equation (1) as:
N
C
  log 2 (1  SNRi )
B i 1
where N  5 and
(4)
SNRi is the signal to noise ratio of
th
C
The quantity,
, is known as the spectral efficiency
B
of the communication system. It is the capacity of
the system per hertz of bandwidth. It is quoted in
bits/sec/Hz. Helenius et al [6] have shown that the
SNR , which varies as a function of frequency, can
be calculated for a crosstalk coupled twisted pair
telephone line, i.e. a practical SISO system, from
equation (2):
SNR( f ) SISO 
1
N0
2
 h( f )   1 ( f )
S( f )
(2)
Here
N 0 is the noise which exists on the line and
this noise is often dominated by broadcast radio
interference in the bandwidth of interest. S ( f ) is
the power spectral density of the signal propagating
down the line. h( f ) i i is the directly connected
th
voltage gain between the i transmitter and the
2
i th receiver. h( f ) i i is thus a measure of the power
gain. The normalised equal level far end crosstalk
(EL-FEXT) [6],  ( f ) , is a measure of the crosstalk
as a function of frequency and is the ratio of
h( f ) i i to the sum of the indirect voltage gains due
the i pair.
In the context of radio systems, Foschini and Gans et
al [4] of Lucent Technologies have proposed using a
transmitter antenna array and a receiver antenna
array to create multiple channels over the same
spectral bandwidth. This has the effect of increasing
the capacity for a given amount of bandwidth, i.e. an
increase in the spectral efficiency, beyond what
would be expected using a SISO system. This system
of using N transmitting antennas and N receiving
antennas is known as a multiple-input/multipleoutput (MIMO) communication system model.
In a five twisted pair cable, the emphasis is on the
spectral efficiency of the sub-bands which the cables
can support. It is proposed that by using a MIMO
communication system on a five twisted-pair cable,
that a potential increase in the spectral efficiency in
each of the supported sub-bands will occur.
In a five twisted-pair MIMO communication system
there are twenty-five signal paths to be considered.
There are five direct connection signal paths and
twenty indirect signal paths arising from crosstalk.
The system can be described by a 5 x5 matrix,
h(i, j ) , where each element is the complex voltage
gain of the twenty-five paths. The diagonal elements
of h (i, j ) , i  j represent the direct connections.
h (i , j ) ,
off-diagonal
elements
of
i  j represent the FEXT. The elements of
h(i, j ) are calculated from equation (5) below:
The
j th adjacent line. It is the sum of
all the possible expressions of h ( f ) i  j for a given
line. An expression for EL-FEXT,  ( f ) , is given
h(i, j )  h(i, j )  exp( j i , j )
by equation (3)
where
to FEXT from the
(5)
h(i, j ) is the absolute voltage gain of a
th
given signal path between the i transmitter and the
j th receiver and similarly  i, j is the phase angle of
such a signal path. The matrix, h (i, j ) , is frequency
dependant and can thus be calculated for each subband that a cable can support. Further mention of
h(i, j ) from here on will denote it as h for the sake
of clarity.
In work involving a MIMO antenna system,
Anderson J.B. et al [5] proposed using the singular
value decomposition (SVD) algorithm to weight the
data at the transmitter and receiver arrays in such a
way as to create a channel in between them where
the crosstalk or off-diagonal terms are zero and the
gain of the remaining five direct signal paths has
been increased to give them added capacity.
The SVD algorithm creates three matrices from the
matrix, h, such that:
h  U  S  VT
(6)
Both U and V are 5 x 5 complex, unitary matrices
and S is a diagonal matrix consisting of the
eigenvalues of h. If both sides of this equation are
multiplied by U-1 and V-T respectively and since
U  U 1  I and (V.V-1)T = I where I is the identity
matrix, then an expression for S is as follows in
equation (7):
S  U 1  h  V T
(7)
It is then proposed that upon evaluating h for the
channel and computing the U-1 and V-T matrices, the
channel be weighted at the transmitter array by U-1
and at the receiver array by V-T. Thus the gain of the
MIMO communication system model is the
diagonalised matrix, S, without any FEXT.
Foschini and Gans et al [4] have shown that the
general expression for the spectral efficiency of a
MIMO system is given by equation (8):
The eigenvalues are normalised with respect to the
largest eigenvalue occurring in any frequency subband, B . This normally occurs at the lowest
frequency sub-band in use on the line. Thus, the
quantity  k will be this set of five normalised
eigenvalues for a given frequency sub-band, B .
The size of the sub-band, B , was set at
approximately 500 kHz.
To compute the spectral efficiency of such a system,
its SNR must also be considered. In the previous
expression for the SNR given by equation (2), the
term  ( f ) represented the ratio of h( f ) to the
total of the indirect voltage gains due to crosstalk
from all neighbouring telephone lines. If the gain of
the MIMO system is described by the diagonal
matrix S it is clear that the term,
 ( f ) 1 ,
will be
zero for the SNR of a MIMO system. Thus equation
(10) is the expression for the SNR of a MIMO
system as a function of frequency, where it is
assumed that the level of noise, N 0 , is constant
across the band:
SNR( f ) MIMO 
S( f )
N0
(10)
Given the SNR for the case of a MIMO system has
increased over the conventional SISO case and the
inclusion of the eigenvalues in equation (8), a
potential increase in the spectral efficiency,
C
, for
B
the MIMO communication system model of twistedpair telephone cables over the conventional SISO
communication system model of twisted-pair
telephone cables is anticipated.
IV MEASUREMENTS AND RESULTS
N
C
  log 2 1  SNR  k 
B k 1
(8)
Again in the case of a five twisted-pair bundle of
telephone lines, N  5 . The expression,  k , is the set
of eigenvalues for the power transfer function matrix
of the system.
k
are the eigenvalues of the matrix, H, which is the
product of the channel matrix, h and its conjugate
transpose, h*. H is given by:
H  h  h*
(9)
The voltage gain between two terminals, either as a
direct connection or as a crosstalk coupled
connection was measured as the S-parameter, S 21 .
The crosstalk-coupled connection was observed
experimentally when S 21 was measured by exciting
one twisted-pair and measuring on the far end of
another under matched conditions. The direct
connection was observed experimentally when S 21
was measured by exciting a given twisted-pair and
measuring on the far end of the same twisted-pair.
Measurements of S 21 were made in the frequency
range 300kHz – 100MHz over 201 sub-bands, each
of bandwidth approximately 500 kHz using Hewlett
Packard (Agilent) HP875313B and Anritsu 37369A
microwave network analysers (MNA) along 100m
length of five twisted pair cable. The spectrum of the
noise and EMI emanating from the pair was
measured on an Advantest R4131C spectrum
analyser, and was examined over a band ranging
from above 50 Hz to 200 MHz. It was found that
through most of the band the noise floor was at a
level of –83 dBm. Significant EMI was noted from
broadcast f.m. radio at around 100 MHz and also
from broadcast television signals from 200 MHz
upwards. The most significant of these was at level
of –53 dBm at 104 MHz. Thus the worst case
SNR is –53 dBm. Details of these measurements are
discussed in previous work by the authors [7].
The normalised power gain for the crosstalk and
direct connections along one twisted pair are
compared in figure (2). This shows the presence of
crosstalk is quite significant from 50 MHz upwards
as the power gain of the direct connection decreases.
For a SISO system this effect disimproves the
SNR . The slight increase in gain at around 100
MHz appears to be an artefact of the FFT used to
remove non-causal crosstalk.
Using equation (4), the measurements of magnitude
and phase of S 21 in the frequency domain form the
elements of the matrix h for any given sub-band,
B , between 300 kHz and 100 MHz. It was
decided that h be evaluated 201 times. The matrix,
H  h  h* was calculated and normalised for each
sub-band from 300 kHz to 100 MHZ and its
eigenvalues,  k , were obtained. The off-diagonal
terms of the matrix, h, will be used to evaluate the
term,  ( f ) .
.
Figure (3): The five normalised eigenvalues
calculated by SVD for each of 201 frequency subbands between 300 kHz and 100 MHz.
The eigenvalues of the orthogonalised system are
shown in Figure (3). This shows each of the five
eigenvalues, represented by a different line, and their
variation with frequency. These eigenvalues were
normalised with respect to the highest eigenvalue,
which was found to be at the lowest frequency of
measurement, i.e. 300 kHz.
Figure (2): The normalised power gain for a direct
connection and for typical crosstalk at each of 201
frequency sub-bands between 300 kHz and 100
MHz.
efficiency for the MIMO communication system
model.
The mean value of spectral efficiency in bits/sec/Hz
for the five twisted-pair MIMO communication
system is approximately 107. This compares with
18.9 for the five twisted-pair SISO system. This
represents a five fold increase in the average spectral
efficiency. The standard deviation of spectral
efficiency for the MIMO system is approximately
13.8 bits/sec/Hz, whereas the standard deviation of
the SISO system is approximately 10.5 bits/sec/Hz.
However, by inspection of Figure (5), it can be seen
that the MIMO system has less variation with
frequency than the SISO system. It may be noted that
up to a frequency of approximately 50 MHz, the
magnitudes of the five eigenvalues are similar.
Figure (4) The largest eigenvalue and the normalised
power gain of the average direct connections.
The curves in figure (4) show a rapid decrease in
normalised power gain of the average direct
connections for frequencies above 50 MHz. This
would cause the SNR of a SISO communication
system to drop quite abruptly, limiting the SISO
capacity. In contrast, for the case of the MIMO
system, the capacity is dominated by the largest
eigenvalue which does not fall away as rapidly with
frequency. This, combined with removal of FEXT,
results in significantly improved capacity in the
MIMO system.
An expression for the total capacity of a five twistedpair bundle of telephone cable over 201 frequency
sub-bands, B , based on the SISO communication
system model is given by:
Figure (5): The calculated spectral efficiency, at each
of 201 frequency sub-bands between 300 kHz and
100 MHz, on a five twisted-pair telephone cable as a
MIMO and SISO communication system.
201 5
C   log 2 1  SNR( f ) SISO   BM
M 1 k 1
(11)
Similarly, an expression for the total capacity of a
five twisted-pair bundle of telephone cable over 201
frequency sub-bands based on the MIMO
communication system model is given by:
C
201 5
 log 1  SNR( f )
M 1 k 1
2
MIMO
 k   BM
(12)
Figure (5) shows a plot of the calculated spectral
efficiency at each frequency sub-band, B . These
results indicate a potential increase in spectral
This is because in this frequency range there is little
FEXT and the system acts as five SISO lines.
However, at frequencies from 50 MHz to 100 MHz,
the eigenvalues have increased variance due to the
presence of FEXT. Since the spectral efficiency
depends primarily on the largest eigenvalue, the
potential capacity may be seen in figure (5) to
maintain a high value up to 100 MHz.
V
CONCLUSIONS
Figure (5) clearly shows that a significant potential
improvement in spectral efficiency is achieved by the
use of MIMO techniques when compared to the
spectral efficiency of a conventional SISO
connection. This is thought to be due to cancellation
of the FEXT, extended frequency response of the
largest eigenvalue above 50 MHz and also due to
power being redirected due to the diagonalisation of
the channel.
However, it is acknowledged that this crosstalk may
be slightly higher than in a practical subscriber
situation due to the fact that the twisted pair cable is
wound in a drum. The potential improvement in
capacity is contingent on processing of the data to
achieve this diagonalisation.
Cioffi, John, M., [8] has noted that the potential
capacity for copper cabling may rival that of optical
fibre. The potential capacity increase in an
inexpensive cable using MIMO techniques is
remarkable. The experimental work reported here
suggests a workable bandwidth of 100 MHz along a
cable of approximately 100m in length with an
average spectral efficiency of approximately 107
bits/sec/Hz. For this workable bandwidth of 100
MHz, this corresponds to a capacity of 10.7
Gbits/sec.
VI
ACKNOWLEDGEMENTS
The authors are indebted to Brian Foley, Tony
Grennan, Brendan O’Sullivan and Mark Davis for
many helpful discussions and to Tom Fallon for
technical support.
This research was supported by a Dublin Institute of
Technology Postgraduate Scholarship
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