Transcript Crosstalk and Loop Make-Up Identification for

University of British Columbia, Vancouver, Distinguished Lecture, Feb. 27, 2006
Crosstalk and Loop Make-Up
Identification for DSL Systems
Dr. Stefano Galli
Senior Scientist, Telcordia Technologies
[email protected]
http://www.argreenhouse.com/bios/sgalli
Talk Outline
 DSL
issues
 DSL
Spectrum Management Enablers
Crosstalk Identification
– Loop Make-Up Identification
–
 Results
on Iterative Algorithms for Optimization
 Simulation
results
UBC 2006– 2
Copper
Impairments

“POTS” faults
–
–

–
–
–
–
EMI radio ingress
Multi-pair cable
Impulse noise
Increases with frequency
Bridged tap: up to 10 dB spectral dips
Coupling between different systems on different pairs
Often most significant noise
Multi-pair feeder and distribution cabling
Narrow band frequency spikes
Unshielded drop and inside wire
Impulsive noise hits
–
–

grounds, shorts,
load coils, balance, dBrn, loop length
Crosstalk
Radio ingress noise = Electromagnetic interference (EMI)
–

Central
Office
(CO)
Crosstalk
–

Unshielded drop
and inside wire
Loop loss
–

Loop loss
Short bursts (10s of microseconds) of high power noise
Long-term (hour) error monitoring
Non-linear distortion
–
From phones with no microfilter, some protectors
UBC 2006– 3

Crosstalk is the major impairment of xDSL
Near End Crosstalk (NEXT)
 Far End Crosstalk (FEXT)

Cable
Pair i
NEXT
Pair j
FEXT
UBC 2006– 4
Managing crosstalk
 As
DSL rollout continues, the problem of
crosstalk will become more and more important
for at least two reasons:
Spectral compatibility issues  necessity of impartial
third party for monitoring and resolution
– Performance issues  necessity of multiuser
detection, cancellation, or dynamic management
–
 Systems
engineered to face worst case xtalk
UBC 2006– 5
Dynamic Spectrum Management (DSM)
CO-based ADSL
Power
CO
Today – equal transmit spectra
really bad Crosstalk
CO
Remote
Terminal (RT)
RT
ADSL,
ADSL2+,
or VDSL
Frequency
Tomorrow
Separate
Frequency bands
RT
Frequency
CO
RT
Frequency
Joint Optimization
Power
CO
Power
Power
Power Back-off
CO
RT
Frequency
UBC 2006– 6
Managing crosstalk
–
Crosstalk is NOT random noise – we can control it!

Identify crosstalk sources and couplings
XT1,2
DSL #1
XT1,3
DSL #2
–
Spectrum balancing



–
DSL #3
XT2,3
Balance transmit power levels
Adapt transmit spectra to optimize performance AND minimize crosstalk
BIT RATES APPROXIMATELY DOUBLE
Vectoring


Real-time signal coordination, crosstalk cancellation
BIT RATES APPROXIMATELY TRIPLE
UBC 2006– 7
Input data from DSL Modems & DSLAMs

Double-Ended Loop Test (DELT)
–
–
Requires working DSL service
Now: proprietary TL1 & SNMP interfaces



ADSL2 & 2+ Diagnostics (ITU G.992.3 & .5) - products just out




Bit rates, SNR Margin, Gross Attenuation, Bit loading spectrum
Different formats, often lack accuracy
Standardized formats, accuracy
For each of the 255 subcarriers to 1.1 MHz: Channel Transfer Function H(f),
Quiet Line Noise PSD QLN(f), and Signal-to-Noise Ratio SNR(f)
Aggregate: Line Attenuation, Signal Attenuation, Signal-to-Noise Margin,
Attainable Net Data Rate, Aggregate Transmit Power
Single-ended loop test (SELT), G.selt ITU-T project, vendor
implementations
–
Single-ended modem-based loop & noise tests – no service or enduser modem required
UBC 2006– 8
Extract data from ADSL modems
Power Spectral Density
(PSD) (dBm/Hz)
-40
-60
-80
-100
-120
ADSL received signal at 9 kft
-140
-160
-180
0
26
51 77 102 128 153 179 204 230 255
ADSL DMT Subcarrier Number
ADSL Discrete multi-tone (DMT) modem data:
- 255 tones
- Nearly as good as continuous spectra!
UBC 2006– 9
Crosstalk Identification
SELT Approach
 It is targeted both to the estimation of the pair-to-pair couplings
and to the identification of the source.
 It is useful for crosstalk cancellation/multiuser detection.
 Should not only be modem-based: it may be used before providing
service, measures crosstalk across all bandwidth.

Not much literature on xtalk identification. First papers are recent:
Zeng, C. Aldana, A. Salvekar, J. Cioffi, “Crosstalk Identification in DSL
Systems”, IEEE JSAC, Aug. 2001.
S. Galli, C. Valenti, K. Kerpez, “A Frequency-Domain Approach to
Crosstalk Identification in DSL Systems”, IEEE JSAC, Aug. 2001.
UBC 2006– 10


Traditional approach is in terms of power sums (sum of the pairto-pair NEXT coupling powers of the other pairs
in the binder group).
Engineering is made in terms of the 1% worst case: linear in the
log-log scale, 15 dB per decade of frequency.
Next( f )  S( f ) X N f
1.5
Fext( f )  S ( f ) X F f 2l H ( f )
2
Power-Sum Models !
Power Sum NEXT Loss(dB)
100
90
80
70
60
50
40
30
0.01
0.10
1.00
Frequency(MHz)
10.00
UBC 2006– 11
P1
P2
P3
P4
P5
P6
P7
P8
P9
P10
P11
P12
P13
P14
P15
P16
P17
P18
P19
P20
P21
P22
P23
P24
P25

Individual pair-to-pair couplings: situation is more complex
No smooth curves, high variability, no known models.
Pair-to-Pair NEXT Loss (dB)

80
75
70
65
60
55
50
45
40
0
500
1000
1500
2000
Frequency (kHz)
UBC 2006– 12
Pair-to-Pair NEXT Coupling (dB)
Worst 25 measured pair-to-pair crosstalk couplings out of 300
Dark black line = 99% worst-case model
-40
-50
-60
-70
-80
-90
-100
0
0.16
0.32
0.48
0.64
0.8
0.96
1.12
1.28
1.44
1.6
Frequency (MHz)
UBC 2006– 13
Crosstalk Identification Algorithm





Perform a vast measurement campaign of the pair-to-pair
couplings on several cables.
Create a set of pair-to-pair couplings, choosing them on the basis
of a specific criterion  create a dictionary of ptp couplings.
Multiply the ptp couplings of the dictionary by the PSDs of all the
possible xDSLs (ISDN, ADSL, HDSL, etc.)  create a dictionary
of crosstalk PSDs profiles.
Measure xtalk PSD and search for the “closest” xtalk PSD profile
in the dictionary.
Finding the “closest” PSD profile gives us the most likely xtalk
source and ptp coupling.
UBC 2006– 14
Basis set members for T1 NEXT
-90
NEXT PSD (dBm/Hz)
-95
-100
-105
-110
-115
-120
-125
-130
-135
-140
0
500
1000
1500
2000
Frequency (kHz)
UBC 2006– 15
Vector Choice Methods
 Power: ranking the ptp couplings on the basis of their dB sum
across all frequencies.
 Singular Value Decomposition: choosing only the linear
independent vectors in the dictionary.
Search Methods
 Correlation: Perform a statistical correlation between measured
xtalk PSD and xtalk PSD profiles in the dictionary.
 Multiple Linear Regression: best suited for the identification of
multiple disturbers.
 Matching Pursuit: mathematical formulation of the problem
equivalent to the problem of finding the best sparse
representation of a vector on the basis of an overcomplete
dictionary.
UBC 2006– 16
Crosstalk ID: Problem Statement
Y  yi ii 1N : set of N frequency samples of the measured crosstalk PSD
caused by un unknown DSL disturber
X
(k )

 
( k ) iN
xi i 1
: set of N frequency samples of the k-th basis crosstalk PSD
profile, with 1  k P
Find the single disturber that generates crosstalk Y given the set of all the
crosstalk PSD profiles X, i.e. find relationship between Y and X
Classical regression problem:
yi  a( k )  b( k ) xi( k )  ei( k )
UBC 2006– 17
yi  a( k )  b( k ) xi( k )  ei( k )
The regression coefficients a(k) and b(k) are determined by the condition
that the sum of the squared residuals S(k) is minimum:
S
(k )
N

 
i 1
(k ) 2
ei
N

  yi  a
i 1
(k )

(k ) (k ) 2
 b xi
It is possible to show that the sum of squared residuals can be expressed
in terms of the correlation coefficient:
Minimizing sum of squared
(k )
S
residuals is equivalent to
2
 X (k ) , Y  1  N
finding the maximum
2
correlation coefficient
yi   Y




i 1
UBC 2006– 18
Y  a1 X
Y  y1

  X (1)
(1)
 a2 X
(2)
y2  y N T
X (1)  X ( P )
E
P
( j)
a
X
 E  a  E
 j
j 1
vector containing the measured crosstalk PSD from unknown
disturbers across all N frequencies

a  a1 a2  aP T
E  e1 e2  eN T
 ... aP X
(P)
full rank NxP matrix containing all the PSD profiles
vector of weighting coefficients
vector containing the residuals over all the frequency points
UBC 2006– 19
Y  a  E
• N<<P, matrix  constitutes an overcomplete set of vectors for N
• Number of disturbers M small, M<<P
Problem: find an optimal sparse representation of a
vector from an overcomplete set of vectors.
UBC 2006– 20
Crosstalk: T1
T1 ++HDSL
Crosstalk:
HDSL
-50
Power Spectral Dendity (dBm/Hz)
Power Spectral Density (dBm/Hz)
Individual ptp: HDSL
-55
Individual ptp: T1
-60
-65
-70
-75
0
200
400
600
800 1000 1200
Frequency in kHz
1400 1600
1800 2000
Frequency (kHz)
UBC 2006– 21
SVD allows to drastically reduce computational complexity.
No SVD
(P = 800)
q=[1,1,1,1,1,1,1,1]
~
( P = 8)
1) ISDN
14/14
14/14
2) HDSL
24/24
23/24
3) T1
38/38
36/38
4) ADSL Dn
37/37
37/37
5) SDSL 400
26/26
26/26
6) SDSL 1040
27/28
23/27
7) SDSL 1552
30/31
26/31
8) HDSL2 Up
27/27
29/29
Totals
223/225
214/226
ID rate (%)
99.1%
94.7%
UBC 2006– 22
Loop Response Estimation

TDR wideband reflectometry signals estimate bridged taps, segment lengths
and gauges
Entire DSL band spectral response

Better than just one frequency or one length number
Determine Bridged Tap effects
–
–

Example: Actual loop Vs. 1328 ft equivalent 26 gauge (EWL)
22 Gauge
22 Gauge
650 ft
22 Gauge
813 ft
1400 ft
Loop Loss (dB)
18
16
14
12
10
8
6
Actual loop
4
2
0
1328 ft 26 gauge (EWL)
0
100
200
300
400 500 600 700
Frequency (kHz)
800
900 1000 1100
UBC 2006– 23
Necessity of Loop Qualification
• Not all local loops can support DSL technology
• Before DSL can be deployed, local loops must be tested to see
whether they can support it or not
• This may be obtained on the basis of a detailed loop
characterization
Detailed loop characterization is difficult to obtain because:
1) information kept for POTS service was not detailed
2) loop records are often on paper
3) records are often wrong
 It is necessary to perform measurements 
UBC 2006– 24
Types of Loop Qualification
Single-ended testing:
• Requires test equipment at the central office only
• Measures can be performed at the Central Office without involving
on-site technicians
Double-ended testing:
• Requires equipment at both ends of the loop
• Involves dispatching a technician to the customer’s location
• Transfer function easily estimated
Single-ended testing is more complicated but:
• It is less expensive
• It may allow us to unveil the loop make-up, not only the transfer
function  “loop identification” implies loop qualification
UBC 2006– 25
Loop Make-Up Identification
Estimate loop make-up stick
diagram from single-ended
CO-based TDR measurement
Telco DSL
CO
TDR
1500’
26
gauge
5900’
2000’
26 gauge 24 gauge
1500’
26
gauge
500’
500’
24 gauge 22 gauge
• The test equipment transmits a set of “ad-hoc” designed signals
• When a signal travels on a loop and encounters medium discontinuities
(gauge changes, bridged taps, end of line) part of the signal is reflected
back, i.e. an echo is generated.
• Unwanted spurious echoes are also always present
• The test equipment will process the received echoes
UBC 2006– 26
Echo Modeling
AWG26
Test
Equipment
CO
1500
1000
3000
AWG26
2000
AWG24
CL
AWG24
2
Amplitude (milli-volts)
1
0
-1
-2
-3
-4
0
10
20
30
40
50
60
Time (microseconds)
70
80
90
100
UBC 2006– 27
Echo Modeling
Observation of the superposition of all the echoes
(Test signal: 200 ns Square Pulse, 1 V amplitude)
3
2
Total
Amplitude (milli-volts)
1
0
-1
Spur
-2
-3
Real
-4
0
10
20
30
40
50
60
Time (microseconds)
70
80
90
100
UBC 2006– 28
Echo Modeling
N
r(t )  s(t )   aie (t t i )
(i )
i 1
The following unknown quantities must be estimated:
•
•
•
•
Time of arrival of the echo: ti
Amplitude of the echo: ai
Waveform of the echo (shape): e(i)(t)
Number of non-negligible echoes N
Problems:
• Some echoes are spurious and some are not
• Some echoes overlap
UBC 2006– 29
Echo Modeling
The shape of echo (real or spurious) generated at a discontinuity
depends on the following quantities:
ZL  ZS
• The insertion loss of the echo path: H IL ( f ) 
AZL  B  CZS ZL  DZS
Z  Zb
• The reflection coefficient:  ( f )  a
Z a  Zb
• The transmission coefficient: tf 1  (f)
(f) =-1/3
t(f) = 2/3
(f) = 1
2s(t)/3
s(t)
-s(t)/3
CO
2s(t)/3
CO
(f) =-1/3
t(f) = 2/3
2s(t)/3
-2s(t)/9
4s(t)/9
CO
CO
3
4s(t)/9
UBC 2006– 30
Echo Modeling
The reflection coefficient for the spurious echoes:
Gauge Changes:
( f )  1( f ) i2 ( f ) i 1
Bridged Taps:
( f )  1 0 ( f )1 1( f )1( f ) i
 ( f )  1 0 ( f )1 1( f )1 2 ( f )1( f ) i 1 2 ( f ) j 1 3 ( f ) j
 ( f )  1 0 ( f )1 2 ( f )2 ( f ) i 3 ( f ) i 1
UBC 2006– 31
Echo Modeling – Experimental Validation
AWG24
980 ft
980 ft
2940 ft
AWG24
AWG24
3000 ft di AWG24: 5 V e 5 micro
800
700
600
500
400
Amplitude in(millivolts)
milliVolts
Amplitude
Measurement
Equipment
300
200
100
0
-100
-200
-300
-400
-500
-600
-700
-800
0
1
2
3
4
5
6
7
8 9 10 11 12
Time in microseconds
13
Time (microseconds)
14
15 16
17
UBC 2006– 32
18 19
20
Echo Modeling – Experimental Validation
3000 ft
3000 ft
AWG26
AWG24
500
450
400
Amplitude (millivolts)
Measurement
Equipment
350
300
250
200
150
100
50
0
0
5
10
15
20
25
30
Time (microseconds)
35
40
45
UBC 2006– 33
50
Traditional Signal Processing Approach
•The problem of detecting and resolving signals generated by D sources
has been usually addressed assuming the availability of an array of M>D
sensors.
•It is a combined detection/estimation problem: determine the number of
sources and then estimate their location in time.
•In our case the sources are the discontinuities, the signals are the
echoes and the location in time is the position of the discontinuity.
UBC 2006– 34
Traditional Signal Processing Approach
Problem: Here we have only one sensor!!!
Let’s try to turn our single sensor case into a multi-sensor one and use
MUSIC, ESPRIT, or WSF.
D
r (t1)   ai s(t1  i )  n(t1)
r (t )   ai s(t  i )  n(t )
i
i 1
D
r (t2 )   ai s(t2  i )  n(t2 )
i 1

D
r (tM )   ai s(tM  i )  n(tM )
i 1
UBC 2006– 35
Traditional Signal Processing Approach
 r (t1)   s(t1  1) s(t1  2 )  s(t1   D )   a1   n(t1) 
 r (t )   s(t   ) s(t   )  s(t   )   a   n(t ) 
2
2
1
D  2  
2 
 2  2 1


 
   






 
  

r
(
t
)
s
(
t


)
s
(
t


)

s
(
t


)
a
n
(
t
)
M
2
M
D  D   M 
 M   M 1

r  Sa  n
Similar to the multi-sensor problem but now the
array manifold depends on the shape of the echo
Problems:
• The manifold S requires the knowledge of the shape of the
echo and that all the echoes have the same shapes.
• The real and spurious echoes would still be undistinguishable
from each other.
UBC 2006– 36
Echo Signatures of Discontinuities
120
Unterminated
100
Amplitude
Amplitude in(millivolts)
millivolts
80
60
Gauge Change (positive)
40
20
0
-20
Gauge Change (negative)
Bridged Tap
-40
0
50
100
150
Time in microseconds
Time (microseconds)
200
250
300
UBC 2006– 37
Not much literature on Loop Make-Up identification.
First papers are recent:
S. Galli, D. L. Waring, “Loop Make-up Identification via Single Ended
Testing: Beyond Mere Loop Qualification”, IEEE J. Select. Areas
Commun., vol. 20, no. 5, June 2002.
T. Bostoen, P. Boets, M. Zekri, L. Van Biesen, T. Pollet, and D. Rabijns,
"Estimation of the Transfer Function of a Subscriber Loop by Means of a
One-Port Scattering Parameter Measurement at the Central Office," IEEE
J. Select. Areas Commun., vol. 20, no. 5, June 2002.
UBC 2006– 38
A Novel Step-by-Step Maximum Likelihood
Technique
The identification process is based on analyzing TDR
measurements in such a way that the measurements are
successively mapped to gradually augmented loop makeup topologies until the error between the measured TDR
trace and the simulated TDR waveform of a set of
hypothesized loop topologies becomes sufficiently small.
S. Galli, K. Kerpez, "Single-Ended Loop Make-Up Identification - Part
1 and 2," IEEE Transactions on Instrumentation and Measurement,
vol. 55, no. 2, April 2006.
UBC 2006– 39
A Novel Step-by-Step Maximum Likelihood
Technique
1) Hypothesize all “sensible” topologies and generate corresponding
waveform according to echo model
2) Choose topology whose waveform best matches measured data,
and identify discontinuity
3) Augment chosen topology using auxiliary topologies (infinite length),
generate corresponding waveform, and subtract it from measured data
to obtain a de-embedded TDR trace
4) Identify the next discontinuity
5) Go to 2 using de-embedded trace as measured data until last echo
is found
Rationale:
• Exploit the “deterministic” nature of the twisted-pair.
• The echoes from near discontinuities “hide” the echoes from far
discontinuities  de-embedding
UBC 2006– 40
UBC 2006– 41
0.0000
0
5
10
15
20
25
30
35
-0.0200
26
-0.0400
Gauge Changes
-0.0600
19
Slope
-0.0800
-0.1000
-0.1200
Bridged taps
26-26
Collocated
Bridged taps
-0.1400
-0.1600
24-26
19-19
26-26-26
19-22-26
-0.1800
19-19-19
-0.2000
Index
UBC 2006– 42
Example of Loop ID
0.8
B
0.7
0.6
0.5
SDS
Amplitude (Volts)
0.4
C
0.3
SP2
0.2
0.1
0
SP1
-0.1
B
-0.2
980 ft
-0.3
Measurement
-0.4
Equipment
-0.5
-0.6
2940 ft
A
C
AWG24
A
-0.7
-0.8
980 ft
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
Time (microseconds)
UBC 2006– 43
Example of Loop ID
1
SDS of AWG 26
0.8
SDS of AWG 24
0.6
Amplitude
(Volts)
Amplitude
(millivolts)
0.4
0.2
0
-0.2
SDS of AWG 22
SDS of AWG 19
-0.4
-0.6
-0.8
-1
1
1.5
2
2.5
3
3.5 4 4.5 5
Time (microseconds)
5.5
Time (microseconds)
6
6.5
7
7.5
UBC 2006– 44
Example of Loop ID
0.75
Measured TDR trace
CO
0.5
980 ft
AWG 22
AWG 24
D3
CO
980 ft
AWG 26
0.25
Amplitude
(millivolts)
Amplitude
(Volts)
D5
0
-0.25
CO
980 ft
D8
AWG 24
-0.5
-0.75
CO
-1
980 ft D21
AWG 24
-1.25
1
1.5
2
2.5
3
3.5 4 4.5 5
Time (microseconds)
5.5
Time (microseconds)
6
6.5
7
7.5
UBC 2006– 45
Example of Loop ID
1
Measured TDR trace (same as in Fig. 3)
0.8
0.6
Difference
Amplitude
(Volts)
Amplitude
(millivolts)
0.4
0.2
0
-0.2
Simulated TDR trace
-0.4

-0.6
Measurement

Equipment
-0.8
-1
980 ft
AWG24
1
2
3
4
5
6
7
8 9 10 11 12 13 14 15 16 17 18 19 20
Time (microseconds)
UBC 2006– 46
Time (microseconds)
Example of Loop ID
1
0.8
Measured TDR trace (same as in Fig. 3)
0.6
Difference
Amplitude
(Volts)
Amplitude
(millivolts)
0.4
0.2
0
-0.2
Simulated TDR trace
-0.4
980 ft
-0.6
Measurement

Equipment
-0.8
-1
980 ft
AWG24
1
2
3
4
5
6
7
8 9 10 11 12 13 14 15 16 17 18 19 20
Time (microseconds)
Time (microseconds)
UBC 2006– 47
Enhancement: Multiple Estimate Path Search
Previous loop estimate
1
2
CO
500’
26
AWG
500’
5900’
2000’
26 AWG
24 AWG
24 AWG
3
500’
24 AWG
State
space
1
2
3
Current loop estimate
2nd discont.
……..
……..
1st discontinuity
……..
1st section gauge
……..
……..
…
Reducedstate
Viterbi
estimation
3rd discont.
UBC 2006– 48
Experimental results: EWL error
19 loops representing the variety at a CO. Loops picked so that 5%, 10%, ..., 95% of all
loops at the wire center were shorter. Loops include bridged tap, gauge change, etc.
26 Gauge Equivalent Working Length
(EWL) Estimation Error (ft)
26 Gauge Equivalent Working Length (ft)
538
634 1076 1556 3360 5086 7266 6795 8293 14921
1600
1400
1200
1000
800
600
400
200
0
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Approximate Percent of Wire Center
UBC 2006– 49
Bit Rate Estimation Error (%)
Experimental results: DSL bit rate error
35
538
Working Length (ft)
666 1076 1716 4121 5246 7650 8702 10756 15305
30
25
20
15
10
5
0
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95
Approximate Percent of Wire Center
UBC 2006– 50
G.shdsl Bit Rate (kbps)
Simulation results
2000
Different actual
pair-to-pair
crosstalk coupling
functions
1500
1000
DSM
500
Static spectrum management
0
0
200
400
600
800
1000
1200
1400
ADSL Bit Rate (kbps)
Presented at the IEEE ICC 2005 conference
UBC 2006– 51
Conclusions
 Crosstalk
 Efficient
is not random noise, we can control it
optimization algorithms need:
–
Crosstalk identification
–
Loop make-up identification
 With
optimization, bit rates increase several times
UBC 2006– 52
Back-Up Slides
UBC 2006– 53
Difference in NEXT loss between coupling lengths of 1 kft and 18 kft.
1 kft to 18 kft NEXT Loss
Difference (dB)
3.0
2.5
2.0
1.5
26-AWG
24-AWG
1.0
0.5
0.0
0
100 200 300 400 500 600 700 800 900 1000
Frequency(kHz)
UBC 2006– 54
The probability histogram of working lengths measured in the 1983
loop survey.
Probability Histogram
0.14
0.12
0.1
0.08
0.06
0.04
0.02
0
1
3
5
7
9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39
Loop Working Length (kft)
UBC 2006– 55
The probability histogram of total bridged tap lengths, measured in
the 1983 loop survey (excluding zero lengths)
Probability Histogram
0.12
0.1
0.08
0.06
0.04
0.02
0
0.1
0.5
0.9
1.3
1.7
2.1
2.5
2.9
3.3
3.7
4.1
4.5
4.9
5.3
Total Bridged Tap Length (kft)
UBC 2006– 56
Cable gauge statistics from the 1983 and the 1987-90 Bellcore loop
surveys. In the 1987-90 Bellcore loop surveys, only 0.1% of cabling
overall was 19 gauge, so 19 gauge is omitted from the table
Distance from
CO in kft (km)
% 26-gauge
% 24-gauge
% 19gauge
% 22-gauge
1983
1987-90
1983
1987-90
1983
1987-90
1983
0 (0)
72
67
22
25
6
8
0
5 (1.5)
53
53
35
34
12
13
0
10 (3.0)
30
27
51
52
18
21
1
15 (4.6)
16
4
46
62
36
34
2
20 (6.1)
2
2
34
38
60
60
4
26 (7.6)
-
2
-
7
-
90
-
30 (9.1)
0
-
10
-
69
-
21
Overall
40.4
37.8
35.6
40.4
21.3
21.7
2.7
UBC 2006– 57
Broadband Test Head prototype architecture
DC Signaling
and Off-hook
Termination
GPIB
Oscilloscope
(Tektronix
TDS 430A)
Arbitrary
Function
Generator
(NI 5411)
CH 1
Tip
CH 2
Ring
Relays
(NI 2565)
Trig
Switch
Interface
Sleeve
Ground
Custom circuitry box
(see Appendix for details)
Multimeter
(NI 4060)
PCI Bus
Controller
(PXI-8156B)
Keyboard,
Mouse, Hard
Disk, CD-ROM
LCD
Screen
PXI 1025 Mainframe
UBC 2006– 58
Schematic diagram of our differential TDR
I
P
Loop
Zo/2
Vw1
Pulse
Vdif
Generator
Zo/2
Vw2
Vcm
N

Oscilloscope
+
O
UBC 2006– 59
Measured TDR traces obtained probing a 975 m (3,200 ft) of AWG26
followed by 975 m (3,200 ft) of AWG24.
(Left) Echo response to our differential probing TDR
(Right) Echo response to conventional unbalanced probing
UBC 2006– 60
START
A
Data
Acquisition: d(t)
De-embedding:
e(i+1)(t)=d(t)-h(i)(t)
C
i = 0, BT=0
B
Hypothesize Discontinuities
via Auxiliary Topologies
{Dj(i)}
Augment T(i) with {Dj(i)}:
Tj(i) = T(i)+Dj(i)
Generate Waveforms
{Tj(i)}{hj(i)(t)}
Calculate Metrics
{Tj(i)}{j(i)}
Waveforms
Choose Topology with
Minimum Metric (eq.(19)):
T(i)=Tk(i)  h(i)(t)=hk(i)(t)
Echo exists
on e(i+1)(t)?
NO
END
YES
i=i+1
Estimate t(i) and l(i)
on e(i)(t)
Update Tk(i-1) with l(i).
IDed topology at step i:
T(i)  h(i)(t)
BT = 1
NO
B
YES
BT=1
YES
Bridged Tap?
i = i + 1, BT=0
NO
A
De-embedding:
e(i)(t)=d(t)-h(i)(t)
C
UBC 2006– 61