41
Original scientific paper
 MIDEM Society
Extraction of two wire Loop topology using 
Hybrid Single Ended Loop Testing
M. Bharathi
1
, A.Amsaveni
2
, S. Ravishankar
3
1,2
Kumaraguru College of Technology, Coimbatore, India
3
R. V . College of Engineering, Bangalore, India
Abstract: Performance of the Digital Subscriber Line (DSL) depends on the line topology and the noise power spectral density 
(PSD).  Single ended loop testing (SELT) is the preferred and economical method for identifying the loop topology. In this paper 
SELT based on a combination of Correlation Time Domain Reflectometry (CTDR) and Frequency Domain Reflectometry (FDR) is 
proposed to identify the topology of a two wire line. In CTDR, complementary codes are used to probe the line and the reflections 
are correlated with the probe signal. For lines with multiple discontinuities, a Maximum Likelihood principle is developed along with 
data de-embedding technique. The prediction accuracy of the CTDR is limited but the main advantage is, it does not need any prior 
knowledge of the loop.  To improve the accuracy of prediction, FDR with optimization algorithm is developed. This Hybrid method has 
the advantage of predicting the loop accurately without any prior knowledge of the loop. An improvement to the hybrid method to 
overcome the issues associated with the initial prediction for multiple discontinuity loops is implemented.  The proposed CTDR and 
FDR use the existing modem for probing the line which avoids the need for additional hardware. As the SELT measurements are done 
online, the effect of cross talk and AWGN is considered. The developed algorithm is tested for standard ANSI loops and the results 
shows good prediction capability of this algorithm. However, when there are more number of discontinuities, the contribution of the 
far end reflection in the received echo signal is very feeble and this limits the prediction accuracy of far end discontinuity. 
Keywords: SELT; Correlation Time Domain Reflectometry (CTDR); Frequency Domain Reflectometry (FDR); Hybrid method; 
Complementary Codes; Optimization.
Prepoznava topologije dvožičnih povezav v 
naročniški zanki s hibridno metodo testiranja na 
enem kraju
Izvleček: Učinkovitost digitalne naročniške linije (DSL) je odvisna od njene topologije in šuma moči sprektralne gostote. Za 
določevanje topologije zanke je priporočeno in ekonomično uporabiti testiranje na enem kraju (SELT). V članku je za določevanje 
topologije predlagan SELT na osnovi korelacijske reflektometrije v časovni domeni (CTDR in reklektometrije v frekvenčni domeni (FDR). 
Predlagana metodologija uporablja obstoječ modem in ne zahteva dodatne strojne opreme. SELT meritve so opravljene v živo, zato 
smo upoštevali tudi vplive presluhov in AWGN. Algoritem je testiran za standardne ANSI zanke in rezultati kažejo na njegovo dobro 
sposobnost napovedovanja. 
Ključne besede: SELT; CTDR; FDR; hibridna metodologija; komplementarne kode; optimizacija
* Corresponding Author’s e-mail: Bharathi.m.ece@kct.ac.in 
Journal of Microelectronics, 
Electronic Components and Materials
Vol. 48, No. 1(2018), 41 – 52
1 Introduction
The service provider has to estimate the Quality of Service 
(QoS) afforded over a subscriber loop under realistic cir-
cumstances. Apart from the data rate, QoS also prescribes 
the delay in the transmission (in ms), the packet loss and 
Bit Error Rate (BER). QoS is a function of subscriber line 
conditions which includes the line topology and noise 
Power Spectral Density (PSD). A double ended loop meas-
urement allow easy estimation of loop impulse response 
and the noise PSD, but needs a test device at the far end 
of the loop and is not economical prior to a service com-
mencement. An economical SELT would require a reuse 
of the network operator’s central office (CO) side DSL mo-
dem resources to perform measurements [1].

42
M. Bharathi et al; Informacije Midem, Vol. 48, No. 1(2018), 41 – 52
The physical loop consists of gauge changes, bridge 
taps and loop discontinuities that result in change of 
characteristic impedance. When a signal is injected 
through the line, reflections (echo) will be generated 
from all these discontinuities. These generated ech-
oes are analysed to extract the location and the type 
of discontinuity. S. Galli et al [2-5] have used pulse TDR 
to characterize the loop. A pulse is considered as a 
probe signal and is transmitted through the loop and 
the reflections produced by each discontinuity are 
observed in time. The time domain reflection which 
contains the signature of the loop is then analyzed to 
predict the loop topology. Clustering of the TDR trace 
[3-4] and the use of statistical data [5] are included to 
reduce the time and to increase the accuracy respec-
tively. These techniques provide a good estimation of 
the loop but are computationally intensive and can-
not be easily implemented in current DSL modems. A 
more practical method described by Carine Neus et al 
[7] uses one port scattering parameter S11 in time do-
main to estimates the loop topology. The S11 measure-
ment is however done off line with a vector network 
analyzer over the entire band width [6]. David E. Dodds 
[8, 9] has proposed FDR for identifying the loop impair-
ments. The measurement phase uses a signal genera-
tor to probe the line up to 1.3MHz in steps of 500 Hz 
and the reflections are coherently detected. However 
if there are multiple discontinuities close to each other 
(<100m), detecting all discontinuities in a single step 
is not possible. If the discontinuities are far from each 
other the order of variation of the reflection makes it 
difficult to predict all the discontinuities in a single step. 
SELT and Double Ended Loop Testing (DELT) are to-
gether employed in [10], to predict the loop topol-
ogy. In [11] Genetic Algorithm (GA) based optimization 
method is used to estimate the line topology. In this 
paper [11], S11 is measured from CO end using SELT 
probing and the transfer function (H) measured from 
both the ends using DELT are considered as inputs. An 
initial solution (topology) is assumed and multi objec-
tive optimization algorithm is used to obtain the final 
optimum solution. For both these methods additional 
equipment are needed in the measuring phase and the 
measurement cannot be done on line.
SELT estimation is performed in two phases. In meas-
urement phase the reflections are captured; termed as 
SELT – PMD function in G.SELT [12] and a second phase 
called as interpretation phase when analysis is done 
for topology estimation; termed as SELT-P function in 
G.SELT. The measurement phase of the proposed meth-
od reuses the blocks of the DSL modem and hence only 
a small code is needed that can be easily compiled into 
any modem. In this step the line is sounded sequen-
tially once by employing CTDR and next by employing 
FDR. In the interpretation phase, the first step consists 
in analyzing CTDR results to obtain an approximate es-
timation of the distance and the type of the disconti-
nuities [14, 15]. The topology learning from the CTDR 
application is used to generate an FDR data for the 
estimated loop. In the second step of the interpreta-
tion phase the generated FDR data is compared with 
a target (measured) FDR data in mean squared sense 
to arrive at an exact estimate of the loop topology. The 
analysis of measured data may be performed in the 
modem to a limited extent or offline where more com-
puting resourcesare available. 
Section 2 of this paper details the Correlation Time Do-
main Reflectometry (CTDR) for the initial loop topology 
estimation. In section 3, measurement and interpreta-
tion phase of Frequency Domain Reflectometry (FDR) 
is discussed. Section 4 gives the result of topology es-
timation of standard ANSI loops and the concluding 
remarks are drawn in section 5. 
2 Correlation time domain 
reflectometry  (CTDR) 
Reflections from each discontinuity are characterized 
by the length and type of discontinuities present in 
the loop. The possible echo paths of a line with single 
bridge tap is shown in Figure1.
Figure 1: Representation of a loop with possible echo 
paths
Spread spectrum (SS) techniques using the existing 
modem can be used for identifying the characteristics 
of the loop without scarifying the response resolution. 
In the proposed CTDR method, data is loaded in all the 
subcarriers at a time and the reflections are used for the 
estimation of the loop topology.  The Digital Subscriber 
Line (DSL) modem can work in full duplex mode. It can 
simultaneously transmit and receive data with an ad-
ditional firmware. This firmware helps in the modifica-
tion of the filter coefficients present in the front end 
of the modem. CTDR method does not need any prior 
knowledge of the loop but the accuracy of prediction 
is limited due to the variation in propagation velocity 
with frequency and the gauge of the copper medium. 
A mathematical model for the time domain echo is de-
veloped based on the two port network theory.

43
2.1 Mathematical model for Time domain Echo Signal
The proposed TDR method uses existing Discrete Multi 
Tone (DMT) modem with its bit loading algorithms. The 
received echo signal r(t) for a probe signal p(t) is given by 
 
1
) ( ) (
) (
) (
0
∑
=
+ − =
M
i
t N
i
T t
i
r
e t r  (1)
Where, 
M - number of discontinuities in the line,
N
0
(t) - noise present in the channel 
T
i
 - time of arrival of the i
th
 echo
e
r
(i)
(t) - echo generated by the i
th
 discontinuity given by 
 
) (
) (
* ) ( ) (
) (
t
i
ep
h t p t
i
r
e =   (2)
Where, 
p(t) - probe signal 
h
ep
(i)
(t) - impulse response of the i
th
 echo path. 
Complementary codes which have good autocorrela-
tion property are used as probe signals p(t) [14] and the 
received echo signal r(t) is correlated with the probe 
signal.
 ) ( ) ( ) ( t p t r t W ⊗ =    (3)
U - represents correlation operation. The signal w(t) 
contains the signature of the loop and can be used to 
estimate the loop topology.
2.2 Analysis of CTDR signal 
Correlated signal will have its peak when transmitted 
signal has completed its round trip of any discontinu-
ity. The time difference between the peaks and the 
propagation speed of the (n ) medium are used to esti-
mate the distance of the discontinuity. Complementary 
codes are used as probe signal [14, 15]. With comple-
mentary codes, the correlated signal is 2N times strong-
er and the noise is build up by a factor  
N 2
. Thus SNR 
improvement with complementary code CTDR to di-
rect impulse probe scheme is 
 
N 2 . To further reduce 
the effect of AWGN noise, averaging over number of 
symbols is performed. Noise reduction by averaging 
technique and the use of complementary codes im-
proves the overall SNR significantly.
The attenuation and reflections in the loop reduces the 
strength of the reflected signal from each discontinuity 
and the peaks from distant discontinuities are not clear 
in the correlated signal. To overcome this limitation, 
Maximum Likelihood (ML) principle [14] with data de-
embedding is incorporated. ML principle is employed 
to identify the nature and type of discontinuity one af-
ter the other. Data de-embedding process masks the 
reflections of the identified discontinuity in the overall 
echo signal to unravel the signatures of the unknown 
discontinuities. Thus by incorporating the de-embed-
ding process, overall predictability of the CDTR method 
is enhanced. This improved CTDR method illustrated in 
Figure 2 has the following steps:
1. Estimate the i
th
 discontinuity location from the 
peak position of W(t) (equation 3).
2. Hypothesize discontinuity by considering all the 
possible topologies. 
 
{}
) (i
j
T
 
is the set of all pos-
sible topologies at step i and j = 1,2…N, N is the 
number of possible topologies based on the mag-
nitude of the reflection coefficient. Each possible 
topology consists of the previously identified line 
segments and the hypothesized discontinuity fol-
lowed by an infinite loop section. The unknown 
segment of the loop after the hypothesized dis-
continuity is represented by an infinite loop sec-
tion so as to eliminate any reflection from the un-
known section.
3. Simulate echo for all the possible topologies. 
 
{} ) (
) (
t h
i
j
 is the simulated echo signal for each of 
the topologies in 
 
{}
) (i
j
T , at step i.
4. Generate the error vector e
j
(i)
 in the localized time 
interval t
1
 to t
2
, corresponding to the hypothe-
sized topologies 
 
{}
) (i
j
T at step i. 
 
) ( ) (
2
1
) ( ) (
∑
− =
t
t
i
j
i
j
t h t r e                  (4)
5. Choose the maximum likelihood topology by 
comparing the calculated error (e). The corre-
sponding simulated signal is considered as h
(i)
(t) 
and the topology is T
(i)
. 
6. If the selected topology is bridge tap, set BT=1and 
continue.
7. The de-embedded signal after the removal of i
th 
discontinuity is d
(i+1)
(t) = r(t) – h
(i)
(t).
8. Generate the corresponding correlated signal 
w
(i+1)
(t) 
9. If there is no peak in w
(i+1)
(t) then the hypothe-
sized topology T
(i)
 is the estimated topology. Else 
continue.
10. i=i+1.
11. Estimate i
th
 discontinuity location from the peak 
position of w
(i)
(t).
12. If BT=1 generate T
(i)
 by including a bridge tap with 
T
(i-1
) and continue. Else go to step 2.
13. Generate corresponding h
(i)
.
14. De-embedding: d
(i+1)
(t) = r(t) – h
(i)
(t) 
15. Set BT=0;
16. Go to step 8.
M. Bharathi et al; Informacije Midem, Vol. 48, No. 1(2018), 41 – 52

44
3 Frequency domain reflectometry (FDR)
A FDR measurement method is based on single tone 
excitation. Each tone in a DMT symbol is sounded in-
dividually and its echoes are captured using the DSL 
Modem. As explained above, additional firmware at 
the modem helps to extract the reflections. The total 
received echo signal is the sum of echo signals of indi-
vidual tones and is used in the analysis phase to predict 
the loop topology. The mathematical model for the 
echo signals in frequency domain is developed and is 
used in the optimization algorithm.  
3.1 Mathematical model for FDR
The received echo signal for the n
th
 tone along with the 
effect of noise is given by,
 
() ) ( ) ( (
1
) (
) ∑
=
+ =
M
i
n o n
i
n
f N f R f R
  (5)
Where,
M
-  number of echo paths in the loop
N
0
(f
n
) -  noise in the echo signal. 
R
(i)
(f
n
) 
- received signal from the i
th
 echo path when n
th
 
tone is sounded given by,
 
) ( ) ( ) (
) ( ) (
f Hecho f S f R
i
n n
i
=   (6)
Where,
S(f
n
) - spectrum of the transmitted data (Energy only in 
the n
th
 bin)  
Hecho
(i)
(f) - transfer function of the i
th
 echo path given 
by,
Figure 2: Step by step Maximum Likelihood approach with De-embedding
M. Bharathi et al; Informacije Midem, Vol. 48, No. 1(2018), 41 – 52

45
 
) ( ) ( ) , , ( ) (
) ( ) ( ) 1 ( ) 2 ( ) 1 ( ) (
f f H F f Hecho
i i i i
ρ τ τ τ
−
= … (7)
Here 
 
) , , (
) 1 ( ) 2 ( ) 1 ( − i
F τ τ τ  is a frequency dependent 
function that includes the transmission coefficients of 
all the discontinuities preceding the i
th
 discontinuity 
and  r (i)
(f) is the reflection coefficient of the i
th
 disconti-
nuity. H
(i)
(f) is the line transfer function  [13,14].
 
) (
) ( Li i
e f H
γ −
=
     (8)
Where, 
Li - length of the i
th
 echo path.
γ - Propagation constant which is a function of frequen-
cy, given by 
 
) )( ( C j G L j R ω ω γ + + =
The total received echo signal is sum of echo signals for 
all the transmitted tones.
 
∑ =
n
n
f R f R ) ( ) (
    (9)
R(f)is the received echo signal from all discontinuities as 
seen at the receiver FFT output and contains information 
about these discontinuities. The frequency range of the 
input signal determines the predictable range and reso-
lution of the FDR method.  The minimum measurable 
distance (resolution) increases with range of frequency 
as higher range will have complete periodic information 
even for a shorter length.  Amplitude of the echo signal 
depends on the attenuation in the line and attenuation 
is doubled due to the round trip travel along the loop. 
The lower tones (low frequency tones) suffer less attenu-
ation compared to the higher tones and are essential for 
longer loops. Thus there is a need to balance the con-
trasting requirement between reach and resolution. 
The initial topology estimated by CTDR method is used 
as a guess topology and optimization is carried out 
based on the guess topology.
3.2 Optimization method
The steps involved in this algorithm are
Simulate FDR echo signal for the initial topology (F ) es-
timated using Correlation Time Domain Reflectometry 
 
) , (
ˆ
n
f RΦ , using equation (5).
Obtain the FDR echo signal R(f
n
) from measurements.
Calculate the cost function (MSE)
 
) ( ) , (
ˆ
2
1








− Φ =
∑
=
N
n
n n
f R f R MSE                (10)
Obtain the accurate line topology by minimizing the 
cost function using Nelder-Mead simplex optimization 
algorithm.
Nelder-Mead optimization algorithm [16] iteratively 
improves Ф in terms of line segment lengths until the 
best solution (close match) is found. 
4 Simulation results
The developed Hybrid method is used for the predic-
tion of the ANSI standard telephone lines [13] shown 
in Figure 3. The parameters used for the simulation of 
CTDR and FDR are tabulated in Table.1.
Test loops 1 to 5 are plain lines with different lengths 
and gauge. End of line is the only discontinuity and it is 
considered as an open termination with reflection co-
efficient is 1 and the correlated signal will have a posi-
tive peak. FDR signal for a plain line will be a decaying 
sinusoidal wave satisfying the equation [18,19]
 
) cos( ) exp( ) (
4 3 2 1
a f a f a a f R + − =                (11)
Where, a1, a2, a3and a4 depend on the gauge, length 
and the termination. 
Table 1: Parameters used for Simulation
Parameters Values in CTDR Values in FDR
Total transmitted power
21dBm as specified in DSL 
standard [13]
-36.5dBm/Hz as per PSD mask specified in 
DSL standard[13]
No of bits per tone 2 bits, 4QAM 2 bits, 4QAM
Tone considered 6 - 511 6 – 110 (One tone at a time)
Crosstalk noise [13] 24 ADSL NEXT and FEXT 24 ADSL NEXT and FEXT 
AWGN PSD -130 dBm/Hz -130 dBm/Hz
Velocity of Propagation (VoP) 0.63 C (C- speed of light) --
Number of frames 10000 --
M. Bharathi et al; Informacije Midem, Vol. 48, No. 1(2018), 41 – 52

46
The waveforms and the analysis of plain line are ex-
plained with test loop 2 which is a medium reach (1.83 
Km, 24 AWG) with open end. For this loop, the variation 
of correlation amplitude with reach is shown in Figure 
4.  The peak value of the signal is positive (0.002398) at 
a distance 1.80 Km. 
Figure 4: Correlation amplitude Vs distance for test 
loop2
The possible topologies with the above prediction 
(1.80 Km, open end) and calculated error (e) are tabu-
lated in Table 2, from which the line is understood as 
1.80 Km of 24 AWG. 
Table 2: Possible topologies for Test loop 2
Sl. 
No
Hypothesized 
discontinuity
possible topology
MSE
1 End of loop 
(open)
1.80  Km line, 26 AWG
2.40e-3
2 End of loop 
(open)
1.80 Km line, 24 AWG
8.35e-5
The frequency domain received echo signal for this 
loop (Test loop 2) is shown in Figure 5. The FDR is a de-
caying sinusoidal waveform.
With the initial guess of 1.80 Km, 24AWG (Predicted 
using CTDR), the optimization algorithm is used and 
Figure 6 shows the variation of mean square error with 
the line length for both gauges and the line is predicted 
as 1.83 Km, 24 AWG line. 
Figure 3: TEST loops
M. Bharathi et al; Informacije Midem, Vol. 48, No. 1(2018), 41 – 52

47
Figure 6: Error curve for test loop2
Test Loops 7 to 11 are loops with one or more dis-
continuities. For lines with multiple discontinuities, 
depends on the type of discontinuity and its length, 
the dominant portion of the received signal varies. 
Following are the observations made with different 
discontinuities. 
The influence of the gauge change in the final signal is 
much lesser due to its low reflection coefficient of ~ -0.03. 
The reflection coefficient at the bridge tap is ~ -0.3. 
Hence the influence of the received signal from the 
bridge tap is predominant. 
When the numbers of discontinuities are higher than 
two, the reflection from the later segments of the loop 
is not felt in the overall received signal and these seg-
ments are not predicted with good accuracy. 
In summary, the magnitudes of transmission and re-
flection coefficients of different discontinuities are 
tabulated in Table 3 [2]. 
The analysis of lines with multiple discontinuities is ex-
plained with test loop 11. Figure 7 shows the correlated 
signal amplitude with distance for test loop 11. Nega-
tive peak with amplitude 3.19e-6 at 2.88 Km indicates 
negative reflection coefficient and gauge change or 
bridge taps are the possible topologies.
Figure 7: Correlation amplitude Vs distance for test 
loop 11
All the possible topologies with this observation and 
the mean square error (e) between the simulated ech-
oes for these possible topologies with the received 
echo are listed in Table 4. From this table, topology with 
gauge change (S No1) is identified as the correct topol-
ogy till first discontinuity (T
(1)
). 
The echo due to the identified first segment is removed 
from the received echo. Figure 8(a) shows the de-
embedded signal w
(2)
(t) after removing the reflection 
from identified topology (T
(1)
).  Negative reflection at 
3.49 Km is inferred as bridge tap and the length of the 
second line segment is 0.7Km (3.58Km- 2.88 Km).  Con-
struction of all possible topologies (including the iden-
tified topology segments) is listed in Table 5. The MSE 
helps in identifying the gauge of the line segments. 
With identifying the tap as 26 AWG, w
(3)
(t) is generated 
and the length of the bridge tap is estimated as 0.18Km 
(3.76Km – 3.58 Km). De-embedding the echo based 
on the identified loop segments results in w
(4)
(t) from 
which the third segment of loop is estimated as 0.61Km 
(4.19 Km-3.58 Km) with open end. In w
(5)
(t) there are no 
peaks visible and CTDR estimated topology is shown 
in Figure 8(d). The de-embedding process is shown in 
Figure 8(a-c). 
Figure 5: Frequency Domain Reflectometry signal for 
test loop2
Table 3: Magnitude of Transmission and Reflection co-
efficients of different discontinuities
Sl. No. Type of 
Discontinuity
Reflection 
Coefficient
Transmission 
Coefficient
1. Gauge Change 0.03 0.97
2. Bridge Tap 0.33 0.33* 
3. End of Loop
(Open)
1 0
* one wave will travel along the BT and other wave will 
travel along the next loop section
M. Bharathi et al; Informacije Midem, Vol. 48, No. 1(2018), 41 – 52

48
The CTDR estimation for test loop11 is not complete. 
This is due to the very less contribution of the far end 
reflection in the overall received signal. With this as 
the initial guess, FDR prediction converged to MSE er-
ror of 0.0028. For lines with more discontinuities, the 
CTDR prediction of the number of discontinuities may 
not be complete. As the FDR step in the hybrid method 
focuses only on the accuracy of the segment lengths, 
there is no possibility of correct prediction if the initial 
guess is incomplete in the number of discontinuities. 
This limitation is found to be serious for complex to-
pologies. The hybrid method is improved to address 
this issue by adding a discontinuity in the initial guess 
from CTDR step when the MSE error after global search 
is higher than the set threshold value. This additional 
modification is shown in Figure 9. As the CTDR is ca-
pable of predicting first two discontinuities and from 
practical understanding the maximum number of dis-
continuities is not more than 4, this outer loop is set 
with a maximum limit of two.  
This issue of non convergence for test loop 11 with FDR 
is due to wrong specification of number of discontinui-
ties as the initial guess. The improved hybrid method 
is employed. The converged line topology with im-
proved hybrid method is shown in Figure 10.
Table 4: Possible topologies for first discontinuity (Test loop 11)
Sl.  No Hypothesized discontinuity Possible topology 
(dotted line indicates infinite length)
MSE
1 Gauge change 
 
2.88Km
26 AWG 24 AWG
1.05e-6
2 Bridge tap (Taps with Open end)
 
2.88 Km
26 AWG 26 AWG
26AWG
1.11e-5
3 Bridge tap (Taps with Open end)
 
2.88Km
26 AWG 26 AWG
24 AWG
1.25e-5
4 Bridge tap (Taps with Open end)
 
2.88 Km
24 AWG 24 AWG
24 AWG
1.11e-4
5 Bridge tap (Taps with Open end)
 
2.88 Km
24 AWG 24 AWG
26 AWG
1.03e-4
Table 5: Possible topologies at second discontinuity for test loop 11
Sl. No Hypothesized discontinuity possible topology 
(dotted line indicates infinite length)
MSE
1 Gauge change followed by bridge 
tap(Taps with Open end)
 
2.88Km
26 AWG 24 AWG
0.7Km
24 AWG
26 AWG
4.04e-6
2 Gauge change followed by bridge tap 
(Taps with Open end)
 
2.88Km
26 AWG 24 AWG
0.7Km
24 AWG
24 AWG
4.40e-6
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49
Figure 8: De-embedded signal for test loop 11 
Figure 9: Improved Hybrid method
Figure 10: The convergence for test loop 11
Figure 11: Reflection analysis of test loop 11
The summary of results for all the test loops is present-
ed in Table 6.
The variance in Table 6 is very small which indicates 
that the same optimum topology was obtained with re-
peated trails.  The estimation error is less in the case of 
plain loops and loops with one or more discontinuities. 
For test loop 11, the first two line segments and the first 
bridge tap length are predicted with good accuracy 
but the segment 3, 4 and tap2 length are not accurate. 
Figure 11 shows the schematic representation of 
the reflection from each discontinuity. Strength of 
the reflection from each junction is calculated based 
on the reflection and transmission coefficients for 
comparison. Table 7 compares the % contribution of 
each reflection in the received echo signal as per the 
transmission and reflection coefficients listed in Table 
3. Signal attenuation and gauge are not considered in 
this calculation as the focus is to quantify the effect of 
M. Bharathi et al; Informacije Midem, Vol. 48, No. 1(2018), 41 – 52

50
individual reflections on the final echo. Around 89% of 
the received echo is contributed by the reflections R1, 
R2 and R3. Even though R4 reflection is considered as 
6 %, due to the higher distance of travel, attenuation 
will be higher and hence net overall contribution in the 
received signal will be much lesser than 6%. R5 and R6 
have 2% weightage in the received signal even without 
considering the attenuation effect. This results in very 
feeble contribution in the measured echo. Hence 
accuracy of these line segments, in the predicted 
topology does not influence MSE to a significant level. 
This explains the reason for higher prediction error in 
the segments 3, 4 and Tap 2.   
Analyses are conducted to study the improvement in 
prediction ability with increase in the strength of the 
probe signal PSD (by 3 and 6 dBm/Hz). As shown in 
Table 6: Summary of results using Hybrid method for Telephone Lines 
Test Loop Actual Loop
 Topology (Km)
Initial Estimate 
using CTDR 
(Km) 
% error Estimated 
Topology Using 
CTDR and FDR 
(Km)
% error % Variance 
in the 
estimation
Test Loop1 0.91, 26 AWG 0.94, 26 AWG 3.33 0.91, 26 AWG -- 0
Test Loop2 1.83, 24 AWG 1.80, 24 AWG 1.16 1.83, 24 AWG -- 0
Test Loop3 3.66, 26 AWG 3.87, 26 AWG 5.73 3.66, 26 AWG -- 0
Test Loop4 0.03, 26 AWG -- -- 0.03, 26 AWG -- 0
Test Loop5 4.11,  26 AWG -- -- 4.11, 26 AWG -- 0
Test Loop6 Segment1 – 2.74, 26 AWG 2.75, 26 AWG 4.06 2.74, 26 AWG 0.25 0.04
Segment 2 -1.22, 24 AWG 1.38, 24 AWG 1.21, 24 AWG
Test Loop7 Segment1- 5.03, 26 AWG -- -- 5.01, 26 AWG 0.55 0.3
Segment 2- 0.46, 24 AWG -- 0.45, 24 AWG
Test Loop8 Segment 1 -0.91, 26 AWG 0.94, 26 AWG 4.1 0.91, 26 AWG -- 0.1
Bridge tap-0.15, 26 AWG* 0.17, 26 AWG* 0.15, 26 AWG*
Segment 2- 1.83, 26 AWG 1.90, 26 AWG 1.83, 26 AWG
Test Loop9 Segment 1- 2.74, 26 AWG 2.84, 26 AWG 6.3 2.74, 26 AWG 0.24 0.1
Segment2 -0.61, 24 AWG 0.57, 24 AWG 0.61, 24 AWG
Bridge tap-0.15, 26 AWG* 0.18, 26 AWG* 0.15, 26 AWG*
Segment 3-0.61, 24 AWG 0.70, 24 AWG 0.60, 24 AWG
Test Loop10 Segment 1 - 0.17, 26 AWG 0.18, 26 AWG 7.3 0.17, 26 AWG 0.27 0.2
Bridge tap 1 - 0.12, 26 AWG* 0.08, 26 AWG* 0.12, 26 AWG*
Segment 2- 1.90, 26 AWG 2.01, 26 AWG 1.90, 26 AWG
Bridge tap 2 - 0.24, 26 AWG* 0.26, 26 AWG* 0.24, 26 AWG*
Segment 3  -1.22, 26 AWG 1.31, 26 AWG 1.21, 26 AWG
Test Loop11 Segment 1 – 2.74, 26 AWG 2.88, 26 AWG -- 2.74, 26 AWG 3.06 1.2
Segment 2 – 0.61, 24 AWG 0.7, 24 AWG 0.60, 24 AWG
Bridge tap 1 – 0.46, 26 AWG* 0.18, 26 AWG* 0.44, 26 AWG*
Segment 3- 0.15, 24 AWG 0.61, 24 AWG 0.22, 24 AWG
Bridge tap 2 – 0.46, 26 AWG* -- 0.43, 26 AWG*
Segment 3  -0.15, 24 AWG -- 0.14, 24 AWG
*Indicates Bridge Tap
Table 8, prediction ability improved with these cases. 
However, it must be noted that as per ITU standards 
[13], signal strength increase beyond 3 dBm/Hz is not 
recommended as it induces crosstalk noise in other 
lines. So the allowed strength of the probe signal is 
-33.3 dBm/Hz.
5 Conclusion
The combined CTDR and FDR method is developed for 
the extraction of loop topology of two wire telephone 
lines. CTDR can be employed where there is no initial 
knowledge of the loop. But the accuracy of CTDR esti-
mation is limited.  On the other hand, FDR method can 
predict the topology with higher accuracy but requires 
a reasonable initial knowledge of the topology. The pro-
M. Bharathi et al; Informacije Midem, Vol. 48, No. 1(2018), 41 – 52

51
posed improved hybrid algorithm combines the advan-
tage of both the methods and accurately estimates the 
loop topology without any initial knowledge about the 
loop. Maximum Likelihood procedure with de-embed-
ding is used in this paper to mask the strong reflections 
after identifying the discontinuities. This helps in esti-
mating the far end discontinuities which has minimum 
contribution in the overall reflected signal. Simulation 
results of standard ANSI loops shows that the error in 
the prediction is less than 0.3% for lines with one or two 
discontinuities. For lines with more number of discon-
tinuities the prediction accuracy is around 3% due to 
the feeble contribution of far end reflections in the re-
ceived signal.  This proposed method has the significant 
advantage in the measurement phase as measurement 
can be directly implemented on the DSL modem with 
a minimal additional firmware. The interpretation of the 
measured data can be carried out either online or offline.
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Table 7: Reflection strength contribution (test loop11)
Reflection
Weightage of transmission and Reflection coefficients in the received signal (Excluding the 
attenuation effect)
Sequence of  approximate reflection and 
transmission coefficients
Total
% contribution in the received signal  
(Ri/∑Ri)
R1 0.03 0.03 6.0
R2 0.97*0.33*0.97 0.3104 62.2
R3 0.97*0.33*1*0.33*0.97 0.1024 20.52
R4 0.97 *0.33*0.33*0.33*0.97 0.0338 6.7
R5 0.97*0.33*0.33*1*0.33*0.33*0.97 0.0112 2.2
R6 0.97*0.33*0.33*1*0.33*0.33*0.97 0.0112 2.2
 ∑Ri 0.499  
Table 8: Test loop 11 prediction summary with increased power
  Actual 
length (Km)
Predicted length 
with 
-36.5 dBm/Hz(Km)
Predicted length with
 -33.3 dBm/Hz(Km)
Predicted length with
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Segment 3  (R4) 0.15 0.28 0.22 0.17
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Segment 4 (R6) 0.15 0.35 0.14 0.16
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Arrived: 16. 09. 2017
Accepted: 08. 03. 2018
M. Bharathi et al; Informacije Midem, Vol. 48, No. 1(2018), 41 – 52