Note: Descriptions are shown in the official language in which they were submitted.
CA 02369858 2005-03-21
SINGLE ENDED MEASUREMENT METHOD AND SYSTEM FOR
DETERMINING SUBSCRIBER LOOP MAKE UP
FIELD OF THE INVENTION
The present invention generally relates to determining the make-up of
subscriber
loops in the public switched network and more specifically to methods and
systems that
determine the make-up of subscriber loops via single ended measurements.
BACKGROUND
The mainstay of the telephone company local network is the local subscriber
loop. The great majority of residential customers, and many business
customers,
are served by metallic twisted pair cables connected from a local switch in
the
central office to the subscriber's telephones. When customers request service,
request a change in service, or drop service, these facilities must be
appropriately
connected or arranged in the field, referred to as the "outside plant," and
telephone
companies have specifically trained craft dedicated full time to this task.
Obviously a
1 S company needs to have an understanding of its subscriber loops including
where they are
connected and the location of the flexibility points such as junction boxes,
etc. These
records historically were kept on paper, called "plats," and more recently are
manually entered into a computer database. However, even when entered
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into a database there are still problems associated with keeping the records
accurate and up-
to-date.
Having accurate records of the loop plant is critically important to many
aspects of a
telephone company's business. In addition to the need for accurate records to
provide
traditional voice services, there will be a need for even more accurate and
more detailed
records in order to deploy a whole new class of "xDSL" based services,
including those
based on integrated services digital network (ISDN), high-rate digital
subscriber line
(HDSL), asymmetrical digital subscriber lines (ADSL) and very high rate
digital subscriber
lines (VDSL) technology. These technologies are engineered to operate over a
class of
subscriber loops, such as nonloaded loops (18 kft), or Carrier Serving Area
(CSA) loops (9
to 12 kft). In fact, the need to be able to "qualify" a loop for provision of
one of these
technologies is becoming critical, as the technologies emerge and deployment
begins. The
ability to easily and accurately qualify loops will allow telephone companies
to offer a whole
range of new services; problems and high expenses associated with qualifying
loops can
potentially inhibit deployment and/or lower or forego associated new revenues.
The
unscreened multipair cables in the existing subscriber loop network constitute
the main
access connection of telephone users to the telephone network. Recently, the
demand for
new services such as data, image and video has increased tremendously, and
telephone
companies have planned to deliver broadband ISDN services via fiber optic
local loops.
However, the deployment of fiber optic cables in the access plant will require
at least twenty
years, so that, in the meantime, it is extremely important to fully exploit
the existing copper
cable plant.
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Although there are many different digital subscriber line services, for
example, ISDN
basic access, HDSL, ADSL, VDSL, and Synchronous DSL (SDSL), these services are
not
always available to every customer since copper lines seem to present more
problems
than expected. In fact, the cable length and the presence of load coils and
bridged taps may
deeply affect the performance of DSL services. Unfortunately, loop records are
unreliable
and often don't match the actual loop configuration, so that the existing
databases cannot be
fully exploited.
Loop prequalification is an important issue not only because it can help an
economic
deployment of DSL services, but also because it can help telephone companies
in updating
and correcting their loop-plant records. From this point of view, the
feasibility of accurate
loop make-up identification would have a much higher economic value than
simple DSL
qualificati on.
One way to obtain accurate loop records is to manually examine the existing
records
and update them if they are nussing or inaccurate. This technique is expensive
and time
consuming. Furthermore, new technologies such as xDSL require additional
information that
was previously not kept for voice services, so, there is the potential that
new information
needs to be added to all existing loop records. Test set manufacturers offer
measurement
devices that can greatly facilitate this process, but typically they require a
remote craft
dispatch.
Another way to obtain accurate loop records is by performing a loop
prequalification
test. There are essentially two ways of carrying out a loop prequalification
test: double
ended or single-ended measurements. Double-ended measurements allow us to
easily
estimate the impulse response of a loop by using properly designed training
sequences.
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Double-ended testing, however, requires equipment at both ends of the loop.
Specifically, in addition to equipment at the Central Office (CO) or near end
of the loop,
double-ended testing involves either the presence of a test device at the far
end of the loop
(Smart Jack or MTU), or dispatching a technician to the subscriber's location
(SL) to
install a modem that communicates with the reference modem in the CO. An
exemplary
double-ended system and method that extrapolates voice band information to
determine
DSL service capability for a subscriber loop is described in Lechleider, et
al., Canadian
Patent No. 2,328,216, issued December 2, 2003, entitled "Method and System for
Estimating the Ability of a Subscriber Loop to Support Broadband Services".
In contrast, single ended tests are less expensive and time consuming than
double-ended tests. Furthermore, single-ended testing requires test-equipment
only at the
CO. In fact, no technician dispatching is required and the CO can perform all
the tests in
a batch mode, exploiting the metallic access with full-splitting capability on
the
customer's line. An example of such a single-ended test system is the "MLT"
(Mechanized Loop Testing) product that is included as part of the widely
deployed
automated loop testing system originally developed by the Bell System. The MLT
system utilizes a metallic test bus and full-splitting metallic access relays
on line card
electronics. By this means, a given subscriber loop can be taken out of
service and
routed, metallically, to a centralized test head, where single-ended
measurements can be
made on the customer's loop. The test head runs through a battery of tests
aimed at
maintaining and diagnosing the customer's narrowband (4kHz) voice service,
e.g.,
looking for valid termination signatures via application of DC and AC
voltages. This
system is highly mechanized, highly efficient, and almost universally
deployed. In
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addition, the MLT system is linked to a Line Monitoring Operating System
(LMOS)
thereby providing a means to access and update loop records which are useful
in
responding to customer service requests or complaints. However, because this
system
exclusively focuses on narrowband voice services, the system misses important
loop
make-up features that will be deleterious to supporting broadband services via
DSL
technologies.
Another well known single-ended measurement technique relies on the
observation of echoes that are produced by medium discontinuities to fully
characterize
the link. Specifically, these single-ended measurements typically rely on time
domain
reflectometry (TDR). TDR measurements are analogous to radar measurements in
terms
of the physical principles at work. TDR test systems transmit pulses of energy
down the
metallic cable being investigated and once these pulses encounter a
discontinuity on the
cable a portion of the transmitted energy is reflected or echoed back to a
receiver on the
test system. The elapsed time of arrival of the echo pulse determines its
location, while
the shape and polarity of the echo pulses) provide a signature identifying the
type of
discontinuity that caused the reflection or echo. Basically, if the reflecting
discontinuity
causes an increase in impedance, the echo pulse's polarity is positive; if the
reflecting
discontinuity causes a decrease in impedance, the echo pulse's polarity is
negative. A
bridged tap, for example, produces a negative echo at the location of the tap
and a
positive echo at the end of the bridged tap. Accordingly, a trained
craftsperson is able to
determine the type of fault based on the shape, polarity and sequence of
pulses.
Nevertheless, TDR methods (or, in general, single-ended measurements that rely
on echo pulse signatures) are inaccurate and provide ambiguous results that
even the most
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skilled craftsperson cannot interpret. Because the arrival of the echoes is
dependent on
the location of the discontinuities (or faults) one echo can be masked by
another echo if
the echoes overlap. For example, FIG. lA illustrates an exemplary loop having
three
discontinuities, two of which are bridged taps 500 feet apart. In accordance
with TDR
methods, a pulse 10 is sent from CO 13 to subscriber location 15 on the
subscriber loop
having loop segments 20, 22, 24 and 26. As the pulse traverses the loop it
encounters a
gauge change 30, a first bridged tap 32, and a second bridged tap 34 before
arriving at
SL 15. FIG. 1B depicts the echo response caused by the bridged taps 32 and 34
(the
echoes generated at the gauge change 30 and SL 1 S were filtered from FIG. 1
B). As
FIG. 1B shows it is not possible to detect the two bridged taps via prior art
TDR methods.
In fact, looking at FIG. 1 B, it appears as if only one bridged tap 32 is
present since there
is only one negative 70 - positive 80 transition. However, since the positive
echo 80 is
not weaker than the negative one 70 (as it usually is for bridged taps) it may
be induced
that either the bridged tap is very short or several bridged taps are present.
However,
since the width of the positive echo 70 looks quite large it is very unlikely
that it was a
short bridged tap since a short bridged tap would introduce a small amount of
distortion
and, consequently, a narrower pulse. Therefore, the case of several bridged
taps may be
the most probable, although we cannot say how many there are. As such, TDR
methods
can produce ambiguous results
In addition, prior art TDR methods do not take into account, more
specifically, are
unable to isolate, the effects of spurious echoes. That is, and with reference
to FIG. 1 A,
as pulse 10 arrives at gauge change 30, a portion of pulse 10 is reflected to
generate a first
real echo, and the remaining portion (or refracted portion) travels toward
bridged tap 32.
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At bridged tap 32, reflection and refraction again occur in the process
producing a second
real echo. This second echo pulse (travelling upstream to CO 13) is then
reflected at
gauge change 30 back to bridged tap 32 where a spurious echo pulse is then
reflected to
the CO 13. Although spurious echoes will be more attenuated than real echoes,
they are
added to the real echoes causing the real echo signals between to be
distorted.
Accordingly, spurious echoes enhance the ambiguity inherent in TDR
measurements
because the shape of the echo is used to interpret the type of fault that
caused the echo. In
other words, a craft person interpreting a TDR measurement analyzes a
distorted trace
that does not distinguish spurious echo distortion. More importantly, the
effects of
spurious echoes on the pulse shape cannot be interpreted via human visual
inspection.
Of utility then is a method and system for unambiguously and completely
determining a subscriber loop make-up including detecting the presence and
location of
load coils, gauge changes, and bridged taps and the length of the loop
including the length
of each bridged tap.
SUMMARY
Our invention is a method and system for unambiguously and completely
determining a subscriber loop make-up.
In accordance with one aspect of the present invention there is provided a
method
for determining make-up of a subscriber loop in a communication system, said
make-up
including presence or absence and location of one or more of gauge changes,
bridged
taps, length of the loop including length of each bridged tap, and gauge of
each loop
section, said method comprising the steps of: repetitively applying signals to
the
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subscriber loop to obtain echoes from the subscriber loop; receiving the
echoes based on
said applied signals, said echoes being caused by discontinuities on the
subscriber loop;
and using a mathematical model contained in a processor, determining the make-
up of
the loop based on the received echoes from said repetitively applied signals
by using a
function in the time domain based on said mathematical model separately for
each loop
section that causes an echo.
In accordance with another aspect of the present invention there is provided a
system for determining make-up of a subscriber loop, said make-up including
the
presence or absence and location of one or more of gauge changes and bridged
taps,
length of the loop including the length of each bridged tap, and gauge of each
loop
section; said system comprising: a broadband test head device for repetitively
applying
signals to the subscriber loop to obtain echoes received from the subscriber
loop; access
circuitry connecting said broadband test head device to the subscriber loop;
and a
processor connected to said broadband test head device, said processor
performing the
steps of estimating the arrival time of two successive echoes received from
the
subscriber loop when a signal is applied to said loop through said access
circuitry; and
using a mathematical model determining the make-up of the loop based on the
received
echoes from the repetitively applied signals.
In accordance with yet another aspect of the present invention there is
provided a
system for determining make-up of a subscriber loop, said make-up including
the
presence or absence and location of one or more of gauge changes and bridged
taps, the
length of the loop including the length of each bridged tap, and the gauge of
each loop
section, said system comprising: a transmitter for repetitively applying
broadband signals
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to the subscriber loop; a receiver for receiving echoes from sections of the
subscriber
loop, said echoes being caused by discontinuities on the subscriber loop; and
a processor
containing a mathematical model for determining the make-up of the subscriber
loop
based on the received echoes from the repetitively applied signals, said
processor
computing functions for the discontinuities of the loop sequentially.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. lA depicts an exemplary subscriber loop being tested by time domain
reflectometry;
FIG.1B depicts the echo responses from the bridged taps of FIG. lA;
FIG. 2A depicts an illustrative embodiment of our broadband test head system
for
determining a subscriber loop make-up in accordance with our invention;
FIG. 2B illustratively depicts another illustrative embodiment of a broadband
test
head in accordance with the present invention;
FIG. 3 illustratively depicts an exemplary subscriber loop having a gauge
change
(labeled A) and a subsequent discontinuity (labeled B) present in the loop;
FIG. 4A illustratively depicts an exemplary subscriber loop having a gauge
change in the loop;
FIG. 4B shows the real and spurious echoes produced by the discontinuity
present
in the loop shown in FIG. 4A;
FIG. S depicts an exemplary subscriber loop having a bridged tap (labeled A)
and
a subsequent discontinuity (labeled C) present in the loop;
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FIG. 6A illustratively depicts an exemplary subscriber loop having a bridged
tap in
the loop;
FIG. 6B illustrates a simulation of the real echoes and spurious echoes for
the loop
configuration in FIG. 6A;
FIG. 7A illustrates the method steps of our invention;
FIG. 7B illustrates the substeps of step 710 of FIG. 7A;
FIG. 7C illustrates the substeps of step 730 of FIG. 7A;
FIG. 8A depicts an exemplary loop used to demonstrate the advantages of our
invention;
FIG. 8B illustrates a simulation of the echoes generated by the loop of FIG.
8A with
the real echoes and spurious echoes shown on separate curves;
FIG. 8C illustrates a simulation of the echoes generated by the loop of FIG.
8A with
the real echoes and spurious echoes shown on the same curve;
FIG. 9A illustrates a simulation of the effects of filtering the echo signals
with an
inverse filter in accordance with our invention for the loop of FIG. 8A (the
inverse filter
includes the transfer function of the section of the loop from the CO 13 to
gauge change
805);
FIG. 9B illustrates a simulation of the effects of filtering the echo signals
with an
inverse filter in accordance with our invention for the loop of FIG. 8A (the
inverse filter
includes the transfer function of the sections of the loop from the CO 13 to
bridged tap 807);
FIG. l0A illustrates an experimental setup used to verify our inventive
method;
FIG. lOB illustrates the loop used in the setup of FIG. 10A;
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FIG. lOC depicts the echoes generated by the loop of FIG. lOB on the scope of
FIG.
10A; and
FIG. lOD depicts our simulation of the echoes generated by the loop of FIG.
lOB.
DETAILED DESCRIPTION
_l. System and Broadband Test Head
Turning now to FIG. 2A, there is depicted a system for determining a
subscriber loop
make-up in accordance with an embodiment of our invention. It should be noted
that our
invention is the unambiguous determination of a loop make-up autonomously,
e.g., without
the aid of any human intervention. There may be more than one embodiment of a
system
including our invention. Specifically, FIG. 2A is our invention in a
distributed architecture
wherein the functions necessary to implement our broadband test head inventive
concept is
distributed over a network having functional elements at different locations.
FIG. 2B is our
invention in a non-distributed architecture wherein broadband test head
functionality is done
at the same location, preferably, on the same equipment.
In accordance with the embodiment depicted in FIG. 2A, a broadband test head
device 210 is selectively coupled through access module 211 by switch 215 to
subscriber
loop 220. Switch 215 determines which subscriber loop 220 should be coupled to
broadband test head device 210 in response to control messages transmitted to
communications module 222 from service/repair center 224 over a data
communications
network 226. Data communications network is a typical packet data network
using any of
the commercially available protocols. In accordance with this embodiment of
our invention
customer loops 220 make-up and DSL service capability may be determined via a
mechanized process. In accordance with this embodiment a control message is
sent from
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bureau 224 instructing switch 215 to provide loop access to broadband test
head device 210.
Once broadband test head device 210 accesses the loop 220, the test head
device 210 sends
at least one pulse of a predetermined duration onto the loop 220 thereby
causing echoes at
the various discontinuities existing on the loop 220. The resulting echoes are
subsequently
received at device 210 and used to determine loop make-up in accordance with
our
invention.
As far as the choice of a probing signal is concerned, several choices are
possible.
For example, it is know in the prior art that a half-sine pulse is a good
choice and this pulse
is used in today's high resolution TDRs. A square pulse may also be used,
although it is
commonly claimed that the half-sine pulse leads to higher echo resolution than
the square
pulse. However, this may not necessarily be true and both probing signals
yield similar
responses. However, there may be a practical advantage in using a half-sine
pulse instead of
a square pulse. In fact, a half-sine pulse has more energy at low frequencies
than a square
pulse and this property has a twofold advantage. First, it may be more useful
to detect gauge
changes since the reflection coefficient of a gauge change is characterized by
a low-pass
behavior. Secondly, injecting low frequency pulses in the pair under test
would cause less
crosstalk in adjacent pairs that, at the time of the test, may be supporting
DSL services.
Another advantage of using a half-sine pulse is that it is easier, from an
implementation
point of view, to generate "cleaner" high-amplitude half-sine pulses instead
of high-
amplitude square pulses. However, except for the above mentioned practical
advantages
there is no conceptual difference between the echo response to a square pulse
or to a half-
sine pulse.
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In accordance with this embodiment of our invention, the processing necessary
to
determine the make-up of the loop 220 is not done in central office 13 (the
access CO)
but instead is done at service bureau 224. Specifically, device 210, in
addition to having
means for transmitting and receiving pulses also includes means transmitting
the acquired
data to communications module 222. The signals received at module 222 are
transmitted
over the data communications network to bureau 224. At bureau 224, a processor
230
running the method steps below (and that are stored on memory 231) can
completely
determine loop make-up. In accordance with this distributed processing
embodiment of
our invention, loop make-up is determined in batch mode. That is, data may be
acquired
for a plurality of loops, sent to bureau 224, and processed at a later time.
This
embodiment is particularly advantageous for off peak hour loop make-up
determination
so as not to disrupt customer service.
At bureau 224 the loop make-ups, as determined in accordance with our
invention,
are then used to replace or update existing records in a database 235, or if
no records
exist, the new make-up is stored as a record in the database 235. It should be
noted that
the system of FIG. 2A is meant to illustrate how our broadband test head
invention may
be implemented as part of a mechanized loop testing system. In fact, as
discussed below,
the essential components of our broadband test head and the method of our
invention may
also be implemented in a metallic time domain reflectometer or in a non-
distributed
architecture.
Turning now to FIG. 2B, there is depicted a broadband test head 2110
in accordance with a second illustrative embodiment of our invention. The
embodiment of FIG. 2B is a non-distributed architecture wherein processing,
and loop make-up, is done at the access location. Here, broadband test
head 2110 comprises an input/output interface 2101 that
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couples the loop 220 tip and ring to a transmitter 2105 and receiver 2106.
Transmitter 2105
and receiver 2106 are coupled to a micro-processor 2109. Memory 2111 is
coupled to
micro-processor 2109 and is used to store the method steps, where applicable,
of the present
invention and may be used to also store results. Although a display is not
shown, broadband
test head 211 may also include a display, wherein echo results are displayed,
and circuitry
for transmitting signals over a data network (as may be required by the
embodiment of FIG.
2A). The micro-processor 2109 executes the method steps, where applicable,
stored in
memory 2111 and is used in performing digital signal processing on the echoes
received by
receiver 2106. As detailed below, by processing the echoes received at the
receiver in
accordance with our method the subscriber loop may be more accurately
determined.
2. ModellinE
In order that our method may be better understood, we will now describe a
mathematical model for describing the echoes. This model is used to determine
the effect
that spurious echoes caused by gauge changes and bridged taps have on
determining the loop
make-up. The effect of spurious echoes, based on the model, is then included
in our method
for determining loop make-up.
2.1 Echo Modelling
It can be shown that the echo signals arriving at a Central Office (CO) (or
more
specifically the broadband test head device receiver) in response to a pulse
being sent out on
a subscriber loop can be expressed as:
r(t) _ ~e~'~(t-~t) (1)
i
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where e~'~(t) is the i'~ echo response and ~t is the echo arrival time in the
CO of the i-th echo.
The echo e~'~(t) can be expressed as a function of its echo path impulse
response hep~ (t)
ec'~ (t) - s(t) ~ hep> (t) , where hep~ (t) = F-' ~K(f )H L~ (.f )P~'~ (.f )~
(2)
In eq.(2), HI~(~ is the insertion loss pertaining to the round trip path from
the CO to the
discontinuity and back to the CO again, the term K(~ takes into account the
role of the
transmission coefficients 2(~ pertaining to previous bridged taps and the
reflection
coefficient p(~ models the effects of the discontinuity on the incident
signal. Each
discontinuity present in the loop will generate an echo whose shape will
depend both on the
kind of discontinuity and on the loop sections on which the echo has traveled.
The observed
signal r(t) will be the sum of a certain number of echoes that might be
overlapping. In fact,
even if the probing signal s(t) is a very short pulse, the medium is very
dispersive and will
broaden the pulse. The longer the loop section, the broader will be the echo
received in the
CO. The shape of the echoes generated by different discontinuities does not
change
significantly from discontinuity to discontinuity. The main difference
consists in the width of
the echo: near discontinuities will generate narrower echoes, whereas far
discontinuities will
generate broader echoes.
Spurious echoes occur because each discontinuity generates both a reflected
and a
refracted signal, so that a part of the signal travels back and forth on the
line, bouncing
between discontinuities, before it arrives at the CO. Obviously, the more the
spurious echo
travels on the line the more attenuation it will exhibit upon arrival at the
CO. However, the
effect of these spurious echoes cannot be neglected since, in some instances,
spurious echoes
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generated at a discontinuity may even be stronger than the real echoes
generated by the
following discontinuities.
More importantly, an accurate analytical model of spurious echoes may be used
to
generate or synthesize spurious echoes and subtract such generated spurious
echoes from the
observation data thereby resolving the ambiguities known in the prior art. The
generation
and subtraction of the spurious echoes from the observation data could be
performed step-
by-step and in parallel with our identification method described below.
In the following subsections we will analyze the main spurious echoes
generated on a
loop by a gauge change and a bridged tap. The spurious echoes are modeled as
real echoes.
For this purpose, we will define their echo path and their reflection
coefficient. The
transmission coefficient can then be expressed as a function of the reflection
coefficient
since the following relationship holds: z( f ) =1 + p( f ) . The determination
of the echo path is
important because it allows us to build the insertion loss transfer function
HIL(~ in eq. (2);
the reflection coefficient will be constituted of several terms, each of which
will account for
the consecutive bouncing.
2.1.1 Spurious Echoes: Gauge Changes
Turning now to FIG. 3, there is depicted an exemplary subscriber loop wherein
two
consecutive gauge changes (labeled A and B) are present in the loop. When a
signal
transmitted from CO 13 arrives at A, an echo is generated and goes back to the
CO 13; this
is a real echo and pertains to the discontinuity in A. After encountering A,
the refracted part
of the signal travels on and arrives at B, where another echo is generated in
accordance with
the reflection coefficient ,oz(fJ. When this second echo arrives back at A,
part of it will be
refracted and will constitute the real echo pertaining to the discontinuity B
and part will be
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reflected back towards B in accordance with the reflection coefficient p~(~.
Theoretically,
the part of signal going back towards B can bounce a infinite number of times
between A
and B, and, at each bouncing, a refracted and a reflected wave will be
generated again. For
this reason, an infinite number of spurious echoes will be received in the CO.
Following the notation of the model in eqs. (1) and(2), it is possible to
prove that the
echo path and the reflection coefficient pertaining to the i-th spurious echo
generated by two
consecutive gauge changes are given by the following (i > 0):
Path = Path from CO to A + 2(i + 1)L + Path from A to CO (3.a)
p(.f ) _ ~p~ (.f )~ '~p2 (.f )~ i+~ (3.b)
Based on eq. 3, we have run simulations and found that spurious echoes due to
gauge
changes are much more attenuated than real echoes. For example, FIG. 4B shows
the real
and spurious echoes produced by the discontinuity present in the loop shown in
FIG. 4A. In
the calculation of the spurious echoes we have considered the first five
spurious echoes, i.e. i
= 1, 2, ..., 5 as given by eqs.(3.a) - (3.b). As such, ignoring the spurious
echoes produced
by gauge changes will not have a major effect on the accuracy of our loop make-
up method.
2.1.2 Spurious Echoes: Bridged Taps
Turning now to FIG. 5, there is depicted an exemplary subscriber loop having a
bridged tap (labeled A) and a gauge change (labeled C) present in the loop.
Actually, the last
discontinuity C can be either a gauge change or another bridged tap, since its
behavior is
described by the reflection coefficient p3(~. When the signal arnves at A, an
echo is
generated and goes back to the CO 13; this is a real echo and pertains to the
discontinuity in
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A. After encountering A, part of the signal travels on and arrives at B and
part travels on
arriving at C. In this case, there are three kinds of spurious echoes of
importance:
1) the spurious echoes that bounce between A and B and go back to the CO;
2) the spurious echoes that bounce between A and B, travel on towards C
and go back to the CO
3) the spurious echoes that bounce between A and C and go back to the CO.
Following the notation of the model in eqs. (1) and (2), the echo paths and
the reflection
coefficients pertaining to the above mentioned types of echoes are given by
the following:
Case 1) i > 0)
Path = Path from CO to A + 2(i +1)LBT + Path from A to CO (4.a)
P(.f ) _ ~1 + Po (.f )~ ~1 '~ P~ (.f )~ ~Pi (.f )~ ~ (4.b)
Case 2) (i ,,'o > 0)
Path = Path from CO to A + 2 i LBT + 2 j L + Path from A to CO (S.a)
P(.f ) _ ~1 '~ Po (.f )~ ~1 '.~ Pi (,f )~ ~1 '~' Az (.f )~ lYi (.f )~ ~ 1 LP2
(.f )~' 1 ~s (.f )~' (S.b)
Case 3) (i > 0)
Path = Path from CO to A + 2(i +1)L + Path from A to CO (6.a)
P(f) _ (1+ po (.f)~ fl+ Pz (f)l fpz (f)l ' (~3 (.f)~'+~ (6.b)
In the case where the consecutive discontinuities are constituted by the same
kind of
gauge, the reflection coefficients in (4.b), (S.b) and (6.b) boil down to the
following
expressions:
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Case 1): p( f ) = 4 _ 1
(7.a)
9 3
8 1 '+' z
Case 2): p( f ) - 27 3 ~,03 ( f )~' (7.b)
Case 3): p( f ) = 9 - 3 ~,03 ( f )~'+' (7.c)
The spurious echoes produced in correspondence to a bridged tap are more
harmful
than those produced by a gauge change. FIG. 6B shows the real echoes and the
first 35
spurious echoes for the loop configuration in FIG. 6A. The 35 spurious echoes
we have
considered are: 5 echoes of case 1 (i = 1, 2, ..., 5 in eqs. (5.a) - (5.b)),
25 echoes of case 2 (i,
j = 1, 2, ..., 5 in eqs. (6.a) - (6.b)) and 5 echoes of type 3 (i = 1, 2, ...,
5 in eqs.(7.a) - (7.b)).
The spurious echoes are still smaller than the real ones but much stronger
than in the gauge
change case and can change the peak sequence, causing the appearance of false
peaks. If the
bridged tap is longer, the spurious echoes are weaker but so are the real
echoes and the peak
sequence will experience a change.
3. Determining the Make-Uu of a Loop
We now turn to our method for unambiguously determining (or identifying) the
make-up of a subscriber loop including identifying the number and location of
load coils,
bridged taps, and gauge changes.
In the course of our work we have found that if some simple assumptions are
satisfied, loop make-up identification may be possible without ambiguity.
These
assumptions are here summarized:
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1. The loop is well behaved, i.e.,(a) the loop is constituted of cables
deployed
following the regular gauging design rule and (b) only simple bridged taps may
be present and the length of each bridged tap is smaller that the length of
the
following loop-section;
2. The loop is terminated on an on-hook telephone and the impedance of an on-
hook telephone can be approximated by an open circuit; and
3. The loop does not have several discontinuities in close proximity
concentrated at
the end of the loop.
If these assumptions are satisfied, it is possible to identify the loop make-
up by just looking
at the position and sign of the peaks of the echoes. The rationale or physical
principle
underlying the above assumption is the realization that the spatial
relationship of the
discontinuities on the loop manifest themselves in a temporal manner via our
measurement
or any TDR measurement. Note however, that even if the above assumptions are
satisfied,
echoes may overlap and it may be possible that some peaks are hidden so that
some
discontinuities may not be detected. Our method will be able to perform loop
make-up
identification without any ambiguity if the loop under investigation satisfies
the above
mentioned four assumptions. For those loops that do not satisfy these
assumptions, it will be
necessary, as described below, to perform additional steps to resolve the
ambiguities, i.e., it
may be necessary to resort to sophisticated signal processing techniques.
Our identification process is performed in several steps. At each step some
partial
information on the loop make-up is calculated and exploited in a subsequent
step. At a high
level, and as indicated in FIG. 7, the identification process can be divided
into four main
phases or steps:
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1. Phase 1 (Step 710, FIG. 7A): Acquire Data;
2. Phase 2 (Step 720, FIG. 7A): Check Consistency of the Loop Record;
3. Phase 3 (Step 730, FIG. 7A): Perform Active Loop Make-up
Identification;
4. Phase 4 (Step 740, FIG. 7A): Resolve Ambiguities.
Once the loop make-up is identified, the loop may then be qualified for DSL
service.
However, where the loop make-up cannot determined without ambiguity, it is
still possible
to exploit the information given via our method to determine the quality of
DSL services
achievable by the loop. In fact, in the case of ambiguous identification, the
possible
configurations that can be attributed to the loop under test are limited and
can be used for
DSL qualification purposes. In this scenario, a worst-case quality of service
can be
determined.
In the following sub-sections, we will describe the functions or steps
performed in
each phase.
3.1 Phase 1 (Step 710): Acduire Data
As FIG. 7A shows at the same time data is being acquired, step 710, it is also
possible, but not required in accordance with our invention, to detect the
presence of load
coils and estimate the noise on the loop under tests, step 712. Step 712 is
optional.
Nonetheless, given that the commercial driver behind unambiguously determining
the make-
up of a loop is deployment of DSL services step 712 will be required in most
cases and by
almost all users of the embodiments depicted in FIG. 2. However, in
implementing our
inventive concept load coil detection and noise estimation are not to be
considered necessary
steps.
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Turning to FIG. 7B, there is illustrated the main sub-steps performed in this
phase,
including the optional steps of load coil detection and noise estimation.
Specifically, FIG.
7B illustrates the substeps of detecting of load coils, step or block 7101,
estimation of the
noise present on the loop, step 7105, and repetitive transmission of suitably
designed
probing signals into the loop and sampling of the received echoes, step 7109.
In addition,
and in accordance with our method, the echoes received at step 7109, may be
stored in
memory, step 7119. In the embodiment depicted in FIG. 2A, the received echoes
may be
transmitted back to the service bureau and stored (step 7119) for later
processing. Or in the
embodiment of FIG. 2B, the received echoes may be stored (step 7119) in local
memory
2111 on the broadband test head 210.
In order to detect loading coils along the line, we measure the input
impedance of the
loop from a few hertz to a few kilohertz; measuring the impedance of a loop is
well known
in the art and any prior art method may be used to perform this step. It is
known that the
presence of loading coils is detected if the behavior of the input impedance
versus frequency
exhibits peaks. If the input impedance of the loop is a decreasing monotonic
function of
frequency, the loop is unloaded. If load coils are detected, the loop cannot
support DSL
services (as is known in the art).
The prior art contains methods for estimating noise on a loop and any of those
methods may be used here. Noise estimation is important because the knowledge
of the
noise level will determine the number of independent snapshots required via
repetitive
probing, step 7109, in order to achieve the desired Signal-to-Noise Ratio
(SNR). In fact,
given that safety, service, and customer satisfaction requirements place an
upper limit on the
energy that can be transmitted on a loop, repetitive probing allows us to
maintain energy
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levels below safety requirements and, at the same time, allows to achieve
desired Signal-to-
Noise Ratio. The process of noise estimation can be limited to a second order
description of
the noise process which may be useful when processing the acquired data for
the resolution
of the echoes. A second order description is sufficient because of the
Gaussian nature of the
noise and may be necessary since crosstalk may introduce colored components in
the noise
spectrum; crosstalk may be present because DSL services might be running on
pairs
adjacent to the pair under test.
As far as the choice of the probing signal is concerned, a compromise on the
width of
the probing signal will need to be made: short pulses give rise to narrow
echoes, whereas
long pulses are able to reach longer distances.
Those of ordinary skill in the art will also note that metallic access to the
cable pair
or subscriber loop is needed only in this step, step 710. Therefore, the loop
is physically
disconnected from the customer only during step 710 and then typically only
for a number of
seconds. Once the data is acquired, the line can be given back to the customer
since all the
further processing can be made in a batch mode off line.
3.2 Phase 2 (Optional Step 720): Compare Acquired Data to Loop Record
Step 720 is an optional step. In step 720 we compare available loop records to
the
previously acquired data. This proves to be a useful way of verifying the
reliability of a pre-
existing loop record for the loop under test.
In particular, at step 720 the correctness of the loop record is verified by
comparing
the loop record with acquired data. Accordingly, we process the data and use
accurate time
windowing to detect if a certain discontinuity is located where the records
indicate. The
verification process will analyze all the discontinuities indicated in the
records starting with
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the ones nearer to the CO. This consistency check will provide the following
phase with
some partial information on the loop make-up. In fact, even though most of the
records are
not updated and, therefore, unreliable, it is reasonable to assume that at
least some of the
information in the database is correct.
3 3 Phase 3 (Std 730): P~orm Active Loop Make-up Identification
During active loop make-up identification, step 730, the data gathered during
step
710 is analyzed and a first attempt to identify the loop make-up is made. If
the consistency
check of the records was able to provide some a priori knowledge on the loop,
this
information is used during the identification process.
The basic parameters to be identified in this phase are the estimation of the
time of
arrival of the echo and its amplitude. The information on the time of arnval
is necessary for
the determination of the location of the discontinuity. Electric signals
propagate in a loop at
a speed of approximately 1.5 ,us per kilofeet, so the time of arnval of an
echo allows us to
locate the distance of the discontinuity from the CO (or broadband test head).
The
knowledge of the amplitude of the echo is necessary to identify the type of
discontinuity that
caused the echo. Specifically, the sign of an echo allows us to determine
whether the
probing signal has passed from a lower to a higher characteristic impedance,
or vice versa.
In addition, the absolute value of the peak of the echo is useful in
determining the kind of
gauges present in the loop. In fact, we can state the following rules that
provide a signature
of the discontinuity:
~ when a signal passes from a loop section with a higher (lower)
characteristic
impedance to a loop section with a lower (higher) one, the echo generated at
the discontinuity is always negative (positive);
~ a bridged tap always produces a negative echo followed by a positive echo;
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~ in the case of bridged tap, the absolute value of the negative peak is
always
higher than the absolute value of the positive peak;
~ the bigger the difference between the characteristic impedance of two loop
sections, the higher the absolute value of the peak generated at the
discontinuity.
Basically, our identification method attempts to detect the discontinuities
nearer to
the CO and, then, moving forward out into the loop detecting, in turn, each
discontinuity.
The determination of the first echoes) does not normally present a problem
since it (they)
will arrive in the CO without being overlapped by previous echoes and because
the first
spurious echoes will arrive later. However, as the identification process
moves forward,
detection of the echoes is more difficult. In fact, the echoes will be
increasingly weaker,
broader and overlapping with each other and with spurious echoes. The main
problem of
detecting far discontinuities is due to the broadening of the echo caused by
the dispersive
nature of the medium. In fact, a broad echo could hide a subsequent and weaker
echo,
making the detection of discontinuities occurring after other discontinuities
extremely
difficult. A possible way to limit widening effect of the medium is to process
the received
signal or echoes in the order received to compensate for the dispersive
behavior of the
medium. In the case of digital communications, the effect of a dispersive
channel is to
broaden the transmitted pulse thus leading to inter-symbol interference. In
digital
communications, the solution to the problem of inter-symbol interference is an
equalizer, i.e.
a device that compensates for the dispersive behavior of the channel. In our
case, we have to
process a signal that is not digital in nature and this limits our freedom in
the choice of the
equalizer. In fact, since we cannot act on the digital structure of the
signal, the only thing we
can do is to act on the channel characteristics. There is only one equalizer
that does not take
CA 02369858 2001-11-28
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into account the digital structure of a received signal: the zero-forcing
equalizer, that in our
case turns out to be a filter with a transfer function equal to the inverse of
the transfer
function of the channel.
On the basis of the above considerations, the identification method should
proceed as
indicated below and by FIG. 7C:
1. identify the location and type of the i'i' discontinuity on the loop by
processing
the received echoes in pairs, step 7301 (processing includes using the echo
time of arnval and amplitude and signature rules to determine, respectively,
the location and type of discontinuity, step 7302) ;
2. compute the transfer function of the first through i'h loop sections
identified
up to now, step 7305 (for i > 1, the ith loop section is the loop section
between
the (i - 1)'~' and i'h discontinuities and for i = 1, the i'h loop section is
the loop
section between the CO and first discontinuity);
3. synthesize an inverse filter for the ith loop section based on the computed
transfer function, step 7309; and
4. operate the convolution between the previously synthesized inverse filter
and
the observation data, step 7313 (this operation would be best performed in the
frequency domain by means of FFT/IFFT techniques);
The above steps are then repeated until the last discontinuity in the loop is
found; in
other words, if there are N echoes i is incremented from 1 to N. In principle,
this procedure
is equivalent to "moving" the CO along the line and towards the subscriber's
location, thus
reducing the distance between the CO and the discontinuity to be identified.
It also should
be noted that at step 2, bridged taps should not included in the calculation
of the transfer
function. This is the case because the bridged tap distorts only signals
travelling on it and
the signals do not travel on the bridged tap. In other words, the cumulative
transfer function
26
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is meant to take into account the effect each loop section has on signals
traversing and
signals reflected at discontinuities after the bridged tap do not travel on
the bridged tap.
The main drawback of this procedure is the noise enhancement. Due to the
characteristic of the transfer function of the twisted-pair channel, the
inverse filter will
enhance the high frequency components of the noise. This effect should be
carefully taken
into account when fixing the minimum SNR required. On the other hand, since
the
correlation introduced in the noise samples is known, we can resort to
standard noise
reduction techniques.
An example of the results achievable with this technique is shown in FIGS. 8
and 9.
Let us consider the well behaved loop shown in FIG. 8A; the real and spurious
echoes are
shown in FIG. 8B (separately) and in FIG. 8C (the superposition of real and
spurious
echoes). The first three echoes pertain to the gauge change 805 and the
bridged tap 807.
The first two echoes are negative, so that we can affirm that the first
discontinuity is gauge
change 805. The second and third echo show a negative/positive sequence, so
that we can
say that after the gauge change there is bridged tap 807. However, the last
small positive
peak is due to spurious echoes and not to the echo generated at the end of the
loop (see
FIGS. 8B and 8C), because the echo generated at the end of the loop is hidden
by the
positive echo of the bridged tap. In fact, the echo paths of these last two
echoes differ by
1000 feet only and this corresponds to a time delay of 1.5 ,us, a time delay
that is too small
with respect to the time duration of the positive echo pertaining to the
bridged tap. From the
previous considerations, we can easily detect the first two discontinuities,
so that we can
build the inverse transfer function pertaining to the first two loop sections.
FIGS 9A and 9B
show the effect of inverse filtering on the identification process. The
normalized observed
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realization filtered with the inverse transfer function of the first loop
section, i.e. the loop
section from the CO up to the gauge change, is shown in FIG. 9A. The first two
negative
echoes are more separated, but we still cannot detect the echo pertaining to
the end of the
loop. In fact, we "moved" our reference point only 1000 feet forward. However,
if we filter
the observation data with the inverse transfer function of the first two loop
section, i.e. the
loop section from the CO up to the junction of the bridged tap, we are finally
able to detect
the last echo due to the end of the loop. In fact, as FIG. 9B shows, we have
two peaks
approximately 1.5 ,us apart, and this time difference corresponds to the 1000
feet difference
between the echo path of the positive echo of the bridged tap and of the end
of loop. Around
11.5 ,us, we can also appreciate the spurious echoes.
FIGS. 8B, 8C, 9A, and 9B demonstrate the feasibility of using our method to
determine loop make-up. Though these figures are simulations, we have
verified, within the
limits of commercially available equipment, our method via actual measurement,
as
illustrated in FIGS. 10A, lOB, lOC, and lOD. Our measurement set up is
illustrated in FIG.
l0A and consists of a pulse generator 1001 that is coupled through a balun
1005 to a loop
under test 1020. The output of the pulse generator was a square wave of 5
Volts (on 50
ohms) with a width of 200 ns and a 5 ns rise and fall time. The balun 1005
provides a 50
ohms unbalanced to a 100 ohms balanced conversion. An oscilloscope 1025 is
used to
receive echoes generated on the loop under test 1020. In FIG. lOB, the loop
under tested is
illustrated. It is understood that the equipment, namely generator 1001, balun
1005, and
scope 1025, illustrated in FIG. l0A is located in CO 13. Turning to FIG. lOC,
there is
depicted an oscilloscope traces of the echoes generated by the loop of FIG.
lOB. In FIG.
lOD the loop is simulated in accordance with our method. As FIG. lOD shows the
28
CA 02369858 2005-03-21
simulation and trace match up almost perfectly. The trace region 1037 of FIG.
lOC is
obtained by circuitry of FIG. l0A including balun 1005.
We have done other measuretizents and simulations to verify our measurement
method and have concluded that our method can be used to determine the make-up
of a
S loop. Our measurements, however, also demonstrated that under certain
conditions gauge
changes cannot be detected using the simple set up of FIG. 10A. For distances
on the
order of 5,000 ft (S kft) the amplitude of the reflected echo is on the order
of micro-volts.
Assuming that the white noise has power density spectrum of -120 dBw/Hz over
100 ohms, for a bandwidth of 5 MHz the noise would be in the micro-volt range
as well.
Nonetheless, these shortcomings may be overcome by using high density pulses
and
repetitive probing followed by noise averaging.
It is worth pointing out that the use of our method allows us to simplify the
model
of the echoes given in eqs. (1) and (2). In fact, since our method compensates
for the
distortion of the medium, the arriving echoes will be much more "similar" to
the probing
signal transmitted in the loop, as if we were transmitting on a non-dispersive
channel.
Using the inverse of the transfer function of the first nth loop sections to
detect the echo
generated in the (n + 1 )th loop section does not eliminate all the
distortion; however, we
may model the residual distortion as a simple attenuation. This allows us the
following
simplification of the model (see eq. (2)):
e~'~ (t) = s(t) * he's' (t) - s(t) * (a~8(t)) = ats(t) (8)
On the basis of (8), the model given by eq. ( 1 ) can be rewritten as:
r(t) = E ats(t - ~,1) (9)
i
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This simplification allows us to state the problem of time of arrival and
amplitude estimation
in a simple way.
Another improvement that may be useful in combating the overlapping of
consecutive echoes would be to subtract a "synthesized" echo from the
observation data as
indicated by block 735 of FIG. 7A. Specifically, and with reference to FIG.
7A, once a
discontinuity has been identified (step 730), the echo caused by that
discontinuity could be
generated via software and subtracted during processing, step 735. This "onion
peeling"
technique will ensure that the later arriving echoes will not be hidden by
previously arriving
echoes. In addition our "onion peeling" approach may also be used to remove
the effect of
spurious echoes. It should be noted that step 735 would be done in parallel
with identifying
the loop makeup, step 730. That is, as the method moves out onto the loop
identifying each
discontinuity via the observation data, each discontinuity and spurious echo
will be removed
from the observation in data before identifying the next discontinuity. It
should be noted
that "onion peeling" is optional and our underlying method would work well for
a large
majority of loops currently deployed in the Public Switched Telephone Network.
On the basis of the above considerations, we can now summarize the main steps
of
the identification algorithm.
1. Compute the arrival times of the ith and (i + 1)'~ echoes and determine the
correspondent distances from the CO (this step is representing by block 7302
of FIG. 7C);
2. Determine the sign sequence of the i'h and (i + 1)t'' echoes according to
the
following (block 7302 of FIG. 7C):
~ Negative-Negative: the i'1' discontinuity is a gauge change, from a thinner
to a thicker cable;
~ Negative-Positive: the i'i' discontinuity is a bridged tap or the ith and (i
+
1)th discontinuities are two consecutive gauge changes from thinner to
CA 02369858 2001-11-28
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thicker to thinner cable;
~ Positive-Positive: the i~' discontinuity is a gauge change from thicker to
thinner cables; or
~ Positive-Negative: the i'~' discontinuity is a gauge change from a thicker
to
a thinner cable.
Note that if the loop is well behaved then the only possible transitions are:
~ Negative-Negative: ith discontinuity is a gauge change from thinner to
thicker; or
~ Negative-Positive: the i'h discontinuity is a bridged tap.
3. Compute the absolute value of the peak of the it'' echo and compare it to
simulation results in order to determine the kind of gauge constituting the
itn
loop section, step 7303 (if a bridged tap was detected, proceed in the same
way to identify the (i + 1)~' loop section also);
4. Compute the transfer function of all the loop sections up to the itn
discontinuity (step 7305) (if a bridged tap was detected, do not include the
bridged tap in the transfer function because the echo generated by the
discontinuity following the bridged tap does not "travel" on it and, thus, is
not
distorted by it);
5. Synthesize the inverse filter (step 7309);
6. Operate the convolution between the inverse filter and the observation data
(step 7313);
7. Compute the next echo arrival time (i.e., compute the (i + 2)'h echo
arrival
time), however, if a bridged tap was previously detected, compute the next
two echoes arnval time (i.e., compute the (i + 2)'1' and (i + 3)th echo
arrival
times); and
8. Set i = i +1 if a bridged tap was not detected or set i = i + 2 if a
bridged tap
was detected and repeat items 1 through 7 from the list above until the last
discontinuity is determined.
Note from the list above and FIG. 7C discontinuities are determined by
processing
the echoes in pairs. Note also that bridged taps are afforded special
attention because the
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echo generated by a bridged tap does not travel on the loop section comprising
the bridged
tap. The above seven steps illustrate the main steps followed during Phase 3
of our method.
However, these steps may not be sufficient to achieve unambiguous loop make-up
identification if the four assumptions pointed out earlier are not satisfied.
Below we
describe an approach that can be used to resolve ambiguities.
3.4 Phase 4 (Step 740): Resolution OfAmbiQUities
This method step is the most sophisticated and delicate part of the
identification
process. The problem of resolving an unknown number of closely spaced,
overlapping and
noisy echoes of a signal with a priori known shape is a problem that arises in
many
applications such as radar and sonar processing, geological sounding, etc. In
principle, this is
a combined detection-estimation problem since we have to determine first the
number of
returning echoes and, then, apply an estimation procedure to determine their
location in time.
The usual approach is to assume the availability of an array of M sensors
located in the far
field of the sources, so that the waves generated by each of the D radiating
sources behave
like plane waves.
The signal received by the M sensors is usually modeled as follows:
n (t) s~ (t) n~ (t)
_ ~A(iy ) . . . A(~9D )~ : + : ( 10)
rM (t) SD (t) nM (t)
or, more compactly, as:
r=As+n (11)
where r;(t) is the signal received at the i-th sensor (i = 1, ..., ll~, s~(t)
is the signal generated
by the j-th sensor (j = 1, ..., D), A(~ is the "signature" of a source in the
direction ~ and
n;(t) is an independent noise affecting the i-th sensor. The set of signature
vectors A( ~ is
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also called the array manifold, since it characterizes the directional
properties of the sensor
array. The array manifold may be obtainable in a closed form for simple
spatial geometries
(e.g., linear, circular), or can be measured through field calibration
procedures. By carefully
choosing the array geometry, it is possible to ensure the following property:
for any set of
parameters ~9 with D<M elements, the array manifold vectors are linearly
independent.
There have been several approaches to such problems. First of all we can
recall
Capon's Maximum Likelihood method and Burg's Maximum Entropy method. These
methods have been widely used in the past but their main limitation is due to
the fact that
they use an incorrect model of the measurements: an autoregressive model
instead of an
autoregressive-moving-average model. The first one to exploit the structure of
the data
model using a covariance approach was Pisarenko, even though he considered a
very
particular case: parameter estimation of cissoids in additive noise. The
covariance approach
to the case of sensor arrays of arbitrary form was first developed by Schmidt
and Bienvenu
and Kopp. Their algorithm, widely known as Multiple Signal Classification
(MUSIC)
algorithm, was the first algorithm to exploit the eigenstructure of the
covariance matrix of
the observed data. The basic principle of this sub-space approach lies in the
fact that, when
there are more measurements than signals (D<tl~, the signal component of the
received data
(As) is confined to at most a D-dimensional subspace (the signal subspace) of
the M-
dimendional space of the observations. Since the noise is typically assumed to
possess
energy in all the dimensions of the observation space, the problem is to
extract a low-rank
signal observed in a full-rank noise. There are two other more recent subspace
methods that
are worth mentioning because they are able to provide performances superior to
MUSIC: the
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Estimation of Signal Parameters via Rotational Invariance (ESPRTT) algorithm
and the
Weighted Subspace Fitting (WSF) algorithm.
It would certainly be useful to exploit this vast literature for the
resolution of the
overlapping echoes in the problem of loop make-up identification via single
ended
measurements. The main difference between our case and the model in eqs. ( 10)
- ( 11 ) is
that we do not have the availability of a sensor array. However, it is
possible to reformulate
our observation model in order to provide it with a structure identical to the
model in eqs.
( 10) - ( 11 ). Our observation model is:
r(t) _ ~a;s(t-~; )+v(t) (12)
Assuming that there are D main echoes and sampling the received waveform r(t)
at
M instants, we can write:
D
r(t~ ) _ ~ a; s(ti - ~; ) + n(t~ )
D
r(tz ) _ ~ a; s(t., - ~; ) + n(t~ ) (13)
r=~
D
r(tM ) _ ~ a; S(tM - ~i ) + Yl(tM )
r=~
and, using a matrix notation, we obtain:
r(t~ ) s(t, -~~ ) s(ty~z ) ... s(t~ -~D ) a~ n(t, )
r(tz ) s(tz -~~ ) s(tz -~z ) . .. s(t, -~D ) az + n(tz ) 14
( )
r(tM ) S(tM ~I ) S(tM ~2 ) ~ . . S(tM -~D ) aD 12(tM )
or, equivalently,
r=Sa+n (15)
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CA 02369858 2001-11-28
WO 01/01158 PCT/LTS00/16865
The model in eq. ( 15) has the same structure as the model in eq. ( 11 ), with
the only
difference that now the array manifold for the signal resolution problem is
obtained from the
signal shape. Furthermore, the desired array manifold (linear independence of
the rows of S
for any set of DcM delays) is satisfied provided that we work with finite-span
pulse type
waveforms.
On the basis of the new model structure in eq. (15), we are now able to
exploit the
MUSIC, the ESPRIT and the WSF algorithms previously mentioned to detect the
number of
echoes and estimate their arrival time.
The array manifold S in eq. ( 15) requires the knowledge of the shape of the
echo and
that all the echoes have the same shape. This is impossible to obtain in our
case but it is
possible to define a "reasonable" shape of the echo. In fact, as previously
pointed out above,
the shape of all the echoes is similar and they differ only by their width
which is a function
of their distance from the CO. Moreover, we can make the CO "nearer" to far
discontinuities
by filtering the data with an appropriate filter. This would ensure that the
use of an array
manifold containing echoes of the same shape is a less problematic
approximation. A
possible choice for a "reasonable" shape of the echo could be:
J ~ ( 16)
e(t) = F-1 lexp(-a~)~
where c~ is a parameter that has to be optimized. The choice of an exponential
function is
due to the fact that it is a good approximation for the transfer function of
the twisted pair
channel. The choice of a signal of the kind of ( 16) has another advantage. It
preserves the
linear independence of the array manifold, whereas the piecewise probing
signal would not.
CA 02369858 2001-11-28
WO 01/01158 PCT/US00/16865
When defining a value for the number of samples M, we have to make sure that
we
have D<Nl. Fortunately, the real echoes generated by a loop are limited to a
maximum of ten
to fifteen, but the spurious echoes are virtually infinite. In this sense, the
value for M should
be chosen very high and this could compromise the computational efficiency of
the
algorithm.
With respect to the arrival estimation problem, the use of a sensor array and
the
linear independence of the array ensure that the subspace algorithms can
detect the emitting
sources and separate them from spurious reflections due, for example, to
multipath
phenomena. In fact, a linear combination of two or more direction signatures
will never
provide the "phantom" signature of some different direction. However, this
property is not
maintained in the single-sensor case. In fact, the spurious echoes generated
in a loop will be
considered as real echoes and the algorithm will not be able to isolate them.
The above description has been presented only to illustrate and describe the
invention. It is not intended to be exhaustive or to limit the invention to
any precise form
disclosed. Many modifications and variations are possible in light of the
above teaching.
The applications described were chosen and described in order to best explain
the principles
of the invention and its practical application to enable others skilled in the
art to best utilize
the invention on various applications and with various modifications as are
suited to the
particular use contemplated.
36
