Single-Ended Loop Make-Up Identification—Part I - Semantic Scholar

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Single-Ended Loop Make-Up Identification—Part I: A Method of Analyzing TDR Measurements Stefano Galli, Senior Member, IEEE, and Kenneth J. Kerpez, Fellow, IEEE

Abstract—Loop qualification consists of determining whether a loop can support digital subscriber line (DSL) services or not, and generally, the estimate of the transfer function is sufficient for such purposes. Loop qualification is one of the most important steps that service providers need to address in deploying DSL technology. In this paper, a solution to a more ambitious problem—single-ended automatic loop make-up identification, i.e., the determination of the length and the gauge of all loop sections (including bridged taps) via single-ended testing without human intervention—is proposed. Loop make-up identification will allow operators to more accurately qualify a loop for DSL service and to update and reorder telephone-company loop records, which can be accessed to support engineering, provisioning, and maintenance operations. Despite its potential importance, the possibility of achieving loop make-up identification via single-ended measurements has seldom been addressed in the literature. The use of time-domain reflectometry (TDR) measurements, which are analyzed by a novel step-by-step maximum-likelihood (ML) algorithm, is proposed here to achieve accurate loop make-up identification. In this paper, the proposed algorithm needs no a priori information, whereas in Part II of this study, a means to reduce the computation time of the identification algorithm will be provided, and the case where a statistical characterization of the loop may be available prior to testing will also be considered. Index Terms—Digital subscriber line (DSL), loop qualification, maximum likelihood (ML), time-domain reflectometry (TDR), twisted-pair modeling.

I. I NTRODUCTION

T

HE TELECOMMUNICATIONS industry worked for over a decade to develop digital subscriber line (DSL) technologies to revitalize the embedded copper plant. Now, the industry is reaping the benefits of this effort, bringing megabitper-second connectivity to offices and homes. However, network providers must properly manage the introduction and application of these systems to the local network. Accurate engineering is critical to avoid provisioning failures that would otherwise create customer disappointment, delay, and higher costs. An understanding of subscriber loop make-ups, i.e., length, wire gauge, and location of every loop section including bridged taps and gauge changes, is key to the proper engineering of DSL systems. While some loop records exist, they may be inaccurate or out of date. Knowing the types of systems that are transmitting in a given cable is also critical, because of the resultant crosstalk and the potential need for dynamic spectrum management (DSM).

Manuscript received October 8, 2003; revised December 12, 2005. The authors are with the Telcordia Technologies, Inc., Piscataway, NJ 08854 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TIM.2006.870134

Among the new techniques being used to upgrade the public network are access technologies that use the embedded copper plant to support higher bandwidth services. These technologies include high-bit-rate DSL (HDSL), asymmetric DSL (ADSL), single-line HDSL (SHDSL), very-high-bit-rate DSL (VDSL) and others for which carriers have announced aggressive deployment plans. The new DSL technologies have the potential to become strategically important to an operator’s business plan; however, they must be properly deployed. This involves several engineering tasks, the two most important of which are 1) loop qualification—knowing what type of DSL system and what bit rate can be successfully and reliably provisioned on a given customer’s loop [1]–[7]; 2) spectrum management—an engineering process that allows an operator to place new DSL systems into the plant in compliance with spectral compatibility guidelines and standards, and to troubleshoot field problems suspected of being caused by crosstalk from other systems [8]–[12]. This paper will focus on loop qualification and, in particular, we will describe a technique for achieving accurate loop make-up identification. Maintaining accurate records of the loop plant is important to many aspects of an operator’s business. Beyond supporting traditional voice services, even more accurate and detailed loop records are needed when deploying DSL-based services. These technologies are typically engineered to operate over a class of subscriber loops, such as revised resistance design (RRD) loops (up to 18 kft, 5.49 km), or carrier service area (CSA) loops (up to 12 kft, 3.66 km). Several approaches and tools are being developed to facilitate loop qualification. The most common is mining existing data in loop databases, checking it for accuracy, and then bulk provisioning loops that are candidates for DSL-based service. Sometimes, a combination of loop records and engineering information about feeder route topology is used to obtain an estimate of loop length. Another technique uses loop loss measurements from traditional plain old telephone service (POTS) loop-testing systems to estimate loop length. These approaches use good engineering judgment and result in large populations of loops that are likely candidates to support advanced services. However, a typical approach is to minimize customer disappointment by biasing the techniques toward low probabilities of false-positive results. This is done at the expense of increasing the probability of false-negative results. In other words, the approaches are conservative, and some loops that might support DSL service remain unused or run at low bit rates. Other loop-qualification methods use the adaptation settings of a modem operating over the subscriber loop of interest.

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GALLI AND KERPEZ: SINGLE-ENDED LOOP MAKE-UP IDENTIFICATION: TDR-MEASUREMENT-ANALYSIS METHOD

For example, if a DSL system is operational, the adaptive filter settings contain useful information about the loop. This approach has the disadvantage that a DSL system must first be in operation on the loop that one hopes to qualify. Other techniques use standard dial-up modems that operate over any subscriber loop to glean voice-band information about the loop, in order to predict performance at the higher frequencies of interest to DSL. It would be desirable to have a single-ended testing technique that could estimate the transfer function or identify (and, therefore, qualify) all nonloaded subscriber loops without the need for special equipment or intervention at the subscriber’s location. As also argued in [2], loop make-up identification implies loop qualification and allows telephone companies to update and correct their loop-plant records. Therefore, accurate loop make-up identification can further be used to update records in loop databases, where records can in turn be accessed to support engineering, provisioning, and maintenance operations. The importance of this capability is also confirmed by the creation of a new project in International Telecommunication Union Telecommunication Standardization Sector (ITU-T) SG15 Q4 on single-ended loop test (G.selt). G.selt modems will report single-ended measurements from a single DSL modem, before DSL service is activated, or to analyze DSL lines that are not working. G.selt modems are likely to provide data to a separate analysis engine that interfaces with a DSL operating support system. Despite its importance, there is little published research on algorithms or techniques that allow loop make-up identification or even channel transfer estimation via single-ended testing. For this reason, the interpretation of time-domain reflectometry (TDR) traces to infer loop features has been considered more art than science. To the best of the authors’ knowledge, there are very few published papers on this topic [2]–[7]. In [6] and [7], the use of the one-port scattering parameter to achieve channel transfer function estimation when some a priori information on the loop topology is available is proposed. Although the technique proposed in [6] allows good results on short/mediumlength loops, the assumption that some or all the loop topology is known prior to testing may limit the practical applicability of this technique. Moreover, the effects of the slowly decaying signal (SDS) are not compensated for so that the applicability of the technique is limited to short/medium loops. In this paper, we propose a technique for achieving accurate loop make-up identification (not only loop qualification) without any a priori knowledge on the loop topology. We follow a TDR approach, i.e., probing signals are transmitted onto the loop and echoes reflected by impedance changes are analyzed to infer the unknown loop topology. The proposed technique is flexible and can be exploited either by a technician in the field equipped with a handheld TDR or by placing the testing equipment at the central office (CO). At the CO, the testing equipment can be connected either to the switch’s notest trunk (NTT) or at the DSL access multiplexer (DSLAM) (see [1, Sec. 5] for more details). Previous attempts to use TDR techniques, sometimes coupled to artificial neural-network algorithms, have failed due to the difficulty of the postprocessing of the TDR trace needed to extract all loop features (see, e.g., [6, Introduction]). More-

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over, conventional metallic TDRs are not capable of detecting all echoes. In fact, conventional metallic TDRs cannot detect gauge changes and, moreover, have a serious range limitation that prevents them from reliably detecting echoes farther than a couple of kilofeet from the location of the TDR test head. This limitation is essentially due to two reasons: Conventional TDR methods use unbalanced probing, thus allowing for limited common mode rejection capability; and there is an SDS (see [2, Sec. 5]), which is caused by the distributed RLC nature of the loop, which overlaps with and masks the echoes generated by impedance changes. Methods to overcome these limitations are described here. To increase the common mode rejection capability of conventional TDRs, we propose the use of differential probing to obtain very clean echo responses (see [1, App.] for more details). To remove the SDSs present in all loop sections, we extend in Section IIIA the technique presented in [2], where the exact expression of the SDS of the first loop section was determined (see [2, eq. (10)]). Note that, to the best of the authors’ knowledge, the only other contribution besides [2], which addresses the problem of the removal of the SDS, can be found in [14]. However, the technique proposed there approximates the SDS with a 1/x function and is not as accurate as the one proposed here, which uses the exact expression of the SDS found in [3]. Accurate TDR measurements alone are not sufficient to infer the loop topology without an algorithm able to extract information from the TDR trace. In particular, a major problem arises in a TDR approach since observations available at the receiver consist of an unknown number of echoes, some overlapping, some not, some spurious,1 some not, that exhibit unknown amplitude, unknown time of arrival, and unknown shape. The resolution of such echoes via a single sensor (and not an array) is very complicated and has seldom been addressed in the scientific literature. Moreover, as shown in [4], the conventional approach to echo resolution fails for several reasons. As described in Section III, we propose a novel algorithm based on the maximum-likelihood (ML) principle, which exploits the deterministic nature of the loop and proceeds step by step in identifying loop discontinuities without any a priori knowledge of the loop under test. In Part II of this study [1], we will describe an enhanced version of this approach, which utilizes a multiple-path search, and we will extend the algorithm proposed here to the case where a priori information is available. Moreover, performance results will also be presented. The paper is organized as follows. An overview of echo modeling is given in Section II. A detailed description of the proposed loop-identification algorithm is given in Section III, and a practical example of identification on a measured TDR trace is given in Section IV. Finally, conclusive remarks are drawn in Section V.

1 As better described in [2], we define as real echoes the echoes pertaining to initial encounters with discontinuities, whereas we define as spurious echoes all the echoes caused by successive reflections. The necessity of separating echoes in two categories (“real” and “spurious”) is irrelevant for modeling issues, but it becomes important when loop identification is attempted. In fact, any identification algorithm must be able to discriminate between real echoes (the echoes that indicate the actual presence of a real discontinuity) and spurious echoes (the rereflected and artificial echoes that do not indicate the presence of a discontinuity).

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where Tf is the so-called forward transmission matrix or ABCD matrix. The ABCD coefficients, which are complex functions of frequency, fully characterize the electrical properties of a 2PN and are defined as follows:



V1

I1

I1

V1

; B= ; C= ; D=
. A= V2
I2 =0 I2
V2 =0 V2
I2 =0 I2 V2 =0 (2) Fig. 1. Two-port network with the signal source (generator VS and its internal impedance ZS ) connected to the first port and the load impedance ZL connected to the second port. Applying the Thevenin theorem, the gray part of the circuit can be represented by the input impedance Zin (f ).

II. E CHO M ODELING

For a cable of length l, these coefficients and the corresponding transmission matrix Tf are 

 A = D = cosh γl
Zo sinh γl

B = Zo sinh γl ⇒ Tf =

1cosh γl (3) cosh γl
 C = 1 sinh γl Zo sinh γl Zo

It is possible to derive an analytical time-domain model of the observation of the echoes generated when probing a loop (see [3] for more details). Each discontinuity along 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 (see, e.g., [3, Fig. 15]). It was also reported in [3] that this is an SDS due to the distributed RLC nature of the loop, which is superimposed to the echoes and often masks weak or closely spaced echoes. Although the technique described in [2] allows us to drastically extend the range and sensitivity of a TDR measurement by perfectly compensating for the SDS, it still has some limitations. First of all, the aforementioned distributed RLC nature of the loop is present in all sections along the loop, and may be different from section to section depending on the gauge of that section. Therefore, the exact expression of the SDS reported in [3, eq. (10)] is actually the SDS present in the first section of the cable and its removal by subtracting it from the measured data allows us to better detect the first discontinuity only. Secondly, the technique of subtracting [3, eq. (10)] from the observations does not eliminate the eventually present spurious echoes that may hide weaker echoes or be mistaken as real echoes by the identification algorithm. To overcome these limitations, we propose in Section III-A a technique that allows us to remove both the SDSs present in every section of the loop and all the spurious echoes. This technique, which can be considered an extension of the technique described in [3], is based on a very accurate frequency-domain model of the echoes, which is described in the next section.

As is well known, a loop can be equivalently described by a reciprocal two-port network (2PN) [13]. The relationship between current and voltage (in the frequency domain) at the two ports of a 2PN is given by the following expression (see Fig. 1)2 :





V
B



V2

= Tf

2




D I2 I2

(1)

T f = Tf

(2)

· Tf

(N )

· · · · · · · · Tf

.

(4)

The ABCD parameters allow us to calculate the input impedance of the loop: Input Impedance : Zin (f ) =

AZL + B . CZL + D

(5)

Since an on-hook telephone has very high input impedance, it is reasonable to assume that the load impedance ZL is infinite (see also the considerations made in [2, Sec. 2.2]). In this case, we have (unterm)

Zin

(f ) = lim Zin (f ) = ZL →∞

A = Zo coth(γl). C

(6)

Note that the input impedance of an unterminated and infinitely long cable is equal to the characteristic impedance of the cable

A. Echo Modeling in the Frequency Domain





V1

A

=

I1

C

where γ and Zo are the propagation constant and the characteristic impedance of the cable, respectively. In general, a loop is made of several sections and each section may consist of different cables of different lengths. An important property of the transmission matrix is that it easily allows us to handle multiple connections of 2PNs. For a given network configuration, the overall ABCD matrix of the endto-end circuit is obtained by exploiting the chain rule, i.e., multiplying the ABCD matrices of the single portions of the (i) network. Therefore, if Tf is the forward transmission matrix of the ith section of the loop, the overall forward transmission matrix Tf of the end-to-end circuit consisting of N sections is given by the following relationship:

(1)

2 For ease of notation, hereinafter, the explicit dependence on frequency of A, B, C, D, Zo , γ, ZS , ZL , Vx , and Ix (x = 1, 2) has been omitted.

(unterm)

lim Zin

l→∞

(f ) = Zo .

(7)

Moreover, expressing the transfer function as the ratio of the voltage on the load to the source voltage, we obtain the following relationship: H(f ) =

ZL V2 = . VS AZL + B + CZS ZL + DZS

(8)

The twisted-pair channel can be indeed considered a known channel. In fact, the characteristic impedance and the propagation constant of any cable can be calculated on the basis of accurate measurements. Many accurate models are also

GALLI AND KERPEZ: SINGLE-ENDED LOOP MAKE-UP IDENTIFICATION: TDR-MEASUREMENT-ANALYSIS METHOD

Fig. 2. Comparison of the measured and simulated TDR trace for the topology shown in the upper right part of the plot (probing signal: 5-V 1-µs-wide square pulse). Expressing lengths in meters, 1.5 kft = 457 m, 3 kft = 914 m, and 9 kft = 2743 m.

available for calculating A, B, C, and D, e.g., VUB0, BT0, KPN1, DTAG1, just to name a few [15]. This allows us to calculate very precisely the input impedance of a loop and, therefore, to predict what waveform would be observed when a loop is probed with a signal. In fact, we can write Vloop (f ) =

Zin (f ) VS (f ) Zin (f ) + ZS

(9)

where VS (f ) is the probing signal, ZS is the output impedance of the signal generator, Zin (f ) is the input impedance of the loop, and Vloop (f ) is the voltage across the two wires of the loop. The time-domain waveform vloop (t) (i.e., the TDR trace or reflectogram) can be obtained by taking the inverse Fourier transform of Vloop (f ). As an example of the application of (9), in Fig. 2, we compare the measured TDR trace3 and the corresponding simulated trace for the topology shown in the upper right part of the figure. The simulated curve has been obtained by computing the ABCD matrix of every loop section, applying the chain rule (5) to obtain the overall ABCD matrix of the whole loop, calculating the input impedance (5), computing the TDR trace in the frequency domain as in (9) and, finally, taking the inverse Fourier transform of Vloop (f ). As Fig. 2 clearly shows, the modeling and the measurements are in perfect agreement. Many other experiments not reported here also confirmed the accuracy of the modeling. III. P ROPOSED S TEP - BY -S TEP ML A PPROACH The TDR trace obtained by probing a loop with a pulse consists of an unknown number of closely spaced echoes, some overlapping, some not, some spurious, some not, that exhibit unknown amplitude, unknown time of arrival, and unknown shape. The problem of resolving such echoes is a problem that 3 For details on how measured TDR traces are obtained, see [1, Sec. 7, Appendix].

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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. 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. There is a vast literature for the resolution of overlapping echoes via a sensor array; however, in our case, we do not have the availability of a sensor array (for more details, see [4] and references therein). For this reason, the problem at hand cannot be addressed exploiting known results and requires a novel approach. The main rationale behind the proposed algorithm is the exploitation of the deterministic nature of the twisted pair and the availability of an accurate model of the observations as described in Section II-A. Given the availability of an accurate model of the physical phenomenon of loop echo response, we chose to apply the ML principle in identifying a loop: Hypothesize loop topologies; on the basis of (9), compute the simulated TDR trace that would be observed at the receiver if the hypothesized topologies were true; choose the topology whose corresponding simulated TDR trace best matches the measured TDR trace. In practice, the ML principle cannot be applied exactly as previously stated. The set of all possible loop topologies is too vast, even if only the “reasonable” ones are considered. A loop is constituted of several loop sections made of different gauges and spliced together in a certain number of ways. Although the average number of loop sections constituting a loop is three to four sections, the location of each discontinuity, i.e., its distance from the measurement equipment, is a parameter that can assume a set of nonnumerable values. This is why it is impossible to apply tout court the ML principle previously described to the set of all possible (or reasonable) topologies. It is proposed here to avoid the aforementioned problem by applying the ML identification method on a step-by-step basis to discontinuity types rather than to the topology of the whole loop. Starting with the first discontinuity and ending with the last one, the identification algorithm estimates first its location and then the kind of discontinuity. Doing so, at every step, we restrict to a finite number the possible topologies that have to be hypothesized during the identification process. In fact, there are four possible gauge kinds (AWG 26, 24, 22, and 19) and essentially four main discontinuity types that need to be identified: gauge change, bridged tap, colocated bridged taps, and end of loop. These possibilities are listed in Table I, where all the different (and distinct) types of impedance discontinuities are shown, i.e., gauge change 26 to 24 gauge, 26 to 22 gauge,. . ., 26 gauge bridged tap with 24 gauge next section, 24 gauge bridged tap with 22 gauge next section, etc. As will be explained later, the algorithm hypothesizes discontinuities where the working length is infinite so that some configurations are equivalent. For example, a discontinuity defined as a 26-gauge bridged tap and a 24-gauge next working section has the same response as a 24-gauge bridged tap and a 26-gauge next working section. Therefore, such redundant states are not included in Table I.

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TABLE I ALL POSSIBLE CONFIGURATIONS FOR THE FOUR MAIN DISCONTINUITIES LISTED IN COLUMN 1

In our approach, we hypothesize loop discontinuities by introducing auxiliary topologies that contain the hypothesized discontinuity and additional loop sections of infinite length. At the time a loop discontinuity is hypothesized, the length of the sections following that discontinuity is unknown and auxiliary topologies can be viewed as topologies with incomplete length information where an infinitely long section of cable replaces the section with unknown length. As will be shown in the next section, the use of auxiliary topologies will also allow us to obtain compensated (or deembedded) TDR traces, which will allow us to sequentially remove all the spurious echoes that arrive to the TDR head prior to the echo of the next real discontinuity. In so doing, the first echo present in the deembedded TDR trace is the echo of the next real discontinuity. The use of auxiliary topologies and the technique of deembedding are described with an example in the following section, whereas the flowchart of the proposed loop make-up identification algorithm is introduced and described in detail in

Section III-B. Finally, a brief example of loop identification will be given in Section IV. A. Data Deembedding: Removal of Real and Spurious Echoes Let us consider the topology, and its corresponding measured TDR trace, shown in Fig. 3. The topology has three discontinuities A, B, C. By looking at Fig. 3, we notice the following echoes after the SDS: the negative–positive echo pattern typical of a bridged tap (first two real echoes labeled A and B), the positive real echo C due to the end of the loop, and spurious echoes labeled SP1 (negative) and SP2 (positive). Spurious echoes should be either tagged as spurious or removed from the observation since they could confuse the identification algorithm and be mistaken for real echoes, thus, falsely indicating the presence of additional discontinuities. This can be accomplished computing the input impedance of suitable auxiliary topologies and then using (9). In fact, auxiliary topologies allow

GALLI AND KERPEZ: SINGLE-ENDED LOOP MAKE-UP IDENTIFICATION: TDR-MEASUREMENT-ANALYSIS METHOD

Fig. 3. Measured TDR trace of the topology shown in the lower right corner (probing signal: 5-V 1-µs-wide square pulse). Echoes due to the discontinuities in A, B, and C are indicated together with the initial SDS and spurious echoes (SP1 , SP2 ). Expressing lengths in meters, 980 ft = 299 m, and 2940 ft = 896 m.

Fig. 4. Example of the use of auxiliary topologies: Measured TDR trace of the topology in Fig. 3; simulated TDR trace of the topology in the lower right corner; difference between these two curves. Probing signal: 5-V 1-µs-wide square pulse. Expressing lengths in meters, 980 ft = 299 m.

the isolation of a subset of spurious and real echoes that depend on a specific discontinuity. For example, let us consider the topology in Fig. 4 and its corresponding simulated TDR trace. This topology is constituted of a first section composed of a 980-ft cable of AWG 24, augmented with the auxiliary topology based on a bridged-tap discontinuity composed of two sections of infinitely long AWG24 cable. As will be better explained in Section III-B, the auxiliary topology corresponds to hypothesizing the presence of the bridged tap after the first section of the loop. The topology in Fig. 4 generates only echo A (the first negative echo) and does not generate any other real or spurious echo. Similarly, let us consider the topology shown in Fig. 5 and its corresponding simulated TDR trace. This topology can be viewed as the topology of Fig. 4 with the added information on the length of the bridged tap. This topology generates echoes A, B, and

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Fig. 5. Same as in Fig. 4, but for the auxiliary topology shown in the lower right corner. Expressing lengths in meters, 980 ft = 299 m.

appreciable Type-1 spurious echoes (for the nomenclature of spurious echoes adopted here, see [2, Sec. 2.2]) around 9, 12, and 15 µs, whereas the end of the loop never generates an echo. The use of auxiliary topologies allows us to generate specific real and spurious echoes that can be subtracted from the observations. This is useful when a discontinuity is identified and its effects (both real and spurious echoes) have to be stripped out together with the SDS of that section from the observations in order to enhance the next real echo pertaining to the following discontinuity. For example, the curve labeled “Difference” in Fig. 4 represents the curve obtained by subtracting the simulated TDR trace obtained with the topology in the inset of Fig. 4 (solid line) from the measured TDR trace (the one in Fig. 3). The curve labeled “Difference” in Fig. 4 can be viewed as a compensated (deembedded) TDR trace where echo A has been removed from the original measured TDR trace. Similarly, subtracting the simulated TDR trace obtained on the basis of the topology in Fig. 5 from the measured TDR trace in Fig. 3, we have obtained another compensated TDR trace where echoes A, B, and all the Type-1 spurious echoes due to the bridged tap have been removed. In fact, as shown by the curve labeled “Difference” in Fig. 5, the first visible echo in the waveform is the one pertaining to the end of the loop (echo C), i.e., the last real echo. B. Flowchart of the Proposed Identification Algorithm A high-level flowchart of the proposed loop make-up algorithm is given in Fig. 6, where the following definitions hold: d(t) measured TDR trace; i discontinuity counter; number of all the possible topologies that can be N (i) hypothesized at step i; (i) set of the auxiliary topologies corresponding to {Dj } all the possible hypothesized discontinuities (j = 1, . . . , N (i) ) at step i; (i) {Tj } set of all the possible hypothesized topologies (j = 1, . . . , N (i) )1 at step i;

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Fig. 6. Flowchart of the proposed algorithm for loop make-up identification. (i)

{hj (t)}

set of all the simulated TDR traces (j = 1, . . . , N (i) ) corresponding to the set of all the (i) possible hypothesized topologies {Tj } at step i; (i) {µj } set of all the metrics (j = 1, . . . , N (i) ) pertaining (i) to all the possible hypothesized topologies {Tj } at step i; chosen topology at step i; T (i) simulated waveform corresponding to the chosen h(i) (t) topology T (i) at step i; e(i) (t) deembedded TDR trace; τ (i) , l(i) time of arrival and distance of the echo generated by the ith real discontinuity. At the beginning of every iteration indexed by index i, the algorithm has available a partially identified loop topology T (i−1) and a deembedded TDR trace e(i) (t) obtained by subtracting the simulated TDR trace corresponding to topology T (i−1) from d(t).4 At this point, the algorithm hypothesizes all possible discontinuities that may follow the partially identified

(i)

loop topology T (i−1) via the auxiliary topologies5 {Dj } (j = 1, . . . , N (i) ). There are several ways to reduce the number N (i) of hypothesized auxiliary topologies and speed up identification time; this topic will be addressed in detail in Part II of this study [1]. (i) The set of auxiliary topologies {Dj } are then used to (i−1) augment the basic topology T of the loop partially identified up the current step, so that a set of N (i) hypothesized (i) (i) topologies {Tj } is obtained. The simulated TDR traces hj (t) corresponding to these hypothesized topologies are generated and compared to the measured TDR trace d(t). The metric that has been chosen for comparing the measured TDR trace with the simulated traces is the mean square error (mse). A set of N (i) mses is therefore computed, one for each of the hypothesized topologies at step i: (i) µj

1 = t2 − t1

t2 

2 (i) d(t) − hj (t) dt,

j = 1, . . . , N (i) .

t1

(10) 4 At i = 0, the algorithm has no a priori information on the loop so that no partial topology T (0) is available and the deembedded TDR trace coincides with the original measured TDR trace d(t). If some a priori information is available, e.g., from a loop database, this can be reflected in the initial topology T (0) .

5 At i = 0, the auxiliary topologies that are hypothesized are simply four infinite-length single-section cables, i.e., one for each gauge. Therefore, at the first step, the algorithm estimates the gauge of the first loop section and removes the corresponding SDS. Basically, at step i = 0, the loop make-up identification algorithm proposed here uses the technique presented in [2].

GALLI AND KERPEZ: SINGLE-ENDED LOOP MAKE-UP IDENTIFICATION: TDR-MEASUREMENT-ANALYSIS METHOD

Particular attention must be given to the time interval [t1 , t2 ] on which the mses must be computed since it is difficult to determine it a priori or without visual inspection. At step i, this interval should be (τ (i) , τ (i+1) ), i.e., the interval between the time of arrival of the echo due to the discontinuity currently under identification and the time of arrival of the echo due to the following one. This ensures that the echo generated by the discontinuity under investigation can be fully compared with the simulated ones. However, the problem is that the value of τ (i+1) is still unknown at step i and cannot always be estimated without first performing the ith deembedding [d(t) − h(i) (t)]. Therefore, in practice, the optimal interval cannot be determined exactly. This problem is trivial for the case of human-aided identification because of the possibility of a visual inspection of the plot of the waveforms, but it is of major importance if a totally automated identification procedure has to be implemented. A possible solution to this problem is to measure the mse on several intervals of the kind (tS , te ), where tS = τ (i) and te = τ (i) + αl(l = 1, . . . , M ). The topology that will then be chosen will be the one that achieves more often the minimum of the mse. It has also been experienced that another metric should be used together with the mse: the difference between the peak of the hypothesized topology at step i and the peak of the ith observed echo. In fact, it might happen that even if the mse is relatively small, these two peaks might even be very different, thus indicating a problem. In general, this situation may arise in two cases: if some other discontinuity not tested exists, or if several echoes of same time of arrival add up and look like only a single echo. The former case occurs if the echo detected is due to a line impairment such as bad splice, water in the cable, line unbalance, etc., whereas the latter case occurs when the open branches of the previously identified bridged taps have a length equal (or very close) to the other bridged tap or to the length of the following loop section. In conclusion, a topology should be chosen at step i only if it exhibits the lowest mse and if the peak of the computer-generated waveform is close to the ith observed one. (i) Once the set of metrics {µj }, j = 1, . . . , N (i) , has been computed, the hypothesized topology Tk (i) that has generated (i) the smallest metric µk is chosen  (i) (i) (11) T k(i), where k satisfies µk = min µj . j

(i)

Deembedding is performed by subtracting h(i) (t) = hk (t), the (i) simulated TDR trace corresponding to Tk , from d(t), and the search for the next echo is performed on e(i+1) (t). If an echo is present, the discontinuity counter i is incremented, the echo location l(i) is estimated, and this length information is used (i−1) with a to replace one6 of the infinite-length sections in Tk section of length l(i) . At this point, the topology T (i) estimated at step i is available. Particular attention must be given to the case when bridged taps, single or colocated, are found. In fact, 6 Particular attention must be given to the order in which section lengths are estimated. There may be some intrinsic ambiguity in doing so, but this problem can be eliminated by the technique described in [1, Sec. 3].

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Fig. 7. Example of loop make-up identification. Step i = 0: Estimation of (0) the gauge of the first loop section. After subtracting D2 from d(t), the (1) deembedded TDR trace e (t) is obtained (curve labeled “Difference”).

single (colocated) bridged taps generate two (three) echoes and the algorithm has to deembed these multiple echoes before starting again to hypothesize discontinuities. IV. E XAMPLE OF L OOP M AKE -U P I DENTIFICATION Let us considered the measured TDR in Fig. 3, and let us assume that we have no a priori information on the loop makeup. For the sake of simplicity, throughout the example, we will assume that error-free estimates of the time of arrival (location) of the echoes (discontinuities) are available. This assumption is only made for simplifying the illustration of how the identification algorithm proceeds. Performance results reported in part II of this study are obtained using actual estimates. As mentioned in footnote 5, the four hypothesized auxiliary (0) (0) (0) (0) topologies D1 , D2 , D3 , and D4 are infinitely long singlesection loops of AWG 26, 24, 22, and 19, respectively. The (0) (0) (0) (0) simulated TDR waveforms h1 (t), h2 (t), h3 (t), and h4 (t) of these four topologies are plotted in Fig. 7 together with the measured TDR trace d(t). Clearly, the best match is given by (0) (0) (0) h2 (t), which corresponds to topology T (0) = T2 = D2 , (0) is not a i.e., an infinitely long cable of AWG 24. Since T bridged tap, we proceed with the deembedding, which is done (0) by subtracting h(0) (t) = h2 (t) from d(t). This allows us to (1) obtain e (t) (the curve labeled “Difference” in Fig. 7). A negative echo is clearly visible on e(1) (t) so that the discontinuity counter i is incremented by 1 and the time of arrival of the echo τ (1) = 2.9 µs is estimated, which corresponds to a discontinuity located at l(1) = 980 ft from the measurement equipment. At this point, T (0) is updated with l(1) . Therefore, the topology T (1) identified at step i = 1 is a 980-ft-long AWG-24 cable followed by an unknown discontinuity. (1) Auxiliary topologies Dj (j = 1, . . . , 35) are now generated to augment topology T (1) with hypothesized discontinuities: gauge changes, bridged taps, collocated bridged taps, and end of the loop. The simulated TDR traces hj (i)(t) (j = 1, . . . , 35)

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V. C ONCLUSION

Fig. 8. Example of loop make-up identification. Step i = 1: comparison between the measured TDR trace and the simulated TDR traces of some of (1) the possible hypothesized topologies. The algorithm chooses h8 (t) as the closest waveform (see Table I for the labeling of curves), which corresponds to (1) auxiliary topology D8 . The dotted lines in the topologies represent a section of infinite length. Expressing lengths in meters, 980 ft = 299 m. (1)

corresponding to the augmented topologies Tj are then computed, and some of them are plotted together with the measured TDR trace in Fig. 8 (see Table I for the labeling of the curves). (1) The algorithm selects h(1) (t) = h8 (t) as the waveform closest to d(t). This corresponds to choosing the augmented topology (1) (1) T (1) = T8 , which contains the auxiliary topology D8 , i.e., the augmented topology that contains a single bridged tap with AWG-24 sections of infinite length. After setting the bridged tap flag BT = 1, deembedding is performed, obtaining the compensated TDR trace e(2) (t) = d(t) − h(1) (t) (the curve labeled “Difference” in Fig. 4). An echo is clearly visible on e(2) (t) at 5.8 µs, which corresponds to a new discontinuity located at l(2) = 1.96 kft (0.6 km) from the measurement equipment or, equivalently, at ∆l(2) = l(2) − l(1) = 980 ft (298.7 m) after the first discontinuity. The discontinuity counter i is then incremented to i = 2 and is T (1) updated with ∆l(2) . There is no difference in assigning length ∆l(2) to the bridged tap or to the following working-length section, so that the topology T (2) estimated at step i = 2 is the one shown in Fig. 5. Since BT = 1, the discontinuity counter i is incremented again to i = 3, flag BT is reset to zero, and deembedding is performed again, obtaining e(3) (t) (the curve labeled “Difference” in Fig. 5). An echo is clearly visible around 11.7 µs, which corresponds to l(3) = 3.92 kft (1.19 km) or ∆l(3) = l(3) − l(2) = 2.94 kft (0.9 km) after the last identified discontinuity. Therefore, topology T (2) identified at step i = 2 is updated with ∆l(3) and the topology T (3) identified at step i = 3 is the one given in Fig. 3. (3) Auxiliary topologies Dj (j = 1, . . . , 35) are generated again to augment topology T (3) with hypothesized discontinuities. At this iteration, the algorithm will identify as the most likely discontinuity the end of the loop. Once deembedding is performed, no echo is found on e(4) (t) and identification ceases after having identified i = 3 discontinuities.

We have introduced a technique for determining loop makeups on a loop-by-loop basis using a TDR-based approach. The identification process is based on analyzing TDR measurements in such a way that the measurements are successively mapped to gradually augmented loop make-up topologies until the error between the measured TDR trace and the simulated characteristic of the hypothesized loop topologies becomes sufficiently small. The advantage of the proposed technique is that it can be applied in a mechanized single-ended fashion from either the CO or by a technician in the field using a handheld TDR. Thus, a new “broadband test head” can be installed in the CO, which will automatically and routinely provide up-to-date information on loop make-ups. This information can be input to a provisioning and maintenance system that will retain and correlate the records. This database can in turn be used for a number of important functions, such as loop-plant engineering, loop qualification and provisioning of DSL-based services, DSM, and maintenance of the loop plant. We believe that the capabilities described here and in [8]–[12] are required to fully exploit the power of emerging DSL technologies, and to effectively deal with the increasingly complex and dynamic unregulated local loop environment. In fact, the knowledge of both the loop make-up and the noise or crosstalk environment allows us to calculate precisely the performance of any DSL type [17]. This knowledge can also help enhance the bit rates and reliability of DSL services [16], and enable DSM [8], [9]. R EFERENCES [1] K. J. Kerpez and S. Galli, “Single-ended loop make-up identification—Part II: Improved algorithms and performance results,” IEEE Trans. Instrum. Meas., vol. 55, no. 2, Apr. 2006. [2] D. L. Waring, S. Galli, K. Kerpez, J. Lamb, and C. Valenti, “Analysis techniques for loop qualification and spectrum management,” in Proc. Int. Wire and Cable Symp. (IWCS), Atlantic City, NJ, Nov. 13–16, 2000. [3] S. Galli and D. L. Waring, “Loop make-up identification via single ended testing: Beyond mere loop qualification,” IEEE J. Sel. Areas Commun., vol. 20, no. 5, pp. 923–935, Jun. 2002. [4] S. Galli and K. Kerpez, “Signal processing for single-ended loop makeup identification,” in Proc. IEEE Workshop Signal Processing Advances Wireless Communications (SPAWC), New York, NY, Jun. 5–8, 2005, pp. 368–374. [5] S. Galli, “Improved method for determining subscriber loop make-up by subtracting calculated signals,” U.S. Patent 6 724 859, Apr. 20, 2004. [6] T. Bostoen, P. Boets, M. Zekri, L. van Biesen, T. Pollet, and D. Rabijns, “Estimation of the transfer function of a subscriber loop by means of a one-port scattering parameter measurement at the central office,” IEEE J. Sel. Areas Commun., vol. 20, no. 5, pp. 936–948, Jun. 2002. [7] P. Boets, T. Bostoen, L. van Biesen, and T. Pollet, “Measurement, calibration and pre-processing of signals for single-ended subscriber line identification,” in Proc. IEEE Instrumentation and Measurement Technology Conf. (IMTC), Vail, CO, May 20–22, 2003, pp. 338–343. [8] K. B. Song, S. T. Chung, G. Ginis, and J. M. Cioffi, “Dynamic spectrum management for next-generation DSL systems,” IEEE Commun. Mag., vol. 40, no. 10, pp. 101–109, Oct. 2002. [9] K. Kerpez, D. Waring, S. Galli, J. Dixon, and P. Madon, “Advanced DSL management,” IEEE Commun. Mag., vol. 41, no. 9, pp. 116–123, Sep. 2003. [10] S. Galli, C. Valenti, and K. Kerpez, “A frequency-domain approach to crosstalk identification in xDSL systems,” IEEE J. Sel. Areas Commun., vol. 19, no. 8, pp. 1497–1506, Aug. 2001. [11] C. Zeng, C. Aldana, A. Salvekar, and J. M. Cioffi, “Crosstalk Identification in xDSL systems,” IEEE J. Sel. Areas Commun., vol. 19, no. 8, pp. 1488–1496, Aug. 2001.

GALLI AND KERPEZ: SINGLE-ENDED LOOP MAKE-UP IDENTIFICATION: TDR-MEASUREMENT-ANALYSIS METHOD

[12] S. Galli, K. Kerpez, R. Hausman, and C. Valenti, “Multiuser channel estimation: Finding the best sparse representation of crosstalk on the basis of overcomplete dictionaries,” in Proc. IEEE Global Telecommunications (GLOBECOM) Conf., Taipei, Taiwan, R.O.C., Nov. 17–21, 2002, pp. 1213–1217. [13] T. Starr, J. M. Cioffi, and P. J. Silverman, Understanding Digital Subscriber Line Technology. Englewood Cliffs, NJ: Prentice-Hall, 1999. [14] M. B. Borchert, D. A. Hartzell, E. J. Thomassen, and L. M. Rezac, “Apparatus and method for improving a time domain reflectometer,” U.S. Patent 5 461 318, Oct. 24, 1995. [15] R. F. M. van de Brink, “Cable reference models for simulating metallic access networks,” ETSI, TM6 Permanent Document TM6(97)02, Jun. 1998. [16] K. Kerpez and S. Galli, “Optimization of single-carrier and multi-carrier DSL spectra,” in Proc. IEEE Int. Conf. Communications (ICC), Seoul, Korea, May 16–20, 2005, pp. 1347–1351. [17] The Telcordia DSL Spectral Compatibility Computer website managed by Kenneth J. Kerpez. [Online]. Available: http://net3.argreenhouse.com

Stefano Galli (S’95–M’98–SM’05) received the M.S. and Ph.D. degrees from the University of Rome “La Sapienza,” Rome, Italy, in 1994 and 1998, respectively, both in electrical engineering. He continued as a Teaching Assistant in signal theory at the Information and Communication Department, University of Rome. In October 1998, he joined Bellcore (now Telcordia Technologies), Piscataway, NJ, in the Broadband Networking Research Department, where he is now a Senior Scientist. His main research efforts are devoted to various aspects of x-digital-subscriber-line systems, wireless/wired home networks, wireless communications, power line communications, and optical code-division multiple access. His research interests also include detection and estimation, communications theory, and signal processing. He is the author or coauthor of more than 70 papers and is the holder of several U.S. and international patents. Dr. Galli is a Reviewer for several IEEE journals and conferences, the Chair of the IEEE Communications Society Technical Committee on Power Line Communications, and an Associate Editor for the IEEE SIGNAL PROCESSING LETTERS. He was also a co-Guest Editor for the feature topic Broadband is Power: Internet Access Through the Power Line Network of the IEEE Communications Magazine (May 2003) and a co-Guest Editor for the Special Issue on Power Line Communications of the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS (June 2006). He has served as a member of the Technical Program Committee in many IEEE conferences, as the General co-Chair of the IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC ’05), as the Vice-Chair of the General Symposium of the IEEE International Conference on Communications (ICC ’06), and as the co-Chair of the General Symposium of the IEEE Global Communications Conference (GLOBECOM ’06).

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Kenneth J. Kerpez (S’84–M’89–SM’93–F’04) received the B.S. degree from Clarkson University, Potsdam, NY, in 1983 and the M.S. and Ph.D. degrees from Cornell University, Ithaca, NY, in 1986 and 1989, respectively, all in electrical engineering. Since 1989, he has been at Telcordia Technologies, Inc., Piscataway, NJ, where he initially performed pioneering work on characterizing and coding for high-bit-rate digital subscriber lines, asymmetric digital subscriber lines, and very-highbit-rate digital subscriber lines. He later also worked on wireless hybrid fiber/coax access systems, home networking, residential gateways, and passive-optical-network optical-fiber broadband access systems. He is currently working on broadband service assurance and testing, Internet protocol television, and triple-play services. He is the author of numerous technical papers and is a frequent contributor to industry standards.