Channel Capacity Estimation of Digital Subscriber Lines: a Frequency Domain Approach Carine Neus, Patrick Boets and Leo Van Biesen Vrije Universiteit Brussel Pleinlaan 2, B-1050 Brussels, Belgium
[email protected]
Abstract— In order to identify if a subscriber loop is suitable for a certain Digital Subscriber Line (DSL) service, the transfer function of the loop has to be estimated. Several measurement techniques exist, however Single-Ended Line Testing (SELT) is often preferred by the telecom operators because all necessary measurements can be done at the central office. The SELT data is typically interpreted in the time domain. This paper presents a new approach by doing the identification in the frequency domain. It starts by explaining the drawbacks of the time domain approach. The paper explains how these are avoided by using a frequency domain identification algorithm. Measurement results show this is a viable alternative to the classical time domain identification. Keywords— Digital Subscriber Line (DSL), Single-Ended Line Testing (SELT), loop qualification, transfer function estimation, channel capacity.
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I. INTRODUCTION
HEN a customer requests a certain Digital Subscriber Line (xDSL) service, the first thing the operator needs to do, is verify whether his telephone line can support this service. This is called ‘loop qualification’ and is different for each customer since it depends on the cabling between the customer premises (CP) and the central office (CO). The make-up of this subscriber loop fixes the transfer function, and as a consequence limits the maximum achievable bit rate and as such the possibility to support a certain service. Many topologies are possible, but typically a subscriber loop consists of a cascade of several cable sections, possibly with a different diameter, connecting the CP to the CO. The final channel capacity does not solely depend on the loop make-up, but also on the noise power spectral density (PSD) at both line ends. However, the latter is not considered in this paper. Correct loop qualification is of great important to the operators because an overestimation results in customer dissatisfaction and an underestimation results in loss of potential customers. Hence, the accurate estimation of the
channel capacity is very important and the best way of qualifying a loop for DSL service is by testing it. Nowadays, commercial available instrumentation for the measurement of the transfer function already exists but is based on Double-Ended Line Testing (DELT). It requires a technician at both line extremities in order to quantify the loop transfer function. Dispatching a technician to the customer’s home for each subscription results in expensive prequalification and moreover, requires the cooperation of the customer. Therefore, it is desirable to have a technique that could identify and qualify all the subscriber loops in an automated and highly accurate manner without the intervention of staff at the subscriber’s location. This explains the recent shift of focus to Single-Ended Line Testing (SELT). With SELT, all measurements are performed at the central office side, which eliminates the necessity of dispatching a technician to the customer premises for each qualification. This explains why SELT is gaining much attention lately. However, in contrast to DELT, the loop transfer function cannot be measured directly from SELT data. The loop makeup has to be estimated first and from this, the transfer function and the channel capacity can be calculated. Discovering information about the loop make-up through single-ended line tests is possible with reflectometry. The basic principle is to inject an excitation signal in the subscriber loop under test, at the central office side. The signal propagates along the line and whenever an impedance discontinuity is encountered, a part of the signal is reflected and travels back to the measuring instrument. The measured SELT quantity is the one-port scattering parameter S11, which is the ratio of the reflected to the injected wave [1]. The excitation signal can be a pulse (Time Domain Reflectometry or TDR) or discrete multitone (DMT) symbols (Frequency Domain Reflectometry or FDR). The collected reflections can be analyzed in the time domain (s11(t)) or in the frequency domain (S11(f)), independently of the chosen measurement domain. However, up till now the identification has mainly been attempted by analyzing the one-port scattering parameter s11(t) in the time domain.
This paper proposes a new approach by doing the identification in the frequency-domain. This will avoid some major drawback of the time domain approach. The remainder of this paper is structured as follows. Section II explains the classical time domain identification and highlights the main drawbacks. Section III then proposes a new approach by doing both measurement and identification in the frequency domain. In section IV measurement results are discussed and Section V emphasizes the importance of SELT by describing some possible applications. Section VI summarizes the main conclusions. II. TIME DOMAIN APPROACH A. Time domain reflectometry (TDR) Injecting a pulse into the subscriber line, recording the reflections over time and processing the measured voltage quantities yields the one-port scattering parameter in the time domain s11(t), also called the reflectogram. Fig. 1 gives an example of such a reflectogram for a 500 m segment (0.4 mm diameter), cascaded with a 1500 m segment (0.6 mm diameter). The amount of reflection is given by (1) where Z1 is the characteristic impedance of the line before the discontinuity and Z2 is the characteristic impedance of the line after the discontinuity. Z − Z1 (1) ρ= 2 Z 2 + Z1 As cables with different wire diameters have different characteristic impedances (Z1 ≠ Z2), two cascaded cables will cause a reflection at their junction. Also line ends, bridged taps and load coils are discontinuities causing reflections. By analyzing the measured reflections, the make-up of the subscriber loop can be discovered. By determining the start time of a peak tstart it is possible to compute the line length l with (2) when the velocity of propagation of the twisted pair v is known.
v ⋅ t start (2) 2 The factor 2 comes from the fact that the signal travels forward until it reaches the discontinuity and then travels backward to the central office. l=
B. Time domain identification By analyzing the reflectogram, the loop make-up and thus also the loop transfer function, can be deduced by advanced signal processing techniques. In a previous paper [2], such a loop make-up estimator was reported. FDR was used instead of TDR, but the identification of the most important features was done in the time domain. The complete structure of this loop make-up estimator is depicted in Fig. 2. First, the one-port scattering parameter S11,raw(f), which is the ratio of the reflected wave to the incident wave, is measured by means of a network analyzer directly in the frequency domain using DMT symbols as excitation signals. Several pre-processing operations (denoising, base change) are necessary before transforming S11,preprocessed(f) into its time domain counterpart s11(t), the so-called reflectogram. After the ifft-operation, some more processing is needed to visualize the reflection information in the reflectogram as clearly as possible [3]. Then the most important characteristics of s11,processed(t), called ‘features’ are detected (e.g. the start of a reflection). Subscriber loop Measurement S11,raw(f) Pre-processing S11,preprocessed(f) ifft s11(t) Processing s11,processed(t) Feature Extraction
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Fig. 2. Left: model of the loop make-up estimator described in [2] (time domain appraoch); right: new estimator (frequency domain approach)
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Fig. 1. Time domain reflectogram for a 500 m segment (0.4 mm diameter), cascaded with a 1500 m segment (0.6 mm diameter)
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Using TDR measurements instead of FDR measurements, could resolve point 1, but problems 2 and 3 remain unchanged. Instead of attempting to tackle all these problems, a completely new approach was attempted by doing the identification directly in the frequency domain.
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only the reliable frequency band is taken into account; only the real or imaginary part of the data is used; the data is windowed and zero-padded.
Only then an ifft-operation is applied, this time not to calculate the reflectogram, but in order to bring out the periodicities of the adapted frequency domain signal. Each periodicity will generate a peak. From this, the reasoning system computes the most probable topology and the initial line lengths. Each of these operations will now be discussed. abs(S 11)
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First of all, after converting the one-port scattering parameter S11,preprocessed(f) to the time domain, processing is needed to remove aliasing and leakage. Moreover, due to irregularities on the line, the first few µs can show false reflections [3]. Due to the dispersive nature of twisted pairs, the reflections show long tails. This leads to a reflectogram in which the reflections are superposed. For example in Fig. 1, the second reflection starts while the first one is not completely extinct. This means each k-th peak pk is superimposed on the tail of the preceding peaks pk-1, pk2,…, p1, as such distorting the isolated shape of the individual peaks. This complicates the feature extraction and models are needed to take into account the effects of superposition [2]. The low frequencies (6 first ADSL tones) are often unreliable because the filter on the modem-board is designed to attenuate the frequencies out of the ADSL band. Performing the ifft-operation with these attenuated low frequencies leads to a completely distorted reflectogram. As a consequence the classical time-domain feature extraction becomes impossible in this situation.
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Fig. 2 can be used to situate the new reasoning system. It starts after the pre-processing of S11(f) and delivers the most probable topology and the initial line lengths for optimization. The pre-processing of S11,raw(f) is left unaltered: the signal is smoothed to remove the effects of noise and the measurement base is changed in order to visualize the reflections as clearly as possible (see [3] for more information). But instead of transforming this pre-processed S11(f) directly into the timedomain, first some complementary processing is done. The main concept is to exploit the information in the periodicity of S11(f) (see Fig. 3). S11,preprocessed(f) is periodic due to the constructive and destructive interference of the reflected waves, with a periodicity determined by the line lengths. The first step consists in manipulating the preprocessed data in the following way:
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C. Difficulties The feature extraction of the time domain scattering parameter s11,processed(t) has several drawbacks.
III. FREQUENCY DOMAIN APPROACH
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Once the features of s11,processed(t) are defined, a reasoning system deduces the most probable topology and determines the length of each line section. Finally, a last module optimizes these line lengths by minimizing a cost function with a Maximum Likelihood Estimator algorithm and produces the estimated subscriber loop make-up [4]. This last module works in the frequency domain, but the identification of the features and the reasoning is done in the time-domain. It is also important to mention that physical cable models were used rather than a black box model. Other approaches, like neural networks or models with lots of parameters are also possible but lack physical meaning. Several other research groups are also working on a white box approach [5,6,7,8], but they use modem dependent voltage reflectograms for their measurements. These systems produce the estimated subscriber loop makeup, allowing as such to calculate the transfer function. If the noise characteristics are known, using a direct measurement or a model-based estimation, then a bit rate prediction is possible. However, at the moment no operational SELT-system exists which can predict the subscriber loop capacity with sufficient accuracy. Consequently research in this field is still ongoing.
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Fig. 3. S11 represented in polar (left hand side) and complex notation (right hand side) for a 600 m cable
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A. Reliable frequency band When dealing with field measurements, the reliability of some frequency bands might be unsatisfying. As explained in Section II.C, the filter on the modem-board attenuates the frequencies out of the xDSL band. But some frequency bands can also be distorted due to other causes (e.g. nonlinear balun behavior at low frequencies). Therefore, only the reliable frequency band should be used for the identification. Otherwise, if these unreliable frequencies are taken into account, this will result in a severely distorted time-domain signal. B. Real/imaginary part of the signal The one-port scattering parameter S11(f) is a complex quantity and is usually described by its amplitude (often in dB) and its phase. But S11(f) could be described with its real and imaginary part as well. We chose to work with the complex notation instead of the polar notation because the periodicity is more pure, as can be seen in the example of Fig. 3. This can theoretically be explained as follows. Starting from the linearized definition of S11(f) for a single line (3) S11 ( f ) = − ρ g + (1 − ρ g2 ).e −2γl where ρ g is the reflection at the measurement device due to the mismatch between the characteristic impedance of the line and the impedance of the measurement device, it can be proven that:
ℜ( S11 ( f )) = −ℜ( ρ g ) + e −2αl . cos( −2 β l ) ℑ( S11 ( f )) = −ℑ( ρ g ) + e
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whereas the magnitude is given by : 2
S11( f ) = ρg + e−4αl − 2.e−2αl .(ℜ(ρg ). cos(−2βl ) + ℑ( ρ g ). sin( −2 β l ))
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When comparing with Fig. 3, we recognize the exponentially damped sine when considering S11(f) in complex notation. Performing an ifft on the real or imaginary part, will bring out the present periodicities, while│S11(f)│, consisting of the sum of a sine and a cosine, altered by the real and imaginary part of the generator reflection, will give a poorer signal after performing the Fourier transform. Also with more complex loop make-ups, S11(f) in complex notation will give a better result when performing an ifft. Whether the real or the imaginary part is used, is free since both contain the same amount of periodicity information. C. Windowing and zero-padding Before applying the ifft, the signal should be windowed in order to reduce leakage (e.g. Hanning window). In practice, only a small frequency band is reliable. In that case, the
number of remaining measurement points is low and zeropadding is used in order to improve the resolution. After all these operations, an ifft is performed. As a consequence, the signal is back in the time domain, but due to the executed manipulations, it has not the physical meaning of the reflectogram anymore. Rather, the ifft was used as a tool to bring out the periodicities. IV. RESULTS AND DISCUSSION Measurements were performed in the Alcatel Lab, Antwerp, Belgium. 401 points were measured in the ADSL frequency grid, with a spacing of 4312.5 Hz, from DC up to 1.7MHz. However, only up to 600 kHz was evaluated to be reliable and therefore the higher frequencies were not used in the processing. The 6 lowest tones were present in the measurements, but in order to show that these are not necessary for the identification, they were not used in the algorithm. This means only the frequency band [30, 600] kHz was used. Three types of cables were available: France Telecom 0.4 mm (FT4), France Telecom 0.6 mm (FT6) and British Telecom 0.5 mm (BT5). Fig. 4 compares both time domain signals for the cascade of 1000 m FT4 with 1000 m BT5: the reflectogram s11,processed(t) and the new time domain signal which we call s11,new(t). Clearly, the reflection overlap is strongly reduced. Both reflections are clearly separated in s11,new(t), in contrast to the classical time-domain approach. This reduces ambiguity and allows for a better estimation of the initial line lengths. Each peak in s11,new(t) indicating a reflection, again, with (2), the line lengths can be estimated. We also see there is no more aliasing problem with the new approach, in contrast to the time domain identification. Table 1 shows the results of the new algorithm, giving the loop topology and the initial line lengths, as well as the final loop make-up. The error on the total initial length is less than 6% for all measurements and less than 2% for the total optimized length. The topology was correctly identified for 12 of the 13 cases. The estimated loop make-up is used to compute the transfer function H(f). From this, the channel capacity can be calculated with Shannon’s formula. 2 ⎛ H ( f ) S ( f ) ⎞⎟ ⎜ C = ∫ log 2 1 + df ⎜ ⎟ N( f ) W1 ⎝ ⎠ W2
(7)
As this paper does not deal with the estimation of the noise PSD and as we are interested to see how the error on the estimated loop make-up influences the error on the estimated downstream capacity, a simple noise model is assumed: background additive white Gaussian noise (AWGN) with a PSD of N(f) = -130dBm/Hz.
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Fig. 4. Comparison between the time domain approach (s11,processed) and the frequency domain approach (s11,new) for a cascade of 1000 m (FT4) and 1000 m (BT5)
In addition, we have assumed ADSL transmission with the downstream transmit PSD mask as defined in the standards [9], i.e. S(f) = -40 dBm/Hz in the downstream band [W1, W2] = [163.875, 1104] kHz. Table 1 shows the maximal achievable bit rate for a 12-bit ADC modem. The actual bit rate, based on the actual loop make-up, and the estimated bit rate, based on the estimated make-up after optimization, are compared. The relative error on the capacity is less than 0.5% for all 13 measured loop make-ups.
V. APPLICATIONS Being able to identify the loop make-up via SELT with sufficient accuracy and in an automated way opens up several promising applications. The following subsections give some examples of possible applications.
Actual Length (m)
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FT4 BT FT6 FT4 BT FT6 FT4-BT FT4-FT6 FT4-BT FT4-FT6 FT4-BT-FT6 FT4-BT-FT6 FT4-BT-FT6
400 384 422 960 998 1014 880-591 800-591 1041-537-525 960-1014 960-537-253 1041-307-1014 1041-998-438
A. Estimation of the achievable xDSL service As mentioned in the introduction, correct loop qualification is important to avoid unsatisfied customers due to false greens or loss of revenues due to false reds. A good knowledge of the channel capacity allows estimating the achievable xDSL service for each specific customer. Especially when deploying new demanding services like ADSL2+, VDSL and VDSL2, the knowledge of the channel capacity will be a valuable asset. Certainty about the ability of the line to support the desired DSL allows offering xDSL services in a more cost-effective way. B. Updating records The existing loop make-up records are often missing or incomplete. If it is feasible to perform loop identification via single-ended measurements in an automated way, all the lines of the network could be tested on a regular base. Using this automated system, the information of the local loop could be updated in an accurate and detailed way. Ideally, this will lead to complete and up-to-date records. The complete knowledge of the network strongly facilitates its maintenance and administration for the operators and results in a better service for the customer. C. Detection of channel defects When a line is down or when a modem refuses to make a connection, SELT is the only cost-effective tool to detect a severe channel defect. Performing a new measurement and comparing it with the known loop make-up, helps identifying the location of the cable fault or a bad connector. D. Measurement for competitive local exchange carriers With the liberalization of the European telecommunication market, it has become common for several providers to share a same network infrastructure. In contrast to the incumbent local exchange carrier (ILEC), the competitive local exchange carriers (CLEC) do not have direct access to the subscriber lines. As a consequence, they can only use SELT to measure the line.
TABLE 1 MEASUREMENT RESULTS Error on total Optimized initial length Length (%) (m) 0 393 4 396 5.5 401 4 993 0.2 1012 1.4 1002 5 1052-355 0.6 1006-391 5.2 1034-967-7 1.3 977-1020 2.8 1004-353-436 1.6 982-338-1077 3.2 1023-1219-153
Error on total optimized length (%) 1.8 1 0.3 0.7 1.2 0.2 0.5 0.2 0.4 0.2 0.4 0.1 0.2
Actual bit rate (Mbit/s) 9.216 9.216 9.216 9.216 9.216 9.216 9.216 9.216 8.60383 8.47397 8.89693 7.55014 7.65403
Estimated bit rate (Mbit/s) 9.216 9.216 9.216 9.216 9.216 9.216 9.216 9.216 8.56672 8.50365 8.90064 7.57612 7.67258
Error (%) 0 0 0 0 0 0 0 0 0.4 0.4 0.1 0.3 0.2
VI. CONCLUSIONS
ACKNOWLEDGMENT
Determining the channel capacity from SELT measurements is possible, but far from simple. In contrast to DELT, the loop transfer function cannot be measured directly. Therefore, the loop make-up must be identified first. Once the loop make-up is known, the transfer function can be calculated and the channel capacity can be estimated. But due to the fact that all the measurements can be done from the central office, SELT is often preferred by the telecom operators. As a consequence, research is ongoing to create a fully automated system for the measurement and interpretation of reflectograms of the local access network of telephone companies. This will allow, amongst other possible applications, on-demand qualification tests. Up till now the feature extraction had mainly been attempted by extracting the most important features of the oneport scattering parameter in the time domain s11(t). This paper proposed a new identification approach by analyzing the features of another quantity, namely s11,new(t), which is also a time-domain signal but has no physical meaning and was created from a processed form of the frequency-domain one port scattering parameter S11(f). With this, the three main drawbacks of the time domain approach, namely aliasing, dispersion and unreliable frequency bands are tackled. The main advantage is the possibility to take into account only the reliable frequency bands. This is important since the 6 lower ADSL tones are often unreliable due to the filter on the modem-board, which makes the classical time domain feature extraction impossible. With the new approach, the necessary measurements can be done from the modem-board without any adaptation to by-pass the filter. The measurement campaign confirms the new algorithm leads to good initial lengths, which in turn eases the optimization process and leads to an accurate capacity estimation.
The authors would like to thank Alcatel Research and Innovation in Antwerp Belgium for making the cable lab available to us and in particular Frank Defoort and Geert Ysebaert. REFERENCES [1]
[2]
[3]
[4] [5]
[6]
[7]
[8] [9]
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