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INTERNATIONAL JOURNAL OF ELECTRONICS AND International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME COMMUNICATION ENGINEERING & TECHNOLOGY (IJECET) ISSN 0976 – 6464(Print) ISSN 0976 – 6472(Online) IJECET Volume 4, Issue 4, July-August, 2013, pp. 101-118 © IAEME: www.iaeme.com/ijecet.asp ©IAEME Journal Impact Factor (2013): 5.8896 (Calculated by GISI) www.jifactor.com TOPOLOGY ESTIMATION OF A DIGITAL SUBSCRIBER LINE M.Bharathi#1, S.Ravishankar#2, Vijay Singh#3 #1, #2 Department of Electronics and Communication Engineering, R V College of Engineering Bangalore, India, #3 DRDO, Bangalore ABSTRACT Topology estimation of a Digital subscriber line (DSL) is critical for an operator to commit a quality of service (QoS) requirement. Single Ended Loop Testing (SELT) is the most preferred and economical way for estimating the copper loop topology. A new method employing a combination of complementary code based Correlation Time Domain Reflectometry (CTDR) and Frequency Domain Reflectometry (FDR) for loop topology estimation is developed. Use of existing modem without any additional hardware in the measurement phase is the unique advantage of this method. Since the measurement is done online the effect of cross talk and AWGN is also considered. In this proposed SELT method approximate loop estimation is first obtained from CTDR measurements. An optimization algorithm based on FDR is then used to predict a more accurate loop topology. Employing FDR measured data and the FDR data of the approximate CTDR predicted topology, an objective function is defined. The objective function is then minimized using Nelder-Mead multivariable optimization method to get an accurate loop estimate. Tests carried out on typical ANSI loops shows good prediction capability of the proposed method. No prior knowledge of the network topology is required in this process. For the estimated loop topology capacity in terms of data rate is calculated and is compared with the capacity of the actual loop. Keywords: Digital subscriber line (DSL), Frequency domain Reflectometry (FDR), Correlation time domain Reflectometry (CTDR), and Loop qualification. I. INTRODUCTION It is important for a service operator to evaluate the Quality of Service (QoS) afforded over a subscriber loop under realistic circumstances. Apart from the data rate performance specified for typical services, a QOS also prescribes the delay in the transmission (in ms), the packet loss and BER. Subscriber line conditions include the transfer function of the line which is a function of the line topology and noise Power Spectral Density (PSD). The line topology is unravelled first, and then 101 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME performance is computed for the topology considering AWGN and crosstalk noise. A double ended loop measurement allow easy estimation of loop impulse response and the noise PSD, but needs a test device at the far end of the loop and is not economical prior to a service commencement. An economical method would require a reuse of the network operator’s central office (CO) side DSL modem resources to perform measurements. The physical loop consists of gauge changes, bridge taps and loop discontinuities that result in a change of characteristic impedance. The generated echo from these discontinuities when a signal is injected into the physical loop is analysed to extract details of location and the type of discontinuity. S. Galli et al [1-4] have employed pulse TDR based techniques to characterize the loop. A pulse is considered as a probe signal and is transmitted through the loop and the reflections produced by each discontinuity are observed in time. The time domain reflection which contains the signature of the loop is then analysed to predict the loop topology. Clustering of the TDR trace [2-3] and the use of statistical data [4] are included to reduce the time and to increase the accuracy respectively. These techniques provide a good estimation of the loop but are computationally intensive and cannot be easily implemented in current DSL modems. A more practical method described by Carine Neus et al [6] uses one port scattering parameter S11 in time domain and estimates the loop topology. The S11 measurement is however done off line with a vector network analyser over the entire band width [5]. David E. Dodds [7, 8] has proposed FDR for identifying the loop impairments. In the measurement phase a signal generator is used to probe the line up to 1.3 MHz in steps of 500 Hz and the reflections are coherently detected. However if there are multiple discontinuities close to each other (<100m), detecting all discontinuities in a single step may not be possible. If the discontinuities are far from each other the order of variation of the reflection makes it difficult to predict all the discontinuities in a single step. SELT Estimation is performed in three phases. The measurement phase during which CTDR and FDR measurements are captured; termed as SELT – PMD function in G.SELT [20] and a second phase called as interpretation phase when an analysis is done for topology estimation; termed as SELT-P function in G.SELT. In a third phase the data rate is calculated (i.e again a SELT-P function) for the estimated topology. No separate test equipments are required and the measurement is done online in the bundle without a need to access copper. In this paper the logical interfaces required by G.SELT [20] are retained. However the interpretation and analysis of the data is vendor specific and this paper describes a novel method. The measurement phase of the proposed method reuses the blocks of the current DSL modem and hence only a small code is needed that can be easily compiled into any modem. In this step the line is sounded sequentially once by employing CTDR and next by employing FDR. In the interpretation phase, the first step consists in analysing CTDR results to obtain an approximate estimation of the distance and the type of the discontinuities [9]. The topology learning from the CTDR application is used to generate an FDR data for the estimated loop. In the second step of the interpretation phase the generated FDR data is compared with a target (measured) FDR data in a mean squared sense to arrive at an exact estimate of the loop topology. The analysis of measured data may be performed in the modem to a limited extent or offline where more computing resources are available. In the third phase the capacity is calculated from the accurately predicted topology obtained in the previous loop estimation phase. Good predictability has been observed for a variety of ANSI loops with different reach and with multiple bridge taps [11]. Section II of this paper details the hybrid method for loop topology estimation. In section III measurement and interpretation phase of topology estimation are dealt along with the results for ANSI loop topology. The bit rate of the estimated channel is calculated considering AWGN noise of -140 dBm/Hz and cross talk. 102 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME II. HYBRID METHOD FOR LOOP TOPOLOGY ESTIMATION CTDR method needs no prior knowledge of the loop for topology estimation but the accuracy of prediction is limited due to the variation in propagation velocity with the frequency and the gauge of the copper medium. On the other hand, FDR method can predict the topology with higher accuracy but requires a reasonable initial knowledge of the topology. A hybrid method is developed to overcome these limitations by combining the two methods. Approximate loop topology is obtained with CTDR method and is used as the initial guess for FDR based optimization method for accurate prediction of the topology. The details of the developed CTDR and FDR optimization method are outlined below. A. Complementary CTDR method Spread spectrum (SS) techniques afford a possibility of providing measurements with improved SNR without sacrificing response resolution. Proposed CTDR method uses the DMT modem with its bit loading algorithms [11] for measurement. The PN sequence is distributed over all the tones in every DMT symbol. The carriers employ Quadrature amplitude modulation (QAM) constellation. The frequency domain signal generated by the constellation encoder is converted to a time domain signal p (t ) using inverse discrete Fourier transform (IDFT).This time domain signal p (t ) is transmitted through a loop with an echo transfer function h(t ) and correlated with its echo signal v(t ) at the receiver to obtain the correlated signal W (t ) that is expressed as, W (t ) = p (t ) ⊗ v (t ) = p (t ) ⊗ ( k * p ( t ) * h (t ) ) (1) Where, k is the proportionality constant. If the autocorrelation of the probe signal can be approximated as delta function, then the correlated signal is W (t ) W (t ) = k{ ( L δ (t ) )* h(t ) } (2) Here, L is the number of elements in the code, operator ⊗ represents correlation operation and operator * represents convolution operation. In our implementation complementary codes are used as a probe signal to increase the range of predictability. Complementary codes are set of codes whose out of phase autocorrelation sums to zero. So the sum of the auto correlation of the two member sequence is a delta function [10]. Ak ⊗ Ak + Bk ⊗ Bk = 2Lδ k (3) Where, δ k is the delta function and Ak , Bk are the complementary code pairs of length L. Ideally the auto correlation of the individual sequences ( Ak , Bk ) has side lobes but gets cancelled when added together. The peak of added signal at zero shift will be 2L. A complementary code of L = 2 K is generated with K=10. Tone numbers 0-511 are loaded with 2 bits per tone with this L element code pair. Unipolar version of each of the complementary codes ( Auni , Buni ) [10] and its one’s complementary form ( A ' uni , B ' uni ) are generated and these 4 codes are used to probe the line. B. Application of Complementary codes for loop topology estimation The steps involved in using the complementary codes for the loop topology estimation is shown in Fig.1. 1. Generate complementary codes Ak and Bk . 103 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME 2. Generate the unipolar version and its one’s complemented form for Ak and Bk . 3. For Auni , simulate the reflected signal ( Auni ∗ h(t ) ) where, h(t ) is the impulse response of the channel. 4. For A' uni , simulate the reflected signal ( A ' uni ∗h(t ) ). 5. Obtain the received signal for the sequence Ak r A = Aun i * h(t ) − A'uni *h(t ) 6. Obtain the correlated signal W A = r A ⊗ A k 7. Repeat steps 3-6 for the second Golay sequence to obtain W B . 8. Sum W = W A + W B . Ak Auni h(t ) A + r WA Correlation Auni − h(t ) + W + Buni h(t ) B + r W B Buni Correlation − h (t ) Bk Fig.1. Functional diagram of Complementary CTDR for loop testing The position of the peak in the correlated signal (W) used to estimate the location of discontinuity (d ) is given by v.t max d= (4) 2 Where, v is the velocity of propagation in the twisted pair and tmax is the peak position. The peak amplitude of the signal depends on the length of the loop section and the type of discontinuity (reflection coefficient). Using the first peak amplitude of the correlated signal the reflection coefficient of the first discontinuity can be estimated. The peak amplitude for an open circuit discontinuity (reflection coefficient = 1) for different lengths is plotted in Fig.2. Using Fig.2 as reference, for a CTDR estimated first segment length and amplitude, the reflection coefficient can be calculated. Amplitude for the estimated length ρ (1) ( f ) = (5) Amplitude for the estimated length with ρ = 1 0.07 26 AWG 0.06 24 AWG -3 x 10 0.05 Peak amplitude 2 0.04 0.03 1 0.02 0 7 8 9 10 11 12 0.01 Length of the line (Kft) 0 0 2 4 6 8 10 12 Length of the line (Kft) Fig.2. Peak amplitude variation of the reflected signal with line length 104 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME When the discontinuities are closely spaced it is difficult to distinguish the cross correlation peaks. Step by step ML principle [4] is used in identifying the discontinuity type at the calculated location. Data de-embedding technique is used to mask the reflections of known discontinuities from the measured echo signal to unravel the signatures of the unknown discontinuities. Thus by incorporating the de-embedding process, overall predictability of the CDTR method is enhanced. After identifying each discontinuity (i) in a successive manner, an auxiliary topology ( Aux (i ) ) is formed which consists of all the previously identified discontinuities followed by an infinite loop section. The reflection ( ri ) due to this auxiliary topology is generated and is removed from the total reflection v(t ) to get a de-embedded TDR trace Di . Di = v (t ) − ri ( 6) The trace Di consists of echoes from the rest of discontinuities in the line and is correlated with the input signal p (t ) to arrive Wi (t ) . Wi (t ) is the correlated signal after removal of echoes from the known discontinuities (first i discontinuities) and hence brings out the next peak (i+1) and discontinuity. This process is continued until there is no identifiable peak in the resultant signal. In this way after identifying each discontinuity the reflection due to the identified discontinuity is removed from the total reflection to enhance the predictability of the following discontinuities. The effect of AWGN (-140dBm/Hz) and cross talk is added in the simulation as the measurement is done online. Cross talk is a slowly varying signal across the symbols and so gets cancelled due to the subtraction of the reflected signal (step 5 &7) shown in Fig.1. To mitigate the effect of AWGN noise, averaging over number of symbols is carried out. This averaging improves the signal to noise ratio (SNR) and hence increases the dynamic range. The predicted line topology (Ф) from CTDR contains length and gauge of all the line sections. The prediction accuracy is improved using the proposed FDR based optimization method. This optimization method works by comparing FDR signal of predicted and actual loops. The FDR received signal for the predicted topology Ф is simulated using the mathematical model described in the next section. C. Model for the FDR received signal In FDR method the PN sequence is sent sequentially (one tone in each DMT symbol). The received echo signal is a function of the reflection (ρ) and transmission (τ) coefficients at each discontinuity. The reflection coefficient (ρ) [16] is Za − Zb ρ( f ) = (7 ) Za + Zb Where, Za and Zb are the frequency dependent characteristic impedance before and after the discontinuity. Similarly, τ is given by [16] 2 Za τ(f ) = (8 ) Za + Zb In the above equations, ρ and τ varies with frequency as the characteristic impedance is a function of frequency which is given by [18], R + j ωL Z= (9) G + jωC The frequency dependant RLCG parameters in the above equation are obtained empirically as described in [18] and used in our computation for the transfer function of the 24 AWG and 26 AWG UTP lines. In the equations that follow we assume that the transmitted signal is a Discrete Multitone 105 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME signal with ‘N’ tones conforming to the tone spacing and bandwidths as detailed in the DSL standards [11, 12]. The observed reflected signal along with the effect of noise, when the nth tone is sounded is given by M R ( f n ) = ∑ R (i) ( f n ) + No ( f n ) (10) i = 1 Here R (i ) ( f n) is the received signal from the ith echo path when the nth bin is sounded. Here th No ( f n ) is the noise in the n tone and M is the number of echo paths in the loop. Further, R (i ) ( f n ) = S ( f n ) Hecho(i) ( f n ) (11) Where S ( f n ) is the spectrum of the transmitted data and the Hecho(i ) ( f n ) is the transfer function of the ith echo path and is given by Hecho i) ( fn ) = F (τ (1) ,τ (2) ,... (i −1) )H (i) ( fn )ρ (i) ( fn ) (12) ( τ Here F (τ (1) , τ ( 2) ,...τ (i − 1) ) is a frequency dependant function that includes the transmission coefficients of all the discontinuities preceding the ith discontinuity and ρ (i ) ( f n ) is the reflection coefficient of the ith discontinuity. H (i ) ( f n ) is the transfer function of the round trip path. The total received signal is sum of received signal of over all the tones. R( f ) = ∑ R( fn) (13) n D. FDR Optimization An iterative optimization process based on FDR method is developed. Nelder-Mead algorithm is chosen for this optimization as it can solve the multidimensional unconstrained optimization problems by minimizing the objective function. Tone numbers 6-110 is sounded individually with two bits as lower frequency tone offer lower attenuation and hence better range. The steps involved in this algorithm is 1. Simulate FDR received signal for the guess topology R (Φ, fn ) . 2. Obtain an FDR measurement (R( fn) ) . ˆ 3. Calculate the objective function (MSE) N 2 OE = ∑ R(Φ, fn) − R( fn) ˆ (14) n=1 4. Obtain the accurate line topology by minimize OE using Nelder-Mead simplex optimization algorithm. Nelder-Mead optimization algorithm iteratively improves Ф in terms of line segment lengths until the best solution (close match) is found. This algorithm works with constructing vectors with updating each variable (Each line segment lengths) of Ф, one at a time by increasing 5%. Initial simplex consists of the newly created ‘n’ vectors along with Ф. The algorithm updates the simplex repeatedly until the best solution is found. Nelder-Mead algorithm has a limitation that it can converge to local minima. To overcome this local minima problem optimization is performed with a different initial guess whenever the objective function value is greater than 1e-4. 106 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME The flowchart of the complete proposed method is shown in the Fig.3. Correlation TDR for approximate topology Measured echo Estimate signal in time Estimate discontinuities by Correlate domain discontinuity maximum likelihood with input distance and successive decomposition Approximate topology (Ф) Measured echo Error minimization using signal in freq Nedler- Mead algorithm domain Final predicted Error R^ (fn) R(Ф,fn) topology function FDR based optimization Fig.3. Flow chart of the proposed method III. SIMULATION RESULTS AND DISCUSSION Test loops are defined to emulate possible scenarios as per ITU recommendation 996.1[11] shown in Fig.4, that include a variety of reach, gauge change and bridge taps. The applicability of the method is tested in the presence of AWGN (-140 dBm/Hz ) and the cross talk defined in [11]. 12 Kft Test loop 1 26AWG 9 Kft 4 Kft Test loop 2 26 AWG 24AWG 0.5 Kft 26 AWG Test loop 3 3 Kft 6 Kft 26AWG 26AWG Test loop 4 1.5 Kft 26 AWG 9 Kft 2 Kft 0.5 Kft 0.5 Kft 26 AWG 24 AWG 24 AWG 24 AWG Fig.4. Test loops Test loop1: Correlation results in amplitude versus time lag and is converted to the desired units of amplitude versus distance using equation 4. For test loop 1 the variation of correlation amplitude with distance is shown in Fig. 5. The positive peak indicates the discontinuity as an open end of loop as the other possible discontinuities (bridge tap and gauge change) have negative reflection coefficient [1]. The possible gauge types with 12.71 Kft length and open end termination are listed in Table 1 along with the mean square error between the simulated TDR of the possible topology and the target TDR. For the predicted line (12.71 Kft, 26 AWG), error of 5% in the length is observed which is due to the use of average VoP in the distance calculation. The CTDR predicted topology is used as an initial guess for the FDR based optimization method. 107 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME -6 x 10 8 X: 12.71 Y: 5.318e-006 6 Cross correlation amplitude 4 2 0 -2 -4 -6 0 10 20 30 40 Distance(Kft) Fig.5. Distance Vs correlation amplitude for test loop1 TABLE 1 POSSIBLE TOPOLOGIES FOR TEST LOOP1 Sl. No Hypothesized discontinuity Possible topology MSE 1 End of loop(open) 12.7 Kft line,26 AWG 8.70e-5 2 End of loop(open) 12.7 Kft line, 24 AWG 5.83e-4 The FDR signal for test loop 1 is shown in Fig.6. It is observed that the signal amplitude is low in the order of 1e-3 and the rate of decay is steep. Fig.7 shows the convergence plot using the Nelder-Mead algorithm with CTDR predicted loop as an initial guess. With 16 iterations MSE is converged to 8.05e-6 and the predicted line is 12.0001 Kft 26 AWG. -4 x 10 -5 x 10 8 3 Received echo Signal (Volts) Reflected Signal (Volts) 6 2 4 1 3.2 3.4 3.6 3.8 4 4.2 4.4 4.6 2 0 -2 0 1 2 3 4 Frequency (Hz) 5 x 10 Fig.6. FDR signal for test loop1 -3 Current Function Value: 8.0545e-006 10 -4 10 MSE -5 10 -6 10 0 2 4 6 8 10 12 14 16 Iteration Fig.7. Convergence plot for test loop1 108 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME Test loop2: Fig. 8 shows the correlation amplitude variation with distance for test loop2. The amplitude of the peak at 9.03Kft is -3.54e-6 and indicates a negative reflection coefficient at first discontinuity. All the possible topologies with this observation and their mean square error with actual echo signal are listed in Table 2 -6 x 10 2 Cross correlation amplitude 1 0 -1 -2 -3 -4 X: 9.039 Y: -3.54e-006 -5 0 10 20 30 40 Distance(Kft) Fig.8. Distance Vs correlation amplitude for test loop2 TABLE 2 POSSIBLE TOPOLOGIES AT FIRST DISCONTINUITY (TEST LOOP2) Hypothesized type Possible topology (dotted MSE line indicates infinite length) Gauge change 9.03 Kft 1.05e-6 26 AWG 24AWG Bridge tap 26AWG 1.11e-5 9.03 Kft (Taps with Open end) 26 AWG 26AWG Bridge tap 24AWG 1.25e-5 (Taps with Open 9.03 Kft end) 26 AWG 26AWG Bridge tap 24AWG 1.11e-4 9.03 Kft (Taps with Open 24 AWG 24AWG end) Bridge tap 26AWG 1.03e-4 (Taps with Open 9.03 Kft end) 24 AWG 24AWG From the above table, topology with gauge change (first row in Table 2) is identified as the correct topology till first discontinuity. The correlated signal after the removal of the echo due to first discontinuity ( W1(t ) ) is given in Fig.9 which indicates the next discontinuity at 13.56Kft (segment length = 13.56Kft–9.03Kft). The type of discontinuity is concluded as end of loop as the reflection coefficient of this discontinuity is positive and there is no bridge tap identified previously in the loop. Thus, the CTDR predicted loop topology is 9.03 Kft of 26 AWG followed by 4.53 Kft of 24 AWG. 109 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME -6 x 10 4 3 Cross correlation am plitude X: 13.56 2 Y: 2.915e-006 1 0 -1 -2 -3 0 10 20 30 40 Distance(Kft) Fig.9. De-embedded signal ( W1(t ) )for test loop2 The FDR reflection for this test loop is shown in Fig.10. Fig.11 shows the MSE variation for a range of line sections. This figure indicates the variation of MSE with the prediction accuracy of the individual line segments. Nelder-Mead optimization algorithm with the CTDR predicted loop as an initial guess estimates the line as 9.00 Kft in series with 3.99 Kft and the MSE is 6.62e-06. The convergence plot using Nelder-Mead algorithm is shown in Fig.12. -4 x 10 -6 5 x 10 8 4 Received echo Signal (Volts) Reflected Signal (Volts) 6 3 4 2 2 0 2.5 3 3.5 4 4.5 1 0 -1 -2 0.5 1 1.5 2 2.5 3 3.5 4 4.5 Frequency (Hz) 5 x 10 Fig.10. FDR signal for test loop2 -3 x 10 8 6 MSE 4 2 0 5 4. 5 10 4 9 .5 9 3 .5 8 .5 2 nd lin e len gth 3 8 1s t line le ng th Fig.11. Error surface for test loop 2 110 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME -3 Current Function Value: 6.6225e-006 10 Predicted Topology 9Kft 3.99Kft -4 10 26AWG 24AWG MSE -5 10 -6 10 0 5 10 15 20 25 30 35 Iteration Fig.12.Convergence with final predicted topology for test loop2 Test loop 3: Correlation amplitude versus distance plot for test loop 3 is shown in Fig.13. A bridge tap has two reflections: one from the location of bridge tap with reflection coefficient of ~ (-0.3) and the other from the open end of the bridge tap with reflection coefficient equal to 1. Hence a negative peak followed by positive peak within a very short distance is expected. In Fig.13, the amplitude value of the first peak at 3.107 Kft is -0.001976 which corresponds to negative reflection coefficient. All the possible topologies are listed in Table 3 along with their computed mean square error with actual signal. -3 x 10 1.5 Cross correlation am plitude 1 0.5 0 -0.5 -1 X: 3.107 -1.5 Y: -0.001976 -2 5 10 15 20 25 30 35 40 Distance(Kft) Fig.13. Distance Vs Correlation amplitude for test loop 3 From the table, topology with bridge tap (Second row in Table 3) of 26 AWG lines is identified as the Auxiliary topology ( Aux(1) ) till first discontinuity. The correlated signal after the removal of the echo due to this first identified topology ( W1(t ) ) is given in Fig.14. Further de- embedding using the identified tap length of 0.57Kft (3.67Kft –3.10 Kft) results in W2 (t ) (Fig. 15) which helps in predicting the next segment length as 6.22Kft (9.32Kft – 3.10Kft) and the identified discontinuity is end of loop with open termination. 111 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME TABLE 3 POSSIBLE TOPOLOGIES AT FIRST DISCONTINUITY (TEST LOOP3) Hypothesized Possible topology MSE discontinuity (dotted line indicates infinite length) Gauge change 3.10 Kft 0.0029 26 AWG 24AWG Bridge tap 26AWG 0.0014 (Taps with 3.10 Kft Open end) 26 AWG 26AWG Bridge tap 24AWG 0.0020 (Taps with 3.10 Kft Open end) 26 AWG 26AWG Bridge tap 24AWG 0.0020 3.10 Kft (Taps with 24 AWG 24AWG Open end) Bridge tap 26AWG 0.0018 (Taps with 3.10 Kft Open end) 24 AWG 24AWG -4 -6 x 10 x 10 8 X: 3.672 Cross correlation amplitude Cross correlation amplitude Y : 0.0008338 10 X: 9.322 6 Y : 1.105e-005 4 5 2 0 0 -2 -4 -5 -6 0 10 20 30 40 0 10 20 30 40 Distanc e(Kft) D is tanc e(Kft) Fig.14. De-embedded signal ( W1(t ) )for test loop3 Fig.15. De-embedded signal ( W2 (t ) )for test loop3 The CTDR predicted topology is shown in Fig. 16. 0.57 Kft 26 AWG 3.10 Kft 6.22 Kft 26AWG 26AWG Fig. 16. CTDR predicted topology for test loop 3 112 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME This CTDR predicted topology is used as initial guess for the FDR optimization. The FDR signal for loop 3 is shown in Fig.17. 0.015 Received echo Signal (Volts) 0.01 Reflected Signal (Volts) 0.005 0 -0.005 -0.01 -0.015 0 1 2 3 4 5 Frequency (Hz) 5 x 10 Fig.17. FDR received signal for test loop 3 A sensitivity study of the line segments on the variation of MSE is shown in Fig.18 and it is inferred that the received echo signal is a strong function of the first section of the line. Optimization algorithm predicts the line topology as 3.00 Kft parallel with 6.00 Kft with the bridge tap length of 0.5Kft. Final MSE of 7.11e-6 confirms fully converged solution. 0.2 0.15 MSE 0.1 0.05 0 7 4 6 3.5 3 2.5 5 2 2nd Line Length First line Length Fig. 18. Error surface for test loop 3 Test loop 4: Fig. 19 shows the correlated signal amplitude with distance for test loop 4. The negative peak with amplitude -3.19e-5 at 9.47 Kft indicates negative reflection coefficient and all the possible topologies are analyzed and the discontinuity is identified as gauge change. -6 x 10 1 Cross correlation amplitude 0 -1 -2 X: 9.47 Y: -3.193e-006 -3 -4 0 5 10 15 20 25 30 35 Distance(Kft) Fig.19.Distance Vs Correlation amplitude for test loop 4 113 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME -6 -6 x 10 x 10 3 1 Cross correlation amplitude Cross correlation amplitude X: 13.49 2 Y: 1.668e-006 0 1 -1 0 -2 X: 11.48 Y: -2.79e-006 -1 -3 0 10 20 30 40 50 0 10 20 30 40 50 60 Distance(Kft) Distance(Kft) (a): w1 (t ) (b): w 2 ( t ) -7 x 10 6 X: 13.77 Cross correlation amplitude Y: 3.799e-007 4 2.01 Kft 26 AWG 2 9.47 Kft 2.01 Kft 2.29 Kft 26 AWG 24AWG 24AWG 0 -2 (d): CTDR Predicted Topology 0 10 20 30 40 Distance(Kft) (c): w3 (t ) Fig.20. De-embedded signals for test loop 4 Removing the reflection from this identified segment, W1(t ) (Fig. 20(a)) helps in predicting the next discontinuity of bridge tap at 11.48 Kft (Length of second segment is 11.48Kft-9.47Kft). Construction of possible topologies at the second discontinuity (Table 4) helps in identifying the gauges of all the line segments. De-embedding the next reflection based on the identified information ( W2 (t ) ) helps in predicting the complete topology. TABLE 4 POSSIBLE TOPOLOGIES AT SECOND DISCONTINUITY (TEST LOOP4) Hypothesized discontinuity possible topology (dotted MSE line indicates infinite length) Gauge change followed by 9.47 Kft 2.01 Kft 26AWG 4.04e-6 bridge tap(Taps -Open end) 26AWG 24AWG 24AWG Gauge change followed by 9.47 Kft 2.01 Kft 24AWG 4.40e-6 bridge tap (Taps-Open end) 26AWG 24AWG 24AWG The CTDR estimation for test loop 4 is not complete. This is due to the very less contribution of the far end reflection in the overall received signal. With this as the initial guess, FDR prediction converged to MSE error of 0.0028. As the MSE error is higher than the threshold level (1e-4), further iterations are attempted with modified initial guesses but no improvement on the MSE error is achieved. This issue of non convergence is due to wrong specification of number of discontinuities as the initial guess. To address these types of scenarios, the hybrid method is further improved with 114 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME an added convergence check which adds a discontinuity to the initial guess as given in Fig.21. As the CTDR is capable of predicting first two discontinuities and from practical understanding the maximum number of discontinuities is not more than 4, this outer loop is set with a maximum limit of two. Step 1 : CTDR for initial estimation, Initialize COUNT Step 2 : FDR estimation Update the initial guess, Update the initial guess with Increment COUNT an additional bridge tap, Initialize COUNT No, COUNT < 3 No, COUNT = 3 MSE < 1e-4 Yes Final topology Fig.21. Improved Hybrid method The converged line topology from the modified method is shown in Fig.22. -3 Current Function Value: 2.2193e-005 10 Predicted Topology 1.47 Kft 1.42 Kft 26 AWG 26 AWG 9Kft 1.97Kft 0.75Kft 0.49Kft MSE -4 10 26AWG 24AWG 24AWG 24AWG -5 10 0 50 100 150 200 250 Iteration Fig.22. Convergence with the final predicted topology for test loop 4 First two line segments and the first bridge tap length of test loop4 are predicted with good accuracy but the segment 3, 4 and tap2 length are not accurate. Fig. 23 shows the schematic representation of the reflection from each discontinuity for test loop 4. Strength of the reflection from each junction is calculated based on the reflection and transmission coefficients for comparison. Signal attenuation due to the line length and gauge is not considered in this investigation as the focus is to quantify the effect of individual reflections on the final echo. Table 5 compares the % 115 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME contribution of each reflection in the received signal. More than 90 % of the received signal is contributed by the reflections R1, R2 and R3. Even though R4 reflection is considered as 5 %, due to the higher distance of travel, attenuation will be higher and hence net overall contribution in the received signal will be much lesser than 5%. R5 and R6 have less than 2% weightage in the received signal even without considering the attenuation effect. This results in very feeble contribution in the measured echo. Hence accuracy of these line segments, in the predicted topology does not influence MSE to a significant level. This explains the reason for higher prediction error in the segments 3, 4 and tap 2 of test loop 4. R3 R5 R1 R2 R4 R6 Fig.23. Reflections for test loop4 Line Capacity for a specified transmit energy and margin is obtained based on the SNR profile using water filling algorithm [15]. Number of bits that can be loaded in each tone is calculated by estimating the SNR profile at the receiver. The transfer function of the predicted loop topology needed to compute the SNR is obtained from the Transmission matrix (ABCD) as in [14, 15]. The cross talk and the AWGN noise are also considered in this performance computation. Table 6 provides a comparison of the capacities of the estimated loops. TABLE 5 REFLECTION STRENGTH CONTRIBUTION Weightage of transmission and Reflection coefficients in the received signal (Excluding the attenuation effect) Reflection Sequence of approximate Total % reflection and transmission contribution coefficients in the received signal(Ri/∑Ri) R1 0.03 0.03 6.8 R2 0.97*0.3*0.97 0.2823 64.5 R3 0.97*0.3*1*0.3*0.97 0.0847 19.4 R4 0.97 *0.3*0.3*0.3*0.97 0.0254 5.8 R5 0.97*0.3*0.3*1*0.3*0.3*0.97 0.0076 1.7 R6 0.97*0.3*0.3*1*0.3*0.3*0.97 0.0076 1.7 ∑Ri 0.4376 116 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME TABLE 6 ESTIMATED CAPACITY FOR THE TEST LOOPS Test Actual loop topology Predicted Topology Downstream Downstream Loop capacity of the capacity of the actual predicted loop(Mbps) loop(Mbps) 1 12 Kft,26 AWG 12.0Kft, 26 AWG 1.732 1.732 2 9 Kft, 26 AWG – 9 Kft, 26 AWG – 1.712 1.712 4 Kft 24 AWG 4 Kft 24 AWG 3 3 Kft, 26 AWG – 3 Kft, 26 AWG – 2.812 2.812 (0.5 Kft ,26 AWG)*– (0.5Kft,26AWG)*– 6 Kft, 26 AWG 6 Kft, 26 AWG 4 9 Kft,26 AWG – 9 Kft, 26 AWG – 1.25 1.16 2Kft, 24 AWG – 2 Kft, 24 AWG – (1.5 Kft,26 AWG)* – (1.5Kft,26 AWG) *– 0.5 Kft, 24 AWG – 0.8 Kft, 24 AWG – (1.5 Kft, 26 AWG)*– (1.1Kft,26 AWG)* – 0.5 Kft, 24 AWG 0.7 Kft, 24 AWG * - bridge tap line segments IV. CONCLUSION Performance of a DSL line is estimated with a hybrid SELT method for topology prediction followed by data rate calculation using water filling algorithm. A two step CTDR-FDR combined SELT method is developed to predict the twisted pair loop topology. In the first step CTDR measurements are used to estimate the loop discontinuities as an initial guess. This estimate is further refined using FDR based optimization method with a target (measured) FDR results. Results of selected ANSI test loops show that this method can predict the topology with less than 0.2 % error for single discontinuity loops. For lines with more discontinuities, the prediction accuracy is good for the segments which contribute high for the reflected signal. Since the method is based on matching the estimated loop reflection with the actual reflection; the prediction is not very accurate for loops with segments that do not affect the transfer function significantly. Maximum data rate for the predicted loops are calculated with estimated transfer function using water filling algorithm with considering the cross talk and the AWGN noise. V. REFERENCES [1] Stefano Galli , David L.Waring ,”Loop Makeup Identification Via Single Ended Testing :Beyond Mere Loop Qualification,” IEEE Journal on Selected Areas in Communication, Vol. 20, No. 5, pp. 923-935, June 2002. [2] Stefano Galli, Kenneth J.Kerpez, “Single-Ended Loop Make-up Identification –Part I:A method of analyzing TDR Measurements,” IEEE Transactions on Instrumentation and Measurement, Vol. 55, No. 2, pp. 528-537, April 2006. [3] Stefano Galli , Kenneth J. Kerpez, “Signal Processing For Single-Ended Loop Make-Up Identification,” in proceedings IEEE 6th Workshop on Signal Processing Advances in WireIess Communications, pp. 368-374, 2005. [4] Kenneth J.Kerpez, Stefano Galli, “Single-Ended Loop Make-up Identification –Part II: Improved Algorithms and Performance Results,” IEEE Transactions on Instrumentation and Measurement, Vol. 55, No. 2, pp. 538-548, April 2006. 117 International Journal of Electronics and Communication Engineering & Technology (IJECET), ISSN 0976 – 6464(Print), ISSN 0976 – 6472(Online) Volume 4, Issue 4, July-August (2013), © IAEME [5] Tom Bostoen,Patrick Boets, Mohamed Zekri,Leo Van Biesen, Daan Rabijns, ”Estimation of the Transfer function of a Subscriber Loop by means of a One-port Scattering Parameter Measurement at the Central Office,” IEEE Journal on Selected Areas in Communciations, Vol. 20, No. 5, pp. 936-948, June 2002. [6] Carine Neus,Patrick Boets and Leo Van Biesen, “Transfer Function Estimation of Digital Subscriber Lines with Single Ended Line Testing,” in proceedings Instrumentation and Measurement Technology Conference 2007. [7] David E. Dodds, “Single Ended FDR to Locate and Specifically Identify DSL Loop Impairments,” in proceedings IEEE ICC 2007, pp. 6413- 6418. [8] David E. Dodds, Timothy Fretz, “Parametric Analysis of Frequency Domain Reflectometry Measurements,” in proceedings Canadian Conference on Electrical and Computer Engineering 2007, pp. 1034-1037, 2007. [9] M.Bharathi, S.Ravishankar, “Loop Topology Estimation Using Correlation TDR,” in Proceedings International Conference on Communication, computers and Devices, IIT, Kharagpur, India, December 10-12, 2010. [10] Moshe Nazarathy ,S.A Newton, R.P Giffard, D.S. Moberly .F. Sischka , W.R. Trutna ,S.Foster, “Real Time Long Range Complementary Correlation Optical Time Domain Reflectometer,” Journal of Lightwave Technology, Vol. 7, No. 1, pp. 24-38, January 1989. [11] Test procedures for digital subscriber line (DSL) transceivers, Telecommunication standardization sector of ITU std. G.996.1, 02/2001. [12] Asymmetric digital subscriber line transceivers – 2 (ADSL2), Telecommunication standardization sector of ITU std. G.992.3, 07/2002. [13] Very high speed digital subscriber line transceivers 2 (VDSL 2), Telecommunication standardization sector of ITU std. G.993.2, 02/2006. [14] Dr.Walter Y.Chen , “DSL Simulation Techniques and Standards Development for Digital Subscriber Line Systems”, Macmillan Technical Publishing. [15] T.Starr, J.M.Cioffi, and P. J. Silverman,Eds., Understanding Digital Subscriber Line Technology, New York: Prentice Hall,1999. [16] John D.Ryder , Networks,Lines and Fields, Prentice Hall. [17] Simon Haykins , Communication Systems, 4th edition, John Wiley & Sons. [18] Dr.Dennis J.Rauschmayer, ADSL/VDSL Principles, Macmillan Technical publishing, 1999. [19] Gi-Hong Im, “Performance of a 51.84-Mb/s VDSL Transceiver Over the LoopWith Bridged Taps,” IEEE Transcation on Communications, Vol. 50, No. 5, pp.711-717, May 2002. [20] Single-ended line testing for digital subscriber lines (DSL), Telecommunication standardization sector of ITU std. G.996.2, 05/2009. [21] Raj Kumar Tiwari, Sachin Kumar and G R Mishra, “A Class Ab Ccii Topology Based on Differential Pair with Modified Output Stage”, International Journal of Electrical Engineering & Technology (IJEET), Volume 4, Issue 1, 2013, pp. 68 - 74, ISSN Print: 0976-6545, ISSN Online: 0976-6553 118

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