COMMITTEE T TELECOMMUNICATIONS Working Group TE.4 Plano, Texas; 2 December 998 TE.4/98-36 CONTRIBUTION TITLE: Equivalent Loss and Equivalent Noise: Figures of Merit for use in Deployment and Spectrum Management SOURCE*: Adtran, Inc. PROJECT: Spectrum Compatibility Project ABSTRACT This contribution builds on current digital service deployment practices by developing equivalent signal (ES), equivalent loss (EL), and equivalent noise (EN) figures of merit. These figures of merit are derived from the ideal DFE and DMT capacity equations in the Draft Spectrum Compatibility Technical Report. Application of the figures of merit to margin calculation is presented. Applications to deployment and spectrum management are discussed. Based on the initial results presented here, we encourage the committee to continue the development of this approach, and its inclusion in the spectrum compatibility report/standard. Introduction Historically, deployment of digital services has been based on the insertion loss at a single frequency and limitations on the number of bridged taps and their lengths. This practice has the appeal of simplicity, both in terms of measurement requirements and calculation requirements. However, when considering modern DSL equipment, it suffers from relatively poor accuracy in predicting the actual performance of a system on a particular loop. In contrast, the current draft spectrum compatibility technical report describes theoretical calculations for DFE margins and capacity to determine whether two technologies are spectrally compatible on a particular loop. While these calculations are relatively simple to perform with today s modern computing platforms, their intended use for deployment or spectrum management is rather unclear. For instance, is it envisioned that would they be used on a case by case basis to determine if a particular technology could be deployed on a particular loop? This contribution develops a middle ground approach, developing figures of merit that could be used for deployment and spectrum management purposes. By using figures of merit, a NOTICE This contribution has been prepared to assist Standards Committee T-Telecommunications. This document is offered to the committee as a basis for discussion and is not a binding proposal on ADTRAN, Inc. The requirements are subject to change in form and numerical values after further study. ADTRAN, Inc. specifically, reserves the right to add to, or amend, the statements contained herein. * CONTACT: Kevin Schneider; email: kevin.schneider@adtran.com; Tel: 256-963-8000; Fax: 256-963-2386
2 of 8 TE.4/98-36 relatively simple test for deployment is still possible (like the historic method), but with somewhat greater accuracy in predicting actual performance. Based on the capacity and DFE margin calculations, two figures of merit are developed: Equivalent Loss (EL) and Equivalent Noise (EN). Both are technology dependent in that they are a function of the bandwidth used by a particular loop technology. These figures of merit are relatively simple to calculate, offering the possibility that handheld test equipment, or the transceivers themselves, can be used to make in-field measurements to compare with the theoretical figure of merit. 2 Discussion The draft Spectrum Compatibility Technical Report [] provides equations for the calculation of DFE margins and the capacity of DMT systems. The Optimal DFE margin calculations can be written in the form Margin db = 0 * log0 exp ln( f _ SNR( f )) df SNR _ reqdb W + () W where W is the Nyquist. The DMT capacity is calculated using C = DMTBW USED 2 S( f ) H( f ) log 2 + df CG Margin (2) 9.75 + db N f 0 ( )0 where the SNR min condition from [] is incorporated into the DMTBW USED, which is the portion of the available DMT that is actually used by data carrying carriers. (CG is the Coding Gain assumed.) If we assume SNR min >>, the DMT calculation can be rewritten in a form that calculates margin for a given data rate: where Margin db = 0log0 ( SNR( f )) df K DMTBW DMTBW USED (3) USED 0ln(2) C K = (9.75 CG) +. (6) ln(0) DMTBW USED which is effectively the required SNR for the given data rate C. We can also rewrite () to eliminate the inverse operations of natural logarithm and exponential to produce a much simpler equation: Margin db = 0log0 ( f _ SNR( f )) df SNR _ reqdb W + (4) W Now, using (3) and (4) and assuming the folded SNR (f_snr) is significantly greater than over the Nyquist band, we can come up with a single equation that approximates the theoretical performance of both DFE based single carrier transceivers and DMT transceivers:
TE.4/98-36 3 of 8 Margin db = 0 * log0 ( SNR( f )) df SNR required( db) (5) where Margin db, is the approximate margin in db, is the Nyquist bandwidth for single carrier systems and the effective bandwidth of the utilized carriers for DMT, and 2 S( f ) H( f ) SNR ( f ) =. (6) N( f ) S(f) is the transmit PSD, H(f) is the loop insertion loss, and N(f) is the noise present at the receiver. Since we have assumed the SNR is large (which eliminated the + term), the signal, loss and noise terms become separable. We then can define the equivalent transmit signal as ES = 0 * log0( S( f ))df the equivalent (insertion) loss of the loop as EL = 20 * log0( H( f ) )df and the equivalent noise on the loop as EN = 0 * log0( N( f ))df Then, the margin calculation in (5) can be approximated by Margin db ( ES EL EN) SNR required ( db) (8) (9) (0) () ES is the equivalent transmit signal PSD level, EL is the equivalent frequency independent loss that results in approximately the same performance as the loop in question, and EN is the equivalent white noise PSD level which gives approximately the same performance as the noise in question. Note that these calculations are performing the mean of the transmit PSD, loss or noise PSD after they have been converted to db. This development illustrates a point that is often misunderstood in spectrum compatibility discussions: transmit power or crosstalk power in and of itself is not the crucial element in spectrum compatibility. Instead, linear calculations (such as the mean) on the PSD after it has been converted to db are important. This is illustrated in Figure, where transmit PSD, loop loss, received PSD, and noise PSD are shown for HDSL operating on CSA 6 with 49 self NEXT. Note that on this db plot, performance is governed by the area (the integral) between the received signal and noise curves. This is quite different than what would be obtained by taking areas or integrals of the PSDs before they are converted to db. Figure 2 shows ES, EL and EN and the actual frequency dependent functions.
4 of 8 TE.4/98-36 -40-50 -60 Transmit PSD Received PSD PSD (dbm/hz) -70-80 -90-00 -0-20 -30 Performance Governed By this Area Crosstalk PSD -40 0 0.2 0.4 0.6 0.8.2.4.6.8 2 x 0 5 Frequency (Hz) Figure. Transmit, Receive and Crosstalk PSDs for HDSL on CSA Loop 6. -20 Loop Attenuation -EL -40 ES Transmit Signal PSD -60 Atten. (db) or PSD (dbm/hz) -80-00 EN Crosstalk PSD -20-40 0 0.2 0.4 0.6 0.8.2.4.6.8 2 Frequency (Hz) x 0 5 Figure 2: Loop Attenuation, Transmit and Crosstalk PSD with EL, ES, and EN for HDSL on CSA Loop 6.
TE.4/98-36 5 of 8 2. Relationship to previous work Previously, in TE.4/96-66, a concept of equivalent 26 AWG loop length was presented. In that contribution, the proposed method of developing equivalent loop length was through empirical models based on test loops. Bridged taps were considered separately. This contribution offers an approach to calculating equivalent 26 AWG loop length, based on theoretical cable characteristics.. By using EL, we also include the effect of bridged taps in the equivalent loop length. To get an equivalent length of 26 AWG cable, the EL can be computed for the loop in question and compared to a table of values for the EL of 26 AWG. Note that EL is technology dependent (just like the approach in TE.4/96-66), since the bandwidth is a function of the technology used. Table shows the EL for 2BQ ISDN, 2BQ HDSL and ADSL-type technologies for 26 AWG cable as a function of length. EL was calculated using khz sampling of the loss and trapezoidal integration, with 35 Ohm terminations for the 0-40 and 0-96 khz calculations, 00 Ohms for the others. In Tables 2 and 3, EL for the ANSI T.60 and CSA loops are presented. Table 2 shows EL for ISDN 2BQ and ADSL-type transmission on the ANSI T.60 loops, along with the single Nyquist frequency loss used in ISDN deployment. Table 3 shows EL for HDSL 2BQ and ADSL-type technology and the single Nyquist frequency loss used for HDSL deployment. (Note: 35 Ohms used for all terminations in Tables 2 & 3.) 2.2 Use in Margin Estimates There are a variety of ways that this data can be used in margin estimates. As an example of the use of ES, EL, and EN, we consider the ideal DFE calculations for HDSL (T.43 Annex B type PSD) on CSA loop 6. From table 3, we find EL 0,96k = 28.2 db. We have calculated ES 0,96k and found it to be 40. dbm/hz and EN 0,96k for 49 disturber self NEXT is 97.3 dbm/hz. (These were shown in Figure 2.) Using Equation, we estimate the margin as 40. 28.2 + 97.3 2.5 = 7.5 db. This is within several tenths of a db of the margin attained through direct calculation. When this method is applied to ADSL calculations, initial tests have shown the upstream margin can generally be predicted within -2 db, with homogeneous or mixed crosstalk. However, we get a bit more variation in the downstream direction. In our initial work, it appears that the choice of bandwidth is most critical. For T.60 loop #7, accuracy to within -2 db is obtained if a downstream bandwidth of 40-300 khz is used. These figures of merit are likely to be more useful individually than simply as part of the Equation calculation. For instance, if EL is known for a loop, it can be substituted (perhaps as equivalent 26 AWG) for the actual loop loss characteristic. Or EN could be used in place of the actual crosstalk PSD for margin calculations. 2.3 Possible Uses in Deployment The calculations that have been presented here can be used in several ways to assist in deployment of DSL technologies. First, EL gives a concise characterization of the loop for a particular technology. In this way, EL could be used directly, or as a part of an Equivalent 26 AWG approach to characterizing loops. Second, EN can be used with EL to qualify loops based on measured noise levels. Using EL and EN for different technologies, quick estimates of achievable performance levels can be obtained. This could be very useful in a loop unbundling environment.
6 of 8 TE.4/98-36 EN can also be used for spectrum management purposes. For instance, if the EN of a new xdsl technology matches the EN of an existing technology over a certain frequency band, it might be considered to be spectrally equivalent to the existing technology. Or if the new technology s EN is significantly less than that of the existing technology, the new technology might be termed to have superior spectral compatibility. Rather than use EN directly, it might also be used indirectly in the development of new spectrum management PSD templates for spectrally equivalent or more spectrally friendly classes of technology. Table 4 shows EN as a function of bandwidth for 49-disturber HDSL and ISDN crosstalk, as defined by the transmit spectra definitions in T.43 annex B. The 40-550 khz case is illustrated in Figure 3. The results of Table 4 were calculated assuming the -piece crosstalk model, using trapezoidal integration with 00 Hz increments. Also shown are the EN for Crosstalk + -40 dbm/hz noise floor. For the wide bandwidth cases, these may provide a more accurate estimate of the actual impact that the crosstalk has on system performance. Table. EL for 26 AWG Cable as a function of Length & Length EL (db) @ (khz) (kft) 0-40 0-96 20-40 40-300 40-550 40-00 5 0.4 5.6 5.47 20.07 23.49 30.23 5.5.4 7.8 7.04 22.08 25.84 33.25 6 2.42 8.75 8.60 24.0 28.20 36.28 6.5 3.43 20.32 20.7 26. 30.55 39.3 7 4.43 2.89 2.73 28.2 32.90 42.33 7.5 5.44 23.46 23.29 30.4 35.26 45.36 8 6.44 25.03 24.86 32.5 37.6 48.39 8.5 7.45 26.60 26.42 34.6 39.96 5.4 9 8.46 28.7 27.98 36.8 42.32 54.44 9.5 9.46 29.74 29.55 38.9 44.67 57.46 0 20.47 3.3 3. 40.2 47.03 60.49 0.5 2.47 32.88 32.67 42.22 49.38 63.52 22.48 34.45 34.23 44.23 5.73 66.54.5 23.48 36.02 35.79 46.25 54.09 69.57 2 24.49 37.59 37.36 48.26 56.44 72.59 2.5 25.50 39.6 38.92 50.27 58.79 75.62 3 26.50 40.73 40.48 52.29 6.5 78.65 3.5 27.5 42.30 42.05 54.30 63.50 8.67 4 28.5 43.87 43.6 56.32 65.85 84.70 4.5 29.52 45.44 45.7 58.33 68.2 87.72 5 30.53 47.0 46.73 60.34 70.56 90.75 5.5 3.53 48.58 48.30 62.36 72.92 93.78 6 32.54 50.5 49.86 64.37 75.27 96.80 6.5 33.54 5.72 5.42 66.39 77.62 99.83 7 34.55 53.29 52.98 68.40 79.98 02.85 7.5 35.56 54.86 54.55 70.4 82.33 05.88 8 36.56 56.43 56. 72.43 84.69 08.9
TE.4/98-36 7 of 8 Table 2. EL for T.60 loops (s for ISDN and ADSL/Lite Technologies) T.60 Loss @ EL (db) @ (khz) Loop # 40 khz 0-40 20-40 40-300 40-550 40-00 47.4 35.6 54.6 70.9 83.2 08.7 2 44. 32.7 53.2 66.5 78.2 99. 3 42.0 30.6 49.0 68.6 78.2 97.4 4 39.5 30.4 45.4 60.2 7.4 93.0 5 37.8 28. 45. 57.5 67.8 86.5 6 37.7 28.9 43.6 68.3 78.5 96.7 7 36.3 27.5 4.9 54.4 63.6 8.9 8 35.8 27.2 43.4 57.7 68.0 89.6 9 36.5 26.0 45.7 52.0 60. 74.3 0 34.6 26.4 4.9 57. 67.2 88.6 34.6 25.6 4.5 5.8 60.3 76.5 2 32.8 25.2 37.6 49.6 58.7 75.9 3 34.4 25. 42.2 5.7 60.2 75.6 4 34.0 25.2 39.6 5.0 60.0 75.8 5 32.2 24.5 37.2 48.3 56.5 72.7 Table 3. EL for CSA loops (s for HDSL and ADSL/Lite Technologies) CSA Loss @ EL (db) @ (khz) Loop # 96 khz 0-96 20-40 40-300 40-550 40-00 36.2 26.4 25.3 37.6 40.4 50.5 2 4.6 26.5 24.2 40.2 39.9 49.0 3 33.2 26.7 26.3 34.4 40.7 53.5 4 39.3 28.7 27. 39. 45. 53.4 5 32.3 27.7 27.8 33.6 39.3 49.8 6 35.0 28.2 27.8 36.3 42.4 54.6 7 40.3 27.5 25.2 38.4 42.8 55.2 8 34.2 26.6 25.9 35.7 43.4 57.0 9 4.5 3.6 30.8 45. 5.4 64.0 0 43.9 35.0 34.5 45.6 53.9 69.9 Table 4. EN for 49-disturber ISDN and HDSL Near End Crosstalk PSD type EN (db) @ (khz) 0-40 0-96 20-40 40-300 40-550 40-00 49-HDSL -06. -97.3-96.5-00.3-8.5-36.6 49-HDSL + N -06. -97.3-96.5-00.3-7.7-29.5 49-ISDN -0. -0.9. --06.8-24.5-32.3-42.6 49-ISDN + N -0. -0.5-06.5-23.5-29.9-35.2
8 of 8 TE.4/98-36 3 Conclusions We have presented a new approach to spectrum compatibility, through the use of figures of merit. Developed from ideal DFE and DMT capacity equations, the Equivalent Loss (EL), Equivalent Noise (EN), and Equivalent Signal (ES) provide a concise characterization of a loop and its environment. These figures of merit can be used estimate of performance of DSL technologies. For single-carrier self-next limited transmission, initial simulations indicate the estimate is quite accurate. For ADSL technology, accuracy in the -2 db range appears to be possible, if the bandwidth is selected correctly. More work is need in this area is needed, as is correlation with measured performance of actual equipment. We present this information to encourage others to explore this area. For spectrum management to be successful, it is important that the basic concepts be presented in a form that that can be grasped by the community. We feel that these figures of merit may aid in this process. EL builds on the accepted practice of deploying digital technology based on a single loss figure. EN provides a similar function for the noise on the loop. In the era of loop unbundling, it will be important to be able to concisely identify the capabilities of the loop. It appears that EL and EN may help provide this function. 4 References [] TE.4/98-002, Proposed Working Draft of Spectrum Compatibility Technical Report, June, 998. [2] TE.4/96-66, R. A. McDonald, An Approach to Estimating Loop Plant Coverage of DSLs, July 996. Figure 3: 49-disturber HDSL and ISDN crosstalk and EN 40-550kHz -90-95 PSD (dbm/hz) -00-05 HDSL Crosstalk -0-5 -20 ISDN Crosstalk HDSL EN -25-30 -35 ISDN EN -40.5 2 2.5 3 3.5 4 4.5 5 5.5 x 0 5 Frequency (Hz)