The Loop Plant Environment

POTS is provisioned to customers by routing twisted wire pairs between the CO and the customer premises (CP) location. The twisted wire pair that connects the CO to the CP is the subscriber loop, which may consist of sections of copper twisted wire pairs of one or more different gauges.

Twisted wire pairs are contained in cables that have large cross-sections near the CO. Within each cable, the twisted wire pairs are grouped into binders of 10, 25, or up to 50 wire pairs, and there could be up to 50 binder groups per cable.

Figure 17 shows the basic architecture of the loop plant in which subscriber loops are provisioned. Each subscriber loop can be divided into three portions of cable: feeder cable, distribution cable, and drop wire. Feeder cables provide links from the CO to a connection point or feeder distribution interface (FDI) in a concentrated customer area. Distribution cables provide links from the FDI to customer locations. The FDI provides connections of the wire pairs in the feeder cable with those in the distribution cable. The drop wires represent the portion of wire that extends from the terminal on a telephone pole to the CP or underground from the pedestal to the CP.

Figure 17. Architecture of the Loop Plant

Because loop-plant construction is completed prior to service request, distribution cables are made available to all existing and potential customer sites. It is common practice to connect a twisted pair from a feeder cable to more than one wire pair in the distribution cable. Multiple connections from a feeder or distribution cable to more than one CP form bridged taps. Typically, only one customer is serviced at one time while the other bridged taps are left open circuited.

The loop plant was originally designed to provision customers with POTS. To ensure proper QoS, design rules were defined for subscriber loop provisioning. One set of rules that govern distribution of twisted wire pairs for voice service from the CO to the CP is the resistance design rules. Implemented in 1980–81 time frame, the design rules are summarized as follows:

• Loop resistance is not to exceed 1,500 Ohms.

• Inductive loading is to be used whenever the sum of all cable lengths, including bridged taps, exceeds 15 kft.

• For loaded cables, 88-mH loading coils are placed at 3 kft from the CO and thereafter at intervals of 6 kft.

• For loaded cables, the total amount of cable, including bridged taps, in the section beyond the loading coil furthest from the CO should be between 3 kft and 12 kft.

• There are to be no bridged taps between loading coils and no loaded bridged taps.

Revised resistance design (RRD) rules are defined in Bellcore Document SR–TSV–002275.³ These rules require that the maximum loop resistance on an 18-kft twisted wire pair between the CO to the CP must be less than 1,300 Ohms and on loops between 18 kft and 24 kft, the maximum resistance is 1,500 Ohms. Loading coils are applied to all loops greater than 18 kft or have loop resistance greater than 1,300 Ohms.

Telephone cables are designed with different wire gauges ranging from 26 American wire gauge (AWG) (thin diameter resulting in higher resistance per unit length) to 19 AWG (thick diameter resulting in lower resistance per unit length). Because distances from the CO to each customer are different, distribution cables are equipped with different wire gauges to meet the resistance-design guidelines and provide service to the maximum number of customers. On long loops, the distribution cables tend to use thicker gauge wire in the regions closer to the subscriber location to minimize the total loop resistance. At the CO, the feeder cables tend to use fine diameter gauges (typically 26 AWG) to maximize the number of wire pairs being served by the CO.

Some customers may be located so far away from the CO that it may not be possible to meet the resistance-design rules. If a subscriber loop is provisioned with a length greater than the maximum defined by the RRD rules, then loading coils must be inserted in the loop to achieve proper voice quality. Note, however, that subscriber loops provisioned with loading coils are not suitable for support of wideband DSL services, because loading coils introduce too much attenuation of the frequencies outside the voice channel, which are required by the DSL system. In short, loading coils must be removed from any subscriber loop that is to support a DSL–based service.

Another set of rules, called carrier serving area (CSA) rules, define the distribution of twisted wire pairs from digital loop carrier (DLC) systems. The radius covered by CSA rules are up to 9 kft of 26-gauge wire and up to 12 kft on 24-gauge wire. The concept of CSA rules was originally developed for provisioning loops from DLC systems in support 56–kbps digital data service (DDS) and later slightly modified for the support of POTS from a DLC system. The CSA rules are defined as follows:

• There should be only nonloaded cable.

• Multigauge cable is restricted to two gauges.

• Total bridged-tap length may not exceed 2.5 kft, and no single bridged tap may exceed 2.0 kft.

• The amount of 26 AWG cable may not exceed a total length of 9 kft, including bridged taps.

• For single gauge or multigauge cables containing only 19, 22, or 24 AWG cable, the total cable length may not exceed 12 kft, including bridged taps.

• The total cable length including bridged taps of a multigauge cable that contains 26-gauge wire may not exceed where L₂₆ is the total length of 26 gauge wire in the cable (excluding any 26 gauge bridged tap) and L_Btap is the total length of bridged tap in the cable. All lengths are in kft.

The above CSA guidelines do not include any wiring in the CO nor any drop wiring and any wiring in the CP.

As the transport medium for wideband signals, the twisted wire pairs introduce linear impairments into the signal. Specifically, the linear impairments are propagation loss, amplitude distortion, and delay distortion. The propagation loss in decibels is directly proportional to the distance of the loop. Amplitude distortion results from the fact that signal components at higher frequencies experience more amplitude loss than the components at low frequencies. To a first order, the amplitude response of the twisted-wire-pair channel rolls off at roughly the square root of frequency. Finally, the delay is such that at low frequencies (less than approximately 10 kHz) there is very sharp variation in the group delay, and at higher frequencies the delay, response is relatively constant.⁴

Test loops have been developed for AWG in T1E1.4 and metric cables in ETSI for ISDN,^{5, 6} HDSL, ^{7, 8, 9} and ADSL² systems. These test loops provide an industry-accepted basis for evaluating the performance of the various DSL systems in the presence of different crosstalk scenarios. J. J. Werner’s The ISDN Environment provides a detailed description of cable modeling.⁴ Several pieces provide a comprehensive list of the test loops used for the North American and European loop environments.^{1, 5–9}

Crosstalk Models

NEXT and FEXT

Crosstalk generally refers to the interference that enters a communication channel, such as twisted wire pairs, through some coupling path. Figure 18 shows two examples of crosstalk generated in a multipair cable. On the left-hand side of Figure 18, signal source transmits a signal at full power on twisted wire pair j. This signal, when propagating through the loop, generates two types of crosstalk into the other wire pairs in the cable. The crosstalk that appears on the left-hand side, in wire pair i, is called near-end crosstalk (NEXT) because it is at the same end of the cable as the cross-talking signal source. The crosstalk that appears on the right-hand side, in wire pair i, is called far end crosstalk (FEXT) because the crosstalk appears on the end of the loop opposite to the reference signal source. In the loop plant, NEXT is generally far more damaging than FEXT because, unlike FEXT, NEXT directly disturbs the received signal transmitted from the far-end after it has experienced the propagation loss from traversing the distance from the far-end down the disturbed wire pair.

Figure 18. NEXT and FEXT in a Multipair Cable

In a multipair cable, relative to one desired receive signal on one twisted wire pair, all of the other wire pairs are sources of crosstalk. For DSL systems, the reference cable size for evaluating performance in the presence of crosstalk is a 50-pair cable.¹ So by reviewing the example shown in Figure 20, it can be seen that relative to the received signal on wire pair i, the other 49 wire pairs are sources of crosstalk (both near-end and far-end).

NEXT Model

As described in several works cited in this tutorial,^{1, 5, 7, 8} for the reference 50-pair cable, the NEXT coupling of signals into other wire pairs within the cable is modeled as

where is the coupling coefficient for 49 NEXT disturbers, is the number of disturbers in the cable, and is the frequency in Hz. Note that the maximum number of disturbers in a 50-pair cable is 49. A signal source that outputs a signal with power spectral density (PSD) will inject a level of NEXT into a near-end receiver that is

So, as illustrated in Figure 21, if there are signals in the cable with the same power spectral density , the PSD of the NEXT at the input to the near-end receiver on wire pair i is

Note from the above expressions that the crosstalk coupling is very low at the lower frequencies and the coupling increases at 15 dB per decade with increasing frequency. For example, at 80 kHz, the coupling loss is 57 dB for 49 disturbers. The loss (in dB) for 49 disturbers at other frequencies may be computed using the following formula:

where L₄₉ is the near-end crosstalk coupling loss in dB and f is the frequency in kHz.

FEXT Model

Correspondingly, in the same 50-pair cable, the FEXT coupling of signals into other wire pairs is modeled as

where is the channel transfer function, is the coupling coefficient for 49 FEXT disturbers, is the number of disturbers, is the coupling path distance, and is the frequency in Hz.

Note that the coupling is small at low frequencies and higher at the larger frequencies. The coupling slope increases at 20 dB per decade with increasing frequency.

Comparison of NEXT with FEXT

If the coupling coefficient for NEXT is compared to that of FEXT, it can be observed that the NEXT coupling is approximately six orders of magnitude greater than that for FEXT. Also notice that the coupling for NEXT increases at 15 dB per decade with increasing frequency where as the coupling for FEXT increases at 20 dB per decade with increasing frequency.

A comprehensive study of loop plant cable characteristics, linear impairments, and crosstalk may be found in J. J. Werner’s The ISDN Environment.⁴ Channel Capacities in the Presence of NEXT and FEXT

Let us assume that a 50-pair cable is filled completely with signals that have the same power spectral density.

Figure 19 contains an example of NEXT and FEXT on a 9-kft, 26-gauge loop. The figure plots the power spectral density (in dBm per Hz) of the transmit signal, the insertion loss of the 9-kft, 26-gauge loop (in dB), the PSDs of the received signal, the 49 NEXT disturbers, and the 49 FEXT disturbers. The bandwidth of the transmit signal is assumed to be approximately 700 kHz between its half-power points (–3 dB frequencies) with a power spectral density level of –40 dBm per Hz in the passband region. The power spectral density of the received signal is shaped by the insertion loss of the channel, as shown in Figure 19. For example, at 500 kHz the insertion loss of the channel is 50 dB, and so the resulting receive signal PSD is –90 dBm per Hz, which is 50 dB below its transmit level.

Figure 19. Comparison of NEXT and FEXT Crosstalk Levels

For the special case where the crosstalk comes from signals with the same PSD as that of the corresponding transmitter, NEXT is more specifically referred to as self–NEXT (or simply SNEXT) and FEXT is referred to as self–FEXT (or simply SFEXT). Such is the case in the example of Figure 19.

In addition to the magnitude of the received signal, Figure 19 also shows the magnitudes of the NEXT and FEXT crosstalk power spectral densities. In each case, 49 disturbers in the 50-pair cable are assumed. Also note that the noise floor for the signals shown in the figure is –140 dBm per Hz.

The signal-to-noise ratio (SNR) at the receiver input relative to NEXT is represented by the area between the receive-signal and 49–SNEXT curves in Figure 19. For this near-end crosstalk case, the SNR is approximately 3.7 dB on the 9-kft, 26–AWG loop. Corresponding, the SNR relative to FEXT is represented by the area between the receive-signal and 49–SFEXT curves in Figure 19. For this FEXT case, the SNR is approximately 40 dB on the 9-kft, 26–AWG loop. Note that the SNR relative to NEXT is significantly lower that that for FEXT; hence, a FEXT limited environment is much more desirable than a NEXT limited environment.

To further quantify the effects of NEXT and FEXT, the resulting Shannon (or channel) capacities are computed, which define the theoretical maximum bit rate that can be transmitted over a given channel with a small error rate. In general, the Shannon capacity for a given channel is

where is the channel capacity in bits per second, is the signal-to-noise ratio density at the `r input, and is frequency in Hz. For the case of SNEXT, the channel capacity is 1.7 Mbps, and that for SFEXT is approximately 8.7 Mbps—a difference of approximately 7 Mbps. Clearly, as shown in the above example, NEXT strongly dominates over the effects of FEXT in the DSL environment.

DSL Signal Spectra

This section describes power spectral density of different DSL transmit signals that are deployed in the network. The standards-based DSLs include integrated services digital network (ISDN), high-rate digital subscriber line (HDSL), and DMT–based asymmetric digital subscriber line (ADSL). Other competitive DSLs include CAP and 2B1Q–based symmetric digital subscriber line (SDSL), multirate symmetric digital subscriber line (MSDSL), and CAP–based rate adaptive digital subscriber line (RADSL). The DSLs targeting transmission applications include ISDN, HDSL, SDSL, and MSDSL. Those targeting data access applications are ADSL and CAP RADSL. The following subsections describe the signal power spectra of each DSL. ISDN

ISDN basic rate provides symmetrical transport of 160 kbps on the subscriber line. The line code is 2B1Q, and the corresponding transmit signal power spectral density is expressed as⁵

where f_o = 80 kHz, V_p = 2.5 volts and R = 135 Ohms. The transmit power of ISDN is 13.5 dBm.

In Figure 20, the solid line plots the power spectral density of the ISDN transmit signal. Included in the plot is the effect of a high-pass filter with a cutoff frequency at 2 kHz, which models the transformer coupling of the signal onto the line.

Figure 20. ISDN Transmit Signal and 49–NEXT Spectra

Also shown in Figure 19 (dotted plot) is the PSD of 49–NEXT disturbers from ISDN. As defined in several papers cited in the tutorial,^{1, 5, 7, 8, 10} the noise floor of the system (modeled at the receiver input) is –140 dBm per Hz.

Both the upstream and downstream signals occupy the same frequency band, so an echo canceler is used to separate the two directions of transmission on the subscriber line. In such a system, ISDN is subject to SNEXT. The deployment objective for ISDN is to operate on nonloaded loops that range up to 18 kft in the presence of SNEXT. These include all loops that meet RRD rules.

HDSL

In North America, HDSL is a service that provides the transport of T1 (1.544 Mbps) signals between the CO and the CP. This service is deployed using two subscriber lines, where the bit rate is 784 kbps on each wire pair and half of the T1 payload is carried on each pair. The line code is 2B1Q, and the corresponding transmit signal power spectral density is expressed as

where f_o = 392 kHz, V_p = 2.7 volts and R = 135 Ohms.^{7, 8, 11} The transmit power of the HDSL signal is 13.5 dBm. In Figure 21, the solid line plots the power spectral density of the HDSL signal. Included in this plot (but not shown in the above equation) is a high-pass filter with a 2-kHz cutoff frequency to model the effects of transformer coupling. The dotted plot is the PSD of 49–NEXT disturbers from HDSL.

Figure 21. HDSL Transmit Signal and 49–NEXT Spectra

Both the upstream and downstream signals occupy the same frequency band, so an echo canceler is used to separate the two directions of transmission on the subscriber line. In such a system, HDSL is subject to self-near-end crosstalk (SNEXT). The deployment objectives for HDSL are operation on loops that meet CSA requirements while operating in the presence of SNEXT.

SDSL

Symmetric digital subscriber line (SDSL) defines the transport of symmetric DSL services on a single twisted wire pair. SDSL solutions deployed today are echo cancellation–based and are implemented using CAP and 2B1Q technologies.

The MSDSL bit rates for CAP–based systems considered are 160 kbps, 272 kbps, 400 kbps, 784 kbps, and 1,560 kbps. Each of the CAP–based systems contain a two-dimension eight-state trellis code to provide additional immunity to crosstalk. Figure 22 shows the spectral plots of the MSDSL spectra. The bandwidth of each spectrum is directly proportional to the bit rate, so the 160–kbps signal has the narrowest bandwidth and the 1,560–kbps signal has the widest bandwidth. The line codes for each system are as follows: 160 kbps uses coded 8–CAP, 272 kbps and 400 kbps each use coded 16–CAP, and 784 kbps and 1,560 kbps each use coded 64–CAP. The spectral shaping of each transmit signal is square-root, raised cosine with a roll-off factor of 15 percent. For each bit rate, the spectrum is scaled and shaped for a transmit power of 13.5 dBm.

Figure 22. CAP SDSL Transmit Signal Spectra

Figure 23 shows the 2B1Q SDSL power spectral density plots for four data rates: 160 kbps, 384 kbps, 784 kbps, and 1,560 kbps. Each system uses nonreturn to zero (NRZ) shaping followed by an Nth-order Butterworth filter. The 160–kbps spectrum is the same as that defined for ISDN in T1.601, which defines a second-order Butterworth filter for out of band energy attenuation. The remaining signals use a fourth-order Butterworth filter for out-of-band energy attenuation. The first null in each spectrum defines the signal bandwidth. Note that for 784–kbps and 1,560–kbps systems, the bandwidth of the CAP systems is roughly half that of the 2B1Q systems; so the CAP spectra provide less interference into other systems at the higher frequencies than the 2B1Q systems.

Figure 23. 2B1Q SDSL Transmit Signal Spectra

For SDSL, both the CAP and 2B1Q systems are affected by SNEXT. If the 50-pair cable is deployed with signals having different bandwidths, then consideration must be given to the effect that these different bandwidths have in producing NEXT onto other services. Recall that the NEXT coupling is greater at higher frequencies than at lower frequencies. As described earlier, the NEXT coupling increases at 15 dB per decade with increasing frequency.

Note that the 2B1Q systems (SDSL, ISDN, and HDSL) do not use any coding or forward error correction; the CAP systems use a two-dimension eight-state trellis code that provides a 4-dB asymptotic coding gain. Hence, the CAP systems provide a greater immunity to NEXT.

ADSL

Figure 24 shows the transmit spectra and NEXT spectral plots of the upstream and downstream DMT ADSL channels. DMT ADSL is a variable bit rate system, and the actual bandwidths of the upstream and downstream channels may vary depending on the bit rate and noise environment.

Figure 24. DMT ADSL FDM Signal Spectra

As shown in Figure 24, spectra are idealized, and displaying the maximum possible useful bandwidth for the upstream and downstream channels is displayed. Not shown in Figure 24 are the out-of-band energy levels. Usually, the PSD levels represent the RMS values. However, for ADSL, the PSD levels shown in Figure 24 are peak values as opposed to RMS values to allow for varying gains at different carrier frequencies.¹⁰ No guard band is specified between the upstream and downstream channel; details of the DMT PSD masks are given in the ADSL standard.¹⁰

The spectra shown in Figure 24 use frequency division multiplexing (FDM) to separate the upstream and downstream channel. If the cable has only FDM–based ADSL systems deployed, there is no SNEXT; system performance would be limited by SFEXT. T1.413 also defines an EC version of ADSL, where the downstream channel completely overlaps the upstream channel. In this case, NEXT will be injected between the upstream and downstream channel. The channel most impacted is the upstream channel, where the NEXT from the downstream channel completely covers the upstream band.

CAP RADSL

Figure 25 shows the PSD plots of the CAP RADSL upstream and downstream channels along with their 49-disturber NEXT spectra. The upstream channel PSD mask is –38 dBm per Hz (rms) and that for the downstream channel is –40 dBm per Hz. The upstream channel uses frequencies from 25 kHz to 181 kHz and the downstream channel uses frequencies from 240 kHz up to approximately 1.3 MHz. The complete definition of the CAP RADSL PSD masks are given in Committee T1-Telecommunications’ Draft T1.413 Issue 2.¹²

Figure 25. CAP RADSL Signal and Crosstalk Spectra

CAP RADSL systems have only been deployed using FDM for separation of the upstream and downstream channels. Hence, with CAP RADSL, there is no NEXT generated between the upstream and downstream channels.

T1 AMI

The PSD of the T1 line signal is assumed to be a 50-percent, duty-cycle random alternate mark inversion (AMI) code at 1.544 Mbps. The single-sided PSD is represented by the following expression:

where V_P = 3.6 V, R_L = 100 W , f_o = 1.544 MHz, f_3dB-Shaping = 3.0 MHz is the 3 dB frequency of a third-order Butterworth low-pass shaping filter, and f_3dB-Xfmr = 40 kHz is the high-pass transformer coupling cutoff frequency.

Figure 26 shows a plot of the T1 AMI transmit signal PSD along with a 49-disturber NEXT PSD.

Figure 26. T1 AMI Signal and Crosstalk Spectra

Computation of Performance

To compute the resulting SNR margin, we first need to compute the resulting output signal-to-noise ratio (SNR_out) and then take the difference from the reference SNR value (SNR_ref) that corresponds to a bit error rate (BER) of 10^–7. The first two columns in Table 7 list the SNR_ref values for the uncoded signal constellations considered in this study.¹³ To include the gain effects of trellis code, the coding gain is subtracted from the uncoded signal’s SNR_ref.

Line Code (without Trellis Coding)	SNRref, uncoded (dB)
4–CAP/2–PAM	14.5
8–CAP	18.0
16–CAP/4–PAM	21.5
32–CAP	24.5
64–CAP/8–PAM	27.7
128–CAP	30.6
256–CAP/16–PAM	33.8

Table 7. List of Reference Signal-to-Noise Ratios of Various Line Codes

The output signal-to-noise ratio (SNR_out) of the decision-feedback equalizer in the CAP/QAM receiver is computed by ¹³

The output signal-to-noise ratio of the DFE in the PAM receiver is computed by ⁸

The SNR margin (M) is computed as follows: where G_TCis the coding gain of the trellis code and SNR_{ref, uncoded} is the reference SNR of the uncoded line code (second column in Table 1). Alternatively, this equation may be expressed as where .