9.3 Next vs. Fext | DSL Advances

If we compare the coupling coefficient for NEXT relative to that of FEXT, we see that the near-end crosstalk coupling is approximately six orders of magnitude greater than that for far-end crosstalk. On the other hand, notice that the coupling for NEXT increases at 15 dB per decade with increasing frequency, whereas the coupling for FEXT increases at 20 dB per decade with increasing frequency.

FEXT is an important consideration for ADSL crosstalk into other ADSLs. This is especially important for crosstalk from RT-fed ADSLs; this is a principal topic for work on the Issue 2 spectrum management standard.

A comprehensive study of loop plant cable characteristics, linear impairments, and crosstalk may be found in [1].

9.3.1 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 9.4 contains an example of NEXT and FEXT on a 9000 foot 26-gauge loop. The figure plots the power spectral density (in dBm/Hz) of the transmit signal, the insertion loss of the 9000 foot 26-gauge loop (in dB), and the PSDs of the received signal, the 49 near-end crosstalk disturbers, and the 49 far-end crosstalk disturbers. In this example, the transmit signal is an arbitrary pass-band signal whose bandwidth is approximately 700 kHz between its half-power points (-3 dB frequencies). Its power spectral density in the pass- band region has a level of -40 dBm/Hz. The power spectral density of the received signal is shaped by the insertion loss of the channel as shown in the figure. For example, at 500 kHz the insertion loss of the channel is 50 dB, so the resulting receive signal PSD is -90 dBm/Hz, which is 50 dB below its transmit level.

Figure 9.4. Comparison of NEXT and FEXT crosstalk levels.

graphics/09fig04.gif

For the special case where the crosstalk comes from signals with the same PSD as that of the corresponding transmitter, near-end crosstalk is more specifically referred to as self-NEXT (or simply SNEXT) and far-end crosstalk is referred to as self-FEXT (or simply SFEXT). Such is the case in the example of Figure 9.4.

In addition to the magnitude of the received signal, Figure 9.4 also shows the magnitudes of the NEXT and FEXT crosstalk power spectral densities . In each case, we assume 49 disturbers in the 50-pair cable. Also note that the noise floor for the signals shown in the figure is -140 dBm/Hz.

The area between the "Receive Signal" and "49 SNEXT" curves in Figure 9.4 represents the signal-to-noise ratio (SNR) at the receiver input relative to near-end crosstalk. For this near-end crosstalk case, the SNR is approximately 3.7 dB on the 9 kft 26 AWG loop. Correspondingly, the area between the "Receive Signal" and "49 SFEXT" curves in Figure 9.4 represents the SNR relative to far-end crosstalk. For this far-end crosstalk case, the SNR is approximately 40 dB on the 9 kft 26 AWG loop. Note that the SNR due to NEXT is significantly lower than that due to FEXT; hence, a FEXT limited environment is much more desirable than a NEXT limited environment.

To further quantify the effects of NEXT and FEXT, we compute the resulting Shannon (or channel) capacities, which defines 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 C is the channel capacity in bits/second, SNR ( f ) is the signal-to-noise ratio density at the receiver input, and f is frequency in Hz. For the case of SNEXT, the channel capacity is 1.7 Mb/s and that for SFEXT is approximately 8.7 Mb/s; a difference of approximately 7 Mb/s.

Clearly, as shown in the above example, near-end crosstalk strongly dominates over the effects of far-end crosstalk in the digital subscriber loop environment.

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