9.5 Computation of Spectral Compatibility

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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 . Table 9.2 lists the SNR _ref values [8] for the uncoded signal constellations considered in this study. To include the gain effects of the trellis code, the coding gain is subtracted from the uncoded signal's SNR _ref .

The output signal-to-noise ratio (SNR _out ) of the decision feedback equalizer in the CAP/QAM receiver is computed by [8]

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

Table 9.2. List of Reference Signal-to-Noise Ratios of Various Line Codes

Line Code (without Trellis Coding)	SNR re f -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

The SNR margin ( M ) is computed as follows :

where G _TC is the coding gain of the trellis code and SNR _ref,uncoded is the reference SNR of the uncoded line code (second column in Table 9.2). Alternatively, this equation may be expressed as

where SNR _{ref , coded} = SNR _{ref , uncoded} - G _TC .

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