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f
f 1 * f s f 1 f 1 + f s f 2 * f s f 2 f 2 + f s f N * f s f N f N + f s
2 2 2 2 2 2
Δ f

Figure 9.4 WDM spectrum.

where B is the data rate of a channel. If there are N channels, the total data rate is NB and the total bandwidth
is about NΔf. Therefore, the spectral efficiency is also the ratio of the total data rate to the total bandwidth.
For example, for a direct detection system based on NRZ-OOK, let the bit rate B be 10 Gb/s. If rectangular
pulses are used, the first null of the NRZ spectrum occurs at 10 GHz (see Fig. 4.4) and the signal bandwidth
f in a channel ≅ 20 GHz. If the channel spacing Δf is 20 GHz, the spectral efficiency is 0.5 b/s/Hz. In this
s
example, the overlap between the channel spectra is small and, hence, the cross-talk between the channels
is negligible. The channel spacing is determined by the signal bandwidth in a channel. In this example, if
the channel spacing is less than 20 GHz, there would be a significant overlap of spectra of adjacent channels,
leading to cross-talk. However, if a Nyquist pulse is used instead, the signal bandwidth in a channel is 10 GHz
(see Section 4.8) and in this case, the channel spacing can be reduced by a factor of two compared with the
case of NRZ, which leads to an improvement in spectral efficiency by a factor of two. The spectral efficiency
can also be considerably enhanced using coherent detection. For example, for a system based on QAM-16,
let the symbol rate B be 25 Gsym/s. For QAM-16, the data rate B is B log 16 = 100 Gb/s (see Section 4.9). If
s s 2
the channel spacing Δf = 50 GHz, the spectral efficiency = 2 b/s/Hz. The spectral efficiency can be increased
using higher-order modulation formats such as QAM-64, but these signals suffer from distortions due to fiber
nonlinear effects (see Chapter 10) limiting the maximum achievable transmission reach. Therefore, there is
a trade-off between spectral efficiency and reach. When polarization multiplexing is used, the data rate is
doubled for the given bandwidth and, therefore, the spectral efficiency is doubled compared with the case of
single polarization.
In 2002, the International Telecommunication Union (ITU) standardized the channel wavelengths (or fre-
quencies) of WDM systems on a 100-GHz (≈ 0.8 nm) grid in a wavelength range of 1528.77 nm to 1563.86 nm
as defined by ITU-T G.694.1 [1]. However, for coherent communication systems with a symbol rate of
28 Gsym/s, such a large channel spacing leads to poor spectral efficiency. Recently, ITU standardized the
WDM channels with a frequency spacing ranging from 12.5 GHz to 100 GHz and wider [1].

Example 9.1
Nyquist pulses are used in a single-polarization WDM system based on QAM-64. The symbol rate is
10 Gsym/s and the number of channels is 12. Calculate (a) the channel spacing to have a spectral efficiency
of 6 b/s/Hz, (b) the signal bandwidth in a channel and the total bandwidth of the WDM signal, and (c) the
total data rate.