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402 Fiber Optic Communications

of 7.2 Tb/s. The optical bandwidth occupied by the WDM signal is 28 nm (or 3.5 THz), leading to a spectral
efficiency of 7.2∕3.5 ≅ 2 bit/s/Hz. The spectral efficiency can be increased further by using MPSK or QAM. A
17-Tb/s (161 × 114 Gb/s) polarization-multiplexed WDM signal is transmitted over 662 km using RZ-8PSK
[15]. A spectral efficiency of 4.2 bit/s/Hz was achieved in this experiment [15]. A 32-Tb/s (320 × 114 Gb/s)
polarization-multiplexed RZ-8QAM signal was transmitted over 580 km of SMF-28 with a spectral efficiency
of 4 bit/s/Hz [16]. As the spectral efficiency increases, the transmission distance decreases because of fiber
nonlinear effects (see Chapter 10).

9.4 OFDM

WDM is a FDM technique in which the carriers are typically not orthogonal. A special class of FDM in
which the carriers (or subcarriers) are orthogonal is known as orthogonal frequency-division multiplexing
(OFDM). In a WDM system, if the channel spacing is smaller than the bandwidth of the channels, this leads
to cross-talk and performance degradation. However, in an OFDM system, if the separation between carriers
is smaller than the band width of the data in each carrier, there is a significant spectral overlap between the
neighboring channels and yet there would be no cross-talk or performance degradation because of carrier
orthogonality conditions.
OFDM has drawn significant research interest in optical communications recently [17–33].OFDMis
widely used in wired and wireless communication systems because it is resilient to ISI caused by disper-
sive channels. It has been used for digital audio broadcasting, HDTV terrestrial broadcasting, and wireless
LANS. The first proposal to use orthogonal frequencies for transmission appeared in a 1966 patent by Chang
[34]. In 1969, Salz and Weinstein [35] introduced orthogonal carriers by using the discrete Fourier transform
(DFT). In 1971, Weinstein and Ebert [36] applied the discrete cosine transform (DCT) to a multi-carrier trans-
mission system as part of a modulation and demodulation process. The cyclic prefix, which is an important
aspect of the OFDM system, was proposed in 1980 [37].

9.4.1 OFDM Principle

Consider a multi-carrier communication system as shown in Fig. 9.12. Suppose d (t), d (t), … , d (t) are the
N
2
1
complex data streams to be transmitted:
{
d n0 for 0 < t < T s
d (t)= (9.71)
n
0 otherwise,
X ʃ
d 1 X d ˆ 1
t)
exp(i2π f 1 exp(*i2π f t)
1
d 2 X ∑ Channel X ʃ d ˆ 2

exp(i2π f t) exp(*i2π f t)
2
2
d N X X ʃ d ˆ 3

t) exp(*i2π f t)
exp(i2π f N N

Figure 9.12 A multi-carrier communication system.