8.5. SUBCARRIER MULTIPLEXING 383
can be written as
P(t)=Pb[
1 +
N∑
j= 1mjajcos( 2 πfjt+φj)]
, (8.5.1)
wherePbis the output power at the bias level andmj,aj,fj, andφjare, respectively, the
modulation index, amplitude, frequency, and phase associated with thejth microwave
subcarrier;aj,fj,orφjis modulated to impose the signal depending on whether AM,
FM, or phase modulation (PM) is used.
The power at the receiver would also be in the form of Eq. (8.5.1) if the communi-
cation channel were perfectly linear. In practice, the analog signal is distorted during
its transmission through the fiber link. The distortion is referred to asintermodulation
distortion(IMD) and is similar in nature to the FWM distortion discussed in Section
8.3. Any nonlinearity in the response of the semiconductor laser used inside the optical
transmitter or in the propagation characteristics of fibers generates new frequencies of
the formfi+fjandfi+fj±fk, some of which lie within the transmission bandwidth
and distort the analog signal. The new frequencies are referred to as theintermodula-
tion products(IMPs). These are further subdivided as two-tone IMPs and triple-beat
IMPs, depending on whether two frequencies coincide or all three frequencies are dis-
tinct. The triple-beat IMPs tend to be a major source of distortion because of their
large number. AnN-channel SCM system generatesN(N− 1 )(N− 2 )/2 triple-beat
terms compared withN(N− 1 )two-tone terms. The second-order IMD must also be
considered if subcarriers occupy a large bandwidth.
IMD has its origin in several distinct nonlinear mechanisms. The dynamic response
of semiconductor lasers is governed by the rate equations (see Section 3.5), which
are intrinsically nonlinear. The solution of these equations provides expressions for
the second- and third-order IMPs originating from this intrinsic nonlinearity. Their
contribution is largest whenever the IMP frequency falls near the relaxation-oscillation
frequency. A second source of IMD is the nonlinearity of the power-current curve (see
Fig. 3.20). The magnitude of resulting IMPs can be calculated by expanding the output
power in a Taylor series around the bias power [232]. Several other mechanisms, such
as fiber dispersion, frequency chirp, and mode-partition noise can cause IMD, and their
impact on the SCM systems has been studied extensively [235].
The IMD-induced degradation of the system performance depends on the inter-
channel interference created by IMPs. Depending on the channel spacing among mi-
crowave subcarriers, some of the IMPs fall within the bandwidth of a specific chan-
nel and affect the signal recovery. It is common to introduce composite second-order
(CSO) and composite triple-beat (CTB) distortion by adding the power for all IMPs
that fall within the passband of a specific channel [232]. The CSO and CTB distortion
values are normalized to the carrier power of that channel and expressed in dBc units,
where the “c” in dBc denotes normalization with respect to the carrier power. Typically,
CSO and CTB distortion values should be below−60 dBc for negligible impact on the
system performance; both of them increase rapidly with an increase in the modulation
index.
System performance depends on the SNR associated with the demodulated signal.
In the case of SCM systems, thecarrier-to-noise ratio(CNR) is often used in place of
SNR. The CNR is defined as the ratio of RMS carrier power to RMS noise power at