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178 Fiber Optic Communications

QPSK signal 8-PSK signal

PM

NRZ data stream

Figure 4.51 Generation of an 8-PSK signal.

Fig. 4.22). The optical signal is recombined using a 3-dB coupler to obtain the QPSK signal. The advantage
of this scheme is that both m (t) and m (t) are binary NRZ data streams. An 8-PSK signal can be obtained
Q
I
from a QPSK signal after passing through a phase modulator which changes the phase of the QPSK signal
by ∕4 or 0 depending on whether the electrical driving signal is V ∕4 or zero, respectively (see Fig. 4.51).

This is because an 8-PSK signal is nothing but a phase-modulated QPSK signal. To see that, let us rewrite
Eq. (4.108) in the complex notation
{ [ 2 ] }
s 8-PSK (t)= Ap(t) exp i 2f t +(j − 1) + , j = 1, 2, … , 8
j c 0
8
l = 1, 2, 3, 4
{ [ ] }
(l − 1)2 k
= Ap(t) exp i 2f t + + + 0 , k = 0, 1
c
4 4
j =(2l − 1)+ k
QPSK
= Ap(t)s (t) exp (ik∕4). (4.112)
l
4.9.3 Quadrature Amplitude Modulation

In M-ary ASK, the amplitude of the carrier is modulated in accordance with a message signal with the con-
straint that frequency f and of Eq. (4.21) are constant. This constraint leads to the straight-line constellation
c
of Fig. 4.41. In M-ary PSK, the phase of the carrier is modulated in accordance with a message signal with
the constraint that amplitude A and frequency f of Eq. (4.21) are constant, which leads to the circular con-
c
stellation of Fig. 4.46. However, if we let the amplitude and phase of the carrier vary simultaneously, we get
a modulation scheme known as an M-ary quadrature amplitude modulation (QAM) or M-ary amplitude and
phase-shift keying (APSK). The signal waveform in the interval 0 ≤ t ≤ T maybeexpressedas
s
s (t)= A p(t) cos (2f t + ) j = 1, 2, … , M
j
j
j
c
= m (t) cos (2f t)+ m (t) sin (2f t), (4.113)
I c Q c
where
m (t)= p(t)A cos ( ),
I
j
j
m (t)=−p(t)A sin ( ). (4.114)
Q
j
j
The amplitude of the in-phase carrier cos (2f t) is modulated by m (t) and that of the quadrature carrier
c I
sin (2f t) is modulated by m (t). Hence, this scheme is known as quadrature amplitude modulation. This is
c Q
√
2
2
similar to QPSK, except that the amplitude A (= m + m ∕p(t)) is constant in QPSK whereas it may be
j I Q