Page 198 - Fiber Optic Communications Fund

Optical Modulators and Modulation Schemes 179

A 2

A 3 = A 1 A 1

A 4 = A 2

M = 4 M = 4
(a) (b)
Figure 4.52 4-QAM constellations: (a) circular, (b) rectangular.

M = 16 M = 16
(a) (b)

Figure 4.53 16-QAM constellations: (a) circular, (b) rectangular.

changing in QAM. For example, when M = 4, one possible way of realizing QAM is by choosing A = A ,
1
3
A = A , = 0, = ∕2, = , and = 3∕2. The corresponding constellation is shown in Fig. 4.52(a).
2
1
3
4
4
2
The other possible way is to choose the four corners of a rectangle, A = A = A = A , and = 0, =
1
2
2
3
1
4
∕2, = , and = 3∕2 (Fig. 4.52(b)). This scheme is the same as QPSK. Fig. 4.53 shows 16-QAM
4
3
constellations.
In complex notation, assuming p(t) to be real, the QAM signal waveform may be written as
̃
s (t)= p(t)A exp [i(2f t + )]
j j c m
̃
= p(t)A j exp (i2f t), (4.115)
c
⏟⏟⏟ ⏟⏞⏞⏞⏟⏞⏞⏞⏟
field envelope optical carrier
̃
where A is the complex amplitude which is related to the real amplitude A by
j
j
̃
A = A exp (i ). (4.116)
j
j
m
Thus, the simultaneous amplitude and phase modulation of the carrier are described by the complex variable
̃
A . Fig. 4.54 shows a possible realization of star 16-QAM [12, 13]. An 8-PSK signal can be generated using
j
a QPSK modulator and a phase modulator (see Section 4.9.2). The 8-PSK signal passes through the MZM,