Page 165 - Fiber Optic Communications Fund

146 Fiber Optic Communications

Message signal m(t) PSK signal
PM

Carrier
Acos(2π f c t)

Figure 4.7 Generation of a PSK signal. PM = phase modulator.

be binary data of the form
{
m 1 for bit ‘1’
m(t)= . (4.28)
m 2 for bit ‘0’
The transmitted signal within a bit interval [0, T ] can be written as
b
s(t)= A cos [(t)], (4.29)
where
{
2f t for bit ‘1’
1
(t)= , (4.30)
2f t for bit ‘0’
2
f = f + k m , i = 1, 2. (4.31)
i
f
c
i
k is the frequency modulation index. Suppose the phase (t) in the bit interval [0, T ] is 2f t and the phase
f b 1
(t) in the next interval is 2f t.At t = T , (T −) = 2f T and (T +) = 2f T . This could cause phase
2 b b 1 b b 2 b
discontinuity at the bit boundaries, which is undesirable in some applications. One possible way of avoiding
phase discontinuities is to choose the frequencies such that the phase accumulated over a bit interval is an
integral multiple of 2,
n
f + k m = , n is an integer,
f
c
1
T b
l
f + k m = , l is an integer. (4.32)
f
c
2
T b
Under these conditions, the phase would be continuous throughout and such a scheme is known as continuous
phase frequency-shift keying (CPFSK). Note that the ASK signal has a constant frequency and the amplitude
is varying, whereas FSK is a constant-amplitude signal but the instantaneous frequency is changing with time.
4.5.4 Differential Phase-Shift Keying
When a PSK signal is transmitted, it requires a complex receiver architecture to detect the phase. This is
because the optical signal acquires a phase due to propagation, which fluctuates due to temperature, stress,