B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

4.6 Local Carrier Synchronization 171
Figure 4.24
Television signal
spectra: (a) DSB
signal. (b) signal
transmitted.
(a)
0
DSB spectrum
fc
I
I
fc + 4.5
/, MHz
r0.25 MHz
Audio spectrum
(FM)
(b)
0 fc - 1.25
fc + 4.5
f, MHz
Consider an SSB-SC case where a received signal is
m(t) cos [ (w e + 1'1w )t + 8] - mh (t) sin [ (w e + 1'1w )t + 8]
because of propagation delay and Doppler frequency shift. The local carrier remains as
2 cos W e t. The product of the received signal and the local carrier is e(t), given by
e(t) = 2 cos W e t [m(t) cos (w e t+ 1'1wt + 8) - mh(t) sin (w e t+ 1'1wt + 8)]
= m(t) cos (1'1wt + 8) - mh(t) sin (1'1wt + 8)
+ m(t) cos [(2w e + 1'1w)t + 8] - mh(t) sin [(2w e + 1'1w)t + 8]
bandpass SSB-SC signal around 2w e + 1'1w
(4.28)
The bandpass component is filtered out by the receiver low-pass filter, leaving the output
e 0 (t) as
e 0 (t) = m(t) cos (1'1wt + 8) - mh(t) sin (1'1wt + 8)
(4.29)
If 1'1w and 8 are both zero (no frequency or phase error), then
as expected.
e o (t) = m(t)
In practice, if the radio wave travels a distance of d meters at the speed of light c, then the
phase delay is
8 = -(w e + 1'1w )d / c
which can be any value within the interval [ -rr, +rr] . Two oscillators initially of identical
frequency can also drift apart. Moreover, if the receiver or the transmitter is traveling at a
velocity of Ve , then the maximum Doppler frequency shift would be
Ve
1'1fmax = -Jc
C