Moreover, there is no interrelationship between the two symbol streams.
The S/P converter is actually creating the complex envelope of
the QPSK modulation. The four allowable phase changes are (t)
H{0,
/2,
}, and they correspond to the phase states outlined
in Table 2.2. The signal constellation diagram is given in Fig. 2.23.
The signal constellation has phase trajectories that correspond
to the following absolute phase state table.
The transmitted signal is given as
(2.11)
This is also represented as follows, using the complex envelope notation:
(2.12)
or
(2.13)
where the allowable phase changes are calculated as
(2.14)
Recall that we have inserted an LPF in order to
reduce the out-of-band emissions. This is accomplished
by slowing down the phase trajectories as
the signal travels from one phase state to another.
Using an SRC LPF, we are able to replot the signal
constellation diagram. Here, we see the information
is mapped to the phase and amplitude
change of the carrier signal.
f(t) tan 1 cQ(t)
I(t) d
S(t) A(t) # cos [vct f(t)]
S(t) Re5[a(t) jb(t)] # ejvct6
S(t) a(t) # cos (vct) b(t) # sin (vct)
MODULATION THEORY 65
LPF
+
X
X
cos(wct)
??“sin(wct)
I(t)
Q(t)
S(t)
a(t)
Quadrature Modulator
Tb ??“1
+1
m(t)
LPF
b(t)
S/P
??“1
+1
a(t)
Ts ??“1
+1
b(t)
Ts
2Ts
2Ts
FIGURE 2.
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