Similarly,
the received signal can encounter a quadrature demodulator which acts as a spectral downshifting operator.
In either case, the shifting operations can inject gain and phase imbalance, thus corrupting/distorting
the signal constellation diagram. A simple gain imbalance impairment model is given in Fig. 2.17.
MODULATION THEORY 61
PA
Input Signals
+
X +
??“
X +
??“
cos(wct)
??“sin(wct)
A
A
X
X
cos(wct + ??)
??“sin(wct + ??)
IBB
QBB
I
Q
IR
QR
FIGURE 2.16 Cartesian feedback block diagram and example.
PA +
X
X
cos(wct)
??“sin(wct)
I
Q
A
S(t)
FIGURE 2.17 Gain imbalance model for the quadrature modulator.
Ignoring any nonlinearities in the PA model, the transmit envelope is written as
(2.6)
Moving our attention to the phase imbalance component, the following model assumes the phase offset
between the quadrature sinusoids is not exactly 90 degrees out of phase, and thus, we draw the
diagram in Fig. 2.18 to capture this imbalance.
ZS(t) Z 2cos 2(u) A2 sin 2(u)
The typical quadrature modulator output signal is written as
(2.7)
which can be rewritten as
(2.8)
In the absence of having an accurate phase shifter, the transmitted signal is represented as follows,
where we have used a trigonometric identity given in the appendix of this book:
(2.
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