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AM, FM, and Digital Modulated Systems Chap. 5
g(t)
g(t)
Imaginary
(quadrature)
Imaginary
(quadrature)
y i
¨
¨i
x i
Real
(in phase)
Real
(in phase)
(a)
Figure 5–30
(b)
QPSK and p4
QPSK signal constellations (permitted values of the complex envelope).
These two signal constellations are essentially the same, except for a shift in the carrierphase
reference. † This example of M-ary PSK where M = 4 is called quadrature phase-shiftkeyed
(QPSK) signaling.
MPSK can also be generated by using two quadrature carriers modulated by the x and y
components of the complex envelope (instead of using a phase modulator); in that case,
g(t) = A c e ju(t) = x(t) + jy(t)
(5–91)
where the permitted values of x and y are
and
x i = A c cos u i
(5–92)
y i = A c sin u i
(5–93)
for the permitted phase angles u i , i = 1, 2, ..., M, of the MPSK signal. This situation is illustrated
in Fig. 5–31, where the signal processing circuit implements Eqs. (5–92) and (5–93).
Figure 5–30 gives the relationship between the permitted phase angles u i and the (x i , y i )
components for two QPSK signal constellations. This is identical to the quadrature method of
generating modulated signals presented in Fig. 4–28.
For rectangular-shaped data pulses, the envelope of the QPSK signal is constant.
That is, there is no AM on the signal, even during the data transition times, when there is a
180 phase shift, since the data switches values (say, from +1 to -1) instantaneously. The
† A constellation is an N-dimensional plot of the possible signal vectors corresponding to the possible digital
signals. (See Sec. 3–4.)