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AM, FM, and Digital Modulated Systems Chap. 5
(i.e., compare Fig. 5–33, = 1, with Fig. 5–20b). It is also realized that the PSD for the
complex envelope of bandpass multilevel signals, as described by Eq. (5–102), is essentially
the same as the PSD for baseband multilevel signals that was obtained in Eq. (3–53).
Example 5–12 PSD FOR MPSK AND QAM SIGNALING
Using Eq. (5–102), plot the PSD (as shown in Figure 5–33) for MPSK and QAM signaling for the
case of data having a rectangular pulse shape. See Example5_12.m for the solution.
Equation (5–102) and Fig. 5–33 also describe the PSD for QPSK, OQPSK, and p4
QPSK for rectangular-shaped data pulses when = 2(M = 4) is used. For signaling with
nonrectangular data pulses, the PSD formula can also be obtained by following the same procedure
that gave Eq. (5–102), provided that the appropriate pulse transfer function is used to
replace Eq. (5–100). For example, for raised cosine-rolloff filtering, where f 0 = 1(2T b ), the
PSD of Fig. 5–33 would become P g (f ) = 20 log [|H e (f)|], where H e (f ) is the raised cosine
transfer function of Eq. (3–69) and Fig. 3–26a.
From Fig. 5–33, we see that the null-to-null transmission bandwidth of MPSK or QAM is
B T = 2R>/
(5–103)
when rectangular data pulses are used.
Substituting Eq. (5–103) into Eq. (3–55), we find that the spectral efficiency of MPSK
or QAM signaling with rectangular data pulses is
h = R = / bits>s
(5–104)
B T 2 Hz
where M = 2 is the number of points in the signal constellation. For an M = 16 QAM signal,
the bandwidth efficiency is h = 2 bitss per hertz of bandwidth.
Spectral Efficiency for MPSK, QAM, QPSK, OQPSK,
and p/4 QPSK with Raised Cosine Filtering
The spectrum shown in Fig. 5–33 was obtained for the case of rectangular symbol pulses, and
the spectral sidelobes are terrible. The first sidelobe is attenuated by only 13.4 dB. The sidelobes
can be eliminated if raised cosine filtering is used (since the raised cosine filter has an
absolutely bandlimited frequency response). Referring to Sec. 3–6, we select the 6-dB bandwidth
of the raised cosine filter to be half the symbol (baud) rate in order for there to be no
ISI. That is, f 0 = 1 2 (R/). The raised cosine filter has the disadvantage of introducing AM on
MPSK signals (and modifying the AM on QAM signals). In practice, a square-root raised
cosine (SRRC frequency response characteristic is often used at the transmitter, along with
another SRRC filter at the receiver, in order to simultaneously prevent ISI on the received
filtered pulses and to minimize the bit errors due to channel noise. However, the SRRC filter