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AM, FM, and Digital Modulated Systems Chap. 5
90 occurs for OQPSK signaling (as opposed to 180 for QPSK), since the I and Q data cannot
change simultaneously, because the data are offset.
A p4 quadrature phase-shift keying (p4 QPSK) signal is generated by alternating
between two QPSK constellations that are rotated by p4 = 45 with respect to each other.
The two QPSK constellations, shown in Fig. 5–30, are used alternately as follows: Given a
point on one of the signal constellations that corresponds to two bits of input data, two new
bits are read to determine the next point that is selected from the other constellation. That is,
the two new input bits cause a phase shift of ;45 or ;135, depending on their value. For
example, an 11 could correspond to a phase shift of ∆u = 45, a 10 to ∆u =-45, a 01 to ∆u =
135, and a 00 to ∆u =-135. Since this uses a form of differential encoding, it is called p4
differential quadrature phase-shift keying (p4 DQPSK).
At the receiver, the data on the p4 QPSK signal can be easily detected by using an FM
detector, followed by a resettable integrator that integrates over a symbol (2-bit) period. The
FM detector produces the derivative of the phase, and the integrator evaluates the phase shift
that occurs over the symbol interval. The result is one of the four possible phase shifts, ;45
and ;135. For example, if the detected phase shift at the integrator output is -45, the corresponding
detected data are 10. Data on the p4 QPSK signal can also be detected by using
baseband IQ processing or by using differential detection at the IF [Rappaport, 2002].
Computer simulations indicate that all three of these receiver structures have almost the same
BER error performance [Anvari and Woo, 1991]. In an AWGN channel, the BER performance
of the three differential (noncoherent) detectors is about 3 dB inferior to that of QPSK, but
coherently detected p4 QPSK has the same BER as QPSK (shown in Fig. 7–14). For the case
of nonrectangular data pulses, the AM on p4 QPSK is less than that on QPSK, since the maximum
phase shift for p4 QPSK is 135, compared with 180 for QPSK. But the AM on
OQPSK is even less as it has a maximum phase shift of 90. However, p4 QPSK is easy to
detect and has been adopted for use in TDMA cellular telephone systems. (See Chapter 8.)
The power spectra for these signals are described in the next section.
PSD for MPSK, QAM, QPSK, OQPSK, and p/4 QPSK
The PSD for MPSK and QAM signals is relatively easy to evaluate for the case of rectangular
bit-shape signaling. In this case, the PSD has the same spectral shape that was obtained for
BPSK, provided that proper frequency scaling is used.
The PSD for the complex envelope, g(t), of the MPSK or QAM signal can be obtained
by using Eq. (6–70d). We know that
g(t) =
n=q
a
n=-q
c n f(t - nT s )
(5–99)
where c n is a complex-valued random variable representing the multilevel value during
the nth symbol pulse. f(t) = Π(tT s ) is the rectangular symbol pulse with symbol duration T s .
D = 1T s is the symbol (or baud) rate. The rectangular pulse has the Fourier transform
F(f) = T s a sin pfT s
pfT s
b =/T b a sin /pfT b
b
/pfT b
(5–100)