Here we observe two input symbols and then generate
an output consisting of half??“symbol time waveform.
The four possible transition functions are defined with A as the system design
parameter as
(2.50)
(2.51)
(2.52)
(2.53)
Based on the 2-input symbols or 4 bits, it is easy to show there are 16 half-symbol combinations
that can occur. They are summarized in Table 2.6.
f4 1 (1 A) sin 2Qpt
Ts R f3 1 (1 A) cos 2Qpt
Ts R f2 1 (1 A) sin 2Qpt
Ts R f1 1 (1 A) cos 2Qpt
Ts R(1/22 A 1)
(1/22 A 1)
96 CHAPTER TWO
TABLE 2.6 FQPSK Combinations of Waveform Generation
I/Q channel Q/I channel No. of combinations
4
f1 or f3 4
f2 or f4 4
4
A
A
Asin Qpt
Ts R
Acos Qpt
Ts R
sin Qpt
Ts R
cos Qpt
Ts R
FIGURE 2.79 FQPSK-KF modulation waveform block diagram.
IJF
+
X
X
cos(wct)
??“sin(wct)
I(t)
Q(t)
a(t)
Quadrature Modulator
IJF
b(t)
S/P
Tb
m(t)
PA
Cross-Correlator
The cross-correlated output waveforms are shown in Fig. 2.80 [44]. The solid line corresponds to
the IJF-OQPSK modulation and the dashed line corresponds to the Cross-Correlated Phase Shift
Keying (XPSK) modulation with the design parameter A 0.707107.
It is important to note that this original technique was presented where the output waveforms
were generated at half symbol rate.
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