2.84 [63??“66].
Thus, the previous FQPSK family of modulation schemes worked with a coherent demodulator.
With this new scheme, differential detection is an option for the receiver now. The cross-correlation
operations are scaled and shifted versions of sinusoids and are given below where we have split up
the description into three cases:
FIGURE 2.84 /4-FQPSK waveform block diagram.
CASE 1: I(k) I(k 1) 0
If Q(k) Q(k 1), then
U(t) C11 0.5C1 cos(2(t/Ts k 1)) for (k 1)Ts t (k 0.5)Ts
V(t) Q(k 1) cos((t/Ts k 1))
U(t) C21 0.5C2 cos(2(t/Ts k 1)) for (k 0.5)Ts t kTs
V(t)Q(k) cos((t/Ts k 1))
where we use the following definitions:
C0 2A(I(k 1) I(k))
C1 I(k 1) C0
C2 C0 I(k)
C11 0.5(I(k 1) C0)
C21 0.5(C0 I(k))
A correlation factor (0 to 1)
CASE 2: Q(K) Q(k 1) 0,THEN
U(t) A1 A2 cos((t/Ts k 1)) for (k 1)Ts t kTs
V(t) B1 B2 cos((t/Ts k 1))
where the following definitions
A1 0.5((I(k 1) I(k))
A2 0.5(I(k 1) I(k))
B1 0.5(Q(k 1) Q(k))
B2 0.5(Q(k 1) Q(k))
CASE 3: Q(k 1) Q(k) 0
Simply replace the I(~) and Q(~) by Q(~) and I(~) in the above equations, respectively.
As far as demodulation techniques are concerned, both coherent and noncoherent detection can be
used and will be discussed in latter chapters.
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