22)
This equation is called the phase differential decoding equation. Here, the received phase is subtracted
by a delayed version of itself to produce one of the four allowable phase changes. This operation
is called differential decoding or differential detection, depending where the equation is
implemented in the receiver.
We can best describe the difference between these two descriptions with the receiver block diagrams
in Figs. 2.38 and 2.39; both will make use of the polar coordinate system. In the first diagram,
we implement differential decoding. This means that coherent detection was applied to the received
signal to estimate the symbols that created . Then the differential decoding equation is applied on
the detected symbols to produce .
Next we discuss the differential detection operation where coherent detection is not performed.
Instead, phase differences are applied directly to the received signal. This is a form on noncoherent
detection.
f(k)
u(k)
f(k) u(k) u(k Ts)
f(k)
u(k Ts) u(k)
u(k) u(k Ts) f(k)
Sk e j uk
Sk Sk1 # ejfk
TABLE 2.3 DQPSK Example
Phase State Table
a(t)-b(t)
0??“0 0
0??“1 /2
1??“0 /2
1??“1
f(k)
74 CHAPTER TWO
I(t)
Q(t)
(0, 0)
(0, 1)
(1, 1)
(1, 0)
BPF
R(t)
Quad
Demod
LPF
LPF
Compensate
Channel
Estimation
~
Decision Device
cos(wct)
??“
Ts Symbol
Quantize
Differential Decoding
q (k)
??†f(k)
tan??“1
I(k)
Q(k)
BPF
R(t)
Quad
Demod
LPF
LPF
~ cos(wct)
??“
Ts
Symbol
Quantize
Differential Detection
q (k)
tan??“1
I(k)
Q(k)
??†f(k)
FIGURE 2.
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