4.29). The differential detector output symbol is compared
fk
max
f ^
k
Re erk # r*k
1 # ejf
^
k f f ^
k
max
f ePrki P2
Prk P2
2 Reark # r*k1 # ejf ^
kbf
max
f Prk # ejf
^
k rki P2
max .
?†
f
r e k i
j
i
k i m
m
i
??’
??’
=
??’ ??’
=
??’
??‘
??‘
??†f
0
0
1
2
196 CHAPTER FOUR
Ts
rk
( )*
Xk + jYk Choose
??†fk
For largest
Re{xn}
x0
x1
x2
x3
Conventional Differential Detector
Decision Device
?†
??†f?†
e??“j??†f1 ?†
e??“j??†f2 ?†
e??“j??†f3 ?†
e??“j??†f0
FIGURE 4.29 Multiple symbol DD (N 2 symbols) receiver block diagram.
against all possible phase changes by rotating the symbol to the positive real axis. This is essentially
performing a nearest neighbor operation.
Here we first perform a phase difference operation and then we exhaustively compare this received
phase difference to all the possible transmitted phase differences. Let us say we have transmitted a
p/4-DQPSK modulation then the possible received candidates are
(4.95)
If p/4 was the actual transmitted symbol then the Re{x2} would be the largest and thus we would
choose . The DD output symbol is compared against the complex conjugate of all the possible
phase changes. This was accomplished in order to have a projection onto the real axis.
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