Noncoherent detection of DQPSK is given as
Noncoherent detection of DPSK is given as
Noncoherent detection of MDPSK is given as
The general noncoherent detection form is
where for DPSK
and for DQPSK
Next we will provide a summary for the M-ary QAM (MQAM) modulation schemes. The bit
error rate for 16-QAM in an AWGN channel is given as
Pb
3
8
# erfcaA0.4Eb
No b # c1
3
8
# ercaA0.4Eb
No bd
b 2 2 12 a 22 12
b 1a 0
Pb QAa2g, b2gB
1
2
# expa
(a2 b2)g
2 b # Io (abg)
Ps>2 # QaA2Eblog2M
No
# sin c p
M12 db
Eb
No Pb
1
2
# e
Pb
1
2
# IoaA2Eb
No b # e
2Eb
No e
2Eb
No # a`
k1
(12 1)k # IkaA2Eb
No b
Pb
K
log2M
# erfc cAEb log2M
No
# sin Qp
MRd # e1
1
2
# erfc cAEb log2M
No
# sinQp
MRd f
Pb erfcaAEb
2Nob erfc2aAEb
2Nob
1
2
# erfc3aAEb
2Nob
1
8
# erfc4aAEb
2Nob
Pb 2QaA2Eb
No b # c1 QaA2Eb
No bd
Pb erfcAEb
No
# c1
1
2
# erfcaAEb
Nobd
USEFUL FORMULAS 511
Alternatively represented as
For square MQAM constellation with M even number, we can use the following:
Also written as
For 64-QAM, we have the following:
For 256-QAM, we have the following:
Next we will provide a summary for the M-ary FSK (MFSK) modulation schemes.
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