Noncoherent
detection of orthogonal signaling is given as
Here we have made use of the bit error rate and symbol error rate relationship
which can also be represented as
Noncoherent detection of BFSK is given as
j
j1 # QEs
NoR Ps aM1
j1
(1) j1 # 1
j 1
# (M 1)!
j! # (M 1 j )!
# e
Pb
M
2(M 1)
# Ps
Eblog2M
2No Pb
M
4
# e
Pb
15
64
# erfcaA4Eb
85Nob
225
2048
# erfc2aA4Eb
85Nob
Pb
4
27
# erfcaAEb
7Nob
49
384
# erfc2aAEb
7Nob
Pb
2
log2M
# e
2M 1 2M f # erfcaA Eblog2M
2No(M 1)b # c1 a
1M 1
21M b # erfcaA3Eblog2M
2(M 1)bd
Pb
4
log2M
# e
2M 1 2M f # QaA3Eb
No
# log2M
(M 1)b
Pb
2
log2M
# e
2M 1 2M f # c1 erfaAEb log2M
No
# A 3
2(M 1)bd
Pb
3
8
# erfcaA0.4Eb
No b
9
64
# erfc2aA0.4Eb
No b
Pb
3
4
# QaA4Eb
5Nob
1
2
# Qa3A4Eb
5Nob
1
4
# Qa5A4Eb
5Nob
512 APPENDIX A
Coherent detection of orthogonal signaling is given as
Coherent detection of BFSK is given as
There has also been some work to provide a closed-form expression that takes into account the phase
error in some practical coherent detection techniques. Below we list three commonly used expressions
for the BER of BPSK, QPSK, and OQPSK modulation schemes, given a phase offset of .
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