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7/16/2019 EEE461Lect15 (Noncoherent Systems)
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EEE 461 1
Chapter 7
Error Probabilities forNoncoherent Systems
Huseyin Bilgekul
EEE 461 Communication Systems IIDepartment of Electrical and Electronic Engineering
Eastern Mediterranean University
Noncoherent Detection of OOK Noncoherent Detection of FSK Differential Phase Shift Keying
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Noncoherent Detection Phase is unknown
Use filter and techniques such as envelope detection or
feedback to demodulate signal
H(f) Envelope
DetectorThreshold
detector
Sampler
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Noncoherent Detection
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On-off Keying
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On-off Keying
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On-off Keying
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On-off Keying
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On-off Keying
Optimum threshold value
occurs where densities intersect
Threshold depends on bit SNR,problem in fading channels
Threshold
Pdf if 1 is sent
Rician distributed
Pdf if 0 is sent
Rayleigh distributed noise only case
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On-off Keying
BER depends on the bandwidth of the bandpass filter used.
Pe becomes smaller as Bp is decreased.
Minimum bandwidth allowed with no ISI is Bp=2B=R=1/T
Noncoherent OOK is worse than coherent OOK.
ff
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On-off Keying
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Noncoherent FSK Detector Filters matched to RF pulses for 0 and 1
Decide 0 ifvu< v
LDecide 1 ifv
L> v
u
H1(f)
H0(f)
Env. Det
Env. Det
Comparator
Sampler
Sampler
vu
vL
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Noncoherent FSK Detector
When signal is present in the lower channel, the upper channel is only noisewhich is Rayleigh distributed. The lower channel is signal plus noise and it isRician distributed.
2 2
2 2 2
2 0
22
2
02 22
0 0
0
0 0
u u
L
v vu
u
u
v AL L
LL
L
ve
f v s
v
v v Ae I v
f v s
v
Noise outputs of the upper and lower receiver channels is similar.
0 1 0 20
0 1 0 0 2 0 0 2 00 0
2
( ) ( )1 1
( ) ( ) ( )2 2
( )
e
e u L
f r s f r s
P f r s dr f r s dr f r s dr
P P v v s
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Noncoherent FSK Detector
2 2 2 2 2
2
2
2
2 202 2 20
121 14
2 2
( )
L u
L
b
p o
e u L
v A vuL Lu Lv
A ETB N
e e
P P v v s
vv v Ae I e dv dv
P e P e
The probability of error is thus obtained as:
OOK and FSK are equivalent on Eb/No basis. Noncoherent FSK requires at most 1 dB more Eb/No coherent FSK.
Noncoherent FSK is much easier to build.
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Noncoherent FSK Detector
ff l h h f
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Differential Phase Shift Keying Phase shift keyed signals can not be detected noncoherently.
Using the delayed version of the signal as phase reference partial coherence can be
obtained.
D ff l Ph h f
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Differential Phase Shift Keying For additive white Gaussian noise the BER performance can be obtained and
approximated as:
1
2
=Q (Bandpass Filter Detection)
(Matched Filter Detection)
b
o
be
o
EN
e
EPN
P e
Suboptimum detection (Band pass filter) is similar to that of OOk and FSK.
Optimum demodulation of DPSK requires 1 dB more Eb/NoBPSK.