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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.