Chapter 7 Error Probabilities for Noncoherent Systems

   Noncoherent Detection of OOK Noncoherent Detection of FSK Differential Phase Shift Keying Huseyin Bilgekul EEE 461 Communication Systems II Department of Electrical and Electronic Engineering Eastern Mediterranean University

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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 Detector Sampler

Threshold detector

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Noncoherent Detection

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On-off Keying EEE 461

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On-off Keying EEE 461

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On-off Keying EEE 461

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On-off Keying

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On-off Keying Pdf if 0 is sent Rayleigh distributed noise only case Pdf if 1 is sent Rician distributed Threshold

• •

Optimum threshold value occurs where densities intersect Threshold depends on bit SNR, problem in fading channels EEE 461

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On-off Keying

• • • •

BER depends on the bandwidth of the bandpass filter used.

P

e becomes smaller as B p is decreased.

Minimum bandwidth allowed with no ISI is B p =2B=R=1/T Noncoherent OOK is worse than coherent OOK.

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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 if v

u < v L

Decide 1 if v

L > v u

v

u

H

1 (

f

)

Env. Det Sample

r

Comparator

H

0 (

f

)

Env. Det Sampler

v

L

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Noncoherent FSK Detector

• Noise outputs of the upper and lower receiver channels is similar.

( )   ( )

P e P e

  1 2  0 

u

( 0 1 ) 0 

v L s

2 )  1 2  0  ( )

dr

0   0  ( )

dr

0 • When signal is present in the lower channel, the upper channel is only noise which is Rayleigh distributed. The lower channel is signal plus noise and it is Rician distributed.

 2         0

v u

2

L s

2   

v L

   0 2

e



v u

2

e

 

v L

2 2  2 

A

2 

v u

 0

v u

 2  2 0

I

0      2    

v L v L

 0  0

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Noncoherent FSK Detector

• The probability of error is thus obtained as: 

P e

0  

v L

 2

u



e

 

v L

2

v L



A s

2 ) 2  2  2

I

0      2

P e

 1 2

e



A

2 4  2

P e

 1 2

e

          

v L v u

 2

e



v u

2 1 2

TB p E b N o

 2  2

dv u

 

dv L

• OOK and FSK are equivalent on E b /N o basis.

• Noncoherent FSK requires at most 1 dB more E b /N o coherent FSK.

• Noncoherent FSK is much easier to build.

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Noncoherent FSK Detector EEE 461

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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.

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Differential Phase Shift Keying

• For additive white Gaussian noise the BER performance can be obtained and approximated as:

P e

=Q  

P e

 1 2

e E b N o

  (Bandpass Filter Detection)  

E b N o

 (Matched Filter Detection) • Suboptimum detection (Band pass filter) is similar to that of OOk and FSK.

• Optimum demodulation of DPSK requires 1 dB more E b /N o BPSK.

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