Chapter 7 Error Probabilities for Noncoherent Systems

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Chapter 7Error 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

Envelope Detector
H(f)
Threshold 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
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

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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
  Bp2BR1/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 vu lt vL Decide 1 if vL gt vu

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Noncoherent FSK Detector

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

• 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.

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Noncoherent FSK Detector

• 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
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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

• Suboptimum detection (Band pass filter) is
  similar to that of OOk and FSK.
• Optimum demodulation of DPSK requires 1 dB more
  Eb/No BPSK.