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Detection in Non-Gaussian Noise

Detection in Non-Gaussian Noise. JA Ritcey University of Washington January 2008. Outline. Based on Miller & John B. Thomas IEEE IT 1975 Gaussian noise shows few outliers Impulsive noise is common in practice – lightning, glitches, interference, pulses …

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Detection in Non-Gaussian Noise

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  1. Detection in Non-Gaussian Noise JA Ritcey University of Washington January 2008

  2. Outline • Based on Miller & John B. Thomas • IEEE IT 1975 • Gaussian noise shows few outliers • Impulsive noise is common in practice – lightning, glitches, interference, pulses … • What does LR theory tell us about non-Gaussian noise detection architectures?

  3. Detection Problem • White Noise (iid) • Constant signal • Multiple Observations • Known noise pdf • Weak signal regime • Architecture

  4. Unknown Parameter Issues • This is clear, but • f_n must be known • Amplitude theta must be known • Generally, the amplitude is unknown

  5. Architecture • ZMNL g(.) memory less non-linearity • Accumulate all N data, then threshold

  6. When everything is known…Use the log likelihood ratio

  7. What is Amplitude is unknown, but small (weak-signal regime)

  8. Locally Optimal (LO) Architecture

  9. Generalized Gaussian PDF univariate

  10. Impact of Noise PDF on ZMNL.c indexes the tail decay ratec = 2 is Gaussian c<2 long-tailed

  11. Known Amplitude vs Weak SignalZMNL

  12. Conclusions • Impulsive Noise kills Gauss detector performance –high false alarm rates • Noise pdf impacts the ZMNL • Gaussian – linear ZMNL • Long Tailed – ZMNL suppresses large samples. Why? Large data likely noise • Short Tailed – ZMNL enhances large samples. Why? Large data likely signal

  13. Additional Issues • Simulation • Generating the Noise samples -- still an open problem for Gen Gauss! • Testing and visual impact • Performance (Qo,Qd), ARE, efficacy • Many other impulsive noise models introduced since then • What about dependence? • Non-Gaussian dependent noise?

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