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

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

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

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

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

When everything is known… Use the log likelihood ratio

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

Locally Optimal (LO) Architecture

Generalized Gaussian PDF univariate

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

Known Amplitude vs Weak Signal ZMNL

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

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