TY - GEN
T1 - MATCHED FILTER THRESHOLD ADJUSTMENT FOR SKEWED NOISE USING GRAM-CHARLIER EXPANSION
AU - Yeredor, Arie
N1 - Publisher Copyright:
© 2024 European Signal Processing Conference, EUSIPCO. All rights reserved.
PY - 2024
Y1 - 2024
N2 - A Matched Filter is commonly used as an optimal linear detector of a known signal in a noisy environment. The filter’s output is used in a Likelihood Ratio Test (LRT), which is usually set under the assumption that the filter’s output has a Gaussian distribution, both under the null hypothesis and under the alternative hypothesis. When the noise is Gaussian, this assumption is perfectly justified. When the noise is non-Gaussian, this assumption is usually a good approximation if the filter is “long enough”, thanks to the Central Limit Theorem. However, if the noise is skewed and the filter is relatively short, the distribution of the filter’s output (under both hypotheses) departs from Gaussianity (and is usually too complicated to derive in an explicit form). In this paper we show that if the skewness of the noise is known, the departure of the filter’s output distribution from Gaussianity can be well-approximated using a Gram-Charlier expansion (which depends on the filter’s coefficients), leading to a more accurate determination of the decision threshold, which we derive in closed form. We demonstrate the resulting improvement in the overall decision-error probability in simulation.
AB - A Matched Filter is commonly used as an optimal linear detector of a known signal in a noisy environment. The filter’s output is used in a Likelihood Ratio Test (LRT), which is usually set under the assumption that the filter’s output has a Gaussian distribution, both under the null hypothesis and under the alternative hypothesis. When the noise is Gaussian, this assumption is perfectly justified. When the noise is non-Gaussian, this assumption is usually a good approximation if the filter is “long enough”, thanks to the Central Limit Theorem. However, if the noise is skewed and the filter is relatively short, the distribution of the filter’s output (under both hypotheses) departs from Gaussianity (and is usually too complicated to derive in an explicit form). In this paper we show that if the skewness of the noise is known, the departure of the filter’s output distribution from Gaussianity can be well-approximated using a Gram-Charlier expansion (which depends on the filter’s coefficients), leading to a more accurate determination of the decision threshold, which we derive in closed form. We demonstrate the resulting improvement in the overall decision-error probability in simulation.
KW - Cumulants
KW - Gram-Charlier Expansion
KW - Likelihood Ratio Test
KW - Matched Filter
KW - Skew
UR - http://www.scopus.com/inward/record.url?scp=85208445790&partnerID=8YFLogxK
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AN - SCOPUS:85208445790
T3 - European Signal Processing Conference
SP - 2747
EP - 2751
BT - 32nd European Signal Processing Conference, EUSIPCO 2024 - Proceedings
PB - European Signal Processing Conference, EUSIPCO
T2 - 32nd European Signal Processing Conference, EUSIPCO 2024
Y2 - 26 August 2024 through 30 August 2024
ER -