A Modified Nonlinear Matched Filter for Skewed Noise Based on the Gram-Charlier Expansion

We consider the classical detection problem, of deciding whether a received signal consists of noise only or of a known signal of interest embedded in noise. The classical tool used for such problems is the Matched Filter (MF), which, under the assumption of Gaussian noise, provides the optimal decision rule via the Likelihood Ratio Test (LRT). However, when the noise is non-Gaussian, and, in particular, when the noise is skewed, the MF’s deviation from optimality may become significant. Moreover, often the full probability distribution of the noise is unknown, so the LRT cannot be applied. In this work we proposed a Modified MF (MOMAF), which is based on a "first-order modification" of the LRT, using the Gram-Charlier expansion in terms of the skewness parameter of the noise (assumed to be known). The MOMAF takes an implementation-friendly form, combining multipliers and two Linear, Time-Invariant filters, and reduces to the classical Matched Filter when the noise skewness is zero. We demonstrate the performance improvement of the MOMAF with various distributions of skewed noise in simulation.