A mutual information extension to the matched filter

Matched filters are the optimal linear filters for signal detection under linear channel and white noise conditions. Their optimality is guaranteed in the additive white Gaussian noise channel due to the sufficiency of second-order statistics. In this paper, we introduce a nonlinear filter for signal detection based on the Cauchy-Schwartz quadratic mutual information (CS-QMI) criterion. This filter is still implementing correlation but now in a high-dimensional transformed space defined by the kernel utilized in estimating the CS-QMI. Simulations show that the nonlinear filter significantly outperforms the traditional matched filter in nonlinear channels, as expected. In the linear channel case, the proposed filter outperforms the matched filter when the received signal is corrupted by impulsive noise such as Cauchy-distributed noise, but performs at the same level in Gaussian noise. A simple nonparametric sample estimator for CS-QMI is derived for real-time implementation of the proposed filter.