# On the Detection of Binary Signals in the Presence of Impulse Noise

This presentation focuses on a classical detection problem of binary signals corrupted by impulse noise modeled by a Middleton Class-A (MCA) distribution. This distribution is one of the most accepted models for impulse noise superimposed to additive white Gaussian noise. The optimum detector in such noise consists of optimum operations followed by a conventional combiner. Since the MCA model is expressed as a weighted linear combination of an infinite number of Gaussian densities, there is no closed-form solution for the optimum preprocessor. In this presentation, we start from a two-term model for the MCA noise process. Hereto, we further approximate this model into a dominant term by evaluating the thresholds at which the Gaussian and impulsive terms can be discriminated. Therefore, the optimum preprocessor is approximated by a nonlinear operation in a closed-form solution. Furthermore, we use this approximation to show for the first time how the decision boundaries of binary signals in MCA noise should look like. The second contribution is to generalize this nonlinearity for binary signal transmission over Rayleigh fading channels with diversity. In this context, we derive a closed-form approximation for the optimum combiner in independent and identically distributed MCA channels. For spatial diversity reception, we prove that the conventional maximum ratio combiner approximates the optimum combiner in impulse noise.