Efficient Nonlinear Detector of Binary Signals in Rayleigh Fading and Impulse Interference

The Middleton Class-A (MCA) model is one of the most widely applied models for narrow-band impulsive interference superimposed to additive white Gaussian noise (AWGN). The MCA noise process consists of an infinite number of Gaussian-distributed noise states with different variances. As a result, the optimum detector has irreducible form. Here, our analysis is based on a two-state model, where we further approximate it to a single noise state. Therefore, a log-function reduces the likelihood ratio test (LRT) to a closed-form expression. Since the low-pass equivalent of the noise process can be expressed by in-phase and quadrature (IQ) components. We derive the nonlinear decision rules when the IQ components of noise are independent and identically distributed (i.i.d.). Furthermore, for jointly distributed IQ noise components, we show that the conventional coherent detector over a fading channel with Gaussian noise is still optimum for impulse noise.