Maximum-likelihood Detection of Impulsive Noise Support for Channel Parameter Estimation

In this paper, we consider the problem of estimating channel parameters in the presence of impulsive noise (IN). To that end, two novel maximum-likelihood based IN support detection techniques are proposed for the cases where the IN is modeled to be a deterministic quantity or a random one. For the deterministic case, an exact closed-form expression for the distribution of the joint likelihood statistic is provided whereas, in the random case, an exact expression of its asymptotic distribution is derived. In both cases, the computed distribution of the likelihood statistic enables the joint estimation of the channel parameters and the detection of the IN support with guarantees on the false alarm probability for the samples that are estimated to be in the IN support set. The goodness of the proposed expressions is validated via numerical simulations.