  In this paper, we propose a novel estimator for pilot-aided orthogonal
frequency division multiplexing (OFDM) channels in an additive Gaussian and
impulsive perturbation environment. Due to sensor failure which might happen
because of man-made noise, a number of measurements in high rate communication
systems is often corrupted by impulsive noise. High power impulsive noise is
generally an obstacle for OFDM systems as valuable information will be
completely lost. To overcome this concern, an objective function based on a
penalized atomic norm minimization (PANM) is provided in order to promote the
sparsity of time dispersive channels and impulsive noise. The corresponding
dual problem of the PANM is then converted to tractable semidefinite
programming. It has shown that one can simultaneously estimate the time
dispersive channels in a continuous dictionary and the location of impulsive
noise using the dual problem. Several numerical experiments are carried out to
evaluate the performance of the proposed estimator.
