  In this paper we consider an un-cooperative spectrum sharing scenario,
wherein a radar system is to be overlaid to a pre-existing wireless
communication system. Given the order of magnitude of the transmitted powers in
play, we focus on the issue of interference mitigation at the communication
receiver. We explicitly account for the reverberation produced by the
(typically high-power) radar transmitter whose signal hits scattering centers
(whether targets or clutter) producing interference onto the communication
receiver, which is assumed to operate in an un-synchronized and un-coordinated
scenario. We first show that receiver design amounts to solving a non-convex
problem of joint interference removal and data demodulation: next, we introduce
two algorithms, both exploiting sparsity of a proper representation of the
interference and of the vector containing the errors of the data block. The
first algorithm is basically a relaxed constrained Atomic Norm minimization,
while the latter relies on a two-stage processing structure and is based on
alternating minimization. The merits of these algorithms are demonstrated
through extensive simulations: interestingly, the two-stage alternating
minimization algorithm turns out to achieve satisfactory performance with
moderate computational complexity.
