Most existing approaches to co-existing communication/radar systems assume
that the radar and communication systems are coordinated, i.e., they share
information, such as relative position, transmitted waveforms and channel
state. In this paper, we consider an un-coordinated scenario where a
communication receiver is to operate in the presence of a number of radars, of
which only a sub-set may be active, which poses the problem of estimating the
active waveforms and the relevant parameters thereof, so as to cancel them
prior to demodulation. Two algorithms are proposed for such a joint waveform
estimation/data demodulation problem, both exploiting sparsity of a proper
representation of the interference and of the vector containing the errors of
the data block, so as to implement an iterative joint interference removal/data
demodulation process. The former algorithm is based on classical on-grid
compressed sensing (CS), while the latter forces an atomic norm (AN)
constraint: in both cases the radar parameters and the communication
demodulation errors can be estimated by solving a convex problem. We also
propose a way to improve the efficiency of the AN-based algorithm. The
performance of these algorithms are demonstrated through extensive simulations,
taking into account a variety of conditions concerning both the interferers and
the respective channel states
