  In joint radar-communications (JRC) applications such as secure military
receivers, often the radar and communications signals are overlaid in the
received signal. In these passive listening outposts, the signals and channels
of both radar and communications are unknown to the receiver. The ill-posed
problem of recovering all signal and channel parameters from the overlaid
signal is termed as \textit{dual-blind deconvolution} (DBD). In this work, we
investigate DBD for a multi-antenna receiver. We model the radar and
communications channels with a few (sparse) \textit{continuous-valued}
parameters such as time delays, Doppler velocities, and directions-of-arrival
(DoAs). To solve this highly ill-posed DBD, we propose to minimize the sum of
multivariate atomic norms (SoMAN) that depend on unknown parameters. To this
end, we devise an exact semidefinite program using theories of positive
hyperoctant trigonometric polynomials (PhTP). Our theoretical analyses show
that the minimum number of samples and antennas required for perfect recovery
is logarithmically dependent on the maximum of the number of radar targets and
communications paths rather than their sum. We show that our approach is easily
generalized to include several practical issues such as gain/phase errors and
additive noise. Numerical experiments show the exact parameter recovery for
different JRC scenarios.
