  Recent interest in integrated sensing and communications has led to the
design of novel signal processing techniques to recover information from an
overlaid radar-communications signal. Here, we focus on a spectral coexistence
scenario, wherein the channels and transmit signals of both radar and
communications systems are unknown to the common receiver. In this dual-blind
deconvolution (DBD) problem, the receiver admits a multi-carrier wireless
communications signal that is overlaid with the radar signal reflected off
multiple targets. The communications and radar channels are represented by
continuous-valued range-times or delays corresponding to multiple transmission
paths and targets, respectively. Prior works addressed recovery of unknown
channels and signals in this ill-posed DBD problem through atomic norm
minimization but contingent on individual minimum separation conditions for
radar and communications channels. In this paper, we provide an optimal joint
separation condition using extremal functions from the Beurling-Selberg
interpolation theory. Thereafter, we formulate DBD as a low-rank modified
Hankel matrix retrieval and solve it via nuclear norm minimization. We estimate
the unknown target and communications parameters from the recovered low-rank
matrix using multiple signal classification (MUSIC) method. We show that the
joint separation condition also guarantees that the underlying Vandermonde
matrix for MUSIC is well-conditioned. Numerical experiments validate our
theoretical findings.
