  We study the problem of identifying the parameters of a linear system from
its response to multiple unknown waveforms. We assume that the system response
is a scaled superposition of time-delayed and frequency-shifted versions of the
unknown waveforms. Such kind of problem is severely ill-posed and does not
yield a unique solution without introducing further constraints. To fully
characterize the system, we assume that the unknown waveforms lie in a common
known low-dimensional subspace that satisfies certain properties. Then, we
develop a blind two-dimensional (2D) super-resolution framework that applies to
a large number of applications. In this framework, we show that under a minimum
separation between the time-frequency shifts, all the unknowns that
characterize the system can be recovered precisely and with high probability
provided that a lower bound on the number of the observed samples is satisfied.
The proposed framework is based on a 2D atomic norm minimization problem, which
is shown to be reformulated and solved via semidefinite programming. Simulation
results that confirm the theoretical findings of the paper are provided.
