  In this work we consider the problem of identification and reconstruction of
doubly-dispersive channel operators which are given by finite linear
combinations of time-frequency shifts. Such operators arise as time-varying
linear systems for example in radar and wireless communications. In particular,
for information transmission in highly non-stationary environments the channel
needs to be estimated quickly with identification signals of short duration and
for vehicular application simultaneous high-resolution radar is desired as
well. We consider the time-continuous setting and prove an exact resampling
reformulation of the involved channel operator when applied to a trigonometric
polynomial as identifier in terms of sparse linear combinations of real-valued
atoms. Motivated by recent works of Heckel et al. we present an exact approach
for off-the-grid superresolution which allows to perform the identification
with realizable signals having compact support. Then we show how an alternating
descent conditional gradient algorithm can be adapted to solve the reformulated
problem. Numerical examples demonstrate the performance of this algorithm, in
particular in comparison with a simple adaptive grid refinement strategy and an
orthogonal matching pursuit algorithm.
