  This paper addresses compressed sensing of linear time-varying (LTV) wireless
propagation links under the assumption of double sparsity i.e., sparsity in
both the delay and Doppler domains, using Affine Frequency Division
Multiplexing (AFDM) measurements. By rigorously linking the double sparsity
model to the hierarchical sparsity paradigm, a compressed sensing algorithm
with recovery guarantees is proposed for extracting delay-Doppler profiles of
LTV channels using AFDM. Through mathematical analysis and numerical results,
the superiority of AFDM over other waveforms in terms of channel estimation
overhead and minimal sampling rate requirements in sub-Nyquist radar
applications is demonstrated.
