Affine Frequency Division Multiplexing for Compressed Sensing of Time-Varying Channels

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.