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.

翻译：本文针对无线传播链路中的线性时变信道压缩感知问题，在时延域与多普勒域双重稀疏性假设下，采用仿射频分复用测量技术展开研究。通过将双重稀疏模型与层次化稀疏范式建立严格理论关联，提出一种具备恢复保证的压缩感知算法，用于从AFDM信号中提取线性时变信道的时延-多普勒剖面。通过数学分析与数值实验证明，在亚奈奎斯特雷达应用中，AFDM波形相较于其他波形在信道估计开销与最低采样率要求方面具有显著优势。