This paper addresses channel estimation for linear time-varying (LTV) wireless propagation links under the assumption of double sparsity i.e., sparsity in both the delay and the Doppler domains. Affine frequency division multiplexing (AFDM), a recently proposed waveform, is shown to be optimal (in a sense that we make explicit) for this problem. With both mathematical analysis and numerical results, the minimal pilot and guard overhead needed for achieving a target mean squared error (MSE) while performing channel estimation is shown to be the smallest when AFDM is employed instead of both conventional and recently proposed waveforms.

翻译：本文针对线性时变（LTV）无线传播链路中的信道估计问题展开研究，假设信道具有双重稀疏性，即在时延域和多普勒域均存在稀疏性。近期提出的仿射频分复用（AFDM）波形被证明在此问题中具有最优性（其具体含义将在文中明确阐述）。通过数学分析与数值结果双重验证，相较于传统波形及近期提出的其他波形，采用AFDM进行信道估计时，为实现目标均方误差（MSE）所需的最小导频与保护间隔开销最小。