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：本文研究了在双重稀疏性（即延迟域和多普勒域均具有稀疏性）假设下，线性时变（LTV）无线传播链路的信道估计问题。本文证明，一种近期提出的波形——仿射频分复用（AFDM）——对于该问题具有最优性（具体含义将在文中明确给出）。通过数学分析与数值结果，本文表明，在实现目标均方误差（MSE）的信道估计过程中，采用AFDM所需的导频和保护开销最小，且优于传统波形及近期提出的波形。