  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.
