We derive methods for asymptotic maximum likelihood (ML) estimation of Jakes' Doppler power spectrum parameters from complex noisy estimates of the fading channel. We consider both single-input single-output (SISO) and smart-antenna scenarios and utilize the Whittle approximation to the likelihood to estimate the Doppler spread, noise variance, and channel covariance parameters. Asymptotic Crame´r-Rao bounds (CRBs) for the unknown parameters are derived. We also discuss the initialization of the proposed methods and their generalization to the Ricean-fading scenario. Numerical simulations demonstrate the performance of the proposed methods.