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In this paper we propose a new speed estimation technique, applicable to both mobile and base stations, based on the characteristics in the power spectrum of mobile fading channels. Our analytic performance analysis, verified by Monte Carlo simulations, shows that our low-complexity estimator is not only robust to both Gaussian and non-Gaussian noises, but also insensitive to nonisotropic scattering observed at the mobile. The estimator performs very well in both two- and three-dimensional propagation environments. The robustness against both nonisotropic scattering and line of sight can be further increased, by taking advantage of resolvable paths in wideband fading channels, due to the differences among the Doppler spectra observed at different paths. We also extend this technique to base stations with antenna arrays. By exploiting the spatial information, the proposed space-time estimator exhibits excellent performance over a wide range of noise power, nonisotropic scattering, and line-of-sight component, verified by simulation. The utility of the new method is further demonstrated by applying it to the measured data.