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Reliable estimates of the speed or, equivalently, the perceived channel Doppler spread, are of great importance in mobile cellular systems for optimization of wireless receiver algorithms such as channel estimation, handoff algorithms etc. In this paper we propose a novel speed estimation algorithm based on the derivative of the received channel envelope. We characterize the effects of additive white noise analytically and verify against simulation results. Simulations illustrate high reliability, low complexity, and good robustness of the approach for various propagation conditions. The performance of the algorithm is demonstrated for WCDMA in the speed range from 0 to 250 km/h.