In this paper, the speed of Mobile Station (MS) is estimated based on the derivative and correlation properties of received wave envelope in additive noise and Rayleigh fading channel environments. We derive the effects of noise and nonzero sampling interval on the accuracy of the speed estimation. In addition, we propose a method to correct the estimation errors due to the noise and sampling interval. We compare the proposed method with the speed estimation using level crossing rate. The proposed estimation method shows better performance than the estimation method using level crossing rate when there is background noise.