Characteristic function approach for higher order crossings with application for speed estimation

In this paper, the zero crossing rate (ZCR) of the first derivative of a Rayleigh fading process is expressed in terms of its characteristic function. Based on the ZCR of the slope (first derivative) of the underlying fading process, a mobile speed estimation scheme, constructed by counting the average number of sampling steps in a positive-going (and/or negative-going) fade envelope slope, is proposed. The proposed speed estimation approach requires neither knowledge of the average fade power nor a variable temporal observation window. The computational complexity and the required memory storage are negligibly small. Simulation results show that the proposed speed estimator yields good estimation accuracy, with relatively small estimation error.