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The authors present a low-complexity non-coherent tracking loop based on the gravity of energy window (GEW). Expressions for the proposed tracking loop in a multipath fading channel with Doppler shift environment are derived. The stationary probability density function (PDF) of the phase error and the root-mean-square (RMS) tracking error are obtained by computer simulation. Statistical simulation results show that the new tracking loop can provide much better performance than the conventional non-coherent delay lock loop (DLL) in the presence of Doppler shift.