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Millimeter wave communications show great potentials in many applications, one of which is the high-speed railway(HSR) communication system. However, a major challenge is the Doppler effect caused by the relative-movement between the train and the base station (BS), which leads to fast channel variation. To compensate for the Doppler shift, an accurate channel model is indispensable, and the far-field channel model is generally employed, which assumes that the dimensions of the antenna arrays are negligible compared to the distance between transmitter and receiver. This model is widely used in Cellular systems, but the underlining assumption is not always true for railway communication systems. In this paper, the modeling of the Doppler effect for millimeter wave in HSR communications is conducted, and data-aided Doppler estimation and compensation algorithms are designed based on the new …