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In space scenarios, the communications between the flying transmitters and receivers generally face two difficulties: a long-distance transmission and a high-speed movement. The long-distance transmission decreases the signal-to-noise ratio (SNR) at the receiver and the high-speed movement imposes a dynamic Doppler-shift on the transmitter's carrier frequency. Under the low SNR, the Doppler-shift acquisition requires a long-time accumulation of many received symbols. However, during this long-time period, the dynamic Doppler-shift disperses all symbols' total energy over a wide frequency range, thus causing the energy dispersion problem. To address this problem, we propose a max-min-sliding-window (MMSW) scheme by less noise elements and all signal elements. The large elements (also called max-elements) and small elements (also called min-elements) provide us the cues of possible ranges and impossible ranges, respectively. Also, the sliding-window is adopted to collect all signal elements. The MMSW scheme includes two algorithms (i.e., Generic MMSW and Iterative MMSW). The Generic MMSW algorithm first selects the max-elements and min-elements to construct a narrow max-min-range, then slides a window over this range to derive the signal and noise windows, and finally searches the largest window to obtain the acquisition result. By updating the max-elements and min-elements, the Iterative MMSW algorithm iteratively slides a window over a much narrower max-min-range to further strengthen the signal window. Moreover, the simulations results have demonstrated our MMSW scheme's significant advantages over the existing schemes.