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The message service is the most distinctive part of the BeiDou System (BDS), whose coverage area will be expanded from China & surroundings to the global surface space at BDS-3 stage. This is an innovative integration of a global mobile communications service in a Global Navigation Satellite System (GNSS), with great practical value and significant strategy. However, BeiDou Global Message service relies on the global Medium Earth Orbit (MEO) satellite constellation to achieve the global beam-forming, the space-borne antenna has smaller size and lower receiving gain than regional beam-forming, so a key issue in designing Global Message is the uplink signal synchronization segment to ensure the space-borne message receiver achieves fast and reliable capture of short burst signals at very low carrier-to-noise ratio (C/N0). In this paper comparing with the uplink channel in Radio Determination Satellite Service (RDSS) based on the BDS Geostationary Earth Orbit (GEO) satellites, the signal condition parameters of the optional BeiDou Global Message are calculated. Then the design scheme of the shortest length synchronization segment based on the constant false alarm and specified detection probability is given. According to this, a fast acquisition algorithm for the uplink message receiver based on MEO satellite is proposed. Finally, through software simulation analysis and ground equipment testing the proposed signal design scheme is proved , as well as the fast acquisition algorithm with high-reliability reception of short burst signals in the condition of signal-to-noise ratio lower than 34dBHz. The research results of this paper provide important technical support for the overall design of Global Message service in BDS-3, and will be further tested in the subsequent actual applications. It is also hoped to provide theoretical basis for the continuous optimization of Global Messages in the future BDS.