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In this paper, the problem of acquiring weak Global Navigation Satellite System (GNSS) signals of the next generation systems (such as Galileo and GPS modernization) is addressed and analyzed, focusing the majority of the attention to the Cross Ambiguity Function (CAF) peak splitting problem caused by the presence of sign transition due to the navigation message in the data channel or the secondary code in the pilot channel. A new two steps acquisition strategy has been proposed in order to mitigate the CAF peak impairments. To achieve better acquisition sensitivity, differentially coherent detection scheme has been considered. When two steps acquisition strategy is employed in the differentially coherent detection scheme, the sign transition problem can be solved and much improved acquisition performance can be obtained specifically in a severe weak signal environment. The validity and effectiveness of the proposed technique has been deeply assessed with simulation analysis.