Low Earth Orbit (LEO) satellite navigation signal can be used as an opportunity signal in the case of a Global Navigation Satellite System (GNSS) outage, or as an enhancement by means of traditional GNSS positioning algorithms. No matter which service mode is used, signal acquisi-tion is a prerequisite for providing enhanced LEO navigation services. Compared with the medium orbit satellite, the transit time of the LEO satellite is shorter. Thus, it is of great significance to expand the successful acquisition time range of the LEO signal. Previous studies on LEO signal acquisition are based on simulation data. However, signal acquisition research based on real data is crucial. In this work, the signal characteristics of LEO satellites: power space density in free space and the Doppler shift of LEO satellites are individually studied. The unified symbolic definitions of several integration algorithms based on the parallel search signal acquisition algorithm are given. To verify these algorithms for LEO signal acquisition, a Software Defined Receiver (SDR) is developed. The performance of these integration algo-rithms on expanding the successful acquisition time range is verified by the real data collected from the Luojia-1A satellite. The experimental results show that the integration strategy can expand the successful acquisition time range, and it will not expand indefinitely with the integration duration. The performance of the coherent integration and differential integration algorithms is better than the other two integration algorithms, so the two algorithms are recommended for LEO signal acquisition and a 20 ms integration duration is preferred. The detection threshold of 2.5 is not suitable for all integration algorithms and various integration durations, especially for the Maximum-to-Mean Ratio indicator.