Aiming at the random access technology which has great application prospect in power satellite Internet of Things, the random burst signal acquisition method is studied. The key problem of random burst signal acquisition is the detection of the existence of random burst signal. Firstly, the existence detection problem of random burst signals with precursors is modeled as a composite hypothesis testing problem. The signal-to-noise ratio (SNR) estimation method in the detection problem is analyzed quantitatively, and the calculation method of the theoretical upper bound of the detection performance is analyzed. Then, based on the generalized likelihood ratio (GLRT) test theory, a constant false alarm rate (CFAR) detector is designed, and the engineering implementation method of the detector is derived. Finally, four simulation experiments prove that the method has good detection performance and adaptability to received signal power fluctuations.