This letter aims to improve the active user detection (AUD) and channel estimation (CE) performance in grant-free random access (GFRA) systems with open-loop power control. In particular, the preamble based on the power-split-ratio (PSR) is designed, where the preamble consists of two sub-preambles generated by multiplying the same sequence with different power coefficients. The ratio of two coefficients is defined as PSR, which can be used to eliminate the effects of uncertain power and detect preamble collisions. Based on the designed preamble, a two-step AUD scheme is proposed to detect the sequence and PSR, followed by the CE scheme. Numerical results show that the proposed PSR-based preamble significantly outperforms existing preambles in GFRA systems with open-loop power control.