With the increasing number of users in the Medium-Orbit (MEO) satellite communication system, multi-access interference (MAI) has become an important factor that restricts the reliability and capacity of the system. Additionally, the low carrier-power-to-noise-density ratio (C/N0) resulting from long-distance transmission poses a significant concern. The parallel interference cancellation (PIC) algorithm, utilized within the paradigm of multi-user detection (MUD), exhibits the capability to effectively mitigate the impact of MAI within the same system. Simultaneously, coherent accumulation serves as a means to substantially enhance the correct detection probability (Pcd) at low C/N0. In this study, a signal acquisition method for multi-user spread spectrum satellite receivers is proposed, which employs interference cancellation and coherent accumulation as its core mechanisms. Furthermore, we introduce a power estimation method based on the outcomes of signal acquisition, which can be integrated into the signal reconstruction module of PIC. Finally, we implement the aforementioned algorithms in both simulation and hardware platforms. Remarkably, we observe that when the interference-to-signal ratio (ISR) caused by MAI equals 20 dB, the improved algorithm attains a maximum Pcd of 0.95 within the high signal-to-noise ratio (SNR) region, closely approaching the theoretical limit for the bit error rate (BER). The experimental results prove the effectiveness and feasibility of the acquisition algorithm. In summary, the enhanced algorithm holds vast potential for widespread implementation in multi-user spread spectrum communication systems.