One approach to increasing nuclear magnetic resonance measurement sample throughput is to implement multiple, independent detection sites. However, the presence of radio frequency interference poses a challenge in multi-detector systems, particularly in unshielded coil arrays lacking sufficient electrical isolation. This issue can lead to unwanted coupling of inductive coils, resulting in excitation pulse interference and signal transfer among multiple detection sites. Here we propose a theoretical framework that combines electromagnetic simulation with spin-dynamic calculations. This framework enables the evaluation of coil coupling effects, the design of parallel pulse sequences to mitigate inter-channel coupling, and the separation of composite free induction decays obtained from multiple detectors. The parallel pulse compensation scheme was validated by a 2-channel parallel spectroscopy experiment. These results provide valuable insights for the design of parallel nuclear magnetic resonance hardware and for exploring the limits of parallelization capacity within a fixed magnet system.