This document analyzes the performance of a monopole antenna placed above a 2D electromagnetic band gap (EBG) structure. It summarizes the design and properties of the square mushroom EBG, including its band rejection range from 4.6-7.9 GHz. Simulation results show that when the monopole operates within this range, it exhibits an enhanced bandwidth and smoother radiation pattern compared to a conventional ground plane. However, when the monopole operates outside this range at 8 GHz, the EBG structure performs similarly to a conventional reflector. In conclusion, a 2D EBG can improve monopole antenna performance by suppressing surface waves when it operates within the EBG's band rejection range.