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Deposition of magnetic material onto pre-patterned disks is a promising choice for Bit Patterned Media (BPM) fabrication. Nevertheless, understanding the relationship between recording characteristics and the patterning parameters is still lacking. In this article, we present a theoretical study on the recording and noise properties of the BPM made from pre-patterned substrates through micro magnetic simulation, and propose a new Signal-to-Noise Ratio (SNR) simulating method, which can avoid the complicated calculation of recording signal sensed in GMR head. The dependence of SNR on the lattice geometry, such as dot size, spacing, pillar height and head-media spacing are carefully simulated and discussed. Finally, based on all the simulation, we conclude that 0.5~0.7 is preferred for island fill factor in practical preparation to keep high SNR, and decreasing the head-media spacing is another effective way to improve SNR, especially in the tall pillar situation.