  The cosmic 21 cm signal serves as a crucial probe for studying the
evolutionary history of the Universe. However, detecting the 21 cm signal poses
significant challenges due to its extremely faint nature. To mitigate the
interference from the Earth's radio frequency interference (RFI), the ground
and the ionospheric effects, the Discovering the Sky at the Longest Wavelength
(DSL) project will deploy a constellation of satellites in Lunar orbit, with
its high-frequency daughter satellite tasked with detecting the global 21 cm
signal from cosmic dawn and reionization era (CD/EoR). We intend to employ the
Vari-Zeroth-Order Polynomial (VZOP) for foreground fitting and subtracting. We
have studied the effect of thermal noise, thermal radiation from the Moon, the
Lunar reflection, anisotropic frequency-dependent beam, inaccurate antenna beam
pattern, and RFI contamination. We discovered that the RFI contamination can
significantly affect the fitting process and thus prevent us from detecting the
signal. Therefore, experimenting on the far side of the moon is crucial. We
also discovered that using VZOP together with DSL, after 1080 orbits around the
Moon, which takes about 103 days, we can successfully detect the CD/EoR 21 cm
signal.
