  The Fermi surface in underdoped cuprates is reconstructed by the charge
density wave (CDW) order in the pseudogap phase. Theoretical proposals can be
divided into two classes: one assumes the underlying Fermi surface without CDW
as a conventional large surface; the other assumes small hole-like Fermi
pockets. In both scenarios, we theoretically study the quantum oscillation and
find three evenly spaced peaks in the oscillation spectra. The central dominant
peak is induced by the CDW order. Its effective mass is strongly enhanced as
the CDW vanishes in agreement with experiments. But the two scenarios have
different understandings of the subdominant satellite peaks. In the
large-surface scenario they are induced by the interlayer tunneling between the
bilayer CuO$_{2}$ planes. Their effective masses are also enhanced with
descreasing CDW. In the small-pocket scenario one of the subdominant peaks
comes from the original small Fermi pockets of the pseudogap state. Its
effective mass is nearly independent of the CDW strength and increases
monotonically with the doping. We propose future quantum oscillation
experiments to test these different predictions and thus to clarify the
underlying Fermi surface structure of the pseudogap state.
