  The China Space Station Telescope (CSST) is a forthcoming Stage IV galaxy
survey. It will simultaneously undertake the photometric redshift (photo-z) and
slitless spectroscopic redshift (spec-z) surveys mainly for weak lensing and
galaxy clustering studies. The two surveys cover the same sky area and overlap
on the redshift range. At $z>1$, due to the sparse number density of the spec-z
sample, it limits the constraints on the scale of baryon acoustic oscillations
(BAO). By cross-correlating the spec-z sample with the high density photo-z
sample, we can effectively enhance the constraints on the angular diameter
distances $D_A(z)$ from the BAO measurement. Based on the Fisher matrix, we
forecast a $\geq$ 30 per cent improvement on constraining $D_A(z)$ from the
joint analysis of the spec-z and cross galaxy power spectra at $1.0<z<1.2$.
Such improvement is generally robust against different systematic effects
including the systematic noise and the redshift success rate of the spec-z
survey, as well as the photo-z error. We also show the BAO constraints from
other Stage-IV spectroscopic surveys for the comparison with CSST. Our study
can be a reference for the future BAO analysis on real CSST data. The
methodology can be applied to other surveys with spec-z and photo-z data in the
same survey volume.
