  The intensity mapping of the [CII] 158um line redshifted to the sub-mm window
is a promising probe of the z>4 star formation and its spatial distribution
into the large-scale structure. To prepare the first-generation experiments
(e.g., CONCERTO), we need realistic simulations of the sub-mm extragalactic sky
in spectroscopy. We present a new version of the SIDES simulation including the
main sub-mm lines around 1mm (CO, [CII], [CI]). This approach successfully
reproduces the observed line luminosity functions. We then use our simulation
to generate CONCERTO-like cubes (125-305GHz) and forecast the power spectra of
the fluctuations caused by the various astrophysical components at those
frequencies. Depending on our assumptions on the relation between star
formation rate and [CII] luminosity, and the star formation history, our
predictions of the z~6 [CII] power spectrum vary by two orders of magnitude.
This highlights how uncertain the predictions are and how important future
measurements will be to improve our understanding of this early epoch. SIDES
can reproduce the CO shot noise recently measured at ~100 GHz by the mmIME
experiment. Finally, we compare the contribution of the different astrophysical
components at various redshift to the power spectra. The continuum is by far
the brightest, by a factor of 3 to 100 depending on the frequency. At 300GHz,
the CO foreground power spectrum is higher than the [CII] one for our base
scenario. At lower frequency, the contrast between [CII] and extragalactic
foregrounds is even worse. Masking the known galaxies from deep surveys should
allow to reduce the foregrounds to 20% of the [CII] power spectrum up to z~6.5.
However, this masking method will not be sufficient at higher redshifts. The
code and the products of our simulation are released publicly and can be used
for both intensity mapping experiments and sub-mm continuum and line surveys.
