  Stellar coronal mass ejections (CMEs) from host stars are an important factor
that affects the habitability of exoplanets. Although their solar counterparts
have been well observed for decades, it is still very difficult to find solid
evidence of stellar CMEs. Using the spectral line profile asymmetry caused by
the Doppler shift of erupting plasma, several stellar CME candidates have been
identified from spectral lines formed at chromospheric or transition region
temperatures of the stars. However, a successful detection of stellar CME
signals based on the profile asymmetries of coronal lines is still lacking. It
is unclear whether we can detect such signals. Here we construct an analytical
model for CMEs on solar-type stars, and derive an expression of stellar
extreme-ultraviolet (EUV) line profiles during CME eruptions. For different
instrumental parameters, exposure times, CME propagation directions and stellar
activity levels, we synthesized the corresponding line profiles of Fe IX 171.07
\AA\ and Fe XV 284.16 \AA. Further investigations provide constraints on the
instrumental requirements for successful detection and characterization of
stellar CMEs. Our results show that it is possible to detect stellar CME
signals and infer their velocities based on spectral profile asymmetries using
an EUV spectrometer with a moderate spectral resolution and signal-to-noise
ratio. Our work provides important references for the design of future EUV
spectrometers for stellar CME detection and the development of observation
strategies.
