  We present a new method to calculate fundamental Doppler measurement limits
with a dispersed fixed-delay interferometer (DFDI) in the near infrared
wavelength region for searching for exoplanets around M dwarfs in the coming
decade. It is based on calculating the Q factor, a measure of flux-normalized
Doppler sensitivity in the fringing spectra created with DFDI. We calculate the
Q factor as a function of spectral resolution R, stellar projected rotational
velocity V sini, stellar effective temperature T_eff and optical path
difference (OPD) of the interferometer. We also compare the DFDI Q factor to
that for the popular cross-dispersed echelle spectrograph method (the direct
echelle (DE) method). Given the IR Doppler measurement is likely to be
detector-limited for a while, we introduce new merit functions, which is
directly related to photon-limited RV uncertainty, to evaluate Doppler
performance with the DFDI and DE methods. We find that DFDI has strength in
wavelength coverage and multi-object capability over the DE for a limited
detector resource. We simulate the performance of the InfraRed Exoplanet
Tracker (IRET) based on the DFDI design, being considered for the next
generation IR Doppler measurements. The predicted photon-limited RV uncertainty
suggests that IRET is capable of detecting Earth-like exoplanets in habitable
zone around nearby bright M dwarfs if they exist. A new method is developed to
quantitatively estimate the influence of telluric lines on RV uncertainty. Our
study shows that photon-limited RV uncertainty can be reached if 99% of the
strength of telluric lines can be removed from the measured stellar spectra. At
low to moderate levels of telluric line strength removal (50% to 90%), the
optimal RV uncertainty is typically a factor of 2-3 times larger than
photon-limited RV uncertainty.
