the Epoch of Reionization (EoR). The common denominator of these experiments are the large
data sets produced, contaminated by various instrumental effects, ionospheric distortions, RFI
and strong Galactic and extragalactic foregrounds. In this paper, the first in a series, we present
the Data Model that will be the basis of the signal analysis for the LOFAR (Low Frequency
Array) EoR Key Science Project (LOFAR EoR KSP). Using this data model we simulate realistic
visibility data sets over a wide frequency band, taking properly into account all currently
known instrumental corruptions (e.g. direction-dependent gains, complex gains, polarization
effects, noise, etc). We then apply primary calibration errors to the data in a statistical sense,
assuming that the calibration errors are random Gaussian variates at a level consistent with
our current knowledge based on observations with the LOFAR Core Station 1. Our aim is to
demonstrate how the systematics of an interferometric measurement affect the quality of the
calibrated data, how errors correlate and propagate, and in the long run how this can lead to
new calibration strategies. We present results of these simulations and the inversion process
and extraction procedure. We also discuss some general properties of the coherency matrix
and Jones formalism that might prove useful in solving the calibration problem of aperture
synthesis arrays. We conclude that even in the presence of realistic noise and instrumental
errors, the statistical signature of the EoR signal can be detected by LOFAR with relatively
small errors. A detailed study of the statistical properties of our data model and more complex
instrumental models will be considered in the future.
