  A number of experiments are set to measure the 21-cm signal of neutral
hydrogen from 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.
