  Calibration is a key step in the signal processing pipeline of any radio
astronomical instrument. The required sky, ionospheric and instrumental models
for this step can suffer from various kinds of incompleteness. In this paper we
analyze several important calibration methods, ignoring for now the ionosphere.
The aim is to use established statistical and signal processing tools to
provide a generic method to assess calibratability of an instrument. We show
how currently popular calibration techniques differ in their assumptions and
also discuss their theoretical commonalities. We also study the effect of only
using a sub-set of baselines on the calibration and provide theoretical methods
to analyze excess noise and biases that it might introduce. In order to
simplify the physical interpretation of the results, we introduce a new signal
processing model which is capable of modeling instrumental direction dependent
effects and spectral smoothness of the individual receiver gain within a
beam-formed station. The statistical properties of this model are then studied
by deriving the Cram\'er--Rao bound (CRB). We finally define a mathematical
framework for calibratability of an instrument based on the model used which is
generic and can be used to study different instruments. These theoretical
results are then verified using numerical simulations.
