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

On Identifiability and Estimability of Direction Dependent Calibration of Radio Interferometric Arrays