P. Noorishad, S.J. Wijnholds, A. van Ardenne and J.M. van der Hulst, "Redundancy calibration of phased-array stations", Astronomy & Astrophysics, V545, no. A108, pp1-15, September 2012

Aims. We assess the benefits and limitations of using the redundant visibility information in regular phased-array systems to improve the quality of the calibration.
Methods. Regular arrays offer the possibility of using redundant visibility information to constrain the calibration of the array independently of a sky model and a beam model of the station elements. This requires a regular arrangement of the configuration of array elements and identical beam patterns.
Results. We revised a previously developed calibration method for phased-array stations using the redundant visibility information in the system and applied it successfully to a LOFAR station. The performance and limitations of the method were demonstrated by comparing its application to real and simulated data. The main limitation is the mutual coupling between the station elements, which leads to non-identical beams and stronger baseline-dependent noise. Comparing the variance in the estimated complex gains with the Cramer-Rao Bound indicates that redundancy is a stable and optimum method for calibrating the complex gains of the system.
Conclusions. Our study shows that the use of the redundant visibility does improve the quality of the calibration in phased-array systems. In addition, it provides a powerful tool obtaining system diagnostics. Our results demonstrate that designing redundancy in both the station layout and the array configuration of future aperture arrays is strongly recommended. This is particularly true in the case of the Square Kilometre Array (SKA) with its dynamic range requirement that surpasses any existing array by an order of magnitude.

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