Redundant space calibration of hexagonal and Y-shaped beamforming radars and interferometric radiometers

The calibration of large antenna arrays in the absence of a beamforming point source is a common problem in beamforming radars and interferometric radiometers. In this paper the fundamentals of the redundant space calibration (RSC) method for phase and amplitude are reviewed, pointing out the parallelism between the active and passive cases, the technique is then applied in a general and systematic way to two cases of interest: hexagonal planar and Y-shaped arrays, which are known to be the optimum periodic two-dimensional configurations. In both cases, the system of equations is determined taking into account the available redundancies and symmetries of these structures. The performance of the RSC method is analysed in terms of the propagation of errors in reference phase/amplitude. The technique is then considered for two hexagonal array systems: the Turbulent Eddy Profiler (TEP), a volume-imaging radar of the lower atmosphere developed at the University of Massachusetts, and the Microwave Imaging Radiometer by Aperture Synthesis (MIRAS), an L-band interferometric radiometer to be launched in 2005 in the Earth Explorer Opportunity Mission--Soil Moisture and Ocean Salinity Mission (SMOS) of the European Space Agency (ESA). In the TEP case the proposed scheme stabilizes an otherwise ill-posed inversion problem, and in the MIRAS case it presents an alternative calibration method to the noise-injection one, without any additional hardware required.