Beamformer Design Methods for Radio Astronomical Phased Array Feeds

A major emphasis in current radio astronomy instrumentation research is the use of phased array feeds (PAF) to provide radio telescopes with larger fields of view. One of the challenges of PAF systems is the design of beamformers that provide sufficient sensitivity and known, stable beam pattern structure. High sensitivity has been achieved with the maximum sensitivity beamformer without regard to beam pattern shape. Deterministic beamformers provide the desired pattern shape control, but suffer from a significant reduction in sensitivity. We present a hybrid beamforming method, which balances the tradeoff between high sensitivity and precise beam pattern shape control. A comparison of each of these beamforming methods, using measured data, confirms the advantage of the hybrid approach. The pattern distortions introduced by modeled beamformers can be mitigated with a transformation step, but ultimately it is shown that PAF beamformer design is best done using measured calibrators. A PAF calibration vector quality metric based on minimum description length is also introduced.