Generalised Self-Holography

The recently proposed self-holography method has the potential to reduce the computational resources needed for calibration of individual receive paths in large arrays like LOFAR and SKA significantly. The method relies on forming different beams from which the receive path gains can be reconstructed. Self-holography has been applied successfully with different beamforming schemes. In this contribution, I present a generalised formulation of self-holography capturing any beamforming scheme and use that to assess its robustness to interfering sources. This analysis indicates that the relative gain bias is inversely proportional to the signal-to-interference ratio (SIR) regardless of the beamforming scheme used. This result is corroborated in simulations. However, the chosen beamforming scheme has significant impact on the condition number of the measurement matrix and, hence, on the susceptibility to measurement noise. A beamforming scheme with (nearly) orthogonal beamformer weight vectors is thus to be preferred.