CRB Analysis of the Impact of Unknown Receiver Noise on Phased Array Calibration

In radio astronomy images are made of astronomical objects as they appear at radio frequencies using a technique called aperture synthesis. Signals from several antennas are correlated and integrated over time. The data collected over several hours are further processed to calibrate the instrument and to form an image or intensity map. The calibration and imaging algorithms do not use the autocorrelations because the receiver noise is unstable and hence considered unknown. In literature the Cramer Rao bound for the calibration problem has been derived assuming that the autocorrelations are part of the available data. If the assumption is correct that the autocorrelations do not contain useful information when the receiver noise is unknown, than the CRB for the case that the autocorrelations are not part of the data will be the same. In this paper we will derive the CRB excluding the autocorrelations and show that it indeed does not matter whether the autocorrelations are included or not