Fundamental limits of radio interferometers: calibration and source parameter estimation

Abstract

We use information theory to derive fundamental limits on the capacity to calibrate next-generation radio interferometers, and measure parameters of point sources for instrument calibration, point source subtraction, and data deconvolution. We demonstrate the implications of these fundamental limits, with particular reference to estimation of the 21cm Epoch of Reionization power spectrum with next-generation low-frequency instruments (e.g., the Murchison Widefield Array -- MWA, Precision Array for Probing the Epoch of Reionization -- PAPER), where short time scale instrumental calibration is required due to the impact of the ionosphere on the signal wavefront. Finally, we explore the optimal point source precision available by using a combination of current and prior information. Estimation schemes that incorporate prior information may be advantageous when the measurement precision is comparable to the characteristic refraction scale of the ionosphere.