The effects of correlated noise in phased-array observations of radio sources

Arrays of radio telescopes are now routinely used to provide increased signal-to-noise when observing faint point sources. However, calculation of the achievable sensitivity is complicated if there are sources in the field of view other than the target source. These additional sources not only increase the system temperatures of the individual antennas, but may also contribute significant 'correlated noise' to the effective system temperature of the array. This problem has been of particular interest in the context of tracking spacecraft in the vicinity of radio-bright planets (e.g., Galileo at Jupiter), but it has broader astronomical relevance as well. This paper presents a general formulation of the problem, for the case of a point-like target source in the presence of an additional radio source of arbitrary brightness distribution. We re-derive the well known result that, in the absence of any background sources, a phased array of N indentical antennas is a factor of N more sensitive than a single antenna. We also show that an unphased array of N identical antennas is, on average, no more sensitive than a single antenna if the signals from the individual antennas are combined prior to detection. In the case where a background source is present we show that the effects of correlated noise are highly geometry dependent, and for some astronomical observations may cause significant fluctuations in the array's effective system temperature.