Post-correlation beamformer for time-domain studies of pulsars and transients

We present a detailed analysis of post-correlation beamforming (i.e. beamforming which involves only phased sums of the correlation of the voltages of different antennas in an array), and compare it with the traditionally used incoherent and phased beamforming techniques. Using data from the GMRT we show that post-correlation beamformation results in a many-folds increase in the signal-to-noise for periodic signals from pulsars and several order of magnitude reduction in the number of false triggers from single pulse events like fast radio bursts (FRBs). This difference arises primarily because the post-correlation beam contains less red-noise, as well as less radio frequency interference. The post-correlation beam can also be more easily calibrated than the incoherent or phased array beams. We also discuss two different modes of post-correlation beamformation, viz. (1) by subtracting the incoherent beam from the coherent beam and (2) by phased addition of the visibilities. The computational costs for both these beamformation techniques as well as their suitability for studies of pulsars and FRBs are discussed. Techniques discussed here would be of interest for all upcoming surveys with interferometric arrays. Finally, we describe a time-domain survey with the GMRT using the post-correlation beamformation as a case study. We find that post-correlation beamforming will improve the current GMRT time-domain survey sensitivity by ~ 2 times for pulsars with periods of few 100s of millisecond and by many-folds for even slower pulsars, making it one of the most sensitive surveys for pulsars and FRBs at low and mid radio frequencies.