With 30 antennas and a maximum baseline length of 25 km, the Giant Metrewave Radio Telescope (GMRT) is the premier low-frequency radio interferometer today. We have carried out a study of possible expansions of the GMRT, via adding new antennas and installing focal plane arrays (FPAs), to improve its point-source sensitivity, surface brightness sensitivity, angular resolution, field of view, and U-V coverage. We have carried out array configuration studies, aimed at minimizing the number of new GMRT antennas required to obtain a well-behaved synthesized beam over a wide range of angular resolutions for full-synthesis observations. This was done via two approaches, tomographic projection and random sampling, to identify the optimal locations for the new antennas. We report results for the optimal locations of the antennas of an expanded array (the EGMRT), consisting of the existing 30 GMRT antennas, 30 new antennas at short distances, $leq 2.5$ km from the array centre, and 26 new antennas at long distances, $approx 5-25$ km from the array centre. The collecting area and the field of view of the proposed EGMRT array would be larger by factors of, respectively, $approx 3$ and $approx 30$, than those of the GMRT. Indeed, the EGMRT continuum sensitivity and survey speed with 550-850 MHz FPAs installed on the 45 antennas within a distance of $approx 2.5$ km of the array centre would be far better than those of any existing interferometer, and comparable to the sensitivity and survey speed of Phase-1 of the Square Kilometre Array.
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