Quest for detection of a cosmological signal from neutral hydrogen with a digital radio array developed for air-shower measurements

Digital radio arrays are widely used for the low-frequency radio astronomy as well as for detection of air-showers induced by high-energy cosmic rays and neutrinos. Since the radio emission from air-showers forms short broadband pulses with duration of tens nanoseconds, the data acquisition strategies of cosmic-ray and astronomical arrays have significant differences. To perform precise measurement of cosmic rays, the radio array should have absolute amplitude calibration and record the entire electric field on the antenna in the broad frequency range. These requirements are similar to ones defined for the experiments aimed at the detection of weak signal from neutral hydrogen at redshifts of $z$>10, what led us to the application of our experience with Tunka-Rex to this problem. We are developing new experimental setup comprising of four antenna stations, placed on the area of 100 sq.m. Each antenna station consists of two perpendicular loop antennas measuring electric field in the frequency band of 30-80 MHz. The setup records electric fields from all antennas in portions of 50 $\mu$s reaching the spectral resolution of 20 kHz. We expect a flow of redundant data of about 10 GB/day, and plan to exploit this redundancy in order to decrease systematic uncertainty of the measurements by application of digital beam-forming, matched filtering and RFI suppression with neural networks. In the present contribution we describe the design and calibration of the setup, expected performance and data analysis techniques.