Frequency smearing in full 3D interferometry

Radio astronomy below 30 MHz has never been properly performed because the ionosphere inhibits this on Earth. In order to properly map the sky at these frequencies, the only financially feasible option is to build a radio telescope that comprises many small satellites. Since the observational antennas will be mounted on satellites, rather than on the Earth's surface, the antennas are likely to form a three-dimensional, possibly swarm-like formation. Such a formation will have no preference in direction of observation, which makes filling the full (u, v, w) space an obvious choice, to create a map of the complete celestial sphere at once. Performing interferometry with signals with a larger bandwidth can reduce the amount of visibility data that the satellites need to relay to Earth, assuming correlation is done in space. This can be advantageous if, to avoid man-made radio frequency interference, the satellites are to be deployed in a location far away from Earth. This paper explores the effects that frequency smearing has in this 3D mode of operation, and it is shown to be different from traditional 2D imaging, because the resulting map does not get smeared. Another consequence of correlating with a large bandwidth is bandwidth decorrelation, which is looked into as well. A framework is developed to optimize the sensitivity of the telescope in light of the limited achievable data rate to Earth, in the trade-off between decorrelation and observation bandwidth. Simulation results are presented using the Orbiting Low-Frequency Antennas for Radio Astronomy (OLFAR) concept as a case study.