The dynamics of large superwavelength open systems which are free-standing multi-wire lines with a large number of Josephson junctions, DC bias batteries and other lumped elements is analyzed using direct numerical simulation. Such systems represent the simplest version of the active Josephson antennas proposed in our earlier studies and show promise as terahertz and subterahertz radiation sources. We have studied dependences of the radiation characteristics on the antenna geometry, number of junctions, DC bias current and the lumped elements position and parameters. Detailed simulation results reveal a multitude of phase transitions between the dynamical states, which differ in the number of Josephson junctions synchronized by the excited waves of current and, hence, in the radiation power emitted into open space also as in radiation patterns. It is shown that, in the absence of noise, the Josephson antennas can emit completely coherent radiation.