We study the phase diagram and the excitation spectra of an array of s
mall Josephson junctions at f = 1/2 and arbitrary charge frustration.
We find that the supersolid region in the phase diagram is larger than
the corresponding region at f = 0 and it includes two different phase
s. In the chiral supersolid charges and vortices are arranged in a che
ckerboard pattern on a 2 x 2 supercell analogously to the unfrustrated
case. We find a phase, which we term nonchiral supersolid, which has
no corresponding phase at f = 0. The excitation spectra in the superso
lid regions show particlelike dispersion which is related to the exist
ence of defectons. The defecton condensation leads to superfluidity in
the presence of a charge-ordered background.