  We study the phase diagram and the excitation spectra of an array of small
Josephson junctions at $f=1/2$ and arbitrary charge frustration. We find that
the supersolid region in the phase diagram is larger than the correspondent
region at $f=0$ and it includes two different phases.In the chiral supersolid
(SS) charges and vortices are arranged in a checkerboard pattern on a
$2\:\times \:2$ supercell analogously to the unfrustrated case. We find a new
phase, which we term {\em non-chiral supersolid} (NCSS), which has no
corresponding phase at $f=0$. The excitation spectra in the supersolid regions
show particle like dispersions which is related to the defectons. The defecton
condensation leads to superfluidity in the presence of charge ordered
background.
