  The Phoenix Deep Survey is a multi-wavelength survey based on deep 1.4 GHz
radio imaging, reaching well into the sub-100 microJy level. One of the aims of
this survey is to characterize the sub-mJy radio population, exploring its
nature and evolution. In this paper we present the catalog and results of the
spectroscopic observations aimed at characterizing the optically ``bright''
(R<~ 21.5 mag) counterparts of faint radio sources. Out of 371 sources with
redshift determination, 21% have absorption lines only, 11% show AGN
signatures, 32% are star-forming galaxies, 34% show narrow emission lines that
do not allow detailed spectral classification (due to poor signal-to-noise
ratio and/or lack of diagnostic emission lines) and the remaining 2% are
identified with stars. For the star-forming galaxies with a Balmer decrement
measurement we find a median extinction of A(Ha)=1.9 mag, higher than that of
optically selected samples. This is a result of the radio selection, which is
not biased against dusty systems. Using the available spectroscopic
information, we estimate the radio luminosity function of star-forming galaxies
in two independent redshift bins at z~0.1 and 0.3 respectively. We find direct
evidence for strong luminosity evolution of these systems consistent with L(1.4
GHz) ~ (1+z)^(2.7).
