A sample of over 1000 objects selected from a 1.4 GHz survey made by the Australia Telescope Compact Array ( ATCA ) is used to study the properties of the faint radio source population .
The sample , covering an area of \approx 3 deg ^ { 2 } , is 50 \% complete to 0.2 mJy .
Over 50 \% of the radio sources are found to have optical counterparts brighter then R \approx 21.5 .
Spectroscopic observations of 249 optically identified radio sources have been made , using the 2-degree Field ( 2dF ) facility at the Anglo-Australian Telescope ( AAT ) .
Redshifts and equivalent widths of several spectral features ( e.g. , H \alpha and [ OII ] \lambda 3727 ) sensitive to star formation have been measured .
On the basis of the photometric and spectroscopic data , the optically identified radio sources are classified as ( i ) absorption-line galaxies , ( ii ) star-forming galaxies and ( iii ) Seyfert-like galaxies .

The spectroscopic sample is corrected for incompleteness and used to estimate the 1.4 GHz and H \alpha luminosity functions ( LFs ) and luminosity density distributions .
The 1.4 GHz LF of the star-forming population has a much steeper faint-end slope ( 1.85 ) than the ellipticals ( 1.35 ) .
This implies an increasing preponderance of star-forming galaxies among the optically identified ( i.e. , z \lesssim 1 ) radio sources at fainter flux densities .
The H \alpha LF of the faint radio population agrees with published H \alpha LFs derived from local samples selected by H \alpha emission .
This suggests that the star-forming faint radio population is coincident with the H \alpha selected population .

The 1.4 GHz and H \alpha luminosity densities have been used to estimate the star formation rates ( SFRs ) .
The two SFRs agree , both giving a SFR density of 0.032 M _ { \odot } yr ^ { -1 } Mpc ^ { -3 } in the range z \lesssim 1 .
Radio selection appears to be as effective as H \alpha selection in finding the galaxies which dominate star formation at a given epoch .
Although the sample contains many galaxies lying beyond z \approx 0.3 , it does not reveal a significant rise in the global star formation rate with increasing redshift .
This result suggests that the optical counterparts of galaxies undergoing vigorous star formation at redshifts beyond z \approx 0.3 are generally fainter than R \approx 21 .