The cosmic far infrared background detected recently by the COBE-DIRBE team is presumably due , in large part , to the far infrared ( FIR ) emission from all galaxies .
We take the well-established correlation between FIR and radio luminosity for individual galaxies and apply it to the FIR background .
We find that these sources make up about half of the extragalactic radio background , the other half being due to AGN .
This is in agreement with other radio observations , which leads us to conclude that the FIR-radio correlation holds well for the very faint sources making up the FIR background , and that the FIR background is indeed due to star-formation activity ( not AGN or other possible sources ) .
If these star-forming galaxies have a radio spectral index between 0.4 and 0.8 , and make up 40 to 60 % of the extragalactic radio background , we find that they have redshifts between roughly 1 and 2 , in agreement with recent estimates by Madau et al . of the redshift of peak star-formation activity .
We compare the observed extragalactic radio background to the integral over the \log N - \log S curve for star-forming radio sources , and find that the slope of the curve must change significantly below about 1 { \mu Jy } .
At 1 { \mu Jy } , the faint radio source counts predict about 25 sources per square arcminute , and these will cause SIRTF to be confusion limited at 160 { \mu m } .