  The infrared-radio correlation (IRRC) offers a way to assess star formation
from radio emission. Multiple studies found the IRRC to decrease with
increasing redshift. This may in part be due to the lack of knowledge about the
possible radio spectral energy distributions (SEDs) of star-forming galaxies.
We constrain the radio SED of a complete sample of highly star-forming galaxies
($SFR>100\,\mathrm{M_{\odot}}/\,\mathrm{yr}$) based on the VLA-COSMOS
$1.4\,\mathrm{GHz}$ Joint and $3\,\mathrm{GHz}$ Large Project catalogs. We
reduce archival GMRT $325\,\mathrm{MHz}$ and $610\,\mathrm{MHz}$ observations,
broadening the rest-frame frequency range to $0.3-15\,\mathrm{GHz}$. Employing
survival analysis and fitting a double power law SED, we find that the slope
steepens from a spectral index of $\alpha_1=0.51\pm 0.04$ below
$4.5\,\mathrm{GHz}$ to $\alpha_2=0.98\pm0.07$ above $4.5\,\mathrm{GHz}.$ Our
results suggest that the use of a K-correction assuming a single power-law
radio SED for star forming galaxies is likely not the root cause of the IRRC
trend.
