  We examine the expected radio confusion on the thermal Sunyaev-Zel'dovich
(SZ) effect of galaxy clusters at 28.5 GHz and 90 GHz based on the cluster
radio luminosity function (CRLF) at 1.4 GHz. With the observationally
determined spectral index (${\alpha}$, where $S_{\rm\nu}\propto\nu^{-\alpha}$)
distribution, instead of a single average index $<\alpha>$, we convert the
cluster radio luminosity function at 1.4 GHz to the high frequency ones and
estimate the total radio flux in a cluster. At 28.5 GHz, radio confusion is up
to 10~100% for small clusters ($M\sim 2\times 10^{14}M_{\odot}$) below redshift
z=1, with more severe confusion for smaller and lower redshift clusters. By
contrast, at 90 GHz the confusion is less than 10% for small clusters even at
low redshifts.

Astrophysics