  Accretion of gas onto already virialized structures like galaxy clusters
should give rise to accretion shocks which can potentially accelerate cosmic
rays. Here, we use the radio emission detected from Coma cluster and models of
evolution of cosmic accretion shocks, to constrain the possible contribution of
unresolved galaxy clusters to the cosmic radio background. We assume that Coma
is a typical galaxy cluster and that its entire radio emission is produced by
cosmic rays accelerated in accretion shocks, making our prediction an upper
limit. Our models predict that at lower frequencies accretion shocks can have a
potentially large contribution to the cosmic radio background, while on larger
frequencies, e.g. 5 GHz, their contribution must be lower than < 2-35%,
depending on the models of evolution of accretion shocks that we use.
