  We study the conditions for coherent radiation of an electron bunch driven by
a counterpropagating strong pulsed electromagnetic plane wave. We derive the
spectrum of the coherent radiation and show that it is emitted backwards with
respect to the laser propagation direction and has a very narrow angular
spread. We demonstrate that for a solid density plasma coherent radiation
extends to frequencies up to hundreds of keV thereby enhancing the
low-frequency part of the spectrum by many orders of magnitude. Our analytical
findings are tested with 3D particle-in-cell simulations of an electron bunch
passing through a laser pulse, clearly demonstrating how the coherence can
essentially modify the observed radiation spectrum.
