The general case of induced coherent scattering of plasma waves by a r
elativistic electron beam is considered for noncollinear wave vectors
of interacting waves, specifically, the plasma pump wave, the scattere
d electromagnetic wave, and the high-frequency space-charge wave produ
ced by the combined action of incident and scattered waves. In terms o
f the three-wave interaction model, the general nonlinear dispersion r
elation describing the initial stage of the induced scattering is obta
ined. Both the Raman and Compton mechanisms of scattering are consider
ed. The corresponding amplification factors and the dependence of thes
e factors on the angular characteristics are obtained. The frequencies
of the scattered electromagnetic waves are determined. The possibilit
y of using plasma waves as effective undulators is discussed in relati
on to the free-electron laser realization for obtaining short wave rad
iation by using moderately relativistic electron beams.