  The multiple scattering of ultra relativistic electrons in an amorphous
matter leads to the suppression of the soft part of radiation spectrum (the
Landau-Pomeranchuk-Migdal effect), and also can change essentially the angular
distribution of the emitted photons. A similar effect must take place in a
crystal for the coherent radiation of relativistic electron. The results of the
theoretical investigation of angular distributions and polarization of
radiation by a relativistic electron passing through a thin (in comparison with
a coherence length) crystal at a small angle to the crystal axis are presented.
The electron trajectories in crystal were simulated using the binary collision
model which takes into account both coherent and incoherent effects at
scattering. The angular distribution of radiation and polarization were
calculated as a sum of radiation from each electron. It is shown that there are
nontrivial angular distributions of the emitted photons and their polarization
that are connected to the superposition of the coherent scattering of electrons
by atomic rows ("doughnut scattering" effect) and the suppression of radiation
(similar to the Landau-Pomeranchuk-Migdal effect in an amorphous matter). It is
also shown that circular polarization of radiation in the considered case is
identically zero.
