  Adamjan-Arov (Lax--Phillips) model space is considered as a scattering
representation space for a CMV matrix in context of an extended
Marchenko--Faddeev scattering theory. That is, there exists a basis in which
the multiplication by independent variable is a CMV matrix. This basis as well
as Verblunski coefficients are computed explicitly in terms of Nehari
interpolation. Asymptotically the Verblynski coefficients go to zero. Moreover,
relations between the basis and wandering subspaces are established.
Transformation from scattering representation to spectral representation is
given.
