  A 2D problem of acoustic wave scattering by a segment bearing impedance
boundary conditions is considered. In the current paper (the first part of a
series of two) some preliminary steps are made, namely, the diffraction problem
is reduced to two matrix Riemann-Hilbert problems with exponential growth of
unknown functions (for the symmetrical part and for the antisymmetrical part).
For this, the Wiener--Hopf problems are formulated, they are reduced to
auxiliary functional problems by applying the embedding formula, and finally
the Riemann-Hilbert problems are formulated by applying the Hurd's method.
  In the second part the Riemann-Hilbert problems will be solved by a novel
method of OE-equation.
