  We describe a special case of base change of certain supercuspidal
representations from a ramified unitary group to a general linear group, both
defined over a p-adic field of odd residual characteristic. Roughly speaking,
we require the underlying stratum of a given supercuspidal representation to be
skew maximal simple, and the field datum of this stratum to be of maximal
degree, tamely ramified over the base field, and quadratic ramified over its
subfield fixed by the Galois involution that defines the unitary group. The
base change of this supercuspidal representation is described by a canonical
lifting of its underlying simple character, together with the base change of
the level-zero component of its inducing cuspidal type, modified by a sign
attached to a quadratic Gauss sum defined by the internal structure of the
simple character. To obtain this result, we study the reducibility points of a
parabolic induction and the corresponding module over the affine Hecke algebra,
defined by the covering type over the product of types of the given
supercuspidal representation and of a candidate of its base change.
