Channel state information is crucial to achieving the capacity of
multi-antenna (MIMO) wireless communication systems. It requires estimating the
channel matrix. This estimation task is studied, considering a sparse channel
model particularly suited to millimeter wave propagation, as well as a general
measurement model taking into account hybrid architectures. The contribution is
twofold. First, the Cram{\'e}r-Rao bound in this context is derived. Second,
interpretation of the Fisher Information Matrix structure allows to assess the
role of system parameters, as well as to propose asymptotically optimal and
computationally efficient estimation algorithms