  Channel estimation is of paramount importance in most communication systems
in order to optimize the data rate/energy consumption tradeoff. In modern
systems, the possibly large number of transmit/receive antennas and subcarriers
makes this task difficult. Designing pilot sequences of reasonable size
yielding good performance is thus critical. Classically, the number of pilots
is reduced by viewing the channel as a random vector and assuming knowledge of
its distribution. In practice, this requires estimating the channel covariance
matrix, which can be computationally costly and not adapted to scenarios with
high mobility. In this paper, an alternative view is considered, in which the
channel is a function of unknown deterministic parameters. In this setting, the
problem of designing optimal pilot sequences of smallest possible size is
studied for any parametric channel model. To do so, the Cram{\'e}r-Rao bound
(CRB) for this general channel estimation problem is given, highlighting its
key dependency on the introduced variation space. Then, the minimal size of
pilot sequences and minimal value of the CRB are determined. Moreover, a
general strategy to build optimal minimal length power constrained pilots
sequences is given, based on an estimation of the variation space. The
theoretical results are finally illustrated in a massive MIMO system context.
They conveniently allow to retrieve well known previous results, but also to
exhibit minimal length optimal pilot sequences for a new strategy based on a
nonlinear physical model.
