  The optimization of the pilot overhead in single-user wireless fading
channels is investigated, and the dependence of this overhead on various system
parameters of interest (e.g., fading rate, signal-to-noise ratio) is
quantified. The achievable pilot-based spectral efficiency is expanded with
respect to the fading rate about the no-fading point, which leads to an
accurate order expansion for the pilot overhead. This expansion identifies that
the pilot overhead, as well as the spectral efficiency penalty with respect to
a reference system with genie-aided CSI (channel state information) at the
receiver, depend on the square root of the normalized Doppler frequency.
Furthermore, it is shown that the widely-used block fading model is only a
special case of more accurate continuous fading models in terms of the
achievable pilot-based spectral efficiency, and that the overhead optimization
for multiantenna systems is effectively the same as for single-antenna systems
with the normalized Doppler frequency multiplied by the number of transmit
antennas.
