  Millimeter-wave (mm-Wave) cellular systems are a promising option for a very
high data rate communication because of the large bandwidth available at
mm-Wave frequencies. Due to the large path-loss exponent in the mm-Wave range
of the spectrum, directional beamforming with a large antenna gain is necessary
at the transmitter, the receiver or both for capturing sufficient signal power.
This in turn implies that fast and robust channel estimation plays a central
role in systems performance since without a reliable estimate of the channel
state the received signal-to-noise ratio (SNR) would be much lower than the
minimum necessary for a reliable communication.
  In this paper, we mainly focus on single-antenna users and a multi-antenna
base-station. We propose an adaptive sampling scheme to speed up the user's
signal subspace estimation. In our scheme, the beamforming vector for taking
every new sample is adaptively selected based on all the previous beamforming
vectors and the resulting output observations. We apply the theory of optimal
design of experiments in statistics to design an adaptive algorithm for
estimating the signal subspace of each user. The resulting subspace estimates
for different users can be exploited to efficiently communicate to the users
and to manage the interference. We cast our proposed algorithm as
low-complexity optimization problems, and illustrate its efficiency via
numerical simulations.
