  Fast channel estimation in millimeter-wave (mmWave) systems is a fundamental
enabler of high-gain beamforming, which boosts coverage and capacity. The
channel estimation stage typically involves an initial beam training process
where a subset of the possible beam directions at the transmitter and receiver
is scanned along a predefined codebook. Unfortunately, the high number of
transmit and receive antennas deployed in mmWave systems increase the
complexity of the beam selection and channel estimation tasks. In this work, we
tackle the channel estimation problem in analog systems from a different
perspective than used by previous works. In particular, we propose to move the
channel estimation problem from the angular domain into the transformed spatial
domain, in which estimating the angles of arrivals and departures corresponds
to estimating the angular frequencies of paths constituting the mmWave channel.
The proposed approach, referred to as transformed spatial domain channel
estimation (TSDCE) algorithm, exhibits robustness to additive white Gaussian
noise by combining low-rank approximations and sample autocorrelation functions
for each path in the transformed spatial domain. Numerical results evaluate the
mean square error of the channel estimation and the direction of arrival
estimation capability. TSDCE significantly reduces the first, while exhibiting
a remarkably low computational complexity compared with well-known benchmarking
schemes.
