  Millimeter-wave (mmWave) massive multiple-input-multiple-output (mMIMO) is
reported as a key enabler in the fifth-generation communication and beyond. It
is customary to use a lens antenna array to transform a mmWave mMIMO channel
into a beamspace where the channel exhibits sparsity. This beamspace
transformation is equivalent to performing a Fourier transformation of the
channel. Still, a Fourier transformation is not necessarily the optimal one,
due to many reasons. Accordingly, this paper proposes using a learned
sparsifying dictionary as the transformation operator leading to another
beamspace. Since the dictionary is obtained by training over actual channel
measurements, this transformation is shown to yield two immediate advantages.
First is enhancing channel sparsity, thereby leading to more efficient pilot
reduction. Second is improving the channel representation quality, and thus
reducing the underlying power leakage phenomenon. Consequently, this allows for
both improved channel estimation and facilitated beam selection in mmWave
mMIMO. Besides, a learned dictionary is also used as the precoding operator for
the same reasons. Extensive simulations under various operating scenarios and
environments validate the added benefits of using learned dictionaries in
improving the channel estimation quality and the beam selectivity, thereby
improving the spectral efficiency.
