  We present a beamforming algorithm for multiuser wideband millimeter wave
(mmWave) communication systems where one access point uses hybrid
analog/digital beamforming while multiple user stations have phased-arrays with
a single RF chain. The algorithm operates in a more general mode than others
available in literature and has lower computational complexity and training
overhead. Throughout the paper, we describe: i) the construction of novel
beamformer sets (codebooks) with wide sector beams and narrow beams based on
the orthogonality property of beamformer vectors, ii) a beamforming algorithm
that uses training transmissions over the codebooks to select the beamformers
that maximize the received sumpower along the bandwidth, and iii) a numerical
validation of the algorithm in standard indoor scenarios for mmWave WLANs using
channels obtained with both statistical and raytracing models. Our algorithm is
designed to serve multiple users in a wideband OFDM system and does not require
channel matrix knowledge or a particular channel structure. Moreover, we
incorporate antenna-specific aspects in the analysis, such as antenna coupling,
element radiation pattern, and beam squint. Although there are no other
solutions for the general system studied in this paper, we characterize the
algorithm's achievable rate and show that it attains more than 70 percent of
the spectral efficiency (between 1.5 and 3 dB SNR loss) with respect to ideal
fully-digital beamforming in the analyzed scenarios. We also show that our
algorithm has similar sum-rate performance as other solutions in the literature
for some special cases, while providing significantly lower computational
complexity (with a linear dependence on the number of antennas) and shorter
training overhead.
