  Beamforming for mmWave communications is well-studied in the PHY based on the
channel parameters to develop optimum receiver processing techniques. However,
even before signal processing, antenna structure and radiation parameters
affect the beamforming performance primarily. For example, in contrast to
common belief, narrow beamwidth (bmW) may result in degraded beamforming
performance. In order to address the impairments such as beam misalignments,
outage loss, tracking inability, blockage, etc., an optimum value of the bmW
must be determined. In this paper, assuming a communication system that creates
a beam per cluster, we theoretically investigate the bmW and received power
relation in the cluster level mmWave channels. We adopt ULA structure and
formulate its antenna gain with respect to the bmW. Two beam models are
considered for the main lobe of the array pattern, rectangular and triangular.
We derive bmW-dependent extracted power expressions for two intra-cluster
channel models, 802.11ad and our previous work, RT-ICM. Combining antenna and
channel gains, in case of a beam misalignment, we find that the optimum bmW
that maximizes the received power is larger than the alignment error when the
error itself is larger than the standard deviation of the cluster power-angle
spectrum. Once the alignment error is smaller than the standard deviation, we
confirm that the optimum bmW converges zero. Performing asymptotic analysis of
the received power, we give the formulation and insights that the practical
nonzero bmW values can be achieved although sacrificing subtle from the maximum
received power. Our analysis shows that to reach 95% of the maximum power for
an indoor mmWave cluster, a practical bmW of 7-10 degrees is enough, which can
be created with 18-20 antenna elements. In the simulation section, we show that
the expressions given by the analysis match to the simulated results.
