Beamforming is the primary technology to overcome the high path loss in millimeter-wave (mmWave) channels. Hence, performance improvement needs knowledge and control of the spatial domain. In particular, antenna structure and radiation parameters affect the beamforming performance in mmWave communications systems. In order to address the impairments such as beam misalignments, outage loss, tracking inability, blockage, etc., an optimum value of the beamwidth must be determined. In our previous paper, assuming a communication system that creates a beam per cluster, we theoretically investigated the beamwidth-received power relation in the cluster level mmWave channels. We used uniform linear array (ULA) antenna in our analysis. In this paper, we revisit the analysis and update the expressions for the scenario where we use rectangular uniform planar array (R-UPA) antenna. Rectangular beam model is considered to approximate the main lobe pattern of the antenna. For the channel, we derive beamwidth-dependent extracted power expressions for two intra-cluster channel models, IEEE 802.11ad and our previous work based on ray-tracing (RT-ICM). Combining antenna and channel gains, in case of the perfect alignment, we confirm that the optimum beamwidth converges zero. Performing asymptotic analysis of the received power, we give the formulation and insights that the practical nonzero beamwidth values can be achieved although sacrificing subtle from the maximum received power. Our analysis shows that to reach 95% of the maximum power for a typical indoor mmWave cluster, a practical beamwidth of 3.5 deg is enough. Finally, our analysis results show that there is a 13 dB increase in the maximum theoretical received power when UPA is used over ULA. We show that an 8 x 8 UPA can reach 50% of that maximum received power while the received power is still 10 dB larger than the ULA scenario.
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