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.
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