On Beamforming Gain Models for Performance Evaluation and Analysis of Narrowband and Wideband Wireless Networks

Directional antennas and beamforming techniques that bring promising transmission gain to the wireless links are widely incorporated in the system-level analysis of wireless networks. In many existing studies, the beamforming gain model to calculate the beamforming gain considers beamforming pattern and aligned as well as misaligned cases. However, the channel properties, e.g., the $K$ factor and the spatial distribution of multi-paths, are neglected, which could significantly influence the beamforming gain. In this paper, a general beamforming gain model is appropriately defined, while the traditional beamforming gain model is proved to be only a special case in the proposed general model by considering an oversimplified channel with no angular spread. In light of this, expressions of the received signal amplitude and the beamforming gain are rigorously derived for narrowband fading and wideband statistical mmWave channels, respectively. Thorough comparison between the proposed beamforming gain model and the traditional beamforming gain is provided, which demonstrates and validates that the traditional model incorrectly captures the beamforming gain and thereby, leads to inaccurate system-level network analysis. To this end, the effectiveness and importance of the proposed general beamforming gain model are revealed, particularly for millimeter-wave wideband systems.