Rate Loss due to Beam Cusping in Grid of Beams

We present mean communication rate loss (MCRL) values due to the beam cusping phenomenon inherent to grid of beams based wireless systems, which are widely used/proposed in millimeter-wave and sub-THz bands. We consider array antenna elements with non-zero aperture and axisymmetric radiation pattern with a certain directivity, unlike the ideal isotropic antenna elements widely considered in theoretical papers on array processing and RF beamforming. The array antenna elements have a half power beam width of ninety degrees in this work which is typical of commonly used microstrip patch antenna elements. We perform Monte Carlo numerical experiments to obtain MCRL values for different spatial dimensions of multiple input multiple output (MIMO) systems, different angular fields-of view, and different beamforming codebook sizes. We show that increasing the beam grid density beyond a certain threshold does not help and therefore a certain cusping loss is unavoidable even for continuous beam steering with directive antenna elements. Further, we also show the quantitative impact on the MCRL values as the axisymmetric radiation pattern directivity of the modelled antenna element is increased.