MAC Layer Beamforming: Rate Loss due to Beam Cusping

In this paper, we investigate the mean communication rate loss (MCRL) due to beam cusping with respect to multiple input multiple output (MIMO) spatial dimensions, beamforming codebook sizes, and beam scan spaces for beamforming operations controlled by the medium access control (MAC) layer beamforming protocol. The intractability of the analytical investigation for a closed-form expression leads to the usage of Monte Carlo numerical experiments. For discrete Fourier transform (DFT) beamforming codebooks, the MCRL increases with an increase in the MIMO dimensions while it decreases with an increase in the beam scan space from the array broadside. The MCRL becomes negligible as the number of beams for selection is increased to four times the number of DFT beams. These results will be helpful for determination of MIMO configuration, angular coverage zone, codebook size, and phase-shifter resolution for a minimal MCRL. This is especially relevant for sparse MIMO channels o f millimetre-wave (mmWave) and terahertz (THz) wireless systems in the fifth generation (5G) and beyond mobile networks.