  This paper addresses the beam-selection challenges in Multi-User Multiple
Input Multiple Output (MU-MIMO) beamforming for mm-wave and THz channels,
focusing on the pivotal aspect of spectral efficiency (SE) and computational
efficiency. We introduce a novel approach, the Greedy Interference-Optimized
Singular Vector Beam-selection (G-IOSVB) algorithm, which offers a strategic
balance between high SE and low computational complexity. Our study embarks on
a comparative analysis of G-IOSVB against the traditional IOSVB and the
exhaustive Singular-Vector Beamspace Search (SVBS) algorithms. The findings
reveal that while SVBS achieves the highest SE, it incurs significant
computational costs, approximately 162 seconds per channel realization. In
contrast, G-IOSVB aligns closely with IOSVB in SE performance yet is markedly
more computationally efficient. Heatmaps vividly demonstrate this efficiency,
highlighting G-IOSVB's reduced computation time without sacrificing SE. We also
delve into the mathematical intricacies of G-IOSVB, demonstrating its
theoretical and practical superiority through rigorous expressions and detailed
algorithmic analysis. The numerical results illustrate that G-IOSVB stands out
as an efficient, practical solution for MU-MIMO systems, making it a promising
candidate for high-speed, high-efficiency wireless communication networks.
