Hybrid Terahertz Beamforming Relying on Channel Sparsity and Angular Orthogonality

As the next generation concepts gravitate towards ultra-high frequency bands, such as the terahertz (THz) band having abundant resources, approaching Tbps transmission rates is becoming a reality. In this contact we may exploit the sparsity of the THz channel, which substantially reduces the hardware complexity, since a single RF chain is capable of designing a near-optimal transmit beamformer in a single-carrier single-user THz system. We then reveal the spatial orthogonality experienced in the downlink of a single-carrier THz broadcast system supporting multiple users. The minimum throughput of the users is maximized by specifically designing the hybrid beamformer. Based on the above-mentioned angular orthogonality, we characterise the asymptotically optimal structure of the hybrid beamformer. Specifically, the asymptotically optimal analog beamformer is represented in closed-form, while its asymptotically optimal digital counterpart is formulated by solving a linear-programming problem. As a special example, the asymptotically optimal hybrid beamformer is also obtained in closed-form for a THz multicast system. Moreover, we obtain the closed-form asymptotically optimal hybrid beamformer of a multi-carrier multi-user system, when we maximize the minimum throughput among all the user. Our numerical results explicitly demonstrate the compelling benefits of our hybrid beamforming design.