Joint Inter-Path and Intra-Path Multiplexing for Terahertz Widely-Spaced Multi-Subarray Hybrid Beamforming Systems

Terahertz (THz) communications with multi-GHz bandwidth are envisioned as a key technology for 6G systems. Ultra-massive (UM) MIMO with hybrid beamforming architectures are widely investigated to provide a high array gain to overcome the huge propagation loss at THz band. However, most of the existing hybrid beamforming architectures can only utilize the multiplexing offered by the multipath components, i.e., inter-path multiplexing, which is very limited due to the spatially sparse THz channel. In this paper, a widely-spaced multi-subarray (WSMS) hybrid beamforming architecture is proposed, which improves the multiplexing gain by exploiting a new type of intra-path multiplexing provided by the spherical-wave propagation among $k$ widely-spaced subarrays, in addition to the inter-path multiplexing. The resulting multiplexing gain of WSMS architecture is $k$ times of the existing architectures. For WSMS architecture, a novel design problem is formulated by optimizing the number of subarrays, subarray spacing, and hybrid beamforming matrices to maximize the spectral efficiency, which is decomposed into two subproblems. An optimal closed-form solution is derived for the first hybrid beamforming subproblem, while a dominant-line-of-sight-relaxation algorithm is proposed for the second array configuration subproblem. Extensive simulation results demonstrate that the WSMS architecture and proposed algorithms enhance the spectral efficiency substantially.