On the performance of hybrid beamforming for closely-spaced and randomly located users

Hybrid (analog-digital) beamforming has received tremendous attention for realizing multiuser multiple-input-multiple-output systems at millimeter wave frequencies. However, almost all of the hybrid beamforming literature characterizes the spectral and energy efficiency performance for randomly located user terminals. In stark contrast, this article evaluates and compares the multiuser downlink ergodic sum spectral efficiency (ESSE) using different combinations of analog and digital beamforming techniques when users are closely-spaced. For any given combination of hybrid beamforming, we derive an analytical expression characterizing the loss of per-user ergodic spectral efficiency relative to fully digital beamforming. To get the negligible ESSE loss for both hybrid and fully digital beamforming, we quantify the angle-of-departure separation across multiple users, it is the term associated to the channel correlation induced by the user positions. We show the generality of the derived expression by testing it across a wide range of system dimensions, number of radio-frequency (RF) chains, and signal-to-noise ratios. Our results demonstrate that an extra RF chain may be sufficient to compensate most of the loss in ESSE due to closely-spaced terminals.