DFT-Based Hybrid Beamforming Multiuser Systems: Rate Analysis and Beam Selection

Abstract: This paper considers the discrete Fourier transform (DFT) based hybrid beamforming multiuser system and studies the use of analog beam selection schemes. We first analyze the uplink ergodic achievable rates of the zero-forcing (ZF) receiver and the maximum-ratio combining (MRC) receiver under Ricean fading conditions. We then examine the downlink ergodic achievable rates for the ZF and maximum-ratio transmitting (MRT) precoders. The long-term and short-term normalization methods are introduced, which utilize long-term and instantaneous channel state information (CSI) to implement the downlink power normalization, respectively. Also, approximations and asymptotic expressions of both the uplink and downlink rates are obtained, which facilitate the analog beam selection solutions to maximize the achievable rates. An exhaustive search provides the optimal results but to reduce the time-consumption, we resort to the derived rate limits and propose the second selection scheme based on the projected power of the line-of-sight (LoS) paths. We then combine the advantages of the two schemes and propose a two-step scheme that achieves near optimal performances with much less time-consumption than exhaustive search. Numerical results confirm the analytical results of the ergodic achievable rate and reveal the effectiveness of the proposed two-step method.