On the Performance of User Selection for Zero-Forcing Beamforming in MU-MIMO Downlink Channels with One-Bit ADCs

This paper analyzes the ergodic sum rate of zero-forcing beamforming with semi-orthogonal user selection (ZFBF-SUS) in multiuser multiple-input multiple-output (MU-MIMO) downlink channels with one-bit analog-to-digital converters (ADCs) at the receivers. Although ZFBF-SUS has been widely studied under the conventional assumption of infinite-resolution ADCs, its ergodic performance with one-bit ADC receivers has not been fully characterized. To address this issue, we derive analytical approximations for the ergodic sum rate by considering the achievable rate expression induced by one-bit quantization. For mathematical tractability, the achievable rate of each selected user is approximated as a function of its channel gain under the condition that the selected users are nearly orthogonal and the number of users is sufficiently large. Moreover, the channel gain of each scheduled user is characterized using maximum order statistics of Gamma random variables, while the size of the SUS candidate set is approximated by exploiting the semi-orthogonality condition. We further derive an asymptotic sum-rate expression with respect to the number of users by applying extreme value theory. Simulation results verify the validity of the proposed analytical approximations and show that the derived expressions accurately capture the ergodic sum-rate behavior of ZFBF-SUS with one-bit ADC receivers, especially when the number of users is large and the SUS threshold is properly chosen.