Asymptotic Capacity of Massive MIMO With 1-Bit ADCs and 1-Bit DACs at the Receiver and at the Transmitter

In this paper, we investigate the capacity of massive multiple-input multiple-output (MIMO) systems corrupted by complex-valued additive white Gaussian noise (AWGN) when both the transmitter and the receiver employ 1-bit digital-to-analog converters (DACs) and 1-bit analog-to-digital-converters (ADCs). As a result of 1-bit DACs and ADCs, the transmitted and received symbols, as well as the transmitand receive-side noisy channel state information (CSI) are assumed to be quantized to 1-bit of information. The derived results, applicable to both single-user and multi-user MIMO, show that the capacity of the considered massive MIMO system is 2N and 2M bits per channel use when N is fixed and M goes to infinity and when M is fixed and N goes to infinity, respectively, where M and N denote the number of transmit and receive antennas, respectively. These coincide with the respective capacities with full and noise-free CSI at both the transmitter and the receiver. In both cases, we showed that the derived capacities can be achieved with noisy 1-bit CSI at the massive-side and without any CSI at the other end. Moreover, we showed that the capacity can be achieved in one channel use without employing channel coding, which results in a latency of one channel use.