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

Abstract: 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 transmit- and receive-side channel state information (CSI), are assumed to be quantized to 1-bit of information. The derived results show that the capacity of the considered massive MIMO system is $2N$ and $2M$ bits per channel use when $N$ is fixed and $M\to\infty$ and when $M$ is fixed and $N\to\infty$, respectively, where $M$ and $N$ denote the number of transmit and receive antennas, respectively. These coincide with the respective capacities with full 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 transmitter-end or at the receiver-end, 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.