Ergodic Capacity Analysis of Uplink MU-MIMO Systems With Low-Resolution ADCs

This paper addresses the ergodic capacity for uplink multi-user multiple-input multiple-output (MU-MIMO) systems equipped with low-resolution analog-to-digital converters (ADCs). The nonlinear quantization effect poses a great challenge to conduct the capacity analysis. This is because the well-known Shannon capacity expression is only applicable for linear systems, and it cannot be directly used for the capacity analysis in the nonlinear quantized systems with low-resolution ADCs. To tackle this, we resort to the replica method from statistical physics. Specifically, we elaborately derive the closed-form expression of the ergodic capacity, which is applicable for arbitrary signaling inputs. As a result, explicit capacity expressions are readily obtained for the often-used Gaussian inputs and QAM inputs. With the obtained expressions, we can evaluate the ergodic capacity for various system setups, and can study the impacts of the system parameters (the number of received antennas, the number of users, the number of quantization bits and the channel parameters) on the ergodic capacity. We directly calculate the mutual information between the transmitted signals and the received quantized signals, without performing any additional reception operations, and obtain more fundamental results. Compared to the time-consuming Monte-Carlo simulations, the analytical expressions are highly accurate while significantly saving the computation time. Furthermore, it is shown that with proper system configurations, the capacity loss caused by low-resolution ADCs may be mild, compared with infinite-precision ADCs.