Performance Analysis of Massive MIMO Multi-Way Relay Networks with Low-Resolution ADCs

High power consumption and hardware cost have motivated using low-resolution analog-to-digital converters (ADCs) for practical massive multiple-input multiple-output (mMIMO) systems. In this paper, we consider a general mMIMO multi-way relaying system with a multi-level mixed-ADC architecture in which each antenna is connected to an ADC pair with an arbitrary resolution. By leveraging on Bussgang’s decomposition theorem and Lloyd-Max algorithm for quantization, tight closed-form approximations are derived for the average achievable rates of zero-forcing (ZF) relaying considering both perfect and imperfect channel state information (CSI). To handle such a challenging setup, we develop a novel method for the achievable rate analysis using distributions of the singular values of Gaussian matrices and properties of Haar matrices. We demonstrate that the average achievable rate has an almost linear relation with the square of the average of quantization coefficients pertaining to the ADC resolution profile. In addition, in the medium to high SNR region, the ADC resolutions have a more significant effect on the rate compared to the number of antennas. Our work also reveals that the performance gap between the perfect and imperfect CSI cases is smaller for lower ADC resolutions, hence imperfect CSI is better tolerated at lower resolutions.