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

Abstract

High power consumption and hardware cost are two barriers for practical massive multiple-input multiple-output (mMIMO) systems. A promising solution is to employ low-resolution analog-to-digital converters (ADCs). 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 of 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 zeroforcing (ZF) relaying considering both perfect and imperfect channel state information (CSI). To conquer the challenges caused by multi-way relaying, the complicated ZF beam-forming matrix, and the general mixed-ADC structure, we develop a novel method for the achievable rate analysis using the singularvalue decomposition (SVD) for Gaussian matrices, distributions of the singular values of Gaussian matrices, and properties of Haar matrices. The results explicitly show the achievable rate behavior in terms of the user and relay transmit powers and the numbers of relay antennas and users. Most importantly, it quantifies the performance degradation caused by low-resolution ADCs and channel estimation error. 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 more significant effect on the rate compared to the number of antennas. Our work reveals that the performance gap between the perfect and imperfect CSI cases increases as the average ADC resolution increases. For more insights, simplified achievable rate expressions for asymptotic cases and the uniform-ADC case are obtained. Numerical results verify that the theoretical results can accurately predict the performance of the considered system. Part of this work on the performance analysis of mMIMO multi-way relay networks with low-resolution uniform-ADC structures has been presented at