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Massive multiple-input multiple-output (MIMO) communications using low-resolution analog-to-digital converters (ADCs) is a promising technology for providing high spectral and energy efficiency with affordable hardware cost and power consumption. However, the use of low-resolution ADCs requires special signal processing methods for channel estimation and data detection since the resulting system is severely non-linear. This paper proposes joint channel estimation and data detection methods for massive MIMO systems with low-resolution ADCs based on the variational Bayes (VB) inference framework. We first derive matched-filter quantized VB (MF-QVB) and linear minimum mean-squared error quantized VB (LMMSE-QVB) detection methods assuming the channel state information (CSI) is available. Then we extend these methods to the joint channel estimation and data detection (JED) problem and propose two methods we refer to as MF-QVB-JED and LMMSE-QVB-JED. Unlike conventional VB-based detection methods that assume knowledge of the second-order statistics of the additive noise, we propose to float the elements of the noise covariance matrix as unknown random variables that are used to account for both the noise and the residual inter-user interference. We also present practical aspects of the QVB framework to improve its implementation stability. Finally, we show via numerical results that the proposed VB-based methods provide robust performance and also significantly outperform existing methods. 

Enabling communications in the (sub-)THz band will call for massive multiple-input multiple-output (MIMO) arrays at either the transmit- or receive-side, or at both. To scale down the complexity and power consumption when operating across massive frequency and antenna dimensions, a sacrifice in the resolution of the digital-to-analog/analog-to-digital converters (DACs/ADCs) will be inevitable. In this paper, we analyze the extreme scenario where both the transmit- and receive-side are equipped with fully digital massive MIMO arrays and 1-bit DACs/ADCs, which leads to a system with minimum radio-frequency complexity, cost, and power consumption. Building upon the Bussgang decomposition, we derive a tractable approximation of the mean squared error (MSE) between the transmitted data symbols and their soft estimates. Numerical results show that, despite its simplicity, a doubly 1-bit quantized massive MIMO system with very large antenna arrays can deliver an impressive performance in terms of MSE and symbol error rate.