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In many multiple-input multiple-output (MIMO) communication applications, two-dimensional (2D) rectangular arrays are used and the angular field of interest is different in the azimuth and elevation angle domains. In this paper, we show how to exploit scenarios with users confined to narrow elevation angles by means of 2D rectangular arrays with low-resolution spatial Σ∆ sampling in only one (i.e., the vertical) dimension. We analyze the 2D directions-of-arrival (DoA) estimation performance of MUSIC for such arrays, and illustrate the resulting advantage of the Σ∆ approach over standard one-bit receivers. 

Low-resolution analog-to-digital converters (ADCs) have been considered as a practical and promising solution for reducing cost and power consumption in massive Multiple-Input-Multiple-Output (MIMO) systems. Unfortunately, low-resolution ADCs significantly distort the received signals, and thus make data detection much more challenging. In this paper, we develop a new deep neural network (DNN) framework for efficient and low-complexity data detection in low-resolution massive MIMO systems. Based on reformulated maximum likelihood detection problems, we propose two model-driven DNN-based detectors, namely OBMNet and FBMNet, for one-bit and few-bit massive MIMO systems, respectively. The proposed OBMNet and FBMNet detectors have unique and simple structures designed for low-resolution MIMO receivers and thus can be efficiently trained and implemented. Numerical results also show that OBMNet and FBMNet significantly outperform existing detection methods. 

Spatial ΣΔ sampling has recently been proposed to improve the performance of massive MIMO systems with low-resolution quantization for cases where the users are confined to a certain angular sector, or the array is spatially oversampled. We derive a linear minimum mean squared error (LMMSE) channel estimator for the ΣΔ array based on an element-wise Bussgang decomposition that reformulates the nonlinear quantizer operation using an equivalent linear model plus quantization noise. Both the case of one- and two-bit quantization is considered. We then evaluate the achievable rate of the ΣΔ system assuming that a linear receiver based on the LMMSE channel estimate is used to decode the data. Our numerical results demonstrate that ΣΔ architecture is able to achieve superior channel estimates and sum spectral efficiency compared to conventional low-resolution quantized massive MIMO systems.