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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. 

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. 

The one-bit spatial Sigma-Delta concept has recently been proposed as an approach for achieving low distortion and low power consumption for massive multi-input multi-output systems. The approach exploits users located in known angular sectors or spatial oversampling to shape the quantization noise away from desired directions of arrival. While reducing the antenna spacing alleviates the adverse impact of quantization noise, it can potentially deteriorate the performance of the massive array due to excessive mutual coupling. In this paper, we analyze the impact of mutual coupling on the uplink spectral efficiency of a spatial one-bit Sigma-Delta massive MIMO architecture, and compare the resulting performance degradation to standard one-bit quantization as well as the ideal case with infinite precision. Our simulations show that the one-bit Sigma-Delta array is particularly advantageous in space-constrained scenarios, can still provide significant gains even in the presence of mutual coupling when the antennas are closely spaced. 

We study the uplink performance of a massive multiple-input multiple-output (MIMO) system with one-bit analog to digital converters (ADCs) in the presence of a disruptive jammer. We propose spatial Sigma-Delta (ΣΔ) quantization with an interference cancellation feedback beamformer (FBB ΣΔ) to mitigate the adverse impact of the jammer on the system performance. Then we analyze the performance of this architecture by adopting an appropriate linear model and present a recursive algorithm to calculate the power of the quantization noise. Simulation results show that the spatial FBB ΣΔ architecture can achieve the same symbol error rate as in systems with high-resolution ADCs. 

The uplink performance of a mixed analog-to-digital converter (ADC) massive multiple-input multiple-output (MIMO) architecture with a space-constrained array at the base station (BS) is analyzed. We investigate the effect of spatial correlation and mutual coupling on the spectral efficiency (SE) of the system. First, we analyze to what extent adding a small number of high-resolution ADCs can impact the channel estimation accuracy. Then, we derive a closed-form approximation for the SE. Our analysis demonstrates how a space constraint on a uniform linear array (ULA) can affect the design of a massive MIMO system with low-resolution ADCs. It is shown that by equally spacing a small number of high-resolution ADCs over the array, one can dramatically reduce the performance gap between a system with all low-resolution and all high-resolution ADCs. 

We consider channel estimation for an uplink massive multiple input multiple output (MIMO) system where the base station (BS) uses a first-order spatial Sigma-Delta (Σ△) analog-to-digital converter (ADC) array. The Σ△ array consists of closely spaced sensors which oversample the received signal and provide a coarsely quantized (1-bit) output. We develop a linear minimum mean squared error (LMMSE) estimator based on the Bussgang decomposition that reformulates the nonlinear quantizer model using an equivalent linear model plus quantization noise. The performance of the proposed Σ△ LMMSE estimator is compared via simulation to channel estimation using standard 1-bit quantization and also infinite resolution ADCs. 

For 5G it will be important to leverage the available millimeter wave spectrum. To achieve an approximately omni- directional coverage with a similar effective antenna aperture compared to state-of-the-art cellular systems, an antenna array is required at both the mobile and basestation. Due to the large bandwidth and inefficient amplifiers available in CMOS for mmWave, the analog front-end of the receiver with a large number of antennas becomes especially power hungry. Two main solutions exist to reduce the power consumption: hybrid beam forming and digital beam forming with low resolution Analog to Digital Converters (ADCs). In this work we compare the spectral and energy efficiency of both systems under practical system constraints. We consider the effects of channel estimation, transmitter impairments and multiple simultaneous users for a wideband multipath model. Our power consumption model considers components reported in literature at 60 GHz. In contrast to many other works we also consider the correlation of the quantization error, and generalize the modeling of it to non- uniform quantizers and different quantizers at each antenna. The result shows that as the Signal to Noise Ratio (SNR) gets larger the ADC resolution achieving the optimal energy efficiency gets also larger. The energy efficiency peaks for 5 bit resolution at high SNR, since due to other limiting factors the achievable rate almost saturates at this resolution. We also show that in the multi- user scenario digital beamforming is in any case more energy efficient than hybrid beamforming. In addition we show that if mixed ADC resolutions are used we can achieve any desired trade-off between power consumption and rate close to those achieved with only one ADC resolution.