This paper considers channel estimation and system performance for the uplink of a single-cell massive multiple-input multiple-output (MIMO) system. Each receive antenna of the base station (BS) is assumed to be equipped with a pair of onebit analog-to-digital converters (ADCs) to quantize the real and imaginary part of the received signal. We first propose an approach for channel estimation that is applicable for both flat and frequency-selective fading, based on the Bussgang decomposition that reformulates the nonlinear quantizer as a linear function with identical first-and second-order statistics. The resulting channel estimator outperforms previously proposed approaches across all SNRs. We then derive closed-form expressions for the achievable rate in flat fading channels assuming low SNR and a large number of users for the maximal ratio and zero forcing receivers that takes channel estimation error due to both noise and one-bit quantization into account. The closed-form expressions in turn allow us to obtain insight into important system design issues such as optimal resource allocation, maximal sum spectral efficiency, overall energy efficiency, and number of antennas. Numerical results are presented to verify our analytical results and demonstrate the benefit of optimizing system performance accordingly.

We study the performance of multi-input multioutput (MIMO) channels with coarsely quantized outputs in the low signal-to-noise ratio (SNR) regime, where the channel is perfectly known at the receiver. This analysis is of interest in the context of Ultra-Wideband (UWB) communications from two aspects. First the available power is spread over such a large frequency band, that the power spectral density is extremely low and thus the SNR is low. Second the analogto-digital converters (ADCs) for such high bandwidth signals should be low-resolution, in order to reduce their cost and power consumption. In this paper we consider the extreme case of only 1-bit ADC for each receive signal component. We compute the mutual information up to second order in the SNR and study the impact of quantization. We show that, up to first order in SNR, the mutual information of the 1-bit quantized system degrades only by a factor of 2 compared to the system with infinite resolution independent of the actual MIMO channel realization. With Channel State Information (CSI) only at receiver, we show that QPSK is, up to the second order, the best among all distributions with independent components. We also elaborate on the ergodic capacity under this scheme in a Rayleigh flat-fading environment.

We study the transmitter optimization for the flat multi-input multi-output (MIMO) channel under nonlinear distortion from the digital-to-analog converters (DACs). Our design is based on a minimum mean square error (MMSE) approach, taking into account the effects of the transmitter nonlinearities. Our derivation does not make use of the assumption of uncorrelated white distortion (quantization) errors and considers the correlations of the quantization error with the other signals of the system. Through simulation, we compare the new optimized linear transmitter to previously proposed linear transmitter designs when operating under DACs in terms of uncoded BER.

Abstract-We study the joint optimization of the quantizer and the iterative Decision Feedback Equalizer (IDE) for the flat multiinput multi-output (MIMO) channel with quantized outputs. Our design is based on a minimum mean square error (MMSE) approach, taking into account the effects of quantization. Our derivation does not make use of the assumption of uncorrelated white quantization errors and considers the correlations of the quantization error with the other signals of the system. Through simulation, we compare the provided IDE to the conventional spatial DFE operating on quantized data in terms of uncoded BER.

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