  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 one-bit 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 functionwith 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.
