  We present an analytical framework for the channel estimation and the data
decoding in massive multiple-input multiple-output uplink systems with 1-bit
analog-to-digital converters (ADCs). First, we provide a closed-form expression
of the mean squared error of the channel estimation for a general class of
linear estimators. In addition, we propose a novel linear estimator with
significantly enhanced performance compared with existing estimators with the
same structure. For the data decoding, we provide closed-form expressions of
the expected value and the variance of the estimated symbols when maximum ratio
combining is adopted, which can be exploited to efficiently implement maximum
likelihood decoding and, potentially, to design the set of transmit symbols.
Comprehensive numerical results are presented to study the performance of the
channel estimation and the data decoding with 1-bit ADCs with respect to the
signal-to-noise ratio (SNR), the number of user equipments, and the pilot
length. The proposed analysis highlights a fundamental SNR trade-off, according
to which operating at the right noise level significantly enhances the system
performance.
