  This paper considers training-based transmissions in massive multi-input
multi-output (MIMO) systems with one-bit analog-to-digital converters (ADCs).
We assume that each coherent transmission block consists of a pilot training
stage and a data transmission stage. The base station (BS) first employs the
linear minimum mean-square-error (LMMSE) method to estimate the channel and
then uses the maximum-ratio combining (MRC) receiver to detect the data
symbols. We first obtain an approximate closed-form expression for the uplink
achievable rate in the low SNR region. Then based on the result, we investigate
the optimal training length that maximizes the sum spectral efficiency for two
cases: i) The training power and the data transmission power are both
optimized; ii) The training power and the data transmission power are equal.
Numerical results show that, in contrast to conventional massive MIMO systems,
the optimal training length in one-bit massive MIMO systems is greater than the
number of users and depends on various parameters such as the coherence
interval and the average transmit power. Also, unlike conventional systems, it
is observed that in terms of sum spectral efficiency, there is relatively
little benefit to separately optimizing the training and data power.
