  Using a very low-resolution analog-to-digital convertor (ADC) unit at each
antenna can remarkably reduce the hardware cost and power consumption of a
massive multiple-input multiple-output (MIMO) system. However, such a pure
low-resolution ADC architecture also complicates parameter estimation problems
such as time/frequency synchronization and channel estimation. A mixed-ADC
architecture, where most of the antennas are equipped with low-precision ADCs
while a few antennas have full-precision ADCs, can solve these issues and
actualize the potential of the pure low-resolution ADC architecture. In this
paper, we present a unified framework to develop a family of detectors over the
massive MIMO uplink system with the mixed-ADC receiver architecture by
exploiting probabilistic Bayesian inference. As a basic setup, an optimal
detector is developed to provide a minimum mean-squared-error (MMSE) estimate
on data symbols. Considering the highly nonlinear steps involved in the
quantization process, we also investigate the potential for complexity
reduction on the optimal detector by postulating the common
\emph{pseudo-quantization noise} (PQN) model. In particular, we provide
asymptotic performance expressions including the MSE and bit error rate for the
optimal and suboptimal MIMO detectors. The asymptotic performance expressions
can be evaluated quickly and efficiently; thus, they are useful in system
design optimization. We show that in the low signal-to-noise ratio (SNR)
regime, the distortion caused by the PQN model can be ignored, whereas in the
high-SNR regime, such distortion may cause 1-bit detection performance loss.
The performance gap resulting from the PQN model can be narrowed by a small
fraction of high-precision ADCs in the mixed-ADC architecture.
