  The use of low precision (e.g., 1-3 bits) analog-to-digital convenors (ADCs)
in very large multiple-input multiple-output (MIMO) systems is a technique to
reduce cost and power consumption. In this context, nevertheless, it has been
shown that the training duration is required to be {\em very large} just to
obtain an acceptable channel state information (CSI) at the receiver. A
possible solution to the quantized MIMO systems is joint channel-and-data (JCD)
estimation. This paper first develops an analytical framework for studying the
quantized MIMO system using JCD estimation. In particular, we use the
Bayes-optimal inference for the JCD estimation and realize this estimator
utilizing a recent technique based on approximate message passing. Large-system
analysis based on the replica method is then adopted to derive the asymptotic
performances of the JCD estimator. Results from simulations confirm our
theoretical findings and reveal that the JCD estimator can provide a
significant gain over conventional pilot-only schemes in the quantized MIMO
system.
