  A promising approach to deal with the high hardware cost and energy
consumption of massive MIMO transmitters is to use low-resolution
digital-to-analog converters (DACs) at each antenna element. This leads to a
transmission scheme where the transmitted signals are restricted to a finite
set of voltage levels. This paper is concerned with the analysis and
optimization of a low-cost quantized precoding strategy, referred to as
linear-quantized precoding, for a downlink massive MIMO system under Rayleigh
fading. In linear-quantized precoding, the signals are first processed by a
linear precoding matrix and subsequently quantized component-wise by the DAC.
In this paper, we analyze both the signal-to-interference-plus-noise ratio
(SINR) and the symbol error probability (SEP) performances of such
linear-quantized precoding schemes in an asymptotic framework where the number
of transmit antennas and the number of users grow large with a fixed ratio. Our
results provide a rigorous justification for the heuristic arguments based on
the Bussgang decomposition that are commonly used in prior works. Based on the
asymptotic analysis, we further derive the optimal precoder within a class of
linear-quantized precoders that includes several popular precoders as special
cases. Our numerical results demonstrate the excellent accuracy of the
asymptotic analysis for finite systems and the optimality of the derived
precoder.
