  We present a mathematical analysis of linear precoders for downlink massive
MIMO multiuser systems that employ one-bit digital-to-analog converters at the
basestation in order to reduce complexity and mitigate power usage. The
analysis is based on the Bussgang theorem, and applies generally to any linear
precoding scheme. We examine in detail the special case of the quantized
zero-forcing (ZF) precoder, and derive a simple asymptotic expression for the
resulting symbol error rate at each terminal. Our analysis illustrates that the
performance of the quantized ZF precoder depends primarily on the ratio of the
number of antennas to the number of users, and our simulations show that it can
outperform the much more complicated maximum likelihood encoder for
low-to-moderate signal to noise ratios, where massive MIMO systems are presumed
to operate. We also use the Bussgang theorem to derive a new linear precoder
optimized for the case of one-bit quantization, and illustrate its improved
performance.
