  Transmitting data using the phases on reconfigurable intelligent surfaces
(RIS) is a promising solution for future energy-efficient communication
systems. Recent work showed that a virtual phased massive multiuser
multiple-input-multiple-out (MIMO) transmitter can be formed using only one
active antenna and a large passive RIS. In this paper, we are interested in
using such a system to perform MIMO downlink precoding. In this context, we may
not be able to apply conventional MIMO precoding schemes, such as the simple
zero-forcing (ZF) scheme, and we typically need to design the phase signals by
solving optimization problems with constant modulus constraints or with
discrete phase constraints, which pose challenges with high computational
complexities. In this work, we propose an alternative approach based on
Sigma-Delta ($\Sigma\Delta$) modulation, which is classically famous for its
noise-shaping ability. Specifically, first-order $\Sigma\Delta$ modulation is
applied in the spatial domain to handle phase quantization in generating
constant envelope signals. Under some mild assumptions, the proposed phased
$\Sigma\Delta$ modulator allows us to use the ZF scheme to synthesize the RIS
reflection phases with negligible complexity. The proposed approach is
empirically shown to achieve comparable bit error rate performance to the
unquantized ZF scheme.
