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Transmitting data using the phases on reconfigurable intelligent surfaces(RIS) is a promising solution for future energy-efficient communicationsystems. Recent work showed that a virtual phased massive multiusermultiple-input-multiple-out (MIMO) transmitter can be formed using only oneactive antenna and a large passive RIS. In this paper, we are interested inusing such a system to perform MIMO downlink precoding. In this context, we maynot be able to apply conventional MIMO precoding schemes, such as the simplezero-forcing (ZF) scheme, and we typically need to design the phase signals bysolving optimization problems with constant modulus constraints or withdiscrete phase constraints, which pose challenges with high computationalcomplexities. In this work, we propose an alternative approach based onSigma-Delta ($\Sigma\Delta$) modulation, which is classically famous for itsnoise-shaping ability. Specifically, first-order $\Sigma\Delta$ modulation isapplied in the spatial domain to handle phase quantization in generatingconstant envelope signals. Under some mild assumptions, the proposed phased$\Sigma\Delta$ modulator allows us to use the ZF scheme to synthesize the RISreflection phases with negligible complexity. The proposed approach isempirically shown to achieve comparable bit error rate performance to theunquantized ZF scheme.

Transmitting Data Through Reconfigurable Intelligent Surface: A Spatial Sigma-Delta Modulation Approach