Multiplexing Gain of Modulating Phases Through Reconfigurable Intelligent Surface

This paper investigates the information theoretical limit of a reconfigurable intelligent surface (RIS) aided communication scenario in which the RIS and the transmitter jointly send information to the receiver. The RIS is an emerging technology that uses a large number of passive reflective elements with adjustable phases to intelligently reflect the transmit signal to the intended receiver. While most previous studies of the RIS focus on its ability to beamform and to boost the received signal-to-noise ratio (SNR), this paper shows that if the information data stream is available both at the transmitter and the RIS and the phases at the RIS can be used to modulate data, then the multiplexing gain of the overall channel can potentially be significantly enhanced. Specifically, we show that in a multiple-input multiple-output (MIMO) channel with $M$ transmit antennas and $K$ receive antennas, a RIS with $N$ reflective elements can improve the multiplexing gain from min(M, K) to min(M + N/2 - 1/2, $N$, K). This result is obtained by establishing a connection between the RIS system and the MIMO channel with phase noises and using results for characterizing the information dimension under projection.