On the Capacity Region of Reconfigurable Intelligent Surface Assisted Symbiotic Radios

In this paper, we are interested in reconfigurable intelligent surface (RIS)-assisted symbiotic radio (SR) systems, where an RIS assists a primary transmission by passive beam-forming and simultaneously acts as a secondary transmitter to modulate its own information by periodically adjusting its reflecting coefficients. The above modulation scheme innately enables a new multiplicative multiple access channel (M-MAC), in which the primary and secondary signals are superposed in a multiplicative and additive manner. To pursue the fundamental performance limits of the M-MAC, we focus on the characterization of the capacity region of such systems. Due to the passive nature of RISs, the transmitted signal of the RIS should satisfy the peak power constraint. Under this constraint at the RIS as well as the average power constraint at the primary transmitter (PTx), we analyze the capacity-achieving distributions of the transmitted signals and the optimal reflecting coefficients of the RIS. Then, we derive the maximum achievable rates for both primary and secondary transmissions and characterize the rate region of the M-MAC. It is observed that the secondary transmission can achieve the maximum rate when the PTx transmits signals with the constant envelope. Furthermore, the rate region of the M - MAC is strictly convex and larger than that of the conventional TDMA scheme.