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 beamforming and simultaneously acts as an information transmitter by periodically adjusting its reflecting coefficients. The above modulation scheme innately enables a new multiplicative multiple access channel (M-MAC), where 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 characterize the capacity region of the M-MAC. Then, theoretical analysis is performed to reveal insights into the RIS-assisted SR. It is observed that: 1) the capacity region of the M-MAC is strictly convex and larger than that of the conventional TDMA scheme; 2) the secondary transmission can achieve the maximum rate when the PTx transmits the constant envelope signals; 3) and the sum rate can achieve the maximum when the PTx transmits Gaussian signals and the RIS transmits the constant envelope signals. Finally, extensive numerical results are provided to evaluate the performance of the RIS-assisted SR and verify the accuracy of our theoretical analysis.