On the Capacity Region of Reconfigurable Intelligent Surface Assisted Symbiotic Radios

In this paper, we consider a reconfigurable intelligent surface (RIS)-assisted symbiotic radio (SR) system, where an RIS assists a primary transmission by passive beamforming and simultaneously acts as an information transmitter by periodically adjusting its reflection coefficients. Such RIS functions innately enable a new type of communication channel, called multiplicative multiple access channel (M-MAC), where the primary and secondary signals are superposed in a multiplicative manner. To pursue the fundamental performance limits, in this paper, we focus on characterizing the capacity region for the RIS-assisted SR system. Due to the reflection nature of RISs, the signal transmitted from the RIS elements should satisfy a passive reflection constraint. In particular, we consider two types of passive reflection constraints, one for the case that the amplitudes of the reflection coefficients are fixed but the phases are adjustable, while the other for the case that both the amplitudes and the phases can be adjusted. Under the passive reflection constraints at the RIS as well as the average power constraint at the primary transmitter (PTx), we characterize the capacity region of RIS-assisted SR when the direct link from the PTx to the receiver is blocked. It is observed that: 1) the number of sum-rate-optimal points on the boundary of the capacity region is infinite; 2) for the rate pairs with the maximum sum rate, the optimal amplitude distribution of the primary signal is a continuous Rayleigh distribution, while for the remaining rate pairs on the capacity region boundary, the optimal amplitude distribution of the primary signal is discrete; 3) when both the amplitudes and the phases of the reflection coefficients are adjusted for the RIS, the capacity region is enlarged as compared to the phase-adjusted-only case.