Channel Capacity of RIS-assisted Symbiotic Radios with Imperfect Knowledge of Channels

In reconfigurable intelligent surface (RIS)-assisted symbiotic radio (SR) systems, the RIS transmits information by modulating its information bits over RF signals from a primary transmitter (PTx), and simultaneously, the RIS assists the primary transmission by passive beamforming. Considering the inevitable channel estimation errors arising in practice, in this paper, we are interested in quantifying the effects of imperfect knowledge of channels on the channel capacity for both primary and secondary transmissions in RIS-assisted SR. For the primary transmission, we first derive upper and lower bounds on the achievable rate with channel estimation errors. Based on the derived lower bound, we investigate the minimum number of reflecting elements of an RIS that can enable the performance enhancement of the primary transmission compared to the case without the RIS. For the secondary transmission, exact and asymptotic achievable rates are derived. Finally, extensive numerical results are presented to demonstrate the effects of the channel estimation errors together with the interrelationship between primary and secondary transmissions.