In reconfigurable intelligent surface (RIS)-assisted symbiotic radio (SR) systems, an RIS transmits a secondary signal by modulating its information bits over the radio frequency (RF) signals emitted 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 channel knowledge 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 considering channel estimation errors. Based on the derived lower bound, we investigate an approximate condition on the number of reflecting elements of an RIS that assures the performance enhancement of the primary transmission as compared to the case without the RIS. For the secondary transmission, exact and asymptotic achievable rates are derived, which are not only related to the channel estimation error of the reflecting link but also are related to that of the direct link. Furthermore, we analyze the effects of system parameters, including the number of pilot symbols and the symbol period ratio between the primary and secondary signals, on the achievable rates for both primary and secondary transmissions. Finally, extensive numerical results are presented to verify the effectiveness of the theoretical analysis and show the impact of the channel estimation errors.

中文翻译：

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信道知识不完善的 RIS 辅助共生无线电的信道容量


在可重构智能表面 (RIS) 辅助共生无线电 (SR) 系统中，RIS 通过在主发射器 (PTx) 发射的射频 (RF) 信号上调制其信息位来传输辅助信号，同时 RIS 辅助通过无源波束形成进行主传输。考虑到实践中不可避免的信道估计误差，在本文中，我们有兴趣量化不完善的信道知识对 RIS 辅助 SR 中主传输和辅助传输的信道容量的影响。对于主传输，我们首先考虑信道估计误差得出可实现速率的上限和下限。基于导出的下限，我们研究了 RIS 反射元件数量的近似条件，以确保与没有 RIS 的情况相比，主传输的性能增强。对于二次传输，推导了精确且渐近的可达到速率，该速率不仅与反射链路的信道估计误差有关，而且与直接链路的信道估计误差有关。此外，我们分析了系统参数（包括导频符号的数量以及主信号和辅助信号之间的符号周期比）对主传输和辅助传输可实现的速率的影响。最后，提供了大量的数值结果来验证理论分析的有效性并显示信道估计误差的影响。