Ergodic Capacity Analysis for a STAR-RIS-Segmented Symbiotic Backscatter NOMA System

Abstract

This paper proposes a simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) segmented symbiotic backscatter non-orthogonal multiple access (NOMA) system. Specifically, the STAR-RIS is divided into an enchancing primary signal (EP) zone and a backscatter device (BD) zone. To characterize the overall transmission effectiveness, the metric of sum ergodic capacity (EC) of the considered symbiotic system is established and the corresponding suboptimal approximation solutions are derived in closed-form for three typical NOMA channel conditions. Our results show that the sum EC obeys the scaling law of $\log \left(P_{s}\right)$ where $P_{s}$ is the total transmit power, and is dominated by the weaker one of the transmission and reflection channels. Moreover, our simulation results show that both the instantaneous sum rate and the sum EC derived by the proposed suboptimal solution are very close to the optimal one obtained through exhaustive search. More importantly, the transmission effectiveness of the proposed system is superior to the STAR-RIS-assisted NOMA system and the STAR-RIS-segmented symbiotic backscatter orthogonal multiple access (OMA) system. Additionally, it is shown that as the quantification order of the imperfect channel state information (ipCSI) increases, the sum EC performance gradually improves.