Reconfigurable Intelligent Surface Design for Symbiotic Radio System Through BER Minimization

This paper considers a reconfigurable intelligent surface (RIS) assisted single-input multiple-output (SIMO) sym-biotic radio (SR) system in which an RIS serves as a secondary transmitter (STx) to communicate with a cooperative receiver (C-Rx). The received signals from both primary transmitter (PTx) and the RIS are jointly decoded at the C-Rx using maximum likelihood (ML) detection. In this paper, we are interested in the RIS design to minimize the bit error rate (BER) of the SR system. Considering the coupling effect between the primary and secondary transmissions, we formulate the primary BER minimization problem with the passive energy constraint of each reflecting element at RIS, which can also enhance the secondary BER performance. To solve the formulated problem, a two-step algorithm is proposed based on the semidefinite programming (SDP) and one-dimensional search approaches. Simulation results show that the proposed algorithm outperforms the random beamforming scheme and that the BER performance of both the primary and secondary transmissions are improved when the number of reflective elements in the RIS is sufficiently large. Moreover, even under the random scheme, the BER performance of the secondary transmission is enhanced with growing number of elements at RIS.