Cooperative Constellation and Beamforming Design for Multi-RIS Empowered Symbiotic Radios

This paper considers a multi-reconfigurable intelligent surface (RIS) empowered symbiotic radio (SR) system, where multiple RISs, operating as Internet-of-Things (IoT) devices, are used to transmit their modulated information bits by backscattering the incident primary signal and to assist the primary system simultaneously. Most existing works consider the modulation design for the single RIS scenario while lacking indepth investigation into the multi-RIS scenario. To fill this gap, we are interested in cooperatively optimizing the signal constellation and the associated phase shifts of all IoT devices to enhance the overall symbol error rate performance of both the primary and IoT transmissions. Towards this end, we formulate a problem to maximize the minimum Euclidean distance of the received noise-free signal from a signal detection perspective, subject to the peak amplitude constraints of the signal constellation and the passive reflection constraints of phase shifts. Due to the non-convexity of the formulated problem, an iterative algorithm is proposed to solve it. Besides, the structure of the optimized signal constellations in the absence of the direct link is sketched to draw useful insights. Finally, simulation results are provided to validate the superiority of the proposed cooperative constellation design methodology over the classic constellation design.