Performance of Cooperative Communication System With Multiple Reconfigurable Intelligent Surfaces Over Nakagami-<i>m</i> Fading Channels

In this paper, the advantages of multiple reconfigurable intelligent surfaces (RISs) assisted wireless systems and direct link between two terminals are exploited by considering a cooperative communication system where reflecting links created by multiple RISs and the direct link are combined at the receiver. We mathematically analyze the performance of the cooperative multiple RISs - direct link (RIS-D) system over Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> fading channels by obtaining the symbol error probability (SEP) expression. In addition, the SEP of the single-input single-output (SISO) system without RISs (i.e., there is only direct link between two terminals) is also obtained for convenience in comparison the performance of the cooperative RIS-D and SISO systems. We demonstrate the correctness of the derived expressions via Monte-Carlo simulations. Numerical results show that the SEP of the cooperative RIS-D system significantly lower than that of the SISO system for a certain transmission power of the transmitter. Also, for a certain SEP target, the cooperative RIS-D system can greatly save energy consumption in comparison with the SISO system. Specifically, increasing the number of RISs or the number of reflecting elements (REs) in the RISs can remarkably reduce the SEP of the cooperative RIS-D system. On the other hand, the impacts of the system parameters such as the number of RISs, the number of REs, and the Nakagami- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> fading channels are fully investigated to clearly indicate their influences on the SEP of the cooperative RIS-D system.