Mutualistic Mechanism for RIS-Assisted Symbiotic Radios: How Many Reflecting Elements Are Required?

In RIS-assisted symbiotic radio (SR) systems, the RIS transmits messages by using the spectrum and energy of the primary transmission and simultaneously assists the primary transmission by passive beamforming. Due to the functionality of information transmission, the RIS could not always enhance the primary transmission. Instead, We observe that the performance of the primary transmission in terms of bit error rate (BER) will drop first and then improve with the increase in the number of reflecting elements of the RIS, i.e.,
$K$
. Motivated by this, in this paper, we are interested in a mutualistic condition on
$K$
for RIS-assisted SR, through which, the primary transmission could obtain the performance gain from the RIS. First, we design a transmission scheme for the RIS, which uses the different phase shifts to represent different transmission bits. Then, we optimize the phase shifts of the RIS, based on which, we derive an upper bound on BER for both primary and secondary transmissions. Compared with the BER performance in the absence of the RIS, we derive the mutualistic condition on the number of the reflecting elements
$K$
. Finally, simulation results are provided to verify the effectiveness of the theoretical analysis.