  Symbiotic radio (SR) is a promising technology of spectrum- and
energy-efficient wireless systems, for which the key idea is to use cognitive
backscattering communication to achieve mutualistic spectrum and energy sharing
with passive backscatter devices (BDs). In this paper, a reconfigurable
intelligent surface (RIS) based SR system is considered, where the RIS is used
not only to assist the primary active communication, but also for passive
communication to transmit its own information. For the considered system, we
investigate the EE trade-off between active and passive communications, by
characterizing the EE region. To gain some insights, we first derive the
maximum achievable individual EEs of the primary transmitter (PT) and RIS,
respectively, and then analyze the asymptotic performance by exploiting the
channel hardening effect. To characterize the non-trivial EE trade-off, we
formulate an optimization problem to find the Pareto boundary of the EE region
by jointly optimizing the transmit beamforming, power allocation and the
passive beamforming of RIS. The formulated problem is non-convex, and an
efficient algorithm is proposed by decomposing it into a series of subproblems
by using alternating optimization (AO) and successive convex approximation
(SCA) techniques. Finally, simulation results are presented to validate the
effectiveness of the proposed algorithm.
