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.

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