  Symbiotic radio (SR) communication is a promising technology to achieve
spectrum- and energy-efficient wireless communication, by enabling passive
backscatter devices (BDs) reuse not only the spectrum, but also the power of
active primary transmitters (PTs). In this paper, we aim to characterize the
energy-efficiency (EE) region of multiple-input single-output (MISO) SR
systems, which is defined as all the achievable EE pairs by the active PT and
passive BD. To this end, we first derive the maximum individual EE of the PT
and BD, respectively, and show that there exists a non-trivial trade-off
between these two EEs. To characterize such a trade-off, an optimization
problem is formulated to find the Pareto boundary of the EE region by
optimizing the transmit beamforming and power allocation. The formulated
problem is non-convex and difficult to be directly solved. An efficient
algorithm based on successive convex approximation (SCA) is proposed to find a
Karush-Kuhn-Tucker (KKT) solution. Simulation results are provided to show that
the proposed algorithm is able to effectively characterize the EE region of SR
communication systems.
