Full-Duplex Backscatter Communications in Symbiotic Radio Systems

In this paper, we are interested in a symbiotic radio (SR) system, in which a passive full-duplex backscatter device (BD) is parasitic in an active primary transmission. The primary transmitter (PT) with multiple antennas is designed to broadcast common messages to the primary receiver (PR) and the BD, as well as to support passive information transmission from the BD to the PR. To do so, the full-duplex BD absorbs a fraction of the incident signal from the PT to decode the common messages and simultaneously transmits its own information to the PR by backscattering the remaining part of the incident signal. We derive the achievable rates of the BD transmission with Gaussian and quadrature amplitude modulation codewords. We also formulate a transmit power minimization problem by jointly designing the beamforming vector at the PT and the power splitting factor at the BD. This problem is first solved by the semi-definite relaxation technique together with a one-dimensional linear exhaustive search over the power splitting factor. Then, a suboptimal but low-complexity solution with closed-form expressions is proposed. The simulation results have shown that the proposed suboptimal solution achieves almost the same performance as that obtained by the exhaustive search. In addition, our proposed SR system with the full-duplex BD outperforms the half-duplex system with the time-division-multiplexing mode in general.