Full Duplex Relaying with Intelligent Reflecting Surface: Joint Beamforming and Phase Adjustment

In this paper, an optimization algorithm is proposed for the system, where a decode-and-forward (DaF) protocol based full duplex relay (FDR) and an intelligent reflecting surface (IRS) work together to deliver message signals from a source to a destination. The transmission is carried out in a single time frame due to the full duplex nature of the FDR and IRS. The joint optimization of the beamformers for the multiple antenna sets at the source along with the FDR antenna sets and the phase adjustment of the reflecting elements at the IRS is proposed. Though separate optimizations of the beamformers and the phase adjustment were available previously, the joint one is more challenging due to the increased number of signal paths and the impacts from these new paths. To accommodate conflicting requirements from different paths, the reflecting elements of the IRS are cleverly grouped into the corresponding number of sets, where the requirements are met separately through the optimizations of the phase values of the corresponding group. For the beamformer optimization, we parameterize the beamforming vectors, which results in two concave optimization problems for the source and for the FDR relay. These optimization sets are implemented in an alternating manner to reach a reasonable solution. Simulation results are provided to illustrate the impacts of the proposed algorithm in various implementation scenarios and parameter sets. These results identify the gains the proposed algorithm provides and the scenarios where these gains are expected.