Energy-efficiency optimization and comparison for IRS-assisted bidirectional relay and direct transmissions

Intelligent reflecting surface (IRS) has emerged as a promising technique for achieving high-transmission rate and low-power consumption transmission to meet the requirements of future beyond 5G and 6G communication. In this paper, we optimize and compare the energy-efficiency (EE) of IRS-assisted bidirectional relay transmission (BRT) and bidirectional direct transmission (BDT). In specific, we firstly consider and give the IRS-assisted BRT and BDT models. Then, we give the analyses of signal transmission models and EE for both IRS-assisted BRT and BDT. In addition, to optimize the EE, we give the joint optimization problems for both IRS-assisted BRT and BDT, which incorporate phase shift (PS) and transmit power (TP) optimizations. What's more, to solve the joint optimization problems and obtain the optimal PS, we design complex circle gradient descent algorithm and apply successive convex approximation for both IRS-assisted BRT and BDT, respectively. After that, we introduce Lagrange factors and Karush-Kuhn-Tucker conditions to obtain the close-form expressions of each node's optimal TP for both IRS-assisted BRT and BDT, respectively. Furthermore, with the optimal PS and TP, we provide the analysis of EE comparison between the IRS-assisted BRT and BDT. Simulation results illustrate that when total TP exceeds approximately -5 dBm, the IRS-assisted BRT will consistently outperform IRS-assisted BDT. Meanwhile, when compared with individual optimization, our IRS-assisted BRT and BDT with joint optimization achieve 61.36% and 65.51% improvements in EE, respectively.