Three Efficient Beamforming Methods for Hybrid IRS-aided AF Relay Wireless Networks

In this paper, a hybrid IRS-aided amplify-and-forward (AF) relay wireless network is considered, where an optimization problem is formulated to maximize signal-to-noise ratio (SNR) by jointly optimizing the beamforming matrix at AF relay and the reflecting coefficient matrices at IRS subject to the constraints of transmit power budgets at the source/AF relay/hybrid IRS and that of unit-modulus for passive IRS phase shifts. To achieve high rate performance and extend the coverage range, a high-performance method based on semidefinite relaxation and fractional programming (HP-SDR-FP) algorithm is presented. Due to its extremely high complexity, a low-complexity method based on successive convex approximation and FP (LC-SCA-FP) algorithm is put forward. To further reduce the complexity, a lower-complexity method based on whitening filter, general power iterative and generalized Rayleigh-Ritz (WF-GPI-GRR) is proposed, where different from the above two methods, it is assumed that the amplifying coefficient of each active IRS element is equal, and the corresponding analytical solution of the amplifying coefficient can be obtained according to the transmit powers at AF relay and hybrid IRS. Simulation results show that the proposed three methods can greatly improve the rate performance compared to the existing networks, such as the passive IRS-aided AF relay and only AF relay network. In particular, a 50.0% rate gain over the existing networks is approximately achieved in the high power budget region of hybrid IRS. Moreover, it is verified that the proposed three efficient beamforming methods have an increasing order in rate performance: WF-GPI-GRR, LC-SCA-FP and HP-SDR-FP.