Two efficient beamforming methods for hybrid IRS-aided AF relay wireless networks

Owing to its ability to mitigate the double-fading effect by amplifying the reflected signal, the active intelligent reflecting surface(IRS) has garnered significant attention. In this paper, an amplify-and-forward(AF) relay network assisted by a hybrid IRS consisting of both passive and active units is developed. A signal-to-noise ratio(SNR) maximization problem is formulated, where the AF relay beamforming matrix and the hybrid IRS reflecting coefficient matrices for two-time slots need to be optimized. To address the SNR maximization problem, this paper proposes both a high-performance(HP) method and a low-complexity(LC) method. The HP method is based on the semidefinite relaxation and fractional programming(SDR-FP)algorithm, with rank-1 solutions obtained through Gaussian randomization. For the LC method, the amplification coefficient of each active IRS element is assumed to be equal. The SNR maximization problem is then addressed using the whitening filter,generalized power iteration, and generalized Rayleigh-Ritz(WF-GPI-GRR) approach. Simulation results show that compared with the benchmarks, such as the passive IRS-aided AF relay network, the proposed HP-SDR-FP and WF-GPI-GRR methods achieve significant rate improvements. In particular, the HP-SDR-FP and WF-GPI-GRR methods yield more than a 135.0%rate gain when the transmit power Ps of the source is 10 dBm. Furthermore, the proposed HP-SDR-FP method outperforms the WF-GPI-GRR method in terms of rate performance.