In order to investigate the effect of cooperative Intelligent Reflecting Surface (IRS) in improving spectral efficiency, this paper explores the joint design of active and passive beamforming based on a double IRS-assisted model. First, considering the maximum power constraint of the active vector and the unit modulus constraint of the cooperative passive vector, we establish the non-linear and non-convex optimization problem of multi-user maximization weighted sum rate (WSR). Then, we propose an alternating optimization (AO) algorithm to design the active vector and the cooperative passive vector based on fractional programming (FP) and successive convex approximations (SCA). In addition, we conduct a study on the optimization of the passive reflection vector under discrete phase shift. The simulation results show that the proposed beamforming scheme of double IRS-assisted model performs better than the conventional single IRS-assisted model.

To achieve fast and accurate channel estimation of reconfigurable intelligent surface (RIS)-assisted multiple-input single-output (MISO) systems, we propose an accelerated bilinear alternating least squares algorithm (ABALS) based on parallel factor decomposition. Firstly, we build a tensor model of the received signal, and expand it to obtain the unfolded forms of the model. Secondly, we derive the expression of the estimation problem of two channels based on the unfolded forms to transform the problem into a cost function problem. Furthermore, we solve the cost function problem by introducing a simpler iterative optimization constraint and linear interpolation. Finally, we provide a strategy on the receiver design based on the feasibility conditions discussed in this paper, which can guarantee the uniqueness of the channel estimation problem. Simulation results show that the proposed algorithm can obtain a faster estimation speed and less iteration steps than the alternating least squares (ALS) algorithm, and the accuracy of the two algorithms is very close.