Analysis and Optimization of A Double-IRS Cooperatively Assisted System with A Quasi-Static Phase Shift Design

The analysis and optimization of single intelligent reflecting surface (IRS)-assisted systems have been extensively studied, whereas little is known regarding multiple-IRS-assisted systems. This paper investigates the a double-IRS cooperatively assisted downlink system (D-IRS-C), where multi-antenna base station (BS) serves single-antenna user with help two multi-element IRSs, connected by an inter-IRS channel. channel between any nodes modeled Rician fading. BS adopts instantaneous CSI-adaptive maximum-ratio transmission (MRT) beamformer, IRSs adopt cooperative quasi-static phase shift design. goal to maximize average achievable rate, which can be reflected power equivalent at low estimation adjustment costs computational complexity. First, we obtain tractable expressions in general (Rician factor), pure line sight (LoS), non-line (NLoS) regimes, respectively. Then, jointly optimize shifts these regimes. problems are challenging non-convex problems. We globally optimal closed-form solutions for some cases propose computationally efficient iterative algorithms stationary points other cases. Next, compare complexity optimizing D-IRS-C those counterpart non-cooperatively (D-IRS-NC) single-IRS-assisted (S-IRS) large number elements three Finally, numerically demonstrate notable gains proposed over existing different parameters. To our knowledge, this first work that optimizes design characterizes its advantages D-IRS-NC S-IRS.