# Machine-Learning-Based Optimization for Multiple-IRS-Aided Communication System
## 1 Introduction  
With the increasing demands for higher data rates, higher spectrum and energy efficiency, and ubiquitous connectivity for the beyond-fifth-generation and sixth-generation wireless communication networks [1], many improved wireless technologies have been proposed (e.g., unmanned aerial vehicle communication, satellite communication, Terahertz communication, etc.). Among them, the intelligent reflecting surface (IRS) is regarded as a promising and efficient solution, which uses software-controlled signal reflection to recognize the wireless propagation environment [2]. Specifically, an IRS is made up of many reflectors with reflecting passive elements, each of which can independently change the corresponding amplitude and phase angles of the incident signals [3]. Via the proper design, the reflected signals can be combined coherently at the intended UE, thereby enhancing the desired signal, and/or destructively at non-intended UEs, thereby eliminating co-channel interference. Thus, the quality of the communication link between the transmitter and the intended receiver can be enhanced. Furthermore, because of the IRSs' fundamental characteristics and competitive advantages in terms of optimizing energy and spectrum efficiency, as well as deployment costs, the IRS is expected to outperformother related technologies, such as relays, backscatters, and massive MIMO-based active surface systems [4]. The IRS can provide another path link between the source and end-users, avoiding a communication blockage, which generally requires the careful design of IRS passive beamforming. In other words, the IRS-aided communication system benefits from the passive beamforming gain to maximize and boost the received desired signal power at the UE [5]. Moreover, the BS is generally equipped with multiple antennas for the adequate and proper design of the active beamforming. Hence, the joint design of the beamforming for the BS and IRS can further enhance the network performance. Many recent studies have adopted conventional optimization methods to conduct the jointly optimized beamforming design for IRS-aided wireless networks. More specifically, in [5], the semidefinite relaxation (SDR) technique and alternating procedure were applied to solve the joint optimization problem of the transmitting beamforming and reflecting phase shifts of a single IRS. The joint problem was then addressed in an IRS-assisted NOMA system [6], where the authors presented a difference-of-convex-based approach that overcame the drawbacks of SDR and handled the resulting optimization problem efficiently. In the same context, the authors in [7] jointly optimized RIS phase shift elements and the corresponding transmit power allocation, where the designed framework was developed based on fractional programming, gradient descent, and alternating maximization methods. In [8], the BS beamforming matrix and IRS phases were optimized through fixed-point iteration and manifold approaches to maximize the MISO system's received signal. RIS-aided broadcasting in a physical layer was investigated in [9], where the BS transmit power was minimized to satisfy the needs of UE for quality of service (QoS). In [10], the authors investigated the optimization problem of maximizing the weighted sum rate in the MISO system enhanced by IRS, where the Lagrangian dual transform and an alternating approach were adopted. In [11], the active precoding of the transmit source and the reflection phases of the IRS were jointly tuned in the ideal CSI scenario using an iterative process, aiming to maximize the total rate. Besides all the above systems, which focus on a single IRS-assisted scenario, some works have considered multiple-IRS-assisted systems. A closed-form solution and an SDR-based approach were proposed for the joint beamforming design in [12], while the work in [13] utilized the Lagrangian and Riemannian manifold techniques to solve the BS precoding transmit matrix and phase shifts of deployed IRSs.