# Intelligent Reflective Surfaces for Wireless Networks:
## 3 IRS-Assisted Wireless Networks
### Optimization and Design of IRSs
#### 3.3.4 Multiuser MISO/SIMO Scenarios
It is considered a setup where each IRS is covering a cluster of users, which have NLOS conditions with the BS. The optimization of the IRS phase-shift matrices such that a large number of users are correctly detected is approached. To overcome the coupling between the IRS phase shifts and other variables, such as the detection order and the filter, a sum-rate optimization is used to obtain a decoupled estimate of those variables. Then, the final IRS adjustment is performed via an semidefinite programming (SDP) relaxation of the optimization problem. Simulation results show the performance gains obtained (measured in terms of the number of correctly detected users) with respect to a random phase shift implementation when the IRS phases are properly optimized. In [67], the authors consider a multiuser MISO IRS-assisted NOMA downlink system with NLOS conditions. The IRS-assisted NOMA system is designed to ensure that additional cell-edge users can be served by the BS. Both analytical and simulation results are provided to show the performance of the proposed scheme in terms of the outage probability. Hardware impairments are also analyzed. In [68], the authors address a multiuser MISO IRS-assisted mmWave communication system. The motivation is to enhance the network reliability and connectivity in the presence of random blockages in mmWave, which usually implies NLOS. A stochastic optimization problem based on the minimization of the sum outage probability is formulated, and a stochastic-learning-based robust beamforming design is proposed via a gradient descent algorithm. The numerical results validate the performance benefits of the proposed algorithm in terms of outage probability and effective data rate over baseline strategies (non-IRS, random IRS). In [69], a DRL-based algorithm for the configuration of the IRS and the BS beamformer is developed in a downlink IRS-assisted multiuser MISO system. The proposed DRL-based algorithm obtains the design of the BS precoder and the IRS phase-shift matrix as the output of the DRL NN from the instantaneous channel estate information. Simulation results show that the algorithm is not only able to learn from the environment and improve its behaviour but also obtains comparable but lower performance than [70]. The work in [70] proposes two EE maximization algorithms for the BS transmit power allocation and the IRS phase-shift matrix in a downlink multiuser MISO system with NLOS. The resultsare presented in terms of EE and show that the proposed solution offers higher EE than the Amplify-and-Forward (AF) relay-assisted setup. The authors in [71] present an infrastructure to perform ML tasks at a mobile edge computing (MEC) server with the assistance of an IRS in a multiuser MISO system. Therein, they aim at maximizing the learning performance. Specifically, a minimization of the maximum learning error (MLE) of all participating users is performed by jointly optimizing the transmit power of mobile users, the beamforming vectors of the BS, and the phase-shift matrix of the IRS. An AO-based framework is proposed to optimize the three terms iteratively, where a successive convex approximation (SCA)-based algorithm is proposed to solve the power allocation problem, closed-form expressions are derived to solve the beamforming design problem, and an alternating direction method of multipliers (ADMM)-based algorithm is designed to efficiently solve the phase-shift matrix design problem. Simulation results show significant gains when deploying the IRS over baseline strategies. Several works related to the IRS phase-shift matrix design assume imperfect CSI. In [72; 73] the authors propose a ML approach to optimize both the beamformers at the BS and the IRS phase-shift matrix in a multiuser MISO system. Such an approach employs a deep NN to parametrize the mapping from the received pilots to an optimized system configuration, then a graph neural network (GNN) architecture is considered to capture the interactions among the different users in the cellular network.