# Intelligent Reflective Surfaces for Wireless Networks:
## 3 IRS-Assisted Wireless Networks
### Optimization and Design of IRSs
#### 3.3.1 Single-User SISO Scenario  
In [6] a single-user SISO scheme with LOS conditions has been considered. The authors proved that the optimal IRS phase-shift setting is the setup that aligns the reflected rays to the direct path between the BS and the users. The paper also compares the IRS technology with conventional decode-and-forward (DF) relaying showing that the IRS needs hundreds of reconfigurable elements to reach a behaviour similar to that of the DF relaying. Additionally, the IRS achieves higher energy efficiency (EE) than DF relaying if very high rates are needed. By considering a simple LOS scenario where the IRS is deployed between a BS and the user to assist the communication, the optimized selection of the phase of each discrete element in the IRS leads to phase alignment of the direct path (BS to user) and scattered paths (BS to IRS to users).  
In [50], a point-to-point SISO system assisted with multiple IRSs is considered. The authors present multi-layer perceptron NN architectures that can be trained either with positioning values or the channel coefficients. Both centralized and individual training of the IRSs are proposed. The simulation results show that achievable rates close to the optimum scheme can be achieved.  
Some works consider single-user point-to-point OFDM systems. The authors in [51] approach the optimization of the IRS phase-shift matrix in a single-user SISO OFDM system with blockage of the direct paths between both ends, i.e., NLOS. Specifically, the authors develop a deep reinforcement learning (DRL)-based framework--which requires minimal training overhead--to solve a non-convex optimization problem by considering few active elements at the IRS and imperfect CSI. The results show that the proposed DRL-based framework is near optimum in terms of rate and converge to the solution with perfect CSI. A single-user SISO OFDM IRS-assisted system is considered in [52], where a ML solution to design the IRS phase-shift matrix is employed. The solution exploits DL tools to learn how to predict the proper IRS matrix configuration directly from the sampled channel knowledge. The simulation results show that the proposed solution can achieve near-optimal data rates with negligible training overhead, without any knowledge of the IRS geometry.  
The authors in [53] also consider a system with imperfect CSI. Specifically, a point-to-point SISO with LOS conditions between both ends is assumed. Two solutions for the design of the IRS phase-shift matrix are proposed. In the first approach, the authors employ compressive sensing strategy to construct the channels by considering a few active elements at the IRS. In the second approach, a DL-based solution where the IRS learns how to interact with the incoming signals given the channels coefficients at the active elements. The achievable rates assessed in the proposed solutions approach the upper bound with perfect CSI, with minor training overhead.  
The authors in [54] consider an uplink single-user cellular network and derive an approximation of the achievable data rate by considering a practical IRS implemented via phase shifters with a limited resolution, i.e., discrete phase shifts. A derivation of the required number of phase shifts under a data rate degradation constraint is performed.  
Table 1 summarizes the references related to single-user SISO systems, their system model assumptions, the performance metrics considered for the optimization, and the main results obtained.