# Intelligent Reflective Surfaces for Wireless Networks:
## 3 IRS-Assisted Wireless Networks
### Optimization and Design of IRSs
#### 3.3.3 Single-User MISO/SIMO Scenarios  
The authors in [57] propose a suboptimal semidefinite relaxation algorithm to maximize the total received signal power by a single-user communicating with a multi-antenna  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference** & **System Model** & **Performance Metric** & **Main Results** \\ \hline
[55] & LOS, CNN, & \
\begin{tabular}{c} Tx power \\ and channel gain \\ \end{tabular} &
\begin{tabular}{c} IRS offers higher \\ EE than DF for \\ very high rates \\ \end{tabular} \\ \hline
[50] & \
\begin{tabular}{c} Multiple IRSs, \\ LOS \\ \end{tabular} & Rate &
\begin{tabular}{c} Near-optimal \\ rate \\ \end{tabular} \\ \hline
[51] & \
\begin{tabular}{c} Imperfect CSI, \\ NLOS, DRL \\ \end{tabular} & Rate &
\begin{tabular}{c} Achievable rates \\ close to the obtained \\ with perfect CSI \\ \end{tabular} \\ \hline
[52] & \
\begin{tabular}{c} mmWave, \\ NLOS, OFDM, ML \\ \end{tabular} & Rate &
\begin{tabular}{c} Near-optimal \\ rate with low \\ training overhead \\ \end{tabular} \\ \hline
[53] & \
\begin{tabular}{c} Imperfect CSI, \\ LOS, DL \\ \end{tabular} & Rate &
\begin{tabular}{c} Achievable rates \\ close to the obtained \\ with perfect CSI \\ \end{tabular} \\ \hline
[54] & \
\begin{tabular}{c} Discrete phase shifts \\ at the IRS, NLOS \\ \end{tabular} & Rate &
\begin{tabular}{c} Number of phase \\ shifts required \\ for a given rate \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 1: Single-user SISO approaches.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference** & **System Model** & **Performance Metric** & **Main Results** \\ \hline
[55] & \
\begin{tabular}{c} LOS, CNN, \\ On/Off binary IRS \\ \end{tabular} & SINR &
\begin{tabular}{c} Higher performance \\ than baselines: \\ On-IRS, Off-IRS \\ \end{tabular} \\ \hline
[56] & \
\begin{tabular}{c} multi-IRS, NLOS \\ On/Off binary IRS \\ \end{tabular} & MSE &
\begin{tabular}{c} Lower MSE with \\ single/multiple IRS \\ than baseline: \\ no-IRS \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}
Table 2: Multiuser SISO approaches.  
access point (AP) in LOS conditions. The simulation results exhibit performance gains over baselines (e.g., systems without IRS) in terms of the received signal-to-noise ratio (SNR).  
In [58], a DL-based approach for the design of the IRS phase-shift matrix in a single-user MISO system is proposed. Specifically, a customized deep NN is trained offline by using the unsupervised learning mechanism, which is able to make real-time predictions when deploying online. The simulation results show that the proposed approach offers slightly lower system performance than the semidefinite relaxation based approaches in [57] in terms of rate while it significantly reduces the computation complexity.  
In [59], a DL approach has been developed to tune the IRS phase-shift matrix in real-time by considering a MISO system with LOS, i.e., a direct link is available between both ends. Simulation results show that the DL approach leads to performance comparable to that of conventional approaches while significantly reducing the computational complexity.  
In [60], a DL approach which learns and makes use of the local propagation environment is deployed for the configuration of the IRS phase-shift matrix in a downlink single-user MISO system with LOS conditions and imperfect CSI. The proposed method uses the received pilot signals reflected through the IRS to train the network. The performance of the proposed approach is evaluated in terms of the NMSE between the phases obtained by the proposed algorithm with imperfect CSI and the optimal IRS phases based on perfect CSI.  
Table 3 summarizes the main results, system model assumptions, and evaluation performance metrics of the papers analysed in this subsection.