# Intelligent Reflective Surfaces for Wireless Networks:
## 3 IRS-Assisted Wireless Networks
### Optimization and Design of IRSs
#### 3.3.6 Multiuser MIMO Scenarios  
In [86] the authors address the IRS phase-shift matrix design by considering a low resolution intelligent surface assisting a multiuser system. The IRS is used as a transmitter, which modulates the incoming symbols by adjusting the phases of the reflective elements. The authors consider both the MISO and the MIMO setup, and aim to design the symbol-level IRS modulator to minimize the SER in the SIMO configuration by relaxing the low-resolution phase-shift constraint and solving the problem via a Riemannian conjugate gradient (RCG) algorithm. For the MIMO setup, the symbol-level IRS modulator is iteratively designed by decomposing the original large-scale optimization problem into several sub-problems. Simulation results are presented in terms of the SER by varying the quantization level resolution available to deploy the IRS.  
The authors in [87] study the tradeoff between EE and SE in the uplink of a multiuser MIMO system aided by an IRS equipped with discrete phase shifters. The transmission strategy design is based on the partial CSI of the cascaded channels by assuming NLOS between both ends. The precoding design at the users and the IRS phase-shift matrix configuration are approached to maximize a metric called resource efficiency (RE)--which is flexible to balance the EE and the SE [88]--for both continuous and discrete-phase shifts at the IRS. An optimization framework by leveraging the AO is proposed to face the optimization problem by developing an iterative MMSE method combined with a projected gradient (PG). The simulation results show the efficiency of the developed optimization framework for RE maximization.  
The work in [89] explores optimization-based and data-driven solutions in a multiuser MISO IRS-aided MEC system in a LOS scenario with a multitask AP which is able to perform the joint optimization of the IRS phase-shift matrix and the AP's receive beamforming vectors. A three-step block coordinate descending (BCD) algorithm is first proposed to solve the non-convex maximization problem. In order to reduce the computational complexity, two DL architectures are constructed. The CSI is the input in the first learning architecture, while the second one exploits the users' locations. The two data-driven approaches are trained using data samples generated by the BCD algorithm via supervised learning. The simulation results show a close match between the performance of the optimization-based BCD algorithm and the low-complexity learning-based architectures in terms of the total completed task-input bits at the users in a given time slot.  
Table 6 summarizes the main system model assumptions, the metrics to evaluate the performance, and the main results of the reviewed single-user IRS-assisted MIMO systems.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference** & **System Model** & **Performance Metric** & **Main Results** \\ \hline
[84] & LOS & Rate & Channel rank \\  & & & increases \\ \hline
[85] & LOS & Capacity & Channel rank \\  & & & increases \\ \hline \hline \end{tabular}
\end{table}
Table 5: Single-user MIMO approaches.