# Intelligent Reflective Surfaces for Wireless Networks:
## 3 IRS-Assisted Wireless Networks
### Optimization and Design of IRSs
#### 3.3.4 Multiuser MISO/SIMO Scenarios  
In [24] an IRS-assisted multiuser MISO system with LOS between a common AP and the users is considered. In particular, a practical phase shift model that captures the phase-dependent amplitude variation in the element-wise reflection design at the IRS is proposed. An optimization problem to minimize the total transmit power at the AP by jointly designing the AP transmit precoder and the IRS phase-shift matrix subject to the users' individual SINR constraints is stated. Then, an AO algorithm is proposed to find suboptimal solutions. The simulation results show the asymptotic performance loss of the optimized IRS-assisted system when it is implemented with practical phase shifters and the obtained gains by optimizing with the practical model under consideration. The work in [61] also considers the practical limitations of the IRSs. In particular, the authors have studied the asymptotic achievable rate in an IRS-assisted downlink MISO system. The system model considers a common BS transmitting to \(K\) users by employing time-division multiple access (TDMA) to serve one user at each time slot. Multiple IRSs are deployed in a scheme where some users are IRS-aided and the others are directly served by the BS. The optimality of the asymptotic performance has been analyzed by considering the practical limitations of the IRSs, e.g., the practical reflection coefficients. In this context, an IRS phase-shift matrix design is proposed, which is able to asymptotically achieve the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Reference** & **System Model** & **Performance Metric** & **Main Results** \\ \hline
[57] & Downlink, LOS & Received signal power & Maximization of the received SNR \\ \hline
[58] & LOS, DL & Rate & Low computation complexity \\ \hline
[59] & LOS, DL & MSE & Low computation complexity \\ \hline
[60] & Downlink, LOS, DL, imperfect CSI & NMSE between phases with perfect CSI and phases with imperfect CSI & Near-optimal IRS config. with imperfect CSI \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Single-user MISO/SIMO scenarios. optimal performance. The results are presented in terms of the symbol-error-rate (SER) and the ergodic rate and compared with a baseline strategy without IRS and the AO algorithm proposed in [24]. The authors in [62] consider a multiuser IRS-assisted SIMO system, where the uplink transmissions are reflected by the IRS. An approximated zero-forcing (ZF) equalizer is implemented to cancel the inter-user interference in a decentralized way by optimizing the IRS phase shifters (see [62], Algorithms 1 and 2). The results are presented in terms of the signal-to-interference ratio (SIR) and show better performance than a single daisy chain realization of the algorithm in [63] to compute the equalization vector. Some works related to non-orthogonal multiple access (NOMA) IRS-aided systems have been considered. In [64], an IRS-aided multiuser MISO NOMA downlink transmission framework is proposed. The authors assume NLOS between the users and the BS. An optimization problem to maximize the sum rate is formulated. For adjusting the IRS phase-shift matrix, a deep deterministic policy gradient (DDPG) algorithm, which dynamically learns the resource allocation policy is defined. The proposed framework achieves a sum rate larger than the one assessed with traditional orthogonal multiple access (OMA) networks. In [65], an IRS-assisted NOMA MISO downlink system is considered. The authors consider the joint optimization of the beamforming vectors at the BS and the phase-shift matrix at the IRS to minimize the total transmission power consumption at the BS. The problem is solved via an AO minimization approach and the results exhibit that this solution leads to transmission power reductions by comparing with a baseline strategy, which imposes random phase shifts at the IRS. In [66], the authors consider the uplink of a cluster-based multiuser code-domain NOMA IRS-assisted MISO system.