# A Survey on Optimal Channel Estimation Methods for RIS-Aided Communication Systems
## 2 System Models for RIS-Assisted Systems
### MISO Systems  
The authors in [71; 72] use S-CSI design passive beamformers for MISO systems and a purely S-CSI-based approach for the design of RIS-assisted multi-user downlink systems is proposed in [4]. Furthermore, in [73], the authors use a tensor algorithm and capitalize on the parallel factor (PARAFAC) decomposition to create an efficient iterative algorithm based on the alternating least squares (ALS) concept to answer the channel estimation issue in the downlink of a MISO network. For this reason, an approximate expression is  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**System Setup** & **Antenna Setup** & & **Main Results** \\ \hline \multirow{8}{*}{Multi-user, narrowband} & \multirow{8}{*}{MISO} & \(\bullet\) & User to user straightforward cascaded channel estimation [48; 49; 50]; \\  & & \(\bullet\) & Exploitation common to RIS-BS channel [51] and additional channel sparsity [52; 53]; \\  & & \(\bullet\) & Dual-link (BS-RIS) reflection [54] and anchor nodes [55] to resolve cascaded common offline RIS-BS channel and online RIS-UE channel for estimation; \\  & & \(\bullet\) & Linear minimum mean-squared-error (LMMSE) criterion in the downlink for estimation [56]; \\  & & \(\bullet\) & Matrix factorization/decomposition [44; 57] and additional channel sparsity for estimation [58; 59]; \\  & & \(\bullet\) & Usage of convolutional neural network for estimation based on deep learning techniques [60; 61]; \\  & & \(\bullet\) & Sparse Bayesian learning for separate channel estimation [62]. \\ \hline \multirow{8}{*}{Single-user, broadband} & \multirow{8}{*}{MISO} & \(\bullet\) & Single convolutional neural network for reducing training complexity [63]. \\ \cline{2-3}  & & \(\bullet\) & Deep denoising neural network in mmWave channels for separate channel estimation [64]. \\ \hline \multirow{8}{*}{MISO} & \multirow{8}{*}{MISO} & \(\bullet\) & Usage of orthogonal matching pursuit (OMP) algorithm and exploiting common channel sparsity over different subcarriers [65]; \\  & & \(\bullet\) & Canonical polyadic decomposition tensors for separate channel estimation [66]. \\ \cline{1-1} \cline{2-3}  & & \(\bullet\) & Deep learning techniques which use federated learning [67]; \\ \cline{1-1}  & & \(\bullet\) & Compressed sensing and exploiting dual sparsity of THz MIMO channels [68]; \\ \cline{1-1}  & & \(\bullet\) & Phase shift design schemes in uplink with linear zero forcing (ZF) detection in receiver side [69; 70]; \\ \cline{1-1}  & & \(\bullet\) & Efficient transmission for energy consumption in IoV networks [10] and in passive meta surface-coated devices [11]. \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._established to employ the sum rate and formulate an active-passive joint beamforming design problem. Because of the non-convex constraint, the objective function is intractable and complicates the relationship between the BS transmit beamformer and RIS passive beamformer. In [27], the authors solve this optimization problem by using a proximal policy optimization (PPO) algorithm, which is a powerful reinforcement learning (RL) algorithm from the actor-critic family and outperforms other actor-critic algorithms. In the following subsection, we present the system and channel models for the considered RIS-assisted MISO communication systems, which are similar to those in [71; 72; 73; 74].