# Intelligent Reflective Surfaces for Wireless Networks:
## 3 IRS-Assisted Wireless Networks
### Channel Estimation
#### 3.2.2 OFDM Systems  
In [37] a transmission protocol has been proposed to perform channel estimation for an IRS-enhanced single-user single-input single-output (SISO) orthogonal frequency division multiplexing (OFDM) system. A least squares (LS) derivation for the CSI estimation is performed by assuming that the IRS can be divided into multiple sub-surfaces of adjacent strongly correlated reflecting elements. The proposal is a low-complexity alternative based on the estimation of the strongest signal path. The well known Zadoff-Chu sequence [38] is employed as the pilot sequence during the first sub-frame. The method proposed in [37] provides MSE values lower than those obtained with the On/Off-based algorithm in [39]. In [39], two methods have been developed. One is a semidefinite relaxation (SDR) algorithm that achieves close-to-optimal performance but whose complexity is extremely high for practical scenarios. The other is a low complexity On/Off-based channel estimation method which is based on On/Off state control of the IRS reflecting elements by grouping adjacent elements that present high channel correlation. The gains offered by [37] over [39] come from the reflection power loss and noise enhancement present in the On/Off-based channel estimation method in [39]. The work in [40] considers a three-phase pilot-based channel estimation framework to acquire the overall uplink channels in an IRS-assisted single-input multiple-output (SIMO) system by considering the correlation among the user-IRS-BS reflected channels of the different users (cf. [40], Table 1). The results are presented in terms of the MSE and the proposed method provides a higher performance compared to that of the benchmark scheme that neglects the channel correlation.  
A practical transmission protocol for channel estimation is proposed in [39] for an OFDM SISO system under frequency selective channels with a single cell-edge user and LOS. The authors also employ the technique of flexibly grouping the IRS elements with On/Off states and estimating the combined channel per group which also reduces training overhead and estimation complexity. The results are presented in terms of the achievable rate and compare the system performance under the utilization of the proposed channel estimation technique versus that of the scheme with perfect CSI. The performance loss obtained in the numerical experiments is small.  
In [41], the authors consider a single-user IRS-aided OFDM multiple-input single-output (MISO) system under LOS conditions and propose a deep learning (DL) based channel estimation method. A convolutional neural network (CNN) is designed to estimate both the direct and cascaded channels of the system. The authors propose a single neural network (NN) for first estimating the combined channel and then recovering individual channel estimates for complexity reductions in the training process. Simulation results show that the proposed DL approach achieves a performance better than the On/Off patterns in [39] because when estimating the direct link with all the IRS elements turned off, the corresponding effective channel gain for pilot transmission is smaller and this leads to higher estimation errors. In [42] the authors formulate two low-complexity LS-based estimation methods for frequency-selective fading channels in the uplink of multiuser IRS-aided OFDM SIMO systems. The first strategy is applicable for arbitrary frequency-selective fading channels. The second channel estimation scheme is especially suited for LOS scenarios. The authors also optimize the training designs (pilot tone allocations and IRS time-varying reflection patterns) for each method to minimize the channel estimation error. Comparisons are performed w.r.t. benchmark scenarios regarding pilot tone allocation, which offer a lower performance in the channel estimation process.