## 3 Deep-Learning-Based Channel Estimation Methods
### Model-Driven Deep-Learning-Based Channel Estimation Methods
#### 3.4.1 Model-Driven Channel Estimation Combining LS Algorithm  
As previously mentioned, the conventional LS channel estimation algorithm is computationally simple but leads to poor performance since it ignores the impact of noise. The ComNet proposed by [PERSON] et al. [12] solves the problem using deep learning networks, which provides a reference for subsequent research. As shown in Figure 17, the ComNet is constructed by cascading the channel estimation and the signal detection subnets. In the channel estimation subnet part, the authors utilized a DNN to refine the coarse estimation of the traditional LS algorithm. Specifically, the DNN takes the LS coarse estimation as input and learns from the discrepancies between this initial estimation and the actual channel. Then, the DNN adjusts its parameters through training to minimize the prediction error, resulting in a more accurate channel estimation.  
In 2021, [PERSON] et al. [71] introduced a dual CNN structure to improve the LS algorithm's estimation accuracy with lower complexity than the general CNN-based methods. The initial channel estimation obtained by the LS algorithm is used as the input for the dual CNN, which consists of a spatial-frequency CNN (SFCNN) and an angle-delay CNN  
Figure 16: Components of the model-driven approach.  
Figure 17: ComNet structure [12].  
(ADCNN). In particular, the SFCNN effectively leverages the channel's sparsity to process white noise, while the ADCNN utilizes the channel correlation to reduce interference. These two CNNs are connected through a discrete Fourier transform (DFT) process. Owing to the dual CNN combining the advantages of SFCNN and ADCNN, it exhibits superior NMSE performance to the single-domain CNN in experiments.  
In 2023, [PERSON] et al. [72] innovatively implemented channel estimation on a System on Chip (SoC) based on deep learning. Specifically, the authors proposed a channel estimation method called DNN-augmented LS (LSDNN) for the preamble-based OFDM physical layer. This method employs a fully connected feedforward DNN to process the LS estimation results. Specifically, the DNN uses the initial LS estimation as input, learning from its errors to improve the initial estimation. It does this by minimizing the cost function, thereby refining the LS estimation of the previous preamble. Finally, the proposed LSDNN, the LS algorithm, and the LMMSE algorithm are mapped onto a Zynq multiprocessor SoC (ZMPSoC) platform for extensive experimental comparison. Experimental results verify that the LSDNN has a superior estimation accuracy over the LS and the LMMSE algorithms. However, there is still room for improvement in resource utilization and power consumption.  
To overcome the challenge of SNR mismatch in multipath time-varying channels, [PERSON] et al. [73] introduced a cascaded network called NDR-Net for channel estimation. The NDR-Net consists of a cascade of a noise level estimation subnet (NLE), a DnCNN, and residual learning, and the channel matrix is regarded as an image in this scheme. Firstly, the LS algorithm estimates the coarse value of the channel matrix, which is then inputted into NLE to obtain the noise level estimation. Subsequently, the estimated noise level and the initial noisy channel matrix image are inputted into DnCNN for noise reduction, resulting in a pure noisy image. Finally, the noiseless channel matrix image is obtained by residual learning. Through experimental comparison, the NDR-Net has better estimation accuracy than conventional methods when the SNR is mismatched. In addition, it applies to different Doppler shifts.