## 3 Deep-Learning-Based Channel Estimation Methods
### Data-Driven Deep-Learning-Based Channel Estimation Methods
#### 3.3.2 Application of CNN in Data-Driven Channel Estimation  
CNN is advantageous for channel estimation since it can reduce the computation of feature parameters and automatically select the appropriate training weights. In addition, CNN's excellent feature extraction capability contributes to its excellent image processing performance. Hence, the channel estimation problem can be transformed into an image processing problem in the application, enabling it to learn from the training data and obtain accurate CSI. Figure 15 shows examples of transforming the channel time-frequency response into a 2D image under the Vehicular-A (VehA) channel model [56]. Specifically, Figure 15a,b represent the channel time-frequency response images under the perfect channel model without noise and the noisy channel model with an SNR of 22 dB, respectively. Figure 15: Two-dimensional image examples of the channel time–frequency response: (**a**) under the VehA perfect channel model (without noise); and (**b**) under the VehA noisy channel model (SNR = 22 dB). In 2019, the ChannelNet proposed by [PERSON] et al. [57] with regard to the channel time-frequency response as a low-resolution 2D image and the values are only known at pilot positions. The ChannelNet consists of a super-resolution CNN (SRCNN) and a denoising CNN (DnCNN), which are cascaded into a two-step channel estimator. In the first step, the low-resolution image is enhanced into a high-resolution image by the SRCNN. In the second step, the DnCNN removes the noise effect to obtain a higher-quality image (i.e., an accurately estimated channel). Through experimental verification, the ChannelNet's MSE performance is superior to the ALMMSE algorithm (an approximation to linear MMSE) but inferior to the MMSE algorithm in low SNR. However, the performance of ChannelNet trained at the SNR of 22 dB shows a decreasing trend when the SNR exceeds 23 dB, which indicates that its generalization ability on real noise is not good enough. Notably, this literature is a pioneer in using image processing methods for channel estimation, providing a novel idea for many subsequent studies. Inspired by this, [PERSON] et al. [58] investigated a deep residual channel estimation network (ReEsNet) based on residual learning, which can work in a wide range of scenarios and significantly reduce the complexity while improving estimation accuracy. The numerous convolutional layers in the denoising structure (DnCNN) of ChannelNet [57] lead to a large amount of computation and a long execution time, which greatly consumes memory. For this reason, [PERSON] et al. [59] made improvements and proposed the channel estimation network (CENet). Compared with ChannelNet, CENet also uses SRCNN for image resolution enhancement, with the difference that a convolutional blind denoising network (CBDNet) is used as the denoising structure instead of DnCNN. The CBDNet reduces the overall number of convolutional layers, thereby reducing the complexity of the proposed CNN model. Through experimental comparison, the CENet is superior to the ChannelNet but inferior to the ideal MMSE algorithm in terms of MSE. Furthermore, the author tested the CENet trained with 48 pilots under conditions of different numbers of pilots. The results showed that CENet maintains high performance even with fewer pilots, unlike other methods, which exhibited a significant decrease in performance under the same conditions. Most research utilizing deep learning for channel estimation focuses on constructing complex neural networks, which leads to increased storage and computational requirements. [PERSON] et al. [60] addressed this phenomenon by combining the CNN and Transformer and proposing a lightweight channel estimation Transformer (LCET). This scheme treats the channel response matrix as a 2D image, with the channel features extracted using a lightweight feature extraction CNN (LFEC) and then transmitted to a lightweight-adjusted Transformer (LAT) for channel estimation.