## 3 Deep-Learning-Based Channel Estimation Methods
### Data-Driven Deep-Learning-Based Channel Estimation Methods
#### 3.3.1 Application of DNN in Data-Driven Channel Estimation  
DNN is a fundamental network for deep learning with a simple model, and as such, it was first applied in channel estimation. It allows end-to-end learning, i.e., from the original input to the target output. Figure 14 shows a DNN-based channel estimator proposed in [9], serving as one of the typical examples. In this model, the authors estimated the CSI end-to-end by recovering the transmitted data from the received data, including the pilot and data blocks. Moreover, DNN is highly adaptable and flexible, and its structure and hyperparameters can be modified to accommodate various application scenarios. Figure 12: Performance comparison with the LS algorithm and the original CDP algorithm; (**a**) BER performance comparison; and (**b**) NMSE performance comparison. Figure 13: Structure of a data-driven deep-learning-based channel estimator. In 2020, [PERSON] et al. [51] investigated a DNN-based method that combines channel estimation and pilot design. The proposed DNN model is composed of a dimensionality reduction subnetwork and a reconstruction subnetwork. In the first subnetwork, the fully connected layer is designed to compress the high-dimensional channel vector into low-dimensional received measurements, and this compression process treats the weights in the layer as pilot signals. In the second subnetwork, several cascaded convolutional layers and a fully connected layer are designed to recover the high-dimensional channel. Through experimental comparison, this method exhibits a superior NMSE performance to the simultaneous orthogonal matching pursuit (SOMP) algorithm. Furthermore, when the DNN trained with multi-carrier samples is tested on single-carrier samples, and it still performs well, demonstrating its excellent generalization ability. The interpolation approach is closely connected with the performance of the pilot-based method. In [52], [PERSON] et al. proposed to utilize DNN to replace the interpolation process of the conventional pilot-based method. Firstly, the position index and the channel estimation result of pilot subcarriers are used as training data to train the DNN model. Then, the position index of data subcarriers is used as the input to the DNN, and the channel estimation of data subcarriers is finally obtained. This method does not require prior statistics or matrix inverse operations like the MMSE algorithm and thus has a lower complexity. Moreover, the proposed method exhibited superior estimation accuracy in experiments compared to the LS algorithm, which requires interpolation. Finally, the author tested the model trained with eight multipath paths in conditions with 4, 8, and 12 multipath paths. The BER performance remains almost unchanged, showing the excellent generalization ability of the proposed model. In 2021, [PERSON] et al. [53] developed an online DNN-based channel estimation method under limited pilot conditions. This method can dynamically learn and compute in real time, inferring and updating the DNN weights from the pilot symbols received online without knowing the real channel matrix to adapt to the actual communication environment. The proposed DNN-based method exhibits the strongest robustness in experiments. Furthermore, its estimation accuracy approaches the group orthogonal matching pursuit (GOMP) algorithm and the burst LASSO algorithm while surpassing the MMSE algorithm. Significantly, it surpasses all these methods by orders of magnitude in terms of computational speed. Additionally, the proposed DNN model, trained at an SNR of 30 dB, consistently surpasses the MMSE algorithm in terms of NMSE performance when tested at lower SNR levels. Specifically, the experiments conducted on the 3 GPP SCM TR 25.996  
Figure 14: DNN-based end-to-end channel estimator [9]. and the DeepMIMO channel models can both yield this result, demonstrating the model's strong generalization on lower SNR. In the realm of ocean exploration, underwater acoustic (UWA) communication is pivotal. In 2022, [PERSON] et al.