## 3 Deep-Learning-Based Channel Estimation Methods
### Data-Driven Deep-Learning-Based Channel Estimation Methods
#### 3.3.3 Application of RNN in Data-Driven Channel Estimation  
RNN is not as widely used as other neural networks in channel estimation. However, some researchers have recently delved into RNN-based methods to improve the channel estimation accuracy. Given the time-dependent properties of RNN, it can be used for time-varying channels to improve time-series information processing. Moreover, it is especially well suited for channel estimation in high-speed mobile settings.  
For high-speed mobile environments, channel estimation becomes problematic due to the impact of multipath and Doppler effects, and conventional methods perform poorly due to the limited number of available pilots. Consequently, [PERSON] et al. [63] proposed a frame-by-frame (FBF) channel estimation method based on bi-directional RNN (Bi-RNN) for doubly-selective channels. The goal is to perform end-to-end 2D interpolation after estimating the channel of pilot symbols, thereby obtaining the channel estimation of data symbols. Simulation results demonstrate that the proposed Bi-RNN is robust and adaptive, and the estimation accuracy is superior to some existing deep learning schemes. Although the estimation accuracy is marginally lower than the conventional 2D-LMMSE algorithm, the complexity is reduced by nearly \(10^{6}\) times, making it a viable alternative.  
In 2021, [PERSON] et al. [64] estimated CSI using a variant of LSTM, namely a bi-directional LSTM (Bi-LSTM) neural network. The proposed network model relies on pilot assistance, does not require prior knowledge of channel statistical information, and employs online training with offline deployment. Under the conditions of limited pilots and uncertain channel prior statistics, this model is robust and has a superior symbol error rate (SER) performance over the LSTM and the conventional algorithms (LS and MMSE). The proposed Bi-LSTM can analyze massive data and establish relationships between features, thus having excellent generalization capabilities and applicability to new datasets.  
The gated recurrent unit (GRU) is a lightweight variant with potential developed from LSTM. In 2022, [PERSON] et al. [65] designed an end-to-end channel estimation method based on GRU to recover the transmitted signal from the received signal, thereby estimating the CSI. Through experimental verification, the GRU-based method surpasses the conventional estimation algorithms (LS and MMSE), DNN, and ReEsNet in terms of SER. In 2023, [PERSON] et al. [66] combined LSTM and GRU to develop an LSTM-GRU estimator, which is designed for channel estimation from the received signal. It consists of three parts: the LSTM, the GRU, and the smoothing module. In this framework, the LSTM serves as a minimum absolute filter that denoises the pre-processed received signals, and the GRU module compensates for the information loss in the LSTM module as a compensator. Finally, the model's output is smoothed using batch normalization and convolutional layers. Through experimental comparison, the proposed LSTM-GRU estimator has a superior NMSE performance over the CNN and CGAN estimators. Additionally, the LSTM-GRU trained with a pilot length of 8 is tested in scenarios of varying pilot lengths. The estimation performance of this model does not degrade significantly in the short pilot length range, indicating its outstanding generalization ability.