## 2 Related Work  
In recent years, numerous studies have shown that DL approaches are particularly well suited for CE, and DL is increasingly used in communication systems. Thus, this section reviews previous studies on our major issue. Artificial neural networks (ANNs) attempt to mimic the behaviour of the human brain and are becoming increasingly popular today. Recently, ANNs, also referred to as feed-forward neural networks (FFNN) or recurrent neural networks (RNNs), have been used in CSI-based localisation [6; 7], channel decoding [8; 9], image recognition [10; 11], user localisation, traffic information, service requests, and channel usage [8; 9], and CE and recognition [9; 10]. An FFNNN-based combined symbol detection and CE approach was presented in [9] for the OFDM method with selectable frequency channels. When considering communication networks that are not perfect, the proposed algorithms perform better than the conventional estimators. An online DL-enabled estimator for double selectivity channels was proposed in [11]. Under all test conditions, the proposed algorithm outperformed the traditional linear MMSE estimators. In one paper [10], a model for 1D convolutional neural networks (CNNs) in DL was presented for estimating the channel and retrieving the equalized information. A comparison was made between the 1D CNNs and the FFNNNs, MMSE, and LS estimators regarding bit error rate (BER) and mean square error (MSE) for various modulation schemes. The 1D CNN estimator outperformed its competitors. The ability of deep-learning algorithms to directly capture the features of a given problem without requiring prior knowledge is a significant advantage for channel estimators. RNNs have not been a standard network system in recent years due to the challenges associated with training and computational complexity. Due to the growth of DL theory, RNNs have just entered a phase of rapid development. RNNs are currently successfully used in speech and handwriting recognition [12; 13]. However, the vanishing/exploding gradient problem affects the basic RNN. It also shows how difficult it is for RNNs to learn and maintain long-term memory and that they are limited in their ability to influence data. Long-short-term memories (LSTMs) were suggested to overcome the vanishing gradient issue in [4; 14; 15; 16]. The paper [17] presented a hybrid model and data-driven receiver technique that utilizes LS estimation as well as zero-point equalization to take out the initial features for estimating channels and identifying data. The paper [18] achieved reliable CE using an upgraded extreme learning machine (ELM). LS highlights initial linear characteristics for CE in the model-driven mode. An upgraded ELM network is built using the initial features to refine channel estimates. There are numerous improved variants of LSTM in its historical evaluation, such as BiLSTM, ConvLSTM, GRU, and peephole long short-term memory (peephole LSTM), which offer the best performance in some specialized areas. A bidirectional long short-term memory (BiLSTM) network comprises two LSTMs with forward and backward propagation, and it may concurrently capture forward and backward features [19; 20; 21]. Convolutional long-short-term memory (ConvLSTM) uses the convolution operator to calculate a cell's future state, which is then determined by its neighbours' inputs and previous states [22]. The GRU is a simpler LSTM variant. The GRU architecture used to solve RNN problems with LSTM has a rather complicated structure [5]. [PERSON] et al. [23] compared DL-based CE to least-square (LS) and minimum mean-square error (MMSE) estimators in pilot-assisted channel estimation (PACE). A GRU-based DL strategy is used to extract time and frequency domain features for CE to suppress error propagation of the data pilot-aided process applied to IEEE 802.11p in [24]. In the letter [25], DL helps OFDM recover nonlinearly corrupted transmission data.