# Low-Complexity Convolutional Neural Network for Channel Estimation
## 1 Introduction  
Due to the high variability of the wireless channel, its estimation is recognized as one of the most challenging techniques in many cellular use cases, such as Reconfigurable Intelligent Surface (RIS), mmWaves, massive Multiple-Input Multiple-Output (MIMO), and Open Radio Access Network (O-RAN) for the Radio Unit. To support more stringent requirements of next generation systems, the traditional channel estimation techniques must be improved, as they become a bottleneck due to high complexity or limited accuracy. Conventional methods, such as Least Square (LS) and Minimum Mean Square Error (MMSE), follow mathematical models and are blind to the underlying characteristics of the channels [1]. Commonly, LS offers the lowest accuracy in many scenarios, but has the benefit of not requiring prior information. Thus, it is still considered a valuable choice when implementation is considered [2]. Alternatively, MMSE minimizes the estimation error, but has a higher computational cost requiring channel statistical information [3]. By virtue of the ability to adapt quickly in various environments, Deep Learning (DL) techniques have gained interest in many aspects of wireless communication systems showing promising results [4]. Since DL is purely data-driven, the networks are optimized over large training datasets and can then provide very high levels of accuracy [5]. It has been demonstrated that neural network-based channel estimation outperforms the MMSE technique, as shown in [3, 6]. In particular, ref. [6] demonstrates error improvement up to2 orders of magnitude compared to MMSE channel estimation, while [3] highlights the efficacy with different Doppler frequencies in the transmission channel model. However, a major concern regarding DL solutions is their effectiveness in real-world scenarios, and [7] demonstrates the validity of orthogonal approximate message passing (OAMP) using DL methods and how this approach can improve performance. Generally, in the literature, the neural network design relies on one of three types of Deep Neural Network (DNN) models, namely, Fully Connected (FCDNNs), Convolutional Neural Networks (CNNs) and Recurrent Neural Networks (RNNs). Despite the fact that the performance of the neural network can vary with the design, FCDNNs are usually applied for classification problems, and are less suitable for channel estimation compared to the CNNs and RNNs, as demonstrated in [8]. RNNs are able to keep track of the information history, which is particularly suitable for channel estimation because the information on one symbol is propagated along the slot, as shown in [9]. In particular, the Long Short-Term Memory (LSTM), one of the most common RNNs, has shown the best results in terms of bit error rate (BER) and mean square error (MSE). Whilst the LSTM-based architecture reaches the lowest error rate, it unfortunately requires more complex operations. Therefore, this architecture is not considered a good fit for hardware technology, such as System on Chip (SoC) or Versal [10]. CNNs are traditionally used for image denoising. They are therefore favorably applied to the noisy channel information in order to obtain a clearer version as proved with ChannelNet, one of the first neural networks to be used for channel estimation [11]. Two neural networks, specifically image super-resolution (SR) and image restoration (IR), are used to enhance channel estimation, outperforming the MMSE technique. Another approach is investigated in [12]; the overall proposal includes two neural networks, but one in the user equipment (UE) and the other is in the base station (BS). This setup enables the UE to gather Channel State Information, compressing it to minimize transmission overhead, which results in improved MSE performance at the BS. Similar in [13; 14], it exploits the attention mechanism to focus on the critical features to yield the best channel estimate.