###### Abstract  
This study uses deep learning (DL) techniques for pilot-based channel estimation in orthogonal frequency division multiplexing (OFDM). Conventional channel estimators in pilot-symbol-aided OFDM systems suffer from performance degradation, especially in low signal-to-noise ratio (SNR) regions, due to noise amplification in the estimation process, intercarrier interference, a lack of primary channel data, and poor performance with few pilots, although they exhibit lower complexity and require implicit knowledge of the channel statistics. A new method for estimating channels using DL with peephole long short-term memory (peephole LSTM) is proposed. The proposed peephole LSTM-based channel state estimator is deployed online after offline training with generated datasets to track channel parameters, which enables robust recovery of transmitted data. A comparison is made between the proposed estimator and conventional LSTM and GRU-based channel state estimators using three different DL optimization techniques. Due to the outstanding learning and generalization properties of the DL-based peephole LSTM model, the suggested estimator significantly outperforms the conventional least square (LS) and minimum mean square error (MMSE) estimators, especially with a few pilots. The suggested estimator can be used without prior information on channel statistics. For this reason, it seems promising that the proposed estimator can be used to estimate the channel states of an OFDM communication system. L 2023  
systems to work well, the accuracy of the channel response estimation is very important. Pilots can derive information about the CSI before the transmitted information is detected. The receiver can retrieve the transmitted symbols based on the estimated CSI. Least square (LS) and minimum mean square error (MMSE) are the most popular methods for selecting the optimal estimation strategy. Despite its simplicity, the accuracy of the LS technique is often unsatisfactory. Due to the complex MMSE calculation, prior information on 2 nd order channel statistics and noise variance is required [3]. This study proposes and implements a peephole long short-term memory (peephole LSTM) DL-based CSIE for OFDM wireless communication systems. To the authors' knowledge, this work is the first to use the peephole LSTM DL network as a CSIE. The proposed estimator does not need prior knowledge of the communication channel statistics and powerfully works with limited pilots (under the condition of less CSI). The proposed estimator is data-driven to analyse, recognise, and understand the statistical characteristics of wireless channels suffering from many known interferences such as adjacent channel, inter-symbol, inter-user, inter-cell, co-channel, and electromagnetic interferences and unknown ones. Although an impressively wide range of configurations can be found for almost every aspect of DL, the choice of the loss function is underrepresented when addressing communication problems, and most studies and applications use the 'log' loss function. The main contributions to this paper are:  
* Propose and evaluate a DL-based peephole LSTM model for estimating channel state information and comparing MMSE, LS, and DL approaches for estimating the impulse response of different channels for next-generation 5G cellular mobile communications based on the OFDM system. * Peephole LSTM designs can store data over a long period. This characteristic is extremely useful when we deal with time-series or sequential data. It is processing not only single data points (e.g., images) but also entire data sequences (such as speech or video inputs). It performs better than MMSE, with less complexity, and LS conventional-state estimators. * The proposed estimator is trained for a generated OFDM signal, where the bit error rate (BER) is calculated and compared with the LS and MMSE estimations. During the offline training and the online deployment stages in this preliminary investigation, the wireless channel is presumed to be fixed.