## 1 Introduction
The CNN model is composed of an input layer, convolutional layer, pooling layer, fully connected layer, and output layer. The structure of the 1-D CNN is illustrated in Figure 1a. In [36], the authors proposed a CNN-based RIS-enhanced multiple-input single-output system for the goal of sum-rate maximization. To archive the accurate CSI and improve performance, an ordinary differential equation-based CNN structured in the RIS-orthogonal frequency division multiplexing (OFDM) single antenna receiver was proposed in [37]. In [38], a CNN-based RIS-assisted OFDM with a single-input single-output system was proposed for achieving the maximization of the achievable rate. In [39], the authors presented a long short-term memory (LSTM)-based energy-efficient RIS wireless system where they evaluated the system EE and achievable rate. The study in [40] presented a CNN-based demodulation method for a multi-user RIS wireless system where, for channel modeling, an OFDM system based on MIMO was taken into consideration. In [40], the authors compared the achievement of the proposed demodulation (Demod)-CNN with the conventional method in terms of bit-error rate (BER) and SER. In addition, the temporal neural network (TCN)-based RIS-assisted MIMO wireless communication was presented in [41], where the proposed TCN analyzed the achievable rate in terms of different modulation schemes. LSTM and gated recurrent unit (GRU) are examples of recurrent neural networks (RNNs) that are frequently employed to address sequence difficulties. In comparison to traditional RNN, GRU is designed to store past state information more effectively. The traditional RNN training process's gradient vanishing and gradient explosion problems can be addressed [42]. The hidden unit in the typical RNN structure, which may selectively recall relevant information and discard unnecessary information, is replaced by a gate structure in the GRU and LSTM. The update gate and the reset gate are used in the GRU instead of the input gate, forget gate, and output gate of the LSTM [43]. The training setting can be decreased to produce a quicker convergence speed, provided that the prediction accuracy of the GRU is not less than that of the LSTM. Figure 1b shows the internal cell structure of the GRU network. Figure 1c,d show the structure of LSTM and typical RNN network, respectively. For a system with a one-bit ADC and massive MIMO, in [44], the authors proposed the LSTM-GRU to evaluate the channel matrix and showed better performance. For the purpose of CE of data subcarriers, in [45], the authors proposed a DL-GRU neural network-based OFDM system in which the computing demands may be greatly decreased and achieved a more satisfactory gain than other methods. The performance in the aforementioned studies has a major influence on the SER and BER by using CNN- and RNN-based models. Thus, the combination of 1-D CNN with GRU can be a promising method to achieve high accuracy performance in RIS-assisted communication systems. Motivated by the previous work and enhanced efficacy, herein, a combined DL model, comprising a 1-D CNN and GRU network, is proposed. In terms of SER and BER with various signal-to-noise (SNR) levels, the suggested model outperforms the [40]. The key contributions of the proposed system can be summarized as follows:  
* DL-cascaded model-based effective decoding is proposed for the RIS-assisted MIMO system. The proposed DL model is structured with a 1-D CNN model, which extracts the features in the form of complex numbers of the received channel matrix, and a GRU network, which uses extracted data for obtaining the optimal prediction. * Inter-carrier interference and inter-symbol interference (ISI) are taken into consideration while segmenting the data of the received signals using a 1-D CNN-based feature extractor. For handling the considerable ISI and accelerating the training speed of the model, the GRU layers are utilized. Thus, the combined model enhances demodulation accuracy.