# Deep Learning-Enhanced Autoencoder for Multi-Carrier Wireless Systems
## 1 Introduction
In [27], the authors proposed a novel deep energy EA for noncoherent multicarrier multiuser SIMO (MU-SIMO) systems in fading channels. The EA-based approach, using neural networks for both transmitter and receiver, leverages energy-only input at the decoder and optimizes subcarrier power levels. In [28], the authors proposed a novel peak-to-average power ratio (PAPR) reduction scheme, PRNet, for OFDM systems based on deep AE architecture. The scheme adaptively determines constellation mapping and demapping using DL, minimizing both bit error rate (BER) and PAPR. For fading channels, ref. [29] introduced a radio transformer network (RTN) to counteract fading, but it did not leverage multipath diversity. Similarly, the AE method applying individual OFDM sub-carriers in [29] did not provide diversity advantages. The paper in [30] compared an AE-based OFDM system with IEEE 802.11a Wi-Fi, demonstrating that the AE system adapts better to channel conditions and effectively manages multi-path effects. A CNN-based universal filtered MC system was proposed in [31], where the DL models leverage the typically discarded odd-indexed samples from the received signal. Consequently, the model relies heavily on extensive and diverse training data to perform effectively. A DNN-based MC with AE (MC-AE) for fading channels was proposed in [32], where both modulation and demodulation are handled by neural networks without relying on channel equalizers. The approach improves diversity and coding gains, achieving superior BLER performance over traditional methods, and is extended to MU-MC-AE. Another DNN-based turbo-style MC-AE was proposed in [33] for the OFDM system, incorporating the exchange of extrinsic information between the MC-AE decoder and the soft-decision channel decoder, which adds computational complexity. The gated recurrent unit (GRU) model captures long-term dependencies in sequential data through gating mechanisms, effectively addressing the vanishing gradient problem. GRUs have a simpler structure with fewer parameters than LSTMs, enabling faster training efficiency. Additionally, GRUs require less memory than LSTMs and generalize well with smaller datasets, making them suitable for real-time and resource-constrained applications [34; 35]. Meanwhile, AEs are advantageous for feature extraction and dimensionality reduction, allowing data compression and efficient representation learning, which often enhances performance in downstream tasks [36]. In this paper, we propose a GRU-based MC-AE (GRU-MC-AE) system that leverages the advantages of the GRU model to tackle the previously mentioned challenges. In this paper, we evaluate the BER and block error rate (BLER) performance of the proposed model across various signal-to-noise ratios (SNRs) under both perfect and imperfect channel conditions. Additionally, we calculate the spectral efficiency (SE) and energy efficiency (EE) across various SNR levels. We compare its performance with traditional decoders and other DL-based decoders. The simulation results demonstrate that our proposed GRU-MC-AE model outperforms both conventional and DL-based models. The key contributions of this paper are summarized below:  
* This study proposes a single-user MC-AE system, wherein a DNN model is used for the modulation block and the demodulation block is implemented using a GRU, acting as the encoder and decoder in an AE framework. The encoder employs a linear activation function, which passes the weighted sum of inputs directly to produce continuous outputs and the GRU-based decoder effectively manages the temporal dependencies between subcarriers, enhancing the system's ability to adapt to changing channel conditions. * The suggested method does not require an equalization or domain knowledge because it feeds the decoder both the received signal and the channel state information (CSI) directly. The encoder and decoder are efficiently learned by this totally data-driven method to maximize diversity and coding gains in fading channels.