# Deep Learning-Enhanced Autoencoder for Multi-Carrier Wireless Systems
## 1 Introduction  
Multicarrier (MC) transmission [1] has been recognized and adopted by numerous standards bodies for both wireline and wireless systems [2, 3] due to its effectiveness and reliability. This approach offers several benefits, including resistance to single-frequency interference and enhanced capability to reduce inter-symbol interference (ISI). MC's strength in addressing various channel impairments, such as frequency selectivity and impulse noise, makes it a popular choice in emerging applications like wireless local area networks (WLANs) [4] and power line communications (PLCs) [5]. The core concept of the MC protocol is the decomposition of the spectrum into a series of orthogonal narrowband subchannels, using complex exponentials as carriers of information [6]. Two primary MC techniques are commonly employed: discrete multitone (DMT) [7] for wireline systems and orthogonal frequency-division multiplexing (OFDM) [8], which is predominantly used in wireless applications. Both OFDM and DMT rely on fast Fourier transform (FFT) for spectrum decomposition, and data are transmitted in blocksas a result. Many wireless standards, such as IEEE 802.11, IEEE 802.16, 3 GPP LTE, and LTE-Advanced, utilize an OFDM-based multicarrier system [9]. A variety of sophisticated MC methods built on OFDM have been investigated recently with the goal of improving spectral or energy efficiency. For example, spread OFDM (S-OFDM), using a Walsh-Hadamard spreading matrix, was proposed in [10], where each subcarrier in the OFDM system is modulated using a spread spectrum technique. In [11], the author introduced OFDM with index modulation (OFDM-IM), employing a maximum likelihood (ML) detector to identify the received signal. Compared to traditional OFDM, OFDM-IM offers enhanced reliability and energy efficiency by activating only a subset of subcarriers. This method transmits data bits through active indices in addition to M-ary symbols. The study in [12] revealed that, like conventional OFDM, OFDM-IM has a diversity order of one and examined its error performance. In particular, spread OFDM-IM (S-OFDM-IM) was developed in [13] by applying a spreading code to OFDM-IM to enhance its diversity advantage. This experiment demonstrates that when low-complexity detection techniques, like minimum mean squared error (MMSE)-based detectors, are used, S-OFDM-IM performs better than S-OFDM. Similarly, the dual model OFDM (DM-OFDM) was introduced in [14] and used several distinct signal constellations. Recently, deep learning (DL) has been applied to various areas within the communications field, particularly to address physical layer challenges [15; 16]. DL has also been widely utilized to tackle issues in MC systems [17]. For instance, deep neural networks (DNNs) have been effectively employed to detect OFDM and OFDM-IM signals [18; 19], particularly in the presence of channel impairments. In [20], a convolutional neural network (CNN)-based receiver was designed for joint detection and modulation classification of the received signal. The work in [21] introduced a dual CNN-based decoder for channel estimation in a multiple input multiple output OFDM (MIMO-OFDM) system, aiming to reduce complexity by incorporating an additional neural network, referred to as HyperNet. A long short-term memory (LSTM)-based detector for the OFDM-IM system was proposed in [22]. A Y-shaped net-based bi-directional LSTM (Bi-LSTM) model was proposed for the OFDM-IM system in [23]. The concept of an end-to-end communication system modeled as an autoencoder (AE) in DNNs was first introduced in [24]. In this approach, the transmitter encodes the input data so that the receiver's output is optimized to match the original input. Additionally, ref. [25] demonstrated the ease of implementing these techniques using open-source DNN frameworks and commercially available software-defined radios. Building on these ideas, ref. [26] proposed an AE-based end-to-end communication system capable of handling unknown channel models.