# Design of a SIMO Deep Learning-Based Chaos Shift Keying (Dlcsk) Communication System
## 1 Introduction
### Background  
DL is a powerful tool that can be implemented for solving problems that are complicated to describe through mathematical models [27]. There are two general methods for designing DL-based architectures, namely DL-based receiver design and joint DL-based transceiver design [28]. A DL-based joint transceiver design optimizes the system as an end-to-end auto-encoder [29]. In contrast, a DL-based receiver optimizes one or more blocks in the receiver [30]. As an example of the latter, in [31], the authors suggested a DL-based receiver to indirectly estimate wireless channels and retrieve the signals. They demonstrated that DL-based receivers have the ability to learn the features of wireless channels, including non-linear distortions. Practical wireless channels change over time with a large dynamic range. In this case, NNs can hardly perform well in the detection tasks under different channel coefficients [32]. To overcome this challenge, Deep Transfer Learning (DTL) adopts a NN to extract the time-varying features with a few online training data by transferring knowledge from a source domain to a target domain [33; 34; 35]. Motivated by this approach, in this paper, we try to propose a framework for detection of the chaotic-modulated signals.  
In this study, our focus is on the design of a DL-based receiver that can be easily harmonized with existing CSK transmitters. Recently, DL have attracted a lot of attention because of its effectiveness in data-driven analysis of chaotic dynamics [36]. Some studies have used DL in chaos-based communications [37; 38; 39; 40], however, their methods need further explorations. In [39], the authors proposed an algorithm to demodulate the reference chaotic signals iteratively. In contrast to traditional demodulation methods, utilizing time or frequency resources to improve reliability, the iterative receiver addresses the feature extraction capability of neural networks (NNs). In [40], an intelligent OFDMDCSK demodulator is proposed using an LSTM-aided NN that withdraw the correlations between chaotic modulated OFDM-DCSK signals in order to retrieve the transmitted information. However, the LSTM-aided receiver transmits reference signals that do not carry useful information. A similar problem can be observed in the other proposed DL-based modulations (e.g., in [38; 39]).  
In this paper, we present an innovative Long Short-Term Memory (LSTM)-based receiver that does not require any reference signal transmissions or chaotic synchronization circuits for data detection. The proposed DL-based Chaos Shift Keying (DLCSK) system benefits from other advantages of NNs, such as generalization and fast training. The multi-antenna design of the DLCSK receiver that, uses an LSTM for each antenna is also presented. Many articles have also combined Multi-Antenna technology with Chaos-based communications [41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53]. For instance, a MIMO STBC-DCSK system does not require any complicated channel estimation, carrier synchronization, or rake reception [54]. However, these conventional techniques transmit the reference signals over the channel, which increases the redundancy and complexity of the system. Previous research in the context of neural network ensembles shows that combining network architectures is frequently more accurate than using single networks [55; 56; 57]. The proposed Single Input Multi Output (SIMO) DLCSK focuses on a fusing method to achieve a diversity gain, where the outputs of all LSTMs are combined using a majority voting strategy. This design maintains the advantages of traditional Multi-Antenna and Chaos-based systems, i.e., it does not require rake receivers, CSI, and chaotic synchronization. DLCSK is an appealing candidate for secure data transmission in cloud-based systems [58; 59; 60], vehicular communications [61; 62; 63], and massive MIMO systems [64; 65; 66; 67] due to the aforementioned characteristics.