# Design of a SIMO Deep Learning-Based Chaos Shift Keying (Dlcsk) Communication System
## 1 Introduction  
Chaotic signals are wide-band noise-like signals with robust and reproducible statistical features [1, 2]. Thus, digital modulation using chaotic signals presents an inherently simple solution for robust and secure communications over multi-path fading channels [3, 4]. Chaos-based modulations are generally classified into two main classes [5]. The first is coherent detection schemes, such as the Chaos Shift Keying (CSK) scheme [6], in which data are transmitted in a combination of basis functions obtained from chaotic waveforms. Chaotic synchronization is commonly used in the recovery of basis functions on the receiver side [7, 8, 9]. Theoretically, CSK modulation can achieve the Bit Error Rate (BER) performance of Binary Phase Shift Keying (BPSK) [10]. In application, this performance is not achievable as some problems needs to be solved, namely the recovery of basis functions and the estimation [11, 12, 13, 14, 15, 16]. Since chaotic synchronization is still practically impossible in a turbulent environment [17], coherent schemes can not work properly in utilization.  
The Differential Chaos Shift Keying (DCSK) system [18] is a variant of CSK where the basis functions have a special arrangement and the information can be revealed from the correlation between the parts of the basis functions. In DCSK modulation, each bit durationis divided into two equal slots, where the first slot is allocated to a reference signal whereas the second slot is used to send information-bearing signal. At the receiver side, these two signals are correlated to detect the transmitted bit information. Non-coherent schemes, such as DCSK, do not require Channel State Information (CSI) or chaotic synchronization on the receiver side [19; 20; 21]. The low data rate and energy efficiency of this scheme are significant drawbacks, as half of the bit time interval is used for sending non-information-bearing samples [22; 23; 24; 25]. Moreover, sending the same signal twice negatively affects security [26].  
The problem of basis function recovery from the received signals, independent of modulation, has impeded the progress of coherent chaos-based communications. To tackle this problem, we propose a Deep Learning (DL)-based receiver that enables us to implicitly estimate wireless channels and retrieve the transmitted message. We showed that using a trainable receiver can mitigate the chaotic synchronization problem in the existing correlator receivers.  
Accepting the definitions of coherent and non-coherent chaos-based communications systems introduced in [8], the symbol may be recovered by means of coherent detection, where all possible sample functions are known, or by non-coherent detection, where one or more characteristics of the sample functions are estimated. Although in the proposed receiver, the sample functions are available, but the available information is previously estimated from the transmitted signals. Regarding the above definitions, though the proposed receiver has similarities to the coherent and non-coherent receivers, it does not exactly fit into the conventional categories. Hence, we use the term Deep Learning-based Chaos Shift Keying (\"DLCSK\") to introduce a new category of chaos-based communications systems. Note that, a trained DLCSK receiver can easily work with existing CSK transmitters.  
The proposed scheme shows a BER gain compared to conventional DCSK. This advantage is obtained at the cost of adding an offline training step. In other words, we train the receiver by chaotic reference signals, instead of reference signal transmission in the test phase. When the training process is performed under different channel conditions, NN grasps different chaotic maps and implicitly estimates channel distribution. As a result, DLCSK consumes fewer resources (energy and time) to transmit one bit and shows a more robust behavior.