## 1 Introduction  
Higher data rates and energy efficiency are the core goals when designing new chaos-based communication systems. These goals originate from different aspects, like introducing the new communication standards (4G&5G) and the new challenges related to spectrum distribution to enable massive numbers of devices to access the network. Chaos-based systems, used as spread spectrum communication systems, were proven to be a great candidate for communications of IoT devices that constitute a considerable portion of the newly introduced standards [1]. In this vein, among the significant motives for improving chaos-based systems is the inherent limitations of non-coherent chaos-based systems and the rapid development of new methods that can profit the design of new highly performing chaos-based schemes. In the literature, the non-coherent scheme called Differential Chaos Shift Keying (DCSK) [2] has received significant attention in developing new chaos-based schemes, given its simple detection structure and its proven ability to mitigate the effect of fading channels [3]. It is also one of the most adaptive schemes and has been extensively studied over the last two decades and has seen numerous upgrades in its basic symbol structure. In this sense, various signal processing approaches have been developed to improve its data rate, spectral efficiency, transmit energy efficiency, and Bit-Error-Rate (BER). Among the most notable emerging modulation schemes, index modulation has been primarily explored, given its potential to encode data more optimally and therefore ameliorate the performancesof DCSK systems. Index modulation (IM) was first studied for Orthogonal Frequency Division Multiplexing (OFDM) in [4], where it was shown that IM could be used for more than just the transmit antennas of MIMO systems. IM was then applied to DCSK and Short Reference DCSK (SR-DCSK) using walsh codes in [5] which showed that the application of Code-Index Modulation (CIM) results in a considerable performance enhancement. Walsh codes are combined with a natural number-based mapping method in [6] to improve the data rate of the simple Code-Index Modulation DCSK (CIM-DCSK) while using the same resources. A combination of multiple modulation techniques, such as OFDM, vector modulation, and index modulation, has been proposed as a method for improving the data rate and spectral efficiency of chaos-based systems. The data rate was addressed in [7] with the introduction of superposition coding to Pulse-Position-Modulation DCSK (PPM-DCSK) to enhance multi-user download rates. Permutation index differential chaos shift keying (PI-DCSK) and differential permutation index differential chaos shift keying (DPI-DCSK) modulations were presented in [8; 9], where a permutation is used to encode additional data with a list of codes referring to a series of chaotic references. Sparse codes were used similarly to achieve higher spectral efficiency for the Multi-carrier DCSK systems in [10]. In [11], time-reversal transform is combined with the DCSK design to improve the BER and spectral performances given a land mobile satellite channel model. According to [12], optimal finger selection based on a genetic algorithm can be used to enhance the performance of the MMSE receiver. Orthogonal chaotic generators (OCG) were combined with Walsh codes in [13] to enable multi-user transmissions and achieve higher spectral efficiency than the DCSK systems. General Carrier Indexing (GCI), which uses carrier indexing in a more general and arbitrary form to reduce the number of indexes required for carriers and data bits, was used in [14] to provide higher spectral efficiency than conventional index-based DCSK systems. Combining M-ary modulation with index modulation and multi-carrier transforms in [15] increased data rate but at the expense of much higher complexity.