###### Abstract  
In this paper, a new short reference differential chaos shift keying (SR-DCSK) cooperative communication system based on modified code index modulation, referred to as the MCIM-SR-DCSK-CC system, is proposed. In the proposed MCIM-SR-DCSK-CC system, the information bits are transmitted to both the relay and the destination in the first time slot. On the other hand, in the second time slot, the relay not only forwards the information bits but also sends new information bits to the destination. Specifically, the relay adopts the modified code index modulation to transmit more information bits to the destination. The theoretical bit error rate (BER) expressions of the proposed MCIM-SR-DCSK-CC system are obtained over additive white Gaussian noise (AWGN) and the multipath Rayleigh fading channels. It is demonstrated that the simulation results of BER performance match the theoretical results. The energy efficiency (EE), the data rate, and transmission throughput are carefully analyzed. The performance of the proposed system is better than its competitors'. chaotic communication; cooperative communication; short reference differential chaos shift keying (SR-DCSK); code index modulation 2025  
Recently, index modulation (IM) has been developed as a means to enhance the data rate and energy efficiency of chaos-based communication systems. In the IM technique, a variety of transmission resources, including spreading codes, time slots, subcarriers, and transmit antennas, can be used to transmit information [13; 14]. To achieve higher data rates, the code index modulation (CIM) technique was first used in direct-spread spectrum-sequence communication systems [15; 16]. The M-ary orthogonal multilevel differential chaos shift keying system with code index modulation (CIM-OM-MDCSK) is proposed for high data rate and high spectral efficiency [17]. In the CIM-OM-MDCSK system, the M-ary information signals consist of modulated bits, chaotic signals, and their Hilbert transforms, and the selected Walsh codes with specific indices are used to modulate the multiple information-bearing signals. The modified code index modulation scheme based on multi-carrier M-ary DCSK (MC-MCIM-MDCSK) is proposed for high energy efficiency (EE), better spectral efficiency (SE), and high data rate [18]. The carrier index (CI) scheme that carries additional information bits by activating different subcarriers was proposed in [19; 20]. Then some modified carrier index differential chaos shift keying (CI-DCSK) systems have been proposed to obtain higher data rates, better energy efficiency, and spectrum efficiency. The carrier index M-ary differential chaos shift keying system (CI-MDCSK) transmitted the modulated bits by the active carriers through M-ary DCSK modulation, which is based on the Hilbert transform [21]. The high data rate carrier index differential chaos shift keying (HDR CI-DCSK) is proposed to obtain higher data rates, better energy efficiency, and spectrum efficiency [22]. The multi-carrier DCSK with hybrid index modulation (HIM-MC-DCSK) system is proposed by combining the carrier-number-index technique and carrier-index technique with MC-DCSK modulation to substantially enhance transmission efficiency in wireless communication systems [23]. Spatial diversity has also received considerable attention as another promising technique to combat multipath fading [24; 25]. The use of multiple antennas to transmit redundant signal information can significantly mitigate the impact of multipath propagation. The cooperative communication, which provides transmit diversity by placing a relay between the source and destination, has been proposed as an alternative approach to tackle multipath fading [26]. Moreover, it has been shown in [27; 28; 29] that integrating DCSK with cooperative communication (CC) can substantially enhance the reliability of wireless communication systems. In [30], the partial-sequence CC (PS-CC) scheme is proposed for improving data rate.