# Secure Mimo Communication System with Frequency Hopping Aided OFDM-DCSK Modulation
## 1 Introduction  
In recent years, with the increase of communication equipments, the single-input single-output (SISO) communication system has been unable to meet the needs of more efficient and faster communication [1]. In order to solve this problem, the multiple-input multiple-output (MIMO) communication system using a space resource has become an effective way. Because the performance gain of MIMO communication system can increase linearly with the increase of the number of antennas, the MIMO communication has not only been widely used in the radio frequency (RF) field but also aroused the interest of researchers which are interested in how to apply this scheme to visible light communication (VLC) [2, 3]. At present, the MIMO communication system which is based on space time code (STC) [4] technology has been widely used in 4G and 5G communication systems. At the same time, in order to improve the reliability of the communication system, researchers further transform space time block coding (STBC) [2] in STC into orthogonal STBC or combine it with spatial multiplexing (SM) [1, 3]. Moreover, in recent years, the orthogonal time-frequency space (OTFS) modulation has been proposed to be applied in the MIMO communication system [5], which has advantages of overcoming Doppler interference and low computational complexity [6, 7]. However, compared with the orthogonal frequency division multiplexing (OFDM) scheme, the OTFS might induce security performance degradations [8]. In the last ten years, the chaotic communication in the SISO communication system has attracted much attention due to its good characteristics of non-periodic, wide-band, noise-like, and sensitivity to initial values [9]. Moreover, chaotic communication also has low probability of intercept [10]. The chaotic communication can be divided into coherent chaotic communication and non-coherent chaotic communication according to whether the chaotic synchronization process is needed at the receiver. As defined in the classification of chaotic communication, non-coherent chaotic communication attracts more attention because it does not need a chaotic synchronization process [10]. In non-coherent chaotic communication, differential chaotic phase-shift keying (DCSK) has attained more attention. In recent years, in order to further improve the security of the DCSK, some scholars propose to scramble chaotic sequences [11], other scholars propose to use the internal correlation of chaotic sequences to encode and decode information bits [12]. In addition, some scholars also propose to use time slot sequences to allocate chaotic reference sequences and information-carrying sequences [13]. However, these methods require complex delay line circuits in the process of implementation; at the same time, because of the need to transmit chaotic reference sequences, the communication efficiency will be reduced [14]. In order to remove the delay line circuit of DCSK and improve communication efficiency, some scholars proposed to use OFDM technology to overcome this defect [15; 16]. However, the direct transmission of chaotic reference sequences will degrade the security performance of signal transmissions [17]. Then, Ref. [18] proposed to apply the frequency hopping (FH) to the OFDM system to assist DCSK (FH-OFDM-DCSK) to overcome the defects of DCSK [18]. However, few research studies have been done to utilize the FH aided OFDM-DCSK scheme to enhance the security of MIMO transmissions. A model combining MIMO with DCSK has been proposed in [19; 20], while according to [21], MIMO communication system which combined STBC with DCSK (STBC-DCSK) are divided into two types: those that require channel state information (CSI) and those that do not. Most scholars who still study the STBC-DCSK model focus on how to use the characteristics of DCSK to improve the reliability of MIMO communication system and use MIMO communication technology to improve the communication efficiency of DCSK [19; 22].