# Secure Mimo Communication System with Frequency Hopping Aided OFDM-DCSK Modulation
## 4 Simulation Results  
In this section, firstly, simulation results are provided to investigate the effectiveness of the proposed scheme. Next, we simulate the BER of legitimate users and eavesdroppers as well as the secrecy capacity of the proposed scheme and the benchmark scheme. Simulation results prove that the scheme proposed in this paper can effectively prevent eavesdroppers from obtaining useful information, thus improving the security of the MIMO communication system. In the simulation, we assume that the propagation channels are the AWGN channel and Rayleigh fading channel. In addition, perfect CSI can be obtained at the receiver. There are two transmit antennas at the transmitter and one receive antenna at the receiver. Then, we assume that different subcarrier number \(N\) and chaotic sequences' length \(\beta\) are used in the simulation. In addition, we assume that (1) the eavesdroppers can steal the STBC code information; and (2) the eavesdroppers can steal STBC coding information and chaotic reference sequences. In both cases, the secrecy capacity of STBC and STBC-DCSK [19; 20] will be compared with the proposed scheme. Firstly, in Figure 4, we simulate the theoretical and simulated BER of the proposed system with different \(\beta\) and different \(N\). It can be observed that, over the AWGN channel, the theoretical BER matches the simulated ones, which verify the effectiveness of the proposed scheme. It is noticeable that, when \(N\) is the same in Figure 4a, the BER of the proposed scheme decreases with the increase of \(\beta\). The reason is that the increase of chaotic sequences' length leads the increase of interference between different chaotic sequences. Additionally, we assume that the equalization is applied, the multi carrier interferences are negligible, and \(\beta\) is the same; it can be seen from Figure 4b that, in this assumption, the BER of the proposed scheme is basically the same as the increase of \(N\). In order to verify that the proposed scheme can effectively improve the security of MIMO communication system, we simulate the BER of legitimate users and eavesdroppers over different channels and \(\beta=N\). It can be seen from the BER of eavesdroppers in Figures 5 and 6, either the AWGN channel or the Rayleigh channel, the BER of eavesdroppers is very high when recovering the user data. This is because eavesdroppers do not know the initial values of the chaotic sequences, the method of generating FH module and the way FH module hidden in the chaotic sequences, so eavesdroppers cannot use the chaotic sequences to generate the correct FH module. Without the correct FH module, eavesdroppers could not correctly de-hop, so they could not obtain the correct user data. Therefore, the proposed scheme can effectively improve the security of MIMO communication system. Then, to demonstrate the improved security performance of the MIMO communication system, we simulate the information secrecy capacity of the scheme proposed in this paper and the benchmark scheme (STBC). As shown in Figure 7, Tables 1 and 2, thanks to the FH and chaotic modulation, the secrecy capacity of the proposed scheme is significantly higher than the benchmark MIMO system. Moreover, we can see from Tables 1 and 2 that,  
Figure 4: The theoretical and simulation BER of MIMO-FH-OFDM-DCSK system over the AWGN channel. (**a**) \(N=64\); (**b**) \(\beta=64\). Figure 5: BER of legitimate users and eavesdroppers over AWGN channel. (**a**) BER over the AWGN channel with BPSK; (**b**) BER over the AWGN channel with QPSK. Figure 6: BER of legitimate users and eavesdroppers over the Rayleigh channel. (**a**) BER over Rayleigh channel with BPSK; (**b**) BER over Rayleigh channel with QPSK. after the eavesdropper has stolen the information of MIMO communication system with STBC encoding only, whether it is AWGN channel or Rayleigh fading channel, the secrecy capacity of the benchmark scheme (STBC) is smaller than that of the proposed scheme at any Eb/N0 (dB).