Secure spatial modulation based on two-dimensional generalized weighted fractional Fourier transform encryption

In this paper, a two-dimensional generalized weighted fractional Fourier transform (2DGWFRFT) and constellation scrambling (CS)-based secure spatial modulation (SM) scheme, called 2DGWFRFT-CS-SM, is proposed to enhance the physical layer security (PLS) of the wireless communication system. The proposed scheme is executed by two steps. In the first step, 2DGWFRFT is implemented as the security kernel for PLS provision. In the second step, the parameters of 2DGWFRFT, regarded as the encryption core, control the antenna number rotation to further enhance the security of the SM modulation symbol. Both the 2DGWFRFT signal generation strategy and the SM system including the transfer process have been elaborated to depict the security mechanism of the proposed scheme. Moreover, we give a key extraction algorithm utilized to generate the parameters, which can help scramble the antenna serial number. From the perspective of signal characteristics, the uniqueness of variation in the constellation has been investigated to outperform other cryptography-based encryption algorithms. Finally, the secrecy rates and the energy efficiency of our proposed scheme are theoretically analyzed and evaluated via Monte Carlo simulations, demonstrating that the proposed scheme can achieve a much higher secrecy capacity than artificial noise schemes without requiring additional jamming power consumption and myriad costs of hardware.