On secrecy rate analysis of spatial modulation and space shift keying

Spatial modulation (SM) and space shift keying (SSK) represent transmission methods for low-complexity implementation of multiple-input multiple-output (MIMO) wireless systems in which antenna indices are employed for data transmission. In this paper, we focus our attention on the secrecy behavior of SSK and SM. Using an information-theoretic framework, we derive expressions for the mutual information and consequently compute achievable secrecy rates for SSK and SM via numerical evaluations. We also characterize the secrecy behavior of SSK by showing the effects of increasing the number of antennas at the transmitter as well as the number of antennas at the legitimate receiver and the eavesdropper. We further evaluate the secrecy rates achieved by SM with different sizes of the underlying signal constellation and compare the secrecy performance of this scheme with those of general MIMO and SIMO systems. The proposed framework unveils that SM is capable of achieving higher secrecy rates than the conventional single-antenna transmission schemes. However, it underperfoms compared to a general MIMO system in terms of the achievable secrecy rates.