Physical Layer Security of Generalised Pre-coded Spatial Modulation with Antenna Scrambling

In the last decade or so, physical layer security had been an active research area drawing substantial attentions and collaborative efforts across different societies. Complementary to the conventional application layer security approach dominantly based on cryptography that is potentially vulnerable to quantum computationally capable eavesdropper, physical layer security was envisioned of providing the ultimate security from the information theoretical point of view. This area of research was pioneered by Shannon’s foundation work on secrete communications [1], where the ’one-time pad’ was proposed in order to achieve the perfect security. This landmark finding inspired further intriguing research on the physical layer security of ’wire-tap’ channel [2], where the eavesdropper’s channel between Alice and Eve constitutes a degraded version of the main channel between Alice and Bob. In particular, the important notion of security capacity was formally defined as the capacity difference between the main channel and the eavesdropper’s channel, where a positive security capacity enables physical layer security. The research of physical layer security became much more complicated yet interesting when wireless communications is considered, where the eavesdropper’s channel becomes not necessarily degraded [3], [4], [5] in comparison to the main channel owing to the fast variations of the wireless channel propagation. As a benefit, the classic solution exploited the fast varying Channel State Information (CSI) of the main channel as the security key [6], which was assumed to be only privately known between Alice and Bob. This solution became naturally inappropriate in the graver condition, where the CSI of the main channel became also publicly known to Eve. In this challenging scenario, various signal processing advances appeared particularly in the so-called Multiple Input Multiple Output Multiple Eavesdropper (MIMOME) physical layer security model [7], [8]. More explicitly, when eavesdropper’s channel is optimistically assumed to be known to Alice having multiple antennas, intelligent beam-forming constituted effective solutions. On the other hand, when eavesdropper’s channel is unknown to Alice but its dimension (number of antennas) is known, the technique of generating artificial noise [9] by Alice was found to be powerful, where the artificial noise was pre-processed to lie in the null space of the